the mean of 41, 52, 56, 65, 65, 76, and 89 is 63.43.
Step-by-step explanation:
The mean of the value is 63.43if lines ax-2y=5 and 2x-by =8 intersect at point (11,3), find the value of a and b
Answer:
To find the values of a and b, we need to substitute the coordinates of the given point (11,3) into both equations and solve for a and b.
Substituting (11,3) into the first equation ax-2y=5:
a(11)-2(3)=5
11a-6=5
11a=11
a=1
Substituting (11,3) into the second equation 2x-by =8:
2(11)-b(3)=8
22-3b=8
-3b=-14
b=14/3
Therefore, a=1 and b=14/3.
Answer:
a = 1
b = 4.67 OR 14/3
Step-by-step explanation:
ax - 2y = 5
a(11) - 2(3) = 5
11a - 6 = 5
11a = 11
a = 1
2x - by = 8
2(11) - b(3) = 8
22 - 3b = 8
3b = 14
b = 4.67 OR 14/3
Room and board charged for on-campus students at the local college have increased 3.15 each year since 2000. In 2000, students paid 4,291 for room and board.
Write a function to model the cost of C after t years since 2000
If the trend continues, how much would a student expect to pay for room and board in 2017? Express your answer as a decimal rounded to the nearest hundredth
1) A function to model the cost of C after t years since 2000 is [tex]C = 4,291(1 + 0.0315)^t[/tex]
2)If the trend continues, a student expect to pay for room and board in 2017 is $7862.35 .
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here we need to use exponential function formula to find the cost function . Then,
=> [tex]f(x)=a(1+r)^t[/tex]
Where a is cost for room in 2000 and r is rate of change.
Then model the cost of room and board C after t years since 2000, we can use the formula:
=> [tex]C = 4,291(1 + 0.0315)^t[/tex]
where 0.0315 represents the annual increase of 3.15% expressed as a decimal.
Now we have to find the cost of room and board in 2017, we need to substitute t = 17 (since 2017 is 17 years after 2000) into the function and round the result to the nearest hundredth.
So,[tex]C = 4,291\times(1 + 0.0315)^{17}[/tex]
=>C = 7,862.35
Therefore, a student would expect to pay approximately $7862.35 for room and board in 2017 if the trend continued.
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rico's mixing water and milk in the ratio 20 : 1
The total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1 is 21 liters.
When a ratio of 20:1 is given for milk and water, it means that for every 20 parts of milk, there is 1 part of water. Therefore, the total number of parts in the mixture is 20 + 1 = 21.
We know that Rico mixed 20 liters of milk, which represents 20 parts of the mixture. To find the corresponding volume of water, we can use the ratio given.
The ratio of milk to water is 20:1, which means that for every 20 parts of milk, there is 1 part of water. Thus, the volume of water in the mixture is [tex]\frac{1}{20}[/tex] of the total volume of the mixture.
Volume of water = [tex]\frac{1}{20}[/tex] x Total volume of the mixture
Since we know that the volume of milk is 20 liters, we can substitute that value in the equation to solve for the total volume of the mixture:
20 = ([tex]\frac{20}{21}[/tex]) x Total volume of the mixture
Total volume of the mixture = (20 × 21) ÷ 20
= 420 ÷ 20
= 21 liters
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The complete question is:
What is the total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1?
A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
The final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
The initial balance of the checking account is $350.
If the customer makes two withdrawals, one $50 more than the other, let's assume the smaller withdrawal amount is x. Then, the larger withdrawal amount will be x + $50.
So, the new balance of the checking account after these two withdrawals would be:
$350 - x - (x + $50) = $350 - 2x - $50 = $300 - 2x
After this, the customer makes a deposit of $75, which would increase the balance of the checking account to:
$300 - 2x + $75 = $375 - 2x
Therefore, the final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.
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Complete question:
Write an expression for the new balance using as few terms as possible. A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.
quartile and decile for ungrouped data
A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7
B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17
C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98
D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98
E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147
F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848
What is number?Number is an important part of mathematics, and it is used in virtually every aspect of life.
A) First, we need to arrange the data in order:
[1,1,2,2,2,2,2,3,3,3,3,4,5,6,6,7,7,7,7,9,9]
The median is the middle value of the data set. Since there are 21 values, the median is the average of the [tex]$10^{th}$[/tex] and [tex]$11^{th}$[/tex] values, which is 6.
The first quartile [tex]$Q_1$[/tex] is the median of the lower half of the data set. The lower half of the data set is [1,1,2,2,2,2,2,3,3,3], which has 10 values. The median of this set is the average of the [tex]$5^{th}$[/tex]and [tex]$6^{th}$[/tex] values, which is 2.
The third quartile[tex]$Q_3$[/tex]is the median of the upper half of the data set. The upper half of the data set is [4,5,6,6,7,7,7,7,9,9], which also has 10 values. The median of this set is the average of the[tex]$5^{th}$[/tex] and[tex]$6^{th}$[/tex]values, which is 7.
The interquartile range (IQR) is the difference between the third and first quartiles: IQR =[tex]Q_3[/tex] - [tex]Q_1[/tex]= 7 - 2 = 5.
To find the deciles, we need to divide the data into $10$ equal parts. Since we have 21 data points, we need to find the values that divide the data into groups of $2$. The [tex]$k^{th}$[/tex] decile[tex]$D_k$[/tex] is the[tex]$k \cdot n/10$-th[/tex] value, where $n$ is the number of data points. The deciles are:
$D_1 = 1, D_2 = 2, D_3 = 2, D_4 = 2, D_5 = 3,$
$D_6 = 6, D_7 = 7, D_8 = 7, D_9 = 9$
B) Again, we need to arrange the data in order:
$10,11,12,12,14,14,14,15,15,15,15,16,16,16,17,17,14,14$
The median is the average of the[tex]$9^{th}$[/tex] and[tex]$10^{th}$[/tex] values, which is $15$.
The first quartile $Q_1$ is the average of the[tex]$4^{th}$[/tex] and [tex]$5^{th}$[/tex]values, which is $14$.
The third quartile $Q_3$ is the average of the [tex]$14^{th}$[/tex] and [tex]$15^{th}$[/tex]values, which is $16$.
The interquartile range (IQR) is [[tex]Q_3[/tex] - [tex]Q_1[/tex]= 16 - 14 = 2].
To find the deciles, we need to divide the data into [10] equal parts. Since we have 18 data points, we need to find the values that divide the data into groups of 2. The deciles are:
[[tex]D_1[/tex]= 10, D_2 = 12, D_3 = 14, D_4 = 14, D_5 = 14,]
[[tex]D_6[/tex]= 15, D_7 = 15, D_8 = 16, D_9 = 17]
From the above calculation, it can be seen that the quartiles and deciles of each set of data differ.
This is due to the different values of the data sets and the number of data points in each set.
The quartiles and deciles show different ranges and values which indicate the spread of the data and also help to identify any skewness in the data.
Summarizing, the quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.
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2plus 2 is 4 everybody knows that
NEED HELP ASAP!!! Q) A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, A) if two cards are randomly selected with replacement.
one third
one ninth
two thirds
two sixths
The prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .
What is Prοbability?The prοbability fοrmula establishes the likelihοοd that an event will οccur. It is the prοpοrtiοn οf favοurite websites tο all favοurite websites. P (B) is the prοbability οf an event "B" is hοw the prοbability fοrmula can be stated. The number "n" (B) represents the favοurite mοments οf an event "B."
There are three cards, each labelled with the letter A οr D. Since there are twο A cards, there are a tοtal οf [tex]$2^3 = 8$[/tex] pοssible equally likely οutcοmes when twο cards are drawn with replacement frοm the set.
The pοssible οutcοmes are: AA, AD, DA, DD, AA, AD, DA, DD.
Out οf these eight pοssible οutcοmes, there is οnly οne οutcοme that cοrrespοnds tο drawing twο A cards: AA. Therefοre, the prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .
In οther wοrds,
[tex]$P(A,A) = \boxed{\frac{1}{8}}$[/tex].
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Suma a doua nr naturale este 70.daca se împarte nr mare la cel mic , se obține cățel 4 di restul 10, sa se afle vele 2 numere
Answer:
Los dos números naturales son 12 y 58.
Step-by-step explanation:
Llamemos al número más pequeño "x" y al número más grande "y".
Del problema sabemos que:
x + y = 70 (ya que la suma de los dos números naturales es 70)
Cuando el número mayor se divide por el número menor, el cociente es 4 con un resto de 10. Esto se puede escribir como:
y = 4x + 10 (ya que 4 es el cociente y 10 es el resto)
Ahora podemos sustituir la segunda ecuación en la primera ecuación:
x + (4x + 10) = 70
Simplificando esta ecuación, obtenemos:
5x + 10 = 70
Restando 10 de ambos lados, obtenemos:
5x = 60
Dividiendo ambos lados por 5, obtenemos:
x = 12
Ahora que conocemos x, podemos volver a sustituirlo en una de las ecuaciones anteriores para encontrar y:
y = 4x + 10 = 4(12) + 10 = 58
Por lo tanto, los dos números naturales son 12 y 58.
the null hypothesis is (typically) rejected, when select one: a. the p-value is less than or equal to .5. b. the p-value is less than or equal to .05. c. the p-value exceeds .05. d. the p-value exceeds .5.
The null hypothesis is (typically) rejected, when (b) the p-value is less than or equal to .05.
In hypothesis testing, the Null-Hypothesis represents the default assumption,
whereas the alternative hypothesis represents the claim made by the researcher.
The "p-value" is defined as a probability metric which indicates the likelihood of observing the data, given that the null hypothesis is true.
If the p-value is small (less than or equal to .05), it means that it is unlikely to observe the data, assuming the null hypothesis is true.
Therefore, a p-value less than or equal to .05 is considered statistically significant, and the null hypothesis is typically rejected, the correct option is (b).
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The given question is incomplete, the complete question is
The null hypothesis is (typically) rejected, when select one:
(a) the p-value is less than or equal to .5
(b) the p-value is less than or equal to .05
(c) the p-value exceeds .05
(d) the p-value exceeds .5
Trapezoid ABCD is formed when right triangle EAB is cut by line DC such that DC || AB. Find the volume of the solid generated when the trapezoid is rotated about side DA. Round your answers to the nearest tenth if necessary.
The volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).
What is volume?A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
According to the given information:Given:
DC = 7
DA = 6
DE = 6
AB = 14
Height of the trapezoid:
ED = (DC/AB) * EA = (7/14) * EA = 0.5 * EA
Height = EA - ED = EA - 0.5 * EA = 0.5 * EA
Circumference of the cylindrical shell:
Circumference = 2 * π * AB = 2 * π * 14
Thickness of the cylindrical shell:
Since the trapezoid is being rotated about side DA, the thickness (Δx) will vary along DA. We'll integrate with respect to x from 0 to 6 (the length of DA).
Volume of the solid generated:
Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * EA * Δx]
Substituting EA = DE + DA = 6 + 6 = 12Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * 12 * Δx]
Integrating:
Volume = 2 * π * 14 * 0.5 * 12 * [x] from 0 to 6
Volume = 2 * π * 14 * 0.5 * 12 * (6 - 0)
Volume = 504 * π
Approximating to the nearest tenth:
Volume ≈ 504 * 3.14 ≈ 1586.6 cubic units (rounded to the nearest tenth)
Therefore, the volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).
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The circle graph represents the jobs at a digital animation company with1,620 employees. How many more story artists are there than ?
263 more story artists are there than interns.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number
In actual values
Number of story artists = 1620 x 20% = 1620 x 20/100 = 324
Number of interns = 1620 x 5% = 1620 x 5/100 = 81
Difference = 324 - 81 = 263
Hence, 263 more story artists are there than interns.
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Complete question:
The circle graph represents the jobs at a digital animation company with 1,620 employees. How many more story artists are there than interns?
See the image attached.
y=log(2x+c) for what values of x will the log be positive
For the logarithm to be positive, the argument of the logarithm (i.e., 2x+c) must be greater than zero.
Solve the inequality 2x+c > 0 for x:
2x > -c
x > -c/2
Therefore, for x > -c/2, the logarithm Y=log(2x+c) will be positive.
Jeff is purchasing a car for $28,175 that will depreciate in value 8.5% each year.
Write a function to model the value of p of the car after t years.
If he decides to sell the car after 6 years, what will be the value of his car? Express your answer as a decimal rounded to the nearest hundredth.
The function to model the value of p of the car after t years can be expressed as:
p(t) = 28,175 * (1 - 0.085)^t
where 0.085 represents the percentage of depreciation per year, and t represents the number of years.
To find the value of the car after 6 years, we substitute t = 6 into the function:
p(6) = 28,175 * (1 - 0.085)^6
p(6) = 28,175 * 0.5386
p(6) ≈ 15,199.35
Therefore, the value of Jeff's car after 6 years will be approximately $15,199.35.
Find the answer and explain
Answer:
660cm^2
Step-by-step explanation:
area of 2 triangle= 10×12
= 120cm^2
area of 3 rectangles= (13×15×2)+(10×15)
= 390+150
= 540cm^2
surface area of triangular prism
= 540+120
= 660cm^2
a forecast is defined as a(n) . a. quantitative method used when historical data on the variable of interest are either unavailable or not applicable b. prediction of future values of a time series c. outcome of a random experiment
A forecast is defined as a(n) prediction of future values of a time series which is option B.
Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Companies use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Often, this is based on the anticipated demand for the provided goods and services.
Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.
To predict how trends, like as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts utilise forecasting. Lastly, statisticians may examine the probable effects of a change in business operations via forecasting. Data may be gathered, for example, on how altering company hours affects consumer happiness or how changing particular work conditions affects staff productivity.
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i need help to solve these questions step by step, PLEASEEE THIS DUES TODAY
At a coffee shop, the first 100 customers'
orders were as follows.
Hot
Cold
Small Medium Large
5
48
22
8
12
5
Find the probability a customer ordered a
medium, given that they ordered a hot drink.
P(B|A) =
P(medium | hot) = [? ]
P(ANB)
P(A)
The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 510 and a standard deviation of 270. If a college requires a student to be in the top 30 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?
answer:(round to the nearest integer)
The minimum score that a student must obtain to be in the top 30% of students taking the national standardized examination for college admission is approximately 658.4.
To find the minimum score that a student must obtain to be in the top 30% of students taking the test, we need to find the score that corresponds to the 70th percentile of the distribution.
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 70th percentile is approximately 0.52.
We can use the formula for transforming a score from a normal distribution to a standard normal distribution to find the corresponding score in the original distribution:
z = (x - mu) / sigma
where z is the z-score, x is the score in the original distribution, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.
Rearranging this formula, we get:
x = mu + z * sigma
Substituting the values we have, we get:
x = 510 + 0.52 * 270
x = 658.4
Therefore, to be among the top 30% of test-takers and be eligible for admission to the college, a student must score at least 658.4 on the exam.
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14. assuming p-value is 0.03, what is the conclusion of testing at the 0.10 level of significance whether the fruit drink distributor should sell this drink? a. based on the sample data, there isn't sufficient evidence to conclude that the average rating is more than 4.75. b. based on the sample data, there isn't sufficient evidence to conclude that the average rating is no more than 4.75. c. based on the sample data, there is sufficient evidence to conclude that the average rating is no more than 4.75. d. based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75. e. none of the above.
Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.
If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.
Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.
Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.
Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.
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What is the value of x? sin64°=cosx enter your answer in the box. x = °
Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°
So, if we have given cos64° = cosx and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.
The answer is: x = 26°
Step-by-step explanation:
the mean wait time for a drive-through chain is 193.2 seconds with a standard deviation of 29.5 seconds. what is the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds? (write answer round to whole number like 91%).
The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.
First, we need to calculate the standard error of the mean (SEM) using the formula
SEM = standard deviation / sqrt(sample size)
SEM = 29.5 / sqrt(45) = 4.4
Next, we can standardize the sample mean using the formula
z = (x - μ) / SEM
where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.
For the lower limit, we have
z = (185.7 - 193.2) / 4.4 = -1.70
For the upper limit, we have
z = (206.5 - 193.2) / 4.4 = 3.02
We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.
The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.
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The new, larger coral reef tank will thrill visitors by providing a floor-to-ceiling view of sea creatures swimming through the reef. In the old version of the exhibit, 576,000 gallons of water circulated through the tank over 24 hours. if the volume of the new exhibit is 3 1/2 times larger than the old one, how many gallons per hour will be circulated?
Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.
What is meant by rate?
In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.
If the new exhibit is 3 1/2 times larger than the old one, then its volume is:
[tex]V_{new} = 3.5 * V_{old[/tex]
We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:
576,000 gallons / 24 hours = 24,000 gallons per hour
To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:
Flow rate = [tex]V_{new[/tex] / time
Plugging in the values we have:
Flow rate = (3.5 * [tex]V_{old[/tex]) / time
We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:
24,000 = (3.5 * [tex]V_{old[/tex]) / time
To solve for time, we can multiply both sides by time:
24,000 * time = 3.5 * [tex]V_{old[/tex]
Then we can divide both sides by 24,000:
time = (3.5 * [tex]V_{old[/tex]) / 24,000
Plugging in [tex]V_{old[/tex] = 576,000, we get:
time = (3.5 * 576,000) / 24,000 = 84 hours
Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:
[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).
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Answer:
To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.
To do this, we divide the total gallons by the number of hours:
576,000 gallons / 24 hours = 24,000 gallons per hour
Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.
Let's assume the volume of the old exhibit is x gallons.
The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.
To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.
So, the volume of the new exhibit is 7/2 * x.
Now, we can determine the amount of water circulated per hour in the new exhibit.
To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):
(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour
Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.
Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.
Step-by-step explanation:
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as shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. what is the distance, in feet, between the centers of the two wheels?
The distance between the centers of the two wheels is approximately 11.86 feet.
The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.
Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula
C = πd
Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:
C = πd = π(0.5) = 1.57 feet (approx.)
The length of the conveyor belt is given as 15 feet. So we can write
2C + d = 15
Substituting the value of C, we get
2(1.57) + d = 15
3.14 + d = 15
d = 11.86 feet
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approximately how many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein?
Answer:
Therefore, there are approximately 102 kilocalories in the snack bar.
Step-by-step explanation:
One gram of fat provides 9 kilocalories (kcal), while one gram of carbohydrate and protein provide 4 kcal each. So, to find the total number of kilocalories in the snack bar, we can use the following formula:
Total kcal = (grams of fat * 9) + (grams of carbohydrate * 4) + (grams of protein * 4)
Plugging in the values, we get:
Total kcal = (6 * 9) + (10 * 4) + (2 * 4)
Total kcal = 54 + 40 + 8
Total kcal = 102
Therefore, there are approximately 102 kilocalories in the snack bar.
The answer is approximately 120 kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein.
What are kilocalories? Kilocalories, also known as calories, are a unit of energy used to calculate the amount of energy in food. The number of kilocalories in food is calculated based on the number of grams of protein, carbohydrate, and fat it contains. Kilocalories are used by the body to fuel its processes and maintain its vital functions. The energy in food is released when it is digested, absorbed, and transported to the cells where it is used to produce ATP, the body's primary source of energy. ATP is used to power cellular processes such as metabolism, respiration, and movement. How many kilocalories are in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein? To calculate the number of kilocalories in a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein, we need to know the number of kilocalories per gram of each macronutrient. Protein and carbohydrates each contain 4 kilocalories per gram, while fat contains 9 kilocalories per gram. To calculate the number of kilocalories in the snack bar, we multiply the number of grams of each macronutrient by the number of kilocalories per gram and then add them together. Here is the calculation:6 grams of fat x 9 kilocalories per gram of fat = 54 kilocalories10 grams of carbohydrate x 4 kilocalories per gram of carbohydrate = 40 kilocalories2 grams of protein x 4 kilocalories per gram of protein = 8 kilocalories. Total kilocalories = 54 + 40 + 8 = 102Therefore, a snack bar that contains 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories.
A snack bar with 6 grams of fat, 10 grams of carbohydrate, and 2 grams of protein has approximately 102 kilocalories. This is calculated as follows: (6 grams fat x 9 kcal/g) + (10 grams carbohydrate x 4 kcal/g) + (2 grams protein x 4 kcal/g).
Therefore, answer is 120 kilocalories.
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two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. what is the probability that after they are painted, the cubes can be rotated to be identical in appearance?(2020amc12b problem 20) (a) 64 9 (b) 2048 289 (c) 512 73 (d) 1024 147 (e) 4096
Step-by-step explanation:
with 2 cubes we have 12 faces to paint.
each face has 2 options (black or white).
so, we have a total of 2¹² possible outcomes.
a probability is always the ratio of
desired cases / totally possible cases
so, we need to find a way to express the desired cases of both cubes being painted the same way.
essentially that means we have a totally free choice of painting the faces of the first cube.
that is 2⁶ possible outcomes.
for the second cubes we have then only one basic choice : to repeat the choices done on the first cube.
BUT : we have 6×4 ways to orient the second cube before painting it identically.
6 ways to pick e.g. the front face, and then 4 options to rotate the cube with the same front face for the e.g. top face.
in other words, we have 2⁶ different desired patterns on the first cube and 24 options to repeat the pattern on the second cube.
that means the desired options are 2⁶×1×24
so, the probability for them to be identical is
24×2⁶ / 2¹² = 24/2⁶ = 3/2³ = 3/8 = 0.375
The probability that after they are painted, the cubes can be rotated to be identical in appearance is (a) 64/9
Probability is a branch of mathematics that deals with the study of random phenomena or events with uncertain outcomes.
Let's start by assuming that one of the cubes has the black face facing up. The other cube can be painted in any of the possible ways.
Let's list all the possible configurations for the second cube.
There are six faces, and each can be painted either black or white. Therefore, there are 2⁶ = 64 possible configurations for the second cube.
The cube with the black face facing up has been accounted for separately, so there are 63 configurations that we need to consider.
If the second cube is painted all black or all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the black or white face is facing up.
There are two such configurations. If the second cube has exactly one white face and five black faces, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube has two white faces and four black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has three white faces and three black faces, there are eight ways to position it so that the cubes look identical. There are eight such configurations.
If the second cube has four white faces and two black faces, there are six ways to position it so that the cubes look identical. There are six such configurations.
If the second cube has five white faces and one black face, there are three ways to position it so that the cubes look identical. There are three such configurations
.If the second cube is painted all white, there is only one way to position it so that the cubes look identical, and that is to rotate it so that the white face is facing up. There are two such configurations.
In total, there are 2 + 3 + 6 + 8 + 6 + 3 + 2 = 30 ways to position the two cubes so that they look identical.
There are 63 × 64 possible configurations for the two cubes, so the probability of the cubes being able to be rotated to be identical in appearance is given by:
30/ (63×64) = 64/9
Therefore, the correct answer is (a) 64/9.
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I need help please thank y’all
Solving the given inequality, we get the value of x to be,
x ≥ 16.
What is an inequality?In a mathematical equation with an inequality, both sides must be equal. In inequality, we don't use equations but rather compare two values. The signs greater than (or greater than or equal to), less than (or less than or equal to), or not equal to are used in place of the equal sign.
Here in the question, we have the inequality:
x - 4 ≥ 12
Now to simplify this we will add 4 on both sides,
⇒ x - 4 + 4 ≥ 12 + 4
⇒ x ≥ 16
So, this implies that the value of x is greater than or equal to 16.
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Empirical Rule Khan Academy; all, if not most, of the answers.
I didn't know how to do the assignment, nor did I want to take the time to learn how to do it- so I kept rerolling answers while documenting the question (the variables involved in each of the questions) and then noting down the answers.
Whilst doing this Khan Academy assignment (quiz or whatever) look at the first two numbers near the "less than," "more than," and "living between" part of the question. Proceed to align the next numbers to whichever ones I have on the pdf.
- The answers will be under the numbers that have "and" or "&." I put on the right, with a dash, to note whether it was the question regarding more than, less than, or living between.
This took me a while to do (I was going for 4 stars on Khan). I thought it was worth sharing. Goodluck, folks.
Answer:
dont no ok i dont konow ask an easy one
#
Mrs. Morales wrote a test with 18 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100. Write an equation in slope-intercept form to represent the total number of points on the test. If necessary, write any fraction in decimal form. (Please help ASAP its due tmrw)
By answering the presented question, we may conclude that As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an that the equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.
Let x denote the number of spelling and y the number of vocabulary questions. Because there are a total of 18 questions, we know:
x + y = 18
5x + 10y = 15 points
We must solve for y 5x + 10y = 100 to put this equation in slope-intercept form.
10y = -5x + 100
y = (-1/2)x + 10
As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.
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Savannah recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 5
Bass 12
Drums 14
Keyboard 4
Eighth Grade Students
Instrument # of Students
Guitar 12
Bass 5
Drums 10
Keyboard 8
Based on these results, express the probability that a student chosen at random will play the drums as a percent to the nearest whole number.
The probability that a student chosen at random plays the drums is approximately 34%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A certain event has a chance of 1, while an impossible event has a probability of 0.
The total number of students in the middle school who play the drums is 14 + 10 = 24.
The total number of students in the middle school is:
5 + 12 + 14 + 4 + 12 + 5 + 10 + 8 = 70
The probability of selecting a student who plays the drums at random is:
24/70 = 0.34285714285714286
To express this probability as a percentage, we multiply by 100 and round to the nearest whole number:
0.34285714285714286 * 100 ≈ 34
Therefore, the probability that a student chosen at random plays the drums is approximately 34%.
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Please help with finding the answer
The two missing points on the line are:
(0, -1)
(-5, 0)
And the slope, using these points, is a = -1/5
How to find the missing y-values and the slope?Remember that a general linear equation is:
y = ax + b
Where a is the slope and b is the y-intercept.
If that line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can look at line e and find the two missing y-values, for the first point we have:
(0, -1)
For the second point we have:
(-5, 0)
Using these two, we will get the slope:
a = (0 + 1)/(-5 - 0) = -1/5
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