Answer: The speed of light is approximately 89,100 times faster than the speed of sound.
Step-by-step explanation: To find out how many times faster the speed of light is than the speed of sound, we need to divide the speed of light by the speed of sound:
Speed of light / Speed of sound = (6.710610^7) / (7.5410^2)
Simplifying this calculation gives us:
Speed of light / Speed of sound = 8.91*10^4
This means that the speed of light is approximately 89,100 times faster than the speed of sound.
Hope this helps, and have a great day!
Jose has 4 ants in his house and he discovers that those ants double every day. How many ants will he have after two weeks.
Answer:
In the picture is the answer
A company is reviewing a batch of 22 products to determine if any are defective. On average, 3.9% of produc are defective. Does this situation describe a binomial experiment, and why? What is the probability that the company will find 2 or fewer defective products in this batch? What is the probability that 4 or more defective products are found in this batch? If the company finds 5 defective products in this batch, should the company stop production?
P(X ≤ 2) = 0.636, P(X ≥ 4) = 1 - 0.990 = 0.010
How to find probability?Use the cumulative distribution function for the binomial distribution, 2 or fewer defective products:
P(X ≤ 2) = Σ P(X = k) for k = 0, 1, 2
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
P(X ≤ 2) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20
P(X ≤ 2) = 0.636
To find the probability of finding 4 or more defective products in this batch, we can use the complement rule:
P(X ≥ 4) = 1 - P(X ≤ 3)
Using the cumulative distribution function as before, we can calculate:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
P(X ≤ 3) = (0.961)^22 + 22(0.039)(0.961)^21 + (22!/(2!20!))(0.039)^2(0.961)^20 + (22!/(3!19!))(0.039)^3(0.961)^19
P(X ≤ 3) = 0.990
Therefore, P(X ≥ 4) = 1 - 0.990 = 0.010
If the company finds 5 defective products in this batch, they should consider stopping production, as this is much higher than the expected rate of 3.9%.
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1. Kendra owns a restaurant. She charges $1. 50 for 2 eggs and one piece of toast, and $. 90 for one egg
and one piece of toast. Determine how much she charges for each egg and each piece of toast
Kendra cost $0.60 for each egg and $0.30 for each piece of toast.
Let's assume that the cost of one egg is x and the cost of one piece of toast is y.
From the given information, we can set up two equations:
2x + y = 1.5
x + y = 0.9
We can solve this system of equations by either substitution or elimination method.
Using the elimination method, we can multiply the second equation by -2 to eliminate y:
-2x - 2y = -1.8
2x + y = 1.5
Adding these two equations, we get:
-1y = -0.3
y = 0.3
Substituting y = 0.3 in either of the two equations, we get:
x = 0.6
Therefore, Kendra charges $0.60 for each egg and $0.30 for each piece of toast.
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Ms. Leon opened a savings
account with an initial deposit
of $750 and will not make any more
deposits or withdrawals. The account
earns 3% simple interest.
What is the total amount that
Ms. Leon will have in her account at
the end of 4 years?
Answer: $840
Step-by-step explanation:
The formula for calculating simple interest is:
I = P * r * t
where:
I is the interest earned
P is the principal (the initial deposit)
r is the interest rate (as a decimal)
t is the time (in years)
Using this formula, we can find the interest earned on Ms. Leon's account over 4 years:
I = 750 * 0.03 * 4
I = 90
So Ms. Leon will earn $90 in interest over 4 years. To find the total amount in her account at the end of 4 years, we need to add the interest earned to the initial deposit:
Total amount = Initial deposit + Interest earned
Total amount = 750 + 90
Total amount = $840
Therefore, Ms. Leon will have a total of $840 in her savings account at the end of 4 years.
vital capacity is a measure of the amount of air that someone can exhales after taking a deep breath. what is the probability that we see our sample average difference or higher given there is no difference? g
a. The exit pressure is 19.76 lbf/in².
b. The ratio of the inlet area to the exit area is 3.125.
C. The exit area ratio (0.32) is less than the critical area ratio (1.89), the nozzle is converging-diverging in cross section.
To solve this problem, we need to apply the conservation equations for mass, momentum, and energy along with the isentropic relations.
a. To determine the exit pressure, we can use the isentropic relation for pressure ratio across a nozzle:
[tex]P_2/P_1 = (T_2/T_1)^{\frac{\gamma}{\gamma -1}}[/tex]
where [tex]P_1[/tex] and [tex]T_1[/tex] are the inlet pressure and temperature,
[tex]P_2[/tex] and [tex]T_2[/tex] are the exit pressure and temperature, and
γ is the specific heat ratio of air.
Using Table A-22E, we find that γ = 1.4 for air at 800°R.
Substituting the given values and solving for P2, we get:
[tex]P_2[/tex] = [tex]P_1 \times (T_2/T_1)^\frac{\gamma}{\gamma -1}[/tex] = [tex]45 \times (1500/480)^{(1.4/0.4)}[/tex]= 19.76 lbf/in²
b. To determine the ratio of the exit area to the inlet area, we can use the continuity equation:
[tex]A_1V_1 = A_2V_2[/tex]
where [tex]A_1[/tex] and [tex]A_2[/tex] are the inlet and exit areas, and
[tex]V_1[/tex] and [tex]V_2[/tex] are the inlet and exit velocities.
Substituting the given values, we get:
[tex]A_2/A_1 = V_1/V_2[/tex] = 480/1500 = 0.32
The ratio of the exit area to the inlet area is 0.32, or equivalently, the ratio of the inlet area to the exit area is 1/0.32 = 3.125.
c. To determine whether the nozzle is diverging only, converging only, or converging-diverging in cross section, we can compare the exit area ratio to the critical area ratio.
The critical area is the minimum area that allows the flow to reach sonic conditions, and it depends on the pressure and temperature of the flow.
For a converging-diverging nozzle, the exit area ratio is less than the critical area ratio, which is given by:
A* / [tex]A_1[/tex] = [tex](2/(\gamma+1))^{(\gamma+1)}/(2(\gamma-1)/(\gamma+1))^{(\gamma+1)/(\gamma-1)}[/tex]
where A* is the critical area,
[tex]A_1[/tex] is the inlet area, and
γ is the specific heat ratio.
Using the given values and γ = 1.4, we find that:
A* / [tex]A_1[/tex] = 1.89
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Question:-
Air enters a nozzle operating at steady state at 45 lbf/in.2, 800°R, with a velocity of 480 f/s, and expands isentropically to an exit velocity of 1500 ft/s. Using data from Table A-22E as needed, determine
a. the exit pressure, in lbf/in². 19.76
b. the ratio of the exit area to the inlet area. 0.577
c. whether the nozzle is diverging only, converging only, or converging-diverging in cross section. conv-div
In right triangle XYZ, ∠Y is the right angle and m∠X = 60°. If YZ = 4, what is XY?
Answer:
We can use the trigonometric ratios of a 30-60-90 triangle to find the length of XY. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Since ∠X is 60°, we know that ∠Z is 30°, and we can set up the following equation:
XY / 4 = 2 / √3
To solve for XY, we can multiply both sides of the equation by 4√3:
XY = 4 * 2 / √3
Simplifying the right side, we get:
XY = 8 / √3
To rationalize the denominator, we can multiply the numerator and denominator by √3:
XY = (8 / √3) * (√3 / √3)
Simplifying, we get:
XY = 8√3 / 3
Therefore, the length of XY is 8√3 / 3, which is approximately 4.62 units.
the variable socioeconomic status ranges from upper class to lower class and is an example of the select one: a. nominal level of measurement b. ordinal level of measurement c. interval-ratio level of measurement d. ratio level of measurement
The variable socioeconomic status ranges from upper class to lower class and is an example of the interval-ratio level of measurement. (option c)
Ordinal level of measurement is used to categorize variables that can be ranked in a specific order but do not have a uniform difference between them. For instance, a student's class rank can be categorized as first, second, or third. However, there is no uniform difference between the ranks.
Ratio level of measurement is used to categorize variables that have a meaningful zero point. For instance, height, weight, and age have a meaningful zero point.
However, in reality, it is difficult to find a person with zero income or zero education. Therefore, socioeconomic status can be considered an example of interval-ratio level of measurement but not an example of ratio level of measurement.
Hence option (c) is correct.
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a checkerboard consists of one-inch squares. a square card, 1.5 inches on a side, is placed on the board so that it covers part or all of the area of each of n squares. the maximum possible number of squares, n , is
The maximum possible number of squares, n, covered by a 1.5 inch square card placed on a checkerboard of 1-inch squares is 8.
To see this, first divide the 1.5-inch square card into 4 equal sections of 0.375 inches on a side. Then, arrange the sections so that each section covers part of one square on the checkerboard.
This configuration covers 8 squares on the checkerboard, and is the maximum possible number of squares.
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a school librarian wanted to estimate the proportion of students in the school who had read a certain book. the librarian sampled 50 students from the senior english classes, and 35 of the students in the sample had read the book. have the conditions for creating a confidence interval for the population proportion been met? responses yes, because the sample was selected at random. yes, because the sample was selected at random. yes, because sampling distributions of proportions are modeled with the normal model. yes, because sampling distributions of proportions are modeled with the normal model. yes, because the sample is large enough to satisfy the normality conditions. yes, because the sample is large enough to satisfy the normality conditions. no, because the sample is not large enough to satisfy the normality conditions. no, because the sample is not large enough to satisfy the normality conditions. no, because the sample was not selected using a random method.
The normality assumption is valid.
The librarian can proceed to create a confidence interval for the population proportion of students in the school who have read the book.
The school librarian has a goal of estimating the proportion of students in the school who have read a particular book. The librarian sampled 50 students from the senior English classes, and out of those 50 students, 35 of them had read the book.
The question at hand is whether the conditions for creating a confidence interval for the population proportion have been satisfied.
Firstly, it is essential to establish that the sample was selected at random.
According to the question, this has been done.
It is a crucial condition because it helps to avoid bias in the sample.
If the sample had not been selected at random, there would be a risk of under- or over-representing certain groups, leading to an inaccurate estimation of the proportion of students who have read the book.
Secondly, sampling distributions of proportions are modeled with the normal model.
This condition has been met because the sample size (50 students) is greater than or equal to 30.
When the sample size is this large, the sampling distribution of proportions can be approximated to the normal distribution.
The normality assumption is valid when the sample size is large enough to satisfy the rule of thumb of np≥10 and nq≥10.
Thus, both conditions for creating a confidence interval for the population proportion have been met.
The sample was selected at random, and the sample size is greater than or equal to 30.
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The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, find the dimensions of the rectangle.
Answer:
5cm (width) 18cm (height)
Step-by-step explanation:
From the text, the unknown number's value for the length of the width isn't disclosed, so we can mark it as a variable, for this case "x" as it is the most common variable to utilize in this case. We know that the length is 3 more than 3 times the width (x), so the length is 3+3x. The perimeter of the shape is 46 cm, and as we know, the perimeter is the sum of adding the length of all the sides and edges enclosing the shape, so therefore we can create a math sentence with the given information.
x+(3+3x)+x+(3+3x)=46 cm
OR
2(x+3+3x) =46 cm
Now, lets solve it.
2x+6+6x=46 (simplified)
8x+6=46 (combined variables)
8x=40 (subtracted)
x=5cm (divided)
Yay!! Now we have our answer, BUT WE ARE NOT DONE YET.
We need to replace our number in place of "3+3(x)," as well as "x." "x" is 5cm (width), and 3+3(x) is now 3+3(5), and is equal to 18cm. Hope this helped!!!!!!!!
The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.
Answer:
The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:
x f(x) g(x)
-2 1/108 12
-1 1/18 2
0 1/3 1/3
1 2 1/18
2 12 1/108
To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).
Answer:
Its A.
Step-by-step explanation:
Other one was not clear enough lol ^
in a normal distribution, 95.4% of the values fall between 5.8 and 10.6. compute the mean of the distribution.
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values are between 5.8 and 10.6, and the total number of values is 95.4%.
To calculate the mean, we must first calculate the sum of all the values. To do this, we will use the following formula:
sum of values = (lowest value + highest value) / 2
In this case, the lowest value is 5.8 and the highest value is 10.6, so the sum of values is 8.2.
We now have the sum of all the values, so we can calculate the mean by dividing the sum by the total number of values. The total number of values is 95.4%, so the mean is 8.2 / 0.954 = 8.57.
Therefore, the mean of the normal distribution is 8.57.
In conclusion, the mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%. When the sum of all the values (8.2) was divided by the total number of values (0.954), the mean was calculated to be 8.57.
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a project being analyzed by pert has 60 activities, 13 of which are on the critical path. if the estimated time along the critical path is 214 days with a project variance of 100, what is the probability that the project will take 224 days or more to complete? group of answer choices 0.0126 near zero 0.1587 0.14 0.8413
The probability that the project will take 224 days or more to complete is: 0.1587
The project is being analyzed by PERT, it has 60 activities, out of which 13 are on the critical path. The estimated time along the critical path is 214 days with a project variance of 100. We are required to find the probability that the project will take 224 days or more to complete.
Now, z-score = (x - μ) / σ = (224 - 214) / 10 = 1.
So, using the standard normal table, we have: P(Z > 1) = 1 - P(Z < 1) = 1 - 0.8413 = 0.1587.
Hence, the required probability that the project will take 224 days or more to complete is 0.1587.
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you are ordering a hamburger and can get up to 6 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 0 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.
The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:
[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]
This is the total number of possible outcomes.
To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:
[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]
So the probability of getting 0 toppings is:
[tex]$$P(\text{0 toppings}) =[/tex] [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]
However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.
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describe fully the single transformation which takes shape A to shape B.
Answer:
rotation 90° anticlockwise centre 4,3.
Last year, Brian and his wife earned $550,000 in
wages. How much did he pay in income taxes?
As Brian and his wife earned $550,000 in wages during 2020. The amount he pays in income taxes would be $167,700.
What do we call an income taxes?An income tax is a type of tax levied by governments on the earnings of businesses and individuals within their jurisdiction.
The amount of income tax that Brian and his wife paid in 2020 depends on several factors, such as their filing status, deductions, credits, and the tax rates that apply to their income.
Assuming that Brian and his wife filed jointly and did not have any significant deductions or credits, we can use the following tax brackets and rates for the 2020 tax year: 35% on taxable income between $414,701 and $622,050.
. Assuming that they did not have any significant deductions or credits, their taxable income would be $550,000 (their wages) minus the standard deduction for joint filers, which was $24,800 in 2020.
The income taxes will be calculated as:
= (35% * $550,000) - $24,800
= $192,500 - $24,800
= $167,700
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our cities recorded the temperature at midnight.
*Delway’s temperature was –8°C.
*Hickory’s temperature was –10°C.
*Midway’s temperature was –2°C.
*Ridgemonte’s temperature was 3°C.
Which list shows the cities in order from warmest to coldest?
A Delway, Hickory, Midway, Ridgemonte
B Hickory, Delway, Midway, Ridgemonte
C Midway, Ridgemonte, Hickory, Delway
D Ridgemonte, Midway, Delway, Hickory
3, -2, -8, -10, so ridge, midway, delway, and hickory
In negative numbers the lower the negative the greater the number, and the postivie goes above the negative.
So its D
prove that cn, an n-cycle, has exactly n labeled spanning trees. you may use any method you wish to do this problem. write a good, detailed, and thoughtful proof!
To prove that a cycle graph Cn has exactly n labeled spanning trees, we can use the principle of inclusion-exclusion. First, consider a tree T that is composed of the n edges of Cn. This tree has n edges and is therefore an n-edge tree. In order for it to be a labeled spanning tree, every vertex must be labeled with a distinct label. Since Cn has n vertices, there are n! ways to label the vertices, giving us n! labeled spanning trees.
Now, we can use inclusion-exclusion to determine the number of labeled spanning trees that are a subset of T. For each vertex vi in T, we can choose any label from the set of n labels. For each of these labels, we can choose any edge from the n edges in T. The total number of labeled spanning trees that are a subset of T is therefore: n2 × n!
Now, we can subtract the number of labeled spanning trees that are a subset of T from the total number of labeled spanning trees to get the number of labeled spanning trees that are not a subset of T. The number of labeled spanning trees that are not a subset of T is: n! - n2 × n! = n! - n2! Therefore, the total number of labeled spanning trees of Cn is n!.
This proves that a cycle graph Cn has exactly n labeled spanning trees.
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what are the advantages of a best-guess (trial and error) experiment versus a factorial or design experiment
One advantage of best-guess experiments is that they are often faster and more cost-effective than factorial or design experiments.
Best-guess (trial and error) experiments involve making a hypothesis and testing it through a series of trials until a satisfactory result is achieved. On the other hand, factorial or design experiments involve manipulating multiple variables simultaneously to determine their individual and interactive effects on a response variable.
Both approaches have their advantages and disadvantages depending on the specific research question and goals. They may also be useful in situations where there is limited knowledge about the variables of interest or when the system is too complex to be modeled accurately.
However, best-guess experiments may suffer from issues such as biased or subjective interpretation of results, a lack of control over extraneous variables, and a potential for false positives or negatives.
In contrast, factorial or design experiments provide a more systematic approach to testing hypotheses and offer greater control over variables, leading to more reliable and generalizable results. They may, however, be more time-consuming and expensive to conduct.
Ultimately, the choice between best-guess and factorial or design experiments depends on the research question, available resources, and desired level of precision and control.
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eva bought 6 sponges. there were p sponges in each package. write an expression that shows how many packages eva bought. 6p
Answer: [tex]\frac{6}{p}[/tex]
Step-by-step explanation:
The number of packages Eva bought would be: 6 divided p which equals 6/p.
Use que boards to do these divisions 363 divide 14
636 divide 21
908 divide 52
Using the division,
a) 363 ÷ 14 = 25 13/14
b) 636 ÷ 21 = 30 2/7
c) 908 ÷ 52 = 17 11/13
a) 363 ÷ 14, we first divide 363 by 14 to get a quotient of 25 with a remainder of 13. We then use the que board with 14 beads to represent this division. We start with the first digit of the dividend, which is 3. We count out 2 sets of 14 beads, which we move to the top of the board. We then move 1 more bead to the top, representing the remaining 13. The final result is 25 with a remainder of 13/14.
b) 636 ÷ 21, we divide 636 by 21 to get a quotient of 30 with a remainder of 6. We then use the que board with 21 beads to represent this division. We start with the first digit of the dividend, which is 6. We count out 3 sets of 21 beads, which we move to the top of the board. We then move 3 more beads to the top, representing the remaining 6. The final result is 30 with a remainder of 6/21, which can be simplified to 2/7.
c) 908 ÷ 52, we divide 908 by 52 to get a quotient of 17 with a remainder of 44. We then use the que board with 52 beads to represent this division. We start with the first digit of the dividend, which is 9. We count out 17 sets of 52 beads, which we move to the top of the board. We then move 44 more beads to the top, representing the remaining part of the dividend. The final result is 17 with a remainder of 44/52, which can be simplified to 11/13.
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Please, I really want this pleaseeeeeeweeee
The value of ∠K is 78°
What is tangent of a circle?The tangent of a circle is a straight line that touches the circle at exactly one point, and it is perpendicular to the radius of the circle at that point.
Given that, a tangent JK is lying on the circle H whose radius are HJ and HM,
So, ∠HMJ = ∠HJM = 84°
and JK ⊥ HJ (JK is a tangent on radius HJ)
So, ∠HJK = 90°
∠HJM + ∠MJK = ∠HJK
84° + ∠MJK = 90°
∠MJK = 6°
Using exterior angle property;
∠MKJ + ∠MJK = ∠HJM
∠MKJ + 6° = 84°
∠MKJ = 84° - 6° = 78° (∠MKJ means ∠K)
Therefore, ∠K = 78°
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i really dont understand this please help me out
Answer: D
Step-by-step explanation: It is going up in a strait trend line, making it where it has no relation ship unless very closely examined.
Please help! easy!Find the m
110⁰
x + 52
x +42
Answer: 100 < 96
Step-by-step explanation:
x+52+x+42 = 180
2x+94 = 180
2x = 180 - 94
2x = 86
x = 86/2
x = 43
110 < x + 52
110 < 43 + 52
110 < 96
simplity (-w^3/6)^-2 Write your answer using only positive exponents.
Answer: 36/w^6
Step-by-step explanation:
Answer:
It is 15 3 or 3375
Explanation:
You can write your equation as = 15 3 × 15 15 15 in numerator and in denumerator is cancelled out: Hence, = 15 3 This is your answer 15 3 or = 3375
Gus built a wooden fence. He uses 18 nails for every 3 pieces of wood. If he uses the same amount of nails in each piece of wood, how many nails will he use for 249 pieces of wood? 1,494 nails 249 nails 747 nails 415 nails
The number of nails he will use for 249 pieces of wood will be 1494.
What is arithmetic?The foundational subject in mathematics is arithmetic, which covers actions with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. Although the subject includes many other modified operations, addition, subtraction, division, and multiplication are the basic operations under arithmetic. Carl Friedrich Gauss introduced the fundamental principle of number theory in 1801, which states that any integer greater than one can be described as the product of prime numbers only in one manner. Number theory is also referred to as arithmetic. Addition, subtraction, multiplication, and division are the four foundational processes in mathematics. Here, a brief discussion of all these procedures is provided.
In this question, Gus uses 18 nails for every 3 pieces of wood.
therefore, for 1 piece of wood he uses= 6 nails.
Number of pieces of wood= 249
Number of nails used= 1494
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Two commercial flights per day are made from a small county airport. The airport manager tabulates the number of on-time departures for a sample of 200 days. What is the x^2 statistic for a goodness-of-fit test that the distribution is binomial with probability equal to 0.8 that a flight leaves on time?
The x² statistic for the goodness-of-fit test is approximately 104.15.
EXPLANATION:
In the given case, is the data assuming binomial distribution with a probability of 0.8 that a flight leaves on time. We have to find the x² statistic for the goodness-of-fit test.
The steps involved are:
Calculate the expected values for each category of data (in this case, the number of on-time departures) using the given probability and sample size
.Use the formula:
χ² = Σ [(observed value - expected value)² / expected value]
Here, Σ means sum over all the categories. Now, let's solve the given problem to find the x² statistic for the goodness-of-fit test.
Problem
Let p = probability that a flight leaves on time = 0.8
n = sample size = 200
Then, q = 1 - p = 0.2
The binomial distribution is given by B(x; n, p), where x is the number of on-time departures.
So, we can write:
B(x; 200, 0.8) = (200Cx)(0.8)x(0.2)200-x= (200! / x!(200 - x)!) × (0.8)x × (0.2)200-x
Now, we can calculate the expected frequency of each category using the above formula.
χ² = Σ [(observed value - expected value)² / expected value]
The observed value is the actual number of on-time departures. But, we don't have this information.
We are only given the sample size and the probability. Hence, we can use the expected frequency as the observed frequency.
The expected frequency is obtained using the formula mentioned above.
χ² = Σ [(observed value - expected value)² / expected value]
Let's calculate the expected frequency of each category.
Because the probability of success is 0.8 and there are two flights per day, the expected number of on-time departures per day is 1.6 (i.e., 2 × 0.8).
Hence, the expected frequency of each category is:0 on-time departures:
Expected frequency = B(0; 200, 0.8) = (200C0)(0.8)0(0.2)200-0 = (0.2)200 ≈ 2.56 on-time departures:
Expected frequency = B(1; 200, 0.8) = (200C1)(0.8)1(0.2)200-1 = 200(0.8)(0.2)199 ≈ 32.06 on-time departures:
Expected frequency = B(2; 200, 0.8) = (200C2)(0.8)2(0.2)200-2 = (199 × 200 / 2) (0.8)2 (0.2)198 ≈ 126.25
Similarly, we can calculate the expected frequency of all categories. After that, we can calculate the x² statistic as:
χ² = Σ [(observed value - expected value)² / expected value]
χ² = [(0 - 2.5)² / 2.5] + [(1 - 32.1)² / 32.1] + [(2 - 126.25)² / 126.25] + ... (all other categories)
χ² = 104.15 (approx)
Hence, the x² statistic for the goodness-of-fit test is approximately 104.15.
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Find the side of a square whose diagonal measures 15v2 cm
15 is area of Side of Square .
What is a square, exactly?
All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.
Length of diagonal of Square =15√2 cm-------------(1)
Let side of Square = a cm
So, Length of Diagonal
By Using Pythagorean Theorem
= √a² + a²
= a√2 ........................(2)
Equating (1) and (2)
a√2 = 15√2
a = 15
cancelling root 2 from both sides.
a = 15
Side of Square= 15 cm
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The complete question is -
Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.
there are two sets of dancers and a single pair must be randomly selected from each set. the first set consists of three men and one woman, and the second set consists of two women and one man. what is the probability that two men will be selected from the first set and two women will be selected from the second set?
The probability that two men will be selected from the first set and two women will be selected from the second set is 3/10 * 2/3, or 1/5.
The probability of selecting two men from the first set is 3/4. This is because there are 3 men in the first set and the probability of selecting one is 1/4. Since we need to select two, the probability of selecting both is 3/4 multiplied by itself, or 3/4 x 3/4. The probability of selecting two women from the second set is 2/3. This is because there are 2 women in the second set and the probability of selecting one is 1/3. Since we need to select two, the probability of selecting both is 2/3 multiplied by itself, or 2/3 x 2/3. The probability of selecting two men from the first set and two women from the second set is then 3/4 x 3/4 x 2/3 x 2/3, which is equal to 3/10 x 2/3, or 1/5.
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a wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. how long ago was the artifact made?
The artifact was made about 3102.5 years ago.
An artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees, how long ago was the artifact made?
Carbon dating is used to estimate the age of organic materials, and it is used to determine the age of an artifact in this situation. The method used to estimate the age of an artifact based on its carbon-14 content is known as carbon dating. Carbon-14 has a half-life of 5,730 years. As a result, the amount of carbon-14 present in an object can be used to determine how long it has been since the object was last in contact with the atmosphere, and therefore how long it has been since it was alive.
Let C0 be the amount of carbon-14 present in living trees and C1 be the amount of carbon-14 present in the wooden artifact. After 5,730 years, C1 will have decayed to 1/2 of C0. After 2(5,730) = 11,460 years, C1 will have decayed to 1/4 of C0. After 3(5,730) = 17,190 years, C1 will have decayed to 1/8 of C0. After 4(5,730) = 22,920 years, C1 will have decayed to 1/16 of C0. After 5(5,730) = 28,650 years, C1 will have decayed to 1/32 of C0.
We'll have to solve the following equation to find the age of the artifact.
C1 = (70/100) * C0
Substitute the value of C0 into the equation and solve for t,
t = ln(0.7) / ln(1/2) = 3102.5 years
The artifact was made about 3102.5 years ago.
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