Answer: x=4/3
Step-by-step explanation:
3x-2=2
3x=2+2
3x=4
x=4/3
Find cot0, sin 0, and csc 0, where 0 is the angle shown in the figure.
Give exact values, not decimal approximations.
0
11
8
cot 0 = 0
sin 0 = 0
csc 0 = 0
Answer:
Step-by-step explanation:
sun cos
A business has a savings account that earns a 3% annual interest rate. At the end of 1996, the business had $4,000 in the account. The
formula F
+
100
is used to determine the amount in the savings account.
p(1
a)
. Fis the final amount,
⢠p is the initial investment amount,
. Ris the annual interest rate, and
. Tis the time in years.
To the nearest dollar, how much did the business initially invest in 1991?
To the nearest dollar, the business initially invested approximately $3,449 in 1991.
To determine the initial investment in 1991, we can use the formula F = P(1 + R/100)^T, where F is the final amount, P is the initial investment amount, R is the annual interest rate, and T is the time in years.
In this case, F = $4,000 (the amount in the account at the end of 1996), R = 3% (the annual interest rate), and T = 5 years (1996 - 1991). We need to solve for P, the initial investment amount.
First, let's rewrite the equation: P = F / (1 + R/100)^T
Now, we can plug in the known values: P = 4000 / (1 + 3/100)^5
Next, we calculate the denominator: (1 + 0.03)^5 = 1.159274
Then, we divide the final amount by the denominator to find the initial investment: P = 4000 / 1.159274
Lastly, rounding to the nearest dollar, we get: P ≈ $3,449
So, the business initially invested approximately $3,449 in 1991.
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Casey recently purchased a sedan and a pickup truck at about the same time for a new business. The value of the sedan S, in dollars, as a function of the number of years t after the purchase can be represented by the equation S(t)=24,400(0. 82)^t. The equation P(t)=35,900(0. 71)^t/2 represents the value of the pickup truck P, in dollars, t years after the purchase. Analyze the functions S(t) and P(t) to interpret the parameters of each function, including the coefficient and the base. Then use the interpretations to make a comparison on how the value of the sedan and the value of the pickup truck change over time
Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.
The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.
Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.
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Select the correct answer from each drop-down menu.
Coach Loren asks Kerry to analyze the batting percentages of players on the softball team.
Complete the sentences with the correct terms.
Coach Loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of
.
Kerry could give her the
or the
of the data set.
Answer:
Kerry could give her the range or the standard deviation of the data set.
Step-by-step explanation:
Coach Loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of variability.
Kerry could give her the range or the standard deviation of the data set.
You want your savings account to have a total of $23,000 in it within 5 years. If you invest your money in an account that pays 6.8% interest compounded continuously, how much money must you have in your account now?
You must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.
To achieve a savings account balance of $23,000 in 5 years with an interest rate of 6.8% compounded continuously, you will need to use the formula for continuous compounding: A = P * e^(rt), where A is the future value, P is the principal amount (initial deposit), r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).
In this case, A = $23,000, r = 0.068, and t = 5 years. You need to solve for P, the principal amount:
$23,000 = P * e^(0.068 * 5)
Now, you can solve for P:
P = $23,000 / e^(0.068 * 5)
P ≈ $16,465.55
So, you must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.
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Question 1 2 pts A researcher is interested in determining whether sugar consumption increases memory. She recruits 100 participants and randomly assigns them to one of two groups, sugar vs. No sugar. She then measures their word recall: Sugar group: M = 4. 5, SD = 1. 8, n = 55 • No sugar group: M = 2. 6, SD =. 68, n = 45 1. Is this an example of a quasi-experimental design? (yes or no) 2. What is the dependent variable? 3. What is the independent variable?
1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.
2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.
3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.
The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.
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Find the area of each shaded sector. round to the hundredths place.
To find the area of each shaded sector and round to the hundredths place, I'll need some more information, such as the radius of the circle and the measure of the central angle of the sector. Please provide these details so I can assist you with the calculation.
The area of the shaded sector is 1330.81 ft²
Given, ∠GKH = 26° and ∠JKI = 90°
The area that is not shaded has a total of 90° + 26° = 116°.
A circle has a total angle of 360°, so the area that is shaded must be
360° - 116° = 244°
Given, HK = 25 ft
Radius of circle = 25 ft
We know that the formula for the area of the sector of a circle is
Area = [tex]\frac{\pi \theta r^2}{360^\circ}[/tex]
= (π × 244 × (25)² )/ 360
= 7625π/18
= 1330.81 ft²
Hence, the area of the shaded sector is 1330.81 ft²
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Given question is incomplete, the complete question is below
Find the area of each shaded sector. round to the hundredths place.
Mariana tiene un peso de 175 libras y su nutrióloga le ha otorgado una nueva dieta y ella misma a creado una nueva rutina de ejercicio su comida semanal consiste en lo siguiente 3 libras de pollo, 9 libras de frutas, 15 libras de verduras cocinadas o crudas y solo 1 libra de tortilla o pollo
¿cual es el peso en kilogramos de mariana?
¿cuantos kilos debe conseguir de pollo a la semana?
¿cuantos de fruta?
¿cuantos kg de verduras deberá consumir?
plis es para hoy
El peso de Mariana en kilogramos es aproximadamente 79.378 kg. Debe conseguir 1.361 kg de pollo a la semana, 4.082 kg de frutas y 6.803 kg de verduras.
How to convert Mariana's weight from pounds to kilograms?Para convertir el peso de Mariana de libras a kilogramos, debemos recordar que 1 libra equivale a aproximadamente 0.4536 kilogramos. Por lo tanto:
Peso de Mariana en kilogramos = 175 libras * 0.4536 kg/libra ≈ 79.3792 kg
Entonces, el peso de Mariana es aproximadamente 79.3792 kilogramos.
En cuanto a la cantidad de pollo que Mariana debe conseguir a la semana, la dieta establece que debe consumir 3 libras de pollo. Para convertirlo a kilogramos:
Cantidad de pollo a la semana = 3 libras * 0.4536 kg/libra ≈ 1.3618 kg
Por lo tanto, Mariana debe conseguir aproximadamente 1.3618 kilogramos de pollo a la semana.
De manera similar, para las frutas, la dieta establece 9 libras. Convertimos a kilogramos:
Cantidad de frutas a la semana = 9 libras * 0.4536 kg/libra ≈ 4.0824 kg
Por lo tanto, Mariana debe conseguir aproximadamente 4.0824 kilogramos de frutas a la semana.
Para las verduras, la dieta establece 15 libras. Convertimos a kilogramos:
Cantidad de verduras a la semana = 15 libras * 0.4536 kg/libra ≈ 6.804 kg
Por lo tanto, Mariana debe consumir aproximadamente 6.804 kilogramos de verduras (cocinadas o crudas) a la semana.
En resumen, el peso de Mariana es de aproximadamente 79.3792 kilogramos. Debe conseguir alrededor de 1.3618 kilogramos de pollo, 4.0824 kilogramos de frutas y 6.804 kilogramos de verduras a la semana.
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Katya collects badges from the National Parks Junior Rangers program.
She wants to know how many cases she needs to display her collection. She can fit 8 badges in one case.
There are 207 National Parks that participate in the Junior Ranger badge program.
She does not have the badges for 165 parks. Which equation should she use first to solve this problem?
A)b=207-165
B)207+165
C)42 divided by 8
D)42*8(42 multiplied by 8)
After solving equation, Katya needs 5 or 6 display cases to display all of her badges, depending on how she chooses to group them.
The number of badges Katya has is not explicitly given in the problem. Therefore, we need to first find the total number of badges Katya has earned by subtracting the number of parks for which she doesn't have badges from the total number of participating parks.
The equation to use for this is:
b = 207 - 165
where b is the total number of badges Katya has earned.
Option A is the correct equation, which simplifies to:
b = 42
This means Katya has earned 42 badges.
Next, we need to find out how many display cases Katya needs. We know that she can fit 8 badges in one case, so we can use division to find the number of cases needed:
c = b / 8
where c is the number of cases needed.
Substituting the value of b from the previous equation, we get:
c = 42 / 8
Option C is the correct equation, which simplifies to:
c = 5.25
This means that Katya needs 5 or 6 display cases to display all of her badges, depending on how she chooses to group them.
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Nataly compra una falda, una blusa y un saco con los precios de la lista son s/78,s/65 y s/240 pero al pagar la falda se la dejan a s/69,la blusa a s/52 y el sacon a s/198.¿cuánto se ahorró nataly?
Nataly saved s/64.
Nataly compró una falda, una blusa y un saco por s/78, s/65 y s/240, respectivamente. Pero compró la falda por s/69, la blusa por s/52 y el saco por s/198. ¿Cuánto se ahorró Nataly?The original prices for the items are:
Skirt: s/78
Blouse: s/65
Jacket: s/240
The discounted prices Nataly paid are:
Skirt: s/69
Blouse: s/52
Jacket: s/198
To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:
savings = (78 - 69) + (65 - 52) + (240 - 198)
savings = 9 + 13 + 42
savings = s/64
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a chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. the chi-square test statistic and p -value of the test were 19.02 and 0.025, respectively. which of the following is the correct interpretation of the p -value in the context of the test? responses assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller. assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller. assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger. there is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same. there is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same. there is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.
The correct statement for p-value in chi-square is : Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger, option B.
A test that evaluates how well a model matches real observed data is the chi-square (2) statistic. A chi-square statistic can only be calculated with data that is random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a sizable enough sample. The outcomes of a fair coin flip, for instance, satisfy these requirements.
To test hypotheses, chi-square tests are frequently employed. Given the size of the sample and the number of variables in the relationship, the chi-square statistic examines the magnitude of any differences between the predicted findings and the actual results.
According to the total number of variables and samples used in the experiment, degrees of freedom are utilised in these tests to assess if a certain null hypothesis can be rejected. Like with any statistic, the results are more trustworthy the greater the sample size.
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Complete question:
A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?
A) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller.
B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
C) Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
D) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same.
E) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.
identify B on the following diagram: a: y-axis b origin c quadrant I d x-axis
Answer:
b
Step-by-step explanation:
point B has coordinates (0, 0 ) which is the origin
use the ratio test to determine whether the series is convergent or divergent. [infinity] 13^n N = 1 (n + 1)62n + 1 identify an.
Evaluate the following limit.
lim n → [infinity]
an + 1
an
Since lim n → [infinity]
an + 1
an
We can use the ratio test to determine whether the series ∑(n=1[tex])^(infinity)[/tex][tex]13^n[/tex]/ [(n+1)[tex]6^(2n+1)[/tex]] is convergent or divergent.
We evaluate the limit:
lim n → ∞ [tex]|(13^(n+1) / [(n+2)6^(2n+3)]) / (13^n / [(n+1)6^(2n+1)])|[/tex]
= lim n → ∞ [tex]|(13^(n+1) / 13^n) * [(n+1)6^(2n+1) / (n+2)6^(2n+3)]|[/tex]
= lim n → ∞ [tex]|13 / 6^2| * |(n+1)/(n+2)|[/tex]
= 13/36
Since the limit is less than 1, by the ratio test, the series is convergent.
To find the value of a_n, we can substitute n = 1 into the formula:
a_n = [tex]13^n / [(n+1)6^(2n+1)][/tex]
a_1 = [tex]13 / [(1+1)6^(2+1)] = 13 / (2*6^3)[/tex]
Therefore, a_1 = 13 / 432.
Note that we only needed to find the value of a_1 to apply the ratio test and determine the convergence of the series.
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What is the slope of the line?
Choose the function that the graph represents.
Click on the correct answer.
y = f(x) = log7x
y = f(x)=x7
y = f(x) = 7x
Answer:
y=f(x) = log7x
Just trust me
The graph best represents the function y = f(x) = 7x, an exponential function.
The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.
The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.
The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.
The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.
Thus, the graph best represents the function y = f(x) = 7x, an exponential function.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Unlocked badge showing an astronaut’s boot touching down on the moon
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Solve x by using square roots.
12-(x-2)^2=3
The required solution to the given equation for x using square roots is x = 5 or x = -1.
The quadratic equation is given as follows:
12-(x-2)² = 3
To solve the equation 12-(x-2)² = 3 using square roots, we need to isolate the squared term on one side of the equation and then take the square root of both sides.
We have:
12-(x-2)² = 3
-(x-2)² = -9
(x-2)² = 9
Apply the square root property in the equation,
x-2 = ±√9
x-2 = ±3
x = 2 ± 3
x = 5 or x = -1
Therefore, the solution for x using square roots is x = 5 or x = -1.
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Jorge and his two brothers each water the plants.
Jorge's watering can holds half as much water as
his older brother's watering can. His younger
brother's watering can holds 8 cups. Altogether, the
watering cans hold 2 gallons. How many cups does
Jorge's watering can hold?
Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.
Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.
We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).
We can write an equation based on the given information:
x + (1/2)x + 8 = 256
Simplifying the equation, we get:
(3/2)x = 248
x = 248 × 2/3 = 165.33
Therefore, jorge's watering can holds 4 cups of water.
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The domain of the function is the set of all real numbers, and the range of the function is the set of all real numbers greater than or equal to ------.
The range of the function is the set of all real numbers greater than or equal to -4.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The function assumes values of y = -4 or greater, which represent the range of the graphed function.
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A store sells packages of comic books with a poster. A poster and 2 comics cost $7.50. A poster and 11 comics cost $16.50. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Suppose another store sells a similar package, modeled by a linear function rule with initial value $5.75. Use pencil and paper. Explain which store has the better deal.
The linear function rule is y =
The linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x and for 10 comic books, the second store has the better deal.
What do you mean by Linear function ?A linear function is a mathematical function where the graph of the function is a straight line. It can be written in the form y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis). The slope represents the rate of change of the function, while the y-intercept is the value of the function when x is equal to zero.
To write a linear function rule that models the cost y of a package containing any number x of comic books, we can use the given information to set up a system of equations:
Poster + 2 Comics = $7.50
Poster + 11 Comics = $16.50
We can solve for the cost of the poster and the cost of one comic book by subtracting the first equation from the second:
9 Comics = $9.00
1 Comic = $1.00
Then, we can use the cost of one comic to set up a linear function rule:
y = cost of poster + cost of x comics
y = $6.50 + $1.00x
Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x.
For the second store, the linear function rule is given as y = $5.75 + $1.00x.
To determine which store has the better deal, we can compare the cost of each package for a specific number of comic books. For example, if we want to buy 10 comic books, the cost at the first store would be:
y = $6.50 + $1.00(10) = $16.50
The cost at the second store would be:
y = $5.75 + $1.00(10) = $15.75
Therefore, for 10 comic books, the second store has the better deal. However, for a different number of comic books, the better deal may be at a different store. We can use the linear function rules to compare the costs for any number of comic books
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Solve this: 12C11
And solve the others too
The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84
Also, the number of ways is 30045015
Solving the combination expressionsFrom the question, we have the following parameters that can be used in our computation:
¹²C₁₁
The formula for combination is
ⁿCₓ = n!/[(n - x)! * x!]
So, we have
¹²C₁₁ = 12!/[(12 - 11)! * 11!]
Evaluate
¹²C₁₁ = 12
Using the above as a guide, we have the following:
¹²C₁₀ = 12!/[(12 - 10)! * 10!]
¹²C₁₀ = 66
¹²C₅ = 12!/[(12 - 5)! * 5!]
¹²C₅ = 792
¹²C₁ = 12!/[(12 - 1)! * 1!]
¹²C₁ = 12
¹²C₁₂ = 12!/[(12 - 12)! * 12!]
¹²C₁₂ = 1
⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]
⁵C₄ + ⁵C₃ = 15
⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]
⁵C₃/⁵C₂ = 1
4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]
4⁷C₂ = 84
For the number of ways to get people hired, we have
n = 30
x = 10
So, we have
³⁰C₁₀ = 30!/[(30 - 10)! * 10!]
³⁰C₁₀ = 30045015
Hence, the number of ways to get them hired is 30045015 ways
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The diagram shows a pyramid with a square base.
The triangular faces are congruent isosceles triangles.
(a) Write down the number of planes of symmetry of this pyramid.
Answer:
4
Step-by-step explanation:
You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.
Please hurry I need it ASAP
Answer:
x = 18
Step-by-step explanation:
We Know
(10x - 4) + (x - 14) must equal 180°
Find the value of x.
Let's solve
10x - 4 + x - 14 = 180
11x - 18 = 180
11x = 198
x = 18
So, x = 18 is the answer.
Mrs Gibson is sending a package to her son through the mail the package is a rectangular prism is 12 inches long,12 inches wide and 48 inches high what is the volume in cubic feet
The volume of the package which is 12 inches long, 12 inches wide, and 48 inches high is 6912 inches³ or 4 cubic feet.
Given length of the package which is in rectangular prism shape (L) = 12 inches
similarly, width of the package (W) = 12 inches
height of the package (H) = 48 inches
To know the volume of the package which is in the rectangular prism shape the formula is V= L x W x H
The substituting the given values in the above equation, we can obtain the volume of the package.
So,
L x W x H = 12 x 12 x 48 = 6912 inches³
To convert the cubic inches into the cubic feet we have to divide the obtained value by 1728.
So, [tex]\frac{6912}{1728}[/tex] = 4 feet³
From the above explanation, we can conclude that the volume of the given package of rectangular prism shape is 4 feet³.
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the linear optimization technique for allocating constrained resources among different products is: linear regression analysis. linear tracking analysis. linear disaggregation. linear programming. linear decomposition.
The linear optimization technique for allocating constrained resources among different products is linear programming. (option d).
In the context of allocating constrained resources, linear optimization aims to maximize the output of a system while minimizing the input required to produce that output. This is achieved by formulating the problem as a set of linear equations or inequalities, which represent the constraints on the resources.
The linear equations or inequalities define the relationship between the input and output variables, which are typically expressed as linear functions. These functions represent the production possibilities of each product or activity and the available resources, such as labor, materials, and equipment.
The goal of linear optimization is to find the optimal values of the input and output variables that satisfy the constraints and maximize the objective function. The objective function is a linear function that represents the measure of performance or profitability of the system.
Hence the correct option is (d).
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If Kawan paints the visible outside
surfaces of his shed, what is the
total surface area that he paints?
3 ft
5
8 ft
8ft
8ft
A. 256 ft²
B. 286 ft²
C. 360 ft²
D. 444 ft²
If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².
The area of a triangle of altitude h and base b is given by;
A = 0.5bh
Therefore the area of one triangle face ;
At = 0.5 × 8 × 5
At = 20ft²
Area of a rectangle of length l and breadth b is;
A = lb
Therefore the area of a rectangle face;
Ar = 8 × 3
Ar = 24ft²
We have 2 triangle faces and 2 rectangle face, therefore total surface area as;
A = 2At + 2Ar
A = 2×20 + 2×24
A = 40 + 48
A = 88ft²
Therefore the answer is; 88ft².
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A supermarket has three options for purchasing a brand of cereal:
Standard $2. 49 for 220g
Economy $5. 00 for 725g
Supersize $11. 50 for 2kg
Compare the cost of each for 100g, and order the brands from cheapest to most expensive
A comparison of the cost of each for 100 g indicates that the standard which costs about $1.13 per 100 grams is more expensive than the supersize which costs about $0.69 per 100 g and the supersize is more expensive than the economy which costs $0.575 per 100 g.
The cost per 100 g the standard is more than the cost per 100 g of the supersizeThe cost per 100 g of the supersize is more than the cost of the economy brand per 100 grams.The order of the cost of the brands from cheapest to most expensive can be presented as follows;
Supersize > Economy > StandardWhat is a cost per unit?The cost per unit is the cost of a number of items, divided by the number of units of the item.
The unit cost of the brands of cereal sold at the supermarket are therefore;
Unit cost per 100 gram for Standard = $2.49/220 g × 100 ≈ $1.13/g
Unit cost per gram for Economy = $5.00/725 g × 100 = $100/145/ g ≈ $0.69/g
Unit cost per gram for Supersize = $11.50/2kg × 100 = $1150/2,000 g ≈ $0.575/g
Based on the above unit cost, we get;
1.13 > 0.69 > 0.575
Therefore, the cheapest brand is the supersize with a cost per 100 gram of $0.575/g, followed by the economy, with a cost per 100 grams which is about $0.69/g then the most costly is the standard, with a cost per 100 gram of $1.13/g
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Estimate the area under the curve f(x)=1/x on [1,2] by using 4 approximating rectangles with a) left endpoints, b) right endpoints, then c) take the average.
our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.
To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.
a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.
So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,
f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.
The area of each rectangle is width times height, so the areas are
0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.
Adding these areas together, we get an estimate of the total area under the curve as
0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.
b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are
1.25, 1.5, 1.75, and 2.
The heights are f(x) evaluated at the right endpoint. So, the heights are
f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.
The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as
0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,
which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:
(0.76+0.76) / 2 = 0.76.
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Find the linearization of the function f (x, y) = √x^2 + y^2 at the point (3, 4), and use it to approximate f (2.9, 4.1).
Therefore, the linearization predicts that f(2.9, 4.1) is approximately 4.142.
To find the linearization of the function f(x, y) = √x^2 + y^2 at the point (3, 4), we need to find the partial derivatives of f with respect to x and y, evaluate them at (3, 4), and use them to write the equation of the tangent plane to the surface at that point.
First, we have:
∂f/∂x = x/√(x^2 + y^2)
∂f/∂y = y/√(x^2 + y^2)
Evaluating these at (3, 4), we get:
∂f/∂x(3, 4) = 3/5
∂f/∂y(3, 4) = 4/5
So the equation of the tangent plane to the surface at (3, 4) is:
z - f(3, 4) = (∂f/∂x(3, 4))(x - 3) + (∂f/∂y(3, 4))(y - 4)
Plugging in f(3, 4) = 5 and the partial derivatives, we get:
z - 5 = (3/5)(x - 3) + (4/5)(y - 4)
Simplifying, we get:
z = (3/5)x + (4/5)y - 1
This is the linearization of f(x, y) = √x^2 + y^2 at the point (3, 4).
To approximate f(2.9, 4.1), we plug in x = 2.9 and y = 4.1 into the linearization:
z = (3/5)(2.9) + (4/5)(4.1) - 1
z ≈ 4.142
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be able to plot all of the data above a label. Which should this fraction be?
Step-by-step explanation:
To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.
The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:
3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1
Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).
Therefore, the students should use 1/8 as the fraction for the line plot.