Write a linear function for the data in the table.
X
y
0
8
1
4.5
2
1
3
-2.5
4
-6

a) Sin2θ = 22/20 = 11/10

b) cos 2θ = 2(17/20) = 17/10

c)tan 2θ = 2(11/17) = 22/17

The trigonometric ratios are six functions that relate the angles of a right triangle to the lengths of its sides. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

If sin θ = 11/20

The missing side of the triangle is;

b = √20^ - 11^2

b = 17

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The larger container will hold 500 ounces of soup when filled.

We know that the formula for the volume of cylinder is: V = πr²h

Let us assume that for the smaller container, d₁ represents the diameter, r₁ represents the radius, h₁ represents the height of the container and v₁ represents the volume of the container.

So, using above formula, the volume of the smaller container would be,

v₁ = π × r₁² × h₁

10 = π × r₁² × h₁

For the larger container, d₂ represents the diameter, r₂ represents the radius, h₂ represents the height of the container and v₂ represents the volume of the container.

Using above formula, the volume of the larger container would be,

v₂ = π × r₂² × h₂

The larger container’s diameter is 5​ times larger than the small container’s diameter.

so, we get an equation

⇒ d₂ = 5d₁

⇒ r₂ = 5r₁

Also, the lrger container is 2​ times taller than the small container.

⇒ h₂ = 2h₁

Consider the ratio of volume of larger cotainer to the volume of smaller container.

v₁/v₂ =  (π × r₁² × h₁) / ( π × r₂² × h₂)

10/v₂ =  (r₁² × h₁) / ( (5r₁)² × (2h₁))

10/v₂ =  (r₁² × h₁) / ( 50 × r₁² × h₁)

10/v₂ = 1/50

v₂ = 500 ounces

which is 50 times more than the smaller container.

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The complete question is:

At a farmer’s market, a vendor sells soup that comes in two different-sized containers, both shaped like cylinders. When the small container is filled, it holds10​ ounces of soup. The larger container’s diameter is 5​ times larger than the small container’s diameter, and it is 2​ times taller than the small container. How many ounces of soup will the larger container hold when filled?

By using only the positive exponents , the answer of the expression (2x⁻²y³/3xy⁻⁴) is  (2y⁷)/(3x³)  .

The Exponents, are defined as a shorthand way of representing the repeated multiplication of a base number by itself. The exponent is the small raised number that indicates how many times the base number is multiplied by itself.

For example, in the expression 2⁴, the base number is 2 and the exponent is 4,

We use the law of exponents to simplify the expression :

the expression is : (2x⁻²y³/3xy⁻⁴) ;

by using the rule that : a⁻ⁿ = 1/aⁿ  ;

we get ;

⇒ (2y³y⁴)/(3xx²) ;

On adding the exponents having the same base ,

we get ;

⇒ (2y⁷)/(3x³)  ;

Therefore , the simplified value of (2x⁻²y³/3xy⁻⁴) is (2y⁷)/(3x³) .

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The given question is incomplete , the complete question is

Write answer only using positive exponents , (2x⁻²y³/3xy⁻⁴) .

Answer:

10

Step-by-step explanation:

i love how you look like a dinosaur

Answer:

8(8+7)

Step-by-step explanation:

64+56
8 is the GCF
8(8+7)

The relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value. Hence, option 2 is the correct answer.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that a function is a relationship between inputs where each input is related to exactly one output.

In the given graph (2,2) and (3,2) have the same y value that is two inputs have same output.

Hence, the relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value and option 2 is the correct answer.

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Answer:

0.238

Step-by-step explanation:

Use identities:

Then apply to the left side of the given equation:

Proved

The volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

The volume of a right circular cylinder can be calculated using the formula:

V = π * r² * h

Where r is the radius and h is the height of the cylinder.

Plugging in the values for r and h, we get:

V = π * 7² * 1.5

V = π * 49 * 1.5

V = 73.5 * 1.5

Therefore, V = 110.25

So the volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.

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Answer:

Option B

Step-by-step explanation:

The green graph represents the percentage of calls with the Chicago service center.
For December 1993, the percentage of calls is coming out to at least 95 percent. In addition, the graph is increasing as months go by. Based on these two analysis, the estimate percentage of calls within 10 seconds in January of 1994 is:

Option B: 98

To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.

Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial.  The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.

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Answer: D

Step-by-step explanation: I can't really see everything well but I think it is D

Step-by-step explanation:

These points are in (X, Y) form. What you want to do is plug in the X coordinates into the equation and see if it equals the Y coordinate.

Equation: Y = X + 4

Point A: (-1, 3)

(-1) + 4 = 3

Point B: (2, 6)

(2) + 4 = 6

Point C: (-2, -2)

(-2) + 4 = 2

Point D: (2, 4)

(2) + 4 = 6

Only point A and point B equal their Y coordinate, making A and B the only correct answers.

There were 297 children and 185 adults who swam that day. Let x be the number of children and y be the number of adults who swam that day.

According to the problem, we know that:

x + y = 482 ---(1) (total number of people who swam)
1.5x + 2y = 815.5 ---(2) (total revenue generated)

To solve for x and y, we can use any method of solving a system of linear equations, such as substitution or elimination. Here's how to solve using the substitution method:

From equation (1), we can write:

x = 482 - y

Substituting this into equation (2), we get:

1.5(482 - y) + 2y = 815.5

Simplifying and solving for y, we find:

723 - 1.5y + 2y = 815.5

0.5y = 92.5

y = 185

Substituting this value of y back into equation (1), we find:

x + 185 = 482

x = 297

Therefore, there were 297 children and 185 adults who swam that day.

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Answer:

one fifth would be espressos so 3

Step-by-step explanation:

The statement is true. A confidence interval is a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.

In this case, we are interested in the odds ratio between MI (yes, no) and treatment (placebo, aspirin).

If the 95% confidence interval for the odds ratio between MI and placebo is (1.44, 2.33), this means that we can be 95% confident that the true odds ratio falls between these two values. This implies that the odds of having an MI are between 1.44 and 2.33 times greater for those taking the placebo compared to those taking aspirin.

When we switch the rows so that aspirin is in the first row, we need to take the reciprocal of the upper and lower bounds of the confidence interval to get the new interval. This is because the odds ratio is calculated as the odds of MI for one group divided by the odds of MI for the other group, and switching the groups changes the ratio.

So, if we take the reciprocal of the lower and upper bounds of the original interval, we get:

1/2.33 and 1/1.44

which is the new 95% confidence interval for the odds ratio when aspirin is in the first row. Therefore, the statement is true.

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Answer:

(6 x 1.5 + 4.9) x 4 = 55.6

Step-by-step explanation:

If the sum of three successive integers even numbers is 6000, then their values must be 1998, 2000, and 2002.

In addition tangere is the root of the Latin word integer, which meaning "whole" and "untouched." The word "entire" is derived from the French word entier, which also means entire and integer. The expression was once used to describe a multiple of 1 or the whole part of a mixed number. The definition of the term was given as the collection of all positive integers, which is the same as the collection of all natural numbers. The concept of integer was expanded to include negative integers as the significance of those numbers came to be realized through time. For instance, in his 1765 book Elements of Algebra, Leonhard Euler stated that integers might contain both positive and negative values. Up until about the middle of the 20th century, most European mathematicians ignored negative numbers.

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Answer:

Step-by-step explanation:

yes no yes

Answer:

Step-by-step explanation:

Mariana's quote: 135

Vicent's quote: 34x+67

Say x=1, 34(1)+67=101

For 1 hour of Vincent's work it would be $101.

Say x=2. 34(2)+67=135

Vincent would have to work for two hours to charge the exact same as Mariana.

The hourly rate that the batches of cookies were made is given as follows:

4.85 batches per hour.

The hourly rate is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate is obtained dividing the total production by the time in hours.

The parameters for this problem are given as follows:

Hence the rate is given as follows:

40/8.25 = 4.85 batches per hour.

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5 baskets of tomatoes can make 7 1/2 quarts of tomato sauce.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

Given that, we get 3 quarts of tomato sauce from 2 baskets of tomatoes.

Thus,

2 baskets = 3 quarts

5 baskets = x

Use the method of cross multiplication or butterfly method for multiplication.

x = (3)(5)/2

x = 15/2

x = 7 1/2

Hence, 5 baskets of tomatoes can make 7 1/2 quarts of tomato sauce.

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Answer: D, 25

Step-by-step explanation:

A parallelogram is 360 degrees, and every angle appears twice, so we can set up an equation to solve for the missing variable.

[tex]360 = 2(65) + 2(5y)[/tex]

Multiplying each angle by two shows that each angle appears twice in the shape, and once we multiply the values, we can simplify the equation to:

[tex]360-130=10y[/tex]

360 - 130 is 230, so divide both sides by 10 and you get 23 as the answer.

Answer:

if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price

Step-by-step explanation:

Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the typing rate in characters per minute, we need use arithmetic operation of division.

Divide the number of characters by the number of minutes -

Typing rate = Number of characters / Number of minutes

In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -

Typing rate = 1274 / 7 = 182

Therefore, the typing rate is 182 characters/minute.

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The width of the bedroom is approximately 7.32 feet.

A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.

Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.

Now, we can use the given area of the bedroom to set up an equation:

Area of rectangle = Length x Width

84 = (x+5) x x

Simplifying this equation, we get:

84 = x² + 5x

Rearranging, we get:

x² + 5x - 84 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:

x = (-5 ± √(5² - 4(1)(-84)))/2(1)

Simplifying this, we get:

x = (-5 ± √721)/2

We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:

x = (-5 + √721)/2

x ≈ 7.32 feet

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The inequality represented by the graph is given as follows:

y < 4x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 1, y increases by 4, hence the slope m is given as follows:

m = 4.

The values to the left of the line are shaded, hence the inequality represented by the graph is given as follows:

y < 4x - 2.

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Number of ways are there to choose this focus group where all three students do not all come from the same major is 240,000

It is given that a school have three majors i.ie, business, math and psych

Number of students in business majors is 100

Number of students in math majors is 60

Number of students in psych majors is 40

Total number of students (100+60+40) = 200 students

Three different students are chosen to be interviewed for a focus group.

Therefore, number of student in focus group = 3

Now, number of ways are there to choose this focus group where all three students do not all come from the same major

= [tex]^{100}C_{1} \times ^{60}C_{1}\times^{40}C_{1}[/tex]

= 100×60×40

= 240,000 ways

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The ratio of employees who work in the office to employees who work in the warehouse is 5: 7

A ratio is a comparison of two quantities, and it is expressed as a fraction.

To find the ratio of employees who work in the office to employees who work in the warehouse, we need to first determine the total number of employees. In this case, we add the number of employees in the office (20) to the number of employees in the warehouse (28), which gives us a total of 48 employees.

Next, we can express the ratio of office employees to warehouse employees as a fraction by using the following formula:

Ratio = Quantity of First Term / Quantity of Second Term

In this case, the first term is the number of employees who work in the office (20) and the second term is the number of employees who work in the warehouse (28). So, the ratio of office employees to warehouse employees is:

Ratio = 20 / 28

Simplifying this fraction, we get:

Ratio = 5 / 7

This means that for every 5 employees who work in the office, there are 7 employees who work in the warehouse.

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By induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

1. To prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders, we can use the following steps:

2. Base case: For k = 1, we have a single node, and if we remove the root, there is no tree left.

3. Inductive hypothesis: Suppose that the result holds for some k = n, that is, if we remove the root of an n-th order binomial tree, it results in n binomial trees of the smaller orders.

4. Inductive step: We need to prove that the result also holds for k = n + 1. To do this, we consider a (n + 1)-th order binomial tree. According to the definition, this tree is formed by joining two n-th order binomial trees. Let's call them T1 and T2. If we remove the root of this tree, the two subtrees T1 and T2 will become the n binomial trees of the smaller orders. These n binomial trees are all distinct because they correspond to the different possible combinations of nodes in the two subtrees T1 and T2.

Therefore, by induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

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