Liam bought snacks for his team's practice. He bought a bag of oranges for $2.13 and a 3-pack of juice bottles. The total cost before tax was \$9.45 . Write and solve an equation which can be used to determine , how much each bottle of juice costs?

Answer:

4,050 ft^3

Step-by-step explanation:

Separate the figure into a cube and a square pyramid.

Volume of the cube (a^3):

15 x 15 x 15 = 3,375

3,375 ft^3

Volume of the square pyramid (lwh/3):

15 x 15 x 9/3 = 675

675 ft^3

Add the volumes of both figures:

675 ft^3 + 3,375 ft^3 = 4,050

The volume of the whole figure is 4,050 cubic feet.

Hope this helps!

The confidence interval for the proportion of registered voters who believe illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship is 0.5998 to 0.6602.

To analyze the results of the poll, we can use the given information to calculate the confidence interval.

Given:

- Sample size (n): 904 registered voters

- Proportion who answered "should be" eligible for legal citizenship (p): 63%

- Margin of error (E): 3%

- Confidence level: 95%

To calculate the confidence interval, we can use the formula:

Confidence Interval = p ± (Z * √((p * (1 - p)) / n))

First, let's find the critical value (Z) corresponding to a 95% confidence level. Since the confidence level is 95%, the alpha level (α) is 1 - 0.95 = 0.05. Dividing this by 2 (for a two-tailed test), we have α/2 = 0.025. Looking up this value in the Z-table, we find that the critical value Z is approximately 1.96.

Next, we can substitute the values into the formula and calculate the confidence interval:

Confidence Interval = 0.63 ± (1.96 * √((0.63 * (1 - 0.63)) / 904))

Confidence Interval = 0.63 ± (1.96 * √((0.63 * 0.37) / 904))

Confidence Interval = 0.63 ± (1.96 * √(0.23211 / 904))

Confidence Interval = 0.63 ± (1.96 * 0.0154)

Confidence Interval = 0.63 ± 0.0302

Therefore, the confidence interval for the proportion of registered voters who believe illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship is approximately 0.5998 to 0.6602.

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Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

Answer:

Solution

The correct option is B 29

Quantity of juice =

725

ounce

Each bottle contains 25 ounces of juice.

Number of bottles required

=

Quantity of juice

25

=

725

25

Answer:

y=4x-12

Step-by-step explanation:

The slope of the line is (7-3)/(1-0)=4. The equation of the line is y=4x-12

The linear approximation, denoted as l(x), to the function f(x) = 1/x near x = 4 is given by the equation l(x) = f(a) + f'(a)(x - a). In this case, a = 4, so we need to find f(a), f'(a), and substitute them into the equation to obtain the linear approximation.

First, we find f(a) by substituting a into the function f(x). Thus, f(4) = 1/4.

Next, we need to determine f'(a), which represents the derivative of f(x) with respect to x, evaluated at x = a. The derivative of f(x) = 1/x is found by applying the power rule of differentiation. The derivative f'(x) = -1/x^2. Substituting a = 4, we get f'(4) = -1/(4^2) = -1/16.

Now, we can substitute f(a) and f'(a) into the linear approximation equation. Therefore, l(x) = 1/4 - (1/16)(x - 4).

In summary, the linear approximation l(x) to the function f(x) = 1/x near x = 4 is given by l(x) = 1/4 - (1/16)(x - 4). This approximation provides an estimate of the function's behavior in the vicinity of x = 4 using a linear equation.

To derive the linear approximation, we first determine f(a) by substituting a = 4 into the original function f(x) = 1/x. This yields f(4) = 1/4. Then, we find f'(x), the derivative of f(x) with respect to x, using the power rule of differentiation. The derivative f'(x) = -1/x^2. Evaluating this at x = 4 gives us f'(4) = -1/(4^2) = -1/16. Finally, we substitute f(a) and f'(a) into the linear approximation equation l(x) = f(a) + f'(a)(x - a) to obtain the final expression l(x) = 1/4 - (1/16)(x - 4). This equation provides an approximate representation of the original function near x = 4, allowing us to estimate its behavior using a simpler linear function.

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Answer:

Step-by-step explanation:

The probability of occurring event A is 23% or 0.23.

To find the probability of event A:

Divide the number of events in A to the total number of events.

Number of events in A = 12

Total number of events = 12+20+20

=52

P(A)=Number of events in A/Total number of events

\(=\frac{12}{52}\)

Divide both sides by 12:

\(=\frac{3}{13}\)

\(=0.23\)

\(=23\) %

Hence, the probability of occurring event A is 23% or 0.23.

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The equation that can be represented by the number line is option D: -3 + (-1) = -4.

The equation that can be represented by the number line is option D: -3 + (-1) = -4.

Let's analyze each option:

A. -4 + 1 = -3: This equation does not represent the situation where we start from -4 and move 1 unit to the right on the number line, resulting in -3.

B. -3 + 4 = 1: This equation represents the situation where we start from -3 and move 4 units to the right on the number line, resulting in 1. However, this equation does not match the form of the equation in the options.

C. 3 + (-4) = -1: This equation represents the situation where we start from 3 and move 4 units to the left on the number line, resulting in -1. However, this equation does not match the form of the equation in the options.

D. -3 + (-1) = -4: This equation matches the form of the equation in the options, and it represents the situation where we start from -3 and move 1 unit to the left on the number line, resulting in -4.

Therefore, the equation that can be represented by the number line is option D: -3 + (-1) = -4.

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The equation that could be represented by the number line is  -3+ (-1) = -4 (option D)

Let us check each option and delve into their implications on the number line:

A. -4 + 1 = -3: This equation does not depict the scenario where we initiate from -4 and shift 1 unit towards the right on the number line, yielding -3.

B. -3 + 4 = 1: This equation represents the scenario where we commence from -3 and progress 4 units towards the right on the number line, culminating in 1. Nonetheless, this equation fails to conform to the prescribed structure specified in the options.

C. 3 + (-4) = -1: This equation portrays the scenario where we commence from 3 and proceed 4 units towards the left on the number line, resulting in -1. However, this equation does not align with the prescribed format presented in the options.

D. -3 + (-1) = -4: This equation adheres to the stipulated format outlined in the options, and it accurately represents the scenario where we initiate from -3 and traverse 1 unit towards the left on the number line, leading to -4.

There, the equation that can be aptly represented by the number line is option D: -3 + (-1) = -4.

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The number of individuals who took the quiz is D) 21.

To determine the total number of individuals who took the quiz (N), we need to sum up the frequencies (f) in the given frequency distribution. The frequency (f) represents the number of individuals who obtained each score.

Let's add up the frequencies:

6 + 5 + 5 + 3 + 2 = 21

The total frequency is 21, which means that 21 individuals took the quiz. Each score represents a certain number of individuals who obtained that score, and by adding up all the frequencies, we get the total number of individuals.

Therefore, the correct answer is D. 21.

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The solutions of the equation cos^2(theta) = 0 in the interval [0, 2π) are θ = π/2 and θ = 3π/2.

To find the solutions of the equation cos^2(theta) = 0, we need to determine the values of theta that satisfy this equation in the given interval [0, 2π).

The equation cos^2(theta) = 0 can be rewritten as cos(theta) = 0. This equation represents the points on the unit circle where the x-coordinate is zero.

In the interval [0, 2π), the values of theta that satisfy cos(theta) = 0 are π/2 and 3π/2. At these angles, the cosine function equals zero, indicating that the x-coordinate on the unit circle is zero.

Therefore, the solutions to the equation cos^2(theta) = 0 in the interval [0, 2π) are θ = π/2 and θ = 3π/2, written in radians in terms of π.

It is important to note that there are infinitely many solutions to the equation cos^2(theta) = 0, as cosine is a periodic function. However, in the given interval [0, 2π), the solutions are limited to π/2 and 3π/2.

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We can expand and simplify x(x+7)(x-2) using the distributive property. The distributive property states that:

a(b + c) = ab + ac

In this case, we have:

x(x+7)(x-2) = x(x) + x(7) + x(x-2)

We can then simplify each term:

x(x) = x^2

x(7) = 7x

x(x-2) = x^2 - 2x

When we add these terms together, we get:

2 + 7x + x^2 - 2x = 2x^2 + 5x

And after simplifying, we get:

2x^2 + 5x

Answer:

x³ + 5x² - 14x

Step-by-step explanation:

Simplify:

           (x + 7)(x - 2) = x*x + x * (-2) + 7*x + 7*(-2)

                               = x² - 2x + 7x - 14

Combine like terms. Like terms have same variable with same power. Here, (-2x) and 7x are like terms.

                               = x² + 5x - 14

           x*(x² + 5x - 14) = x*x² + x*5x - x * 14

                                   = x³ + 5x² - 14x

Answer:

Step-by-step explanation:

We have formula and values given:

Substitute the values and calculate:

V = 1/3*12*[(5√7)² + (5√7)(2√7) + (2√7)²] =

   = 4*(25*7 + 10*7 + 4*7) =

   = 4* 273 =

   = 1092 in³

Answer:

t = 9

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

sum the exterior angles and equate to 360

10t + 16t + 53 + 73 = 360 , that is

26t + 126 = 360 ( subtract 126 from both sides )

26t = 234 ( divide both sides by 26 )

t = 9

Answer: 6

Step-by-step explanation:

Answer:

7776

Step-by-step explanation:

Answer:

81 and 9 is the answer I got hope it helps

Answer: $22.12

Step-by-step explanation:

I just did the compound interest formula which is

starting amount * (1. interst rate) ^ number of years

example if you have 100$ and you want to know how much it is worth if it appretiates by 7% of a period of 20 years it would look something like this;

100 * (1.10) ^20 = 672.74$

but since you have to figure out what it was in 2008 which was exactly half way in the period you divide the exponent by half so your formula should be;

I know the answer is right because I asked my teacher and it's correct.

REAL EXAMPLE: 18 * (1.51) ^.5 = 22.12$

The amount should be $22.12.

\(= 18 \times (1.51) ^{.5}\)

= $22.12

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Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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The slope of a line that is parallel to the line containing the points (3, 4) and (2, 6) is -2.

To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line containing these points. We can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where:

m = slope

(x1, y1) = coordinates of the first point (3, 4)

(x2, y2) = coordinates of the second point (2, 6)

Substituting the given values, we get:

m = (6 - 4) / (2 - 3)

m = -2

The slope of the line containing the points (3, 4) and (2, 6) is -2.

Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2.

Therefore, the slope of the parallel line is -2.

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Based on the area of the Mojave desert and the area of the scale drawing, the scale of the map is 1 square inches : 2,500 square miles.

The scale of a map is used to find out how the distance on the map relates to the distance on the ground. It is usually shown as a ratio.

The fact that the area of the Mojave desert is 25,000 square miles but only 10 square inches on the scale drawing means that every 10 square inches on the map is equal to 25,000 actual square miles.

The scale is:

10 square inches : 25,000 square miles

In its simplest form, this is:

10 / 10 square inches : 25,000 / 10 square miles

1 square inch : 2,500 square miles

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Answer:

g(7)= -4

Step-by-step explanation:

10-2(7)

10-14

=-4

The value of g(7) is -4.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

g(x) = 10 - 2x

For x = 7,

g(7) = 10 - 2 x 7

g(7) = 10 - 14

g(7) = -4

Thus,

g(7) = -4.

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The SRED Credit remainder after applying the maximum SRED Credit for this year is $0.

The Scientific Research and Experimental Development (SRED) program provides tax incentives for companies conducting eligible research and development activities. The SRED credit is calculated based on qualified SRED expenses and can be used to reduce the tax liability of a company.

In this case, the qualified SRED expenses for the current year are $10,000. However, the SRED credit remainder is determined after applying the maximum SRED credit for the year. Since the maximum SRED credit has already been applied, the remaining SRED credit is $0.

The taxable loss from the previous year ($50,000) and the part I tax before SRED ($1,500) are not directly relevant to determining the SRED credit remainder. The maximum SRED credit has already been utilized, resulting in a remaining credit of $0.

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The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

D. 1/1679616

Step-by-step explanation:

Answer:

The BEST DEAL Is 32..

Step-by-step explanation:

please mark me brainliestndfollow me because im new in brainly.

To verify that the conclusion of Clairaut's theorem holds for f at the point (0,π/2), we need to check that the partial derivatives of f with respect to x and y are continuous at (0,π/2) and that they are equal at this point. Since e^(π/2) is not equal to π/2, the conclusion of Clairaut's theorem does not hold for f at the point (0,π/2).

First, let's find the partial derivative of f with respect to x:
∂f/∂x = yexy sin(y)
Now, let's find the partial derivative of f with respect to y:
∂f/∂y = exy cos(y) + exy sin(y)
At the point (0,π/2), we have:
∂f/∂x = π/2
∂f/∂y = e^(π/2)
Both partial derivatives exist and are continuous at (0,π/2).
To check that they are equal at this point, we can simply plug in the values:
∂f/∂y evaluated at (0,π/2) = e^(π/2)
∂f/∂x evaluated at (0,π/2) = π/2
Since e^(π/2) is not equal to π/2, the conclusion of Clairaut's theorem does not hold for f at the point (0,π/2).
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125

1) Examining the sequence 1, 8, 27, 64 we can find a pattern like this:

2) As we can see, when we raise to 3rd power we can get the numbers of that sequence.

3) So the next number in that sequence is 125

Answer:

ur welcome

Step-by-step explanation:

this is what i think

please mark brainiest

Answer:

Use the given functions to set up and simplify

f (2). 0

Step-by-step explanation: