Tasha has a gift card to buy tickets to the movie theater. The initial value of the gift card is $120 . The function M(x)=120-12x represents the amount of money, M , in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each.
Complete the statements.
The value of is 60/-60 which is viable/not viable in terms of the given context.

The two questions should you ask are:

The given answers to the above questions, one can be able to know the ranges of values that the four numbers have, as well as their relative positions.

In the event that we know the smallest and biggest numbers, we can be ready to mark those points on the number line and after that put the other two numbers in between them agreeing to their relative positions.

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Answer:

Step-by-step explanation:

This is a trinomial quadratic equation

x^2-9x+8

= x^2 -x-8x+8

= (x-1)(x-8)

The roof area is 468.75 square feet.

To find the roof area, we need to follow these steps:
Determine the rise (vertical distance) using the slope of 9 inches per foot:

Since the run is 10 feet, the rise is 9 inches/foot × 10 feet = 90 inches.
Convert the rise to feet: 90 inches ÷ 12 inches/foot = 7.5 feet.
Calculate the length of the rafter using the Pythagorean theorem:

Rafter length = √(run² + rise²) = √(10² + 7.5²) = √(100 + 56.25) = √156.25 = 12.5 feet.
Determine the total length of the gable roof:

Since the rake slope is 1.25, we have Total length = Rafter length × Rake slope = 12.5 feet × 1.25 = 15.625 feet.
Calculate the roof area:

Roof area = Eaves length × Total length = 30 feet × 15.625 feet = 468.75 square feet.
None of the given options matches the calculated roof area.

It is possible there is a mistake in the question or the provided options.

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Answer: 6(x - (23/2))² = 14x + 1044

Step-by-step explanation:

First, we need to move all the terms to one side of the equation:

6x² - 46x - 312 - 14x = 0

Next, we need to factor out the coefficient of the x² term:

6(x² - (46/6)x) - 312 - 14x = 0

Simplifying:

6(x² - 23x) - 312 - 14x = 0

To complete the square, we need to add and subtract the square of half the coefficient of the x-term inside the parentheses:

6[(x - (23/2))² - (23/2)²] - 312 - 14x = 0

Simplifying:

6(x - (23/2))² - 6(23/2)² - 312 - 14x = 0

Expanding the square term:

6(x - (23/2))² - 1044 - 14x = 0

Finally, adding 1044 to both sides and simplifying:

6(x - (23/2))² = 14x + 1044

The intermediate step after completing the square is:

6(x - (23/2))² = 14x + 1044

Since the 95% confidence interval includes zero, we cannot conclude that the population means are different without conducting the test in part a.

a. Significance test:

Null hypothesis (H0): The population means are equal for females and males (μ1 = μ2).

Alternative hypothesis (H1): The population means are not equal for females and males (μ1 ≠ μ2).

Significance level (α): 0.05

We will use a two-sample t-test for independent samples to compare the means:

Calculate the pooled variance (Sp^2):

Sp^2 ≈ 5.27

Calculate the standard error (SE):

SE ≈ 0.11

Calculate the t-statistic:

t ≈ 1.18

Calculate the degrees of freedom (df):

df = N1 + N2 - 2

df = 1117 + 870 - 2

df = 1985

Comparing the t-statistic and the critical t-value for a two-tailed test with α = 0.05:

t_critical ≈ ±1.96 (from t-distribution table)

Since -1.96 < 1.18 < 1.96, we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to conclude that the population means differ for females and males at a 0.05 significance level.

b. 95% confidence interval:

Calculate the margin of error (ME):

ME = t_critical * SE

ME = 1.96 * 0.11

ME ≈ 0.22

Calculate the difference in means (M_diff):

M_diff = M1 - M2

M_diff = 2.99 - 2.86

M_diff = 0.13

Determine the 95% CI for the difference in means:

CI = (0.13 - 0.22, 0.13 + 0.22)

CI ≈ (-0.09, 0.35)

Since the 95% confidence interval includes zero, we cannot conclude that the population means are different without conducting the test in part a.

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the amount of paint required is dependent on the size of the area that needs to be painted.

In an equation or algebraic expression, an uncertain amount is denoted by a symbol in algebra, which is often a letter. A variable is, in the simplest terms, a quantity that can change and is not fixed. The two primary categories of variables are categorical and numerical. Then, for both categorical and numerical variables, discrete or continuous subcategories are created for each category. In this section, a summary of several categories is provided. a measure that can take many different forms. Something that can alter; the sign of a variable; a variable in a scientific experiment.

Because it is the variable which the homeowner may alter or control, the area of the house that needs to be painted in this scenario is the independent variable. Because it depends on the portion of the home that needs to be painted, the overall quantity of paints that need to be obtained is a variable that is dependent. To put it a different way, the amount of paint required depends on the size of the area that needs to be painted.

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The cross section across a conic section would produce:

Triangle, Circle and Parabola

Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.

However, rectangle is not a conic section.

A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.

In forming a conic section , we could also form an ellipse.

Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola

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only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

How to solve the question?

The mathematical term "indirectly proportional" refers to a relationship in which two variables are related in such a way that when one increases, the other decreases, and vice versa. In other words, the two variables vary in opposite directions.

Out of the four equations given, only one shows an indirect proportional relationship. This equation is:

y=1/x

In this equation, y and x are indirectly proportional. As x increases, the value of 1/x decreases, and therefore, the value of y decreases as well. Similarly, as x decreases, the value of 1/x increases, and the value of y increases as well. This relationship is commonly known as an inverse relationship, where the two variables vary in opposite directions.

On the other hand, the other three equations do not show an indirect proportional relationship. The equation y=5x shows a direct proportional relationship, where y increases as x increases and vice versa. The equation y=-2x+1 is a linear equation with a negative slope, where y decreases as x increases, and y increases as x decreases. Lastly, the equation y=3x+5 is also a linear equation with a positive slope, where y increases as x increases, and y decreases as x decreases.

In summary, only the equation y=1/x shows an indirect proportional relationship, while the other three equations show either a direct proportional or a linear relationship.

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Answer:

35.00 - (0.85x) = remaining amount

Step-by-step explanation:

To find out how much money she has left, we need to subtract this amount from her starting amount of $35.00:

35.00 - 0.85x

Therefore, the expression that shows how much money Pam has left after buying (x) peaches is:

35.00 - 0.85x

The distance between control room to airplane is 41027.5 feet.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here This distance (d) from tower will be the hypotenuse of a right triangle.

The altitude is the side opposite the angle at the tower

The tower is 200' high, therefore, the altitude above the tower.

=> 5200 - 200 = 5000 feet.

Now using sine ratio then,

=> Sin 7° = AC/BC

=> BC = AC/sin 7°

=> BC = 5000/sin 7°

=> BC = d = 41027.5 feet.

Hence the distance between control room to airplane is 41027.5 feet.

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For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.

We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]

[tex]H_1 : µ > µ_0.[/tex].

We have to calculate the P-value for the following observed values test statistic one by one.

a)z = 2.35

The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)

= 1 - P( z≤ 2.35)

Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387

= 0.990613

b) z₀ = 1.53

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.53)

Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008

=0.936992

c) z₀ = 2.00

The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 2.00)

Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275

=0.97725

d) z₀ = 1.85

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.85)

Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157

=0.967843

e) z₀ = -0. 15

The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)

= P( z≤ 0.15 )

Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.

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Starting from the same point when bike riding, two individuals are riding. Tom and Juanita goes on biking in opposite directions to each other. Tom rides at speed of 30 mph and Juanita rides at speed of 30 mph in one hour. This will both be added together. And later will be add both speed in third hour that gives us the final value. The answer of this will be seventy two miles.

[tex]30+30[/tex] in one hour

[tex]30+30[/tex] in second hour

[tex]30+30[/tex] in the third hour

[tex]\boxed{\bold{= 270 \ miles}}[/tex]

Answer:

x=162

Step-by-step explanation:

55+x-87+50=180

x+18=180

x=162

When p=4 and t=24 then substituting these values into the equation 6p + 3q = t we get q=0.

To find the value of q in the equation 6p + 3q = t when p = 4 and t = 24, you can substitute the given values into the equation and solve for q. First, replace p with 4 and t with 24

6(4) + 3q = 24

Simplify the left side of the equation

24 + 3q = 24

Subtract 24 from both sides

3q = 0

Divide both sides by 3

q = 0

Therefore, when p = 4 and t = 24, q is equal to 0.

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The expansion of the polynomial (-p²+4p-3)(p²+2) would be is -p⁴ + 4p³ - 5p² + 8p - 6  

Here we need to expand the polynomial (-p²+4p-3)(p²+2)

To do so we need to multiply each of the term with the first bracketby the each term of second bracket.

So, the expansion of the polynomial (-p²+4p-3)(p²+2) would be,

(-p² + 4p - 3)(p² + 2)

= [p² × (-p² + 4p - 3)] + [2 × (-p² + 4p - 3)]

= [p² × (-p²) + p² × 4p - p² × 3] + (-2p² + 8p - 6)

= (-p⁴ + 4p³ - 3p²) + (-2p² + 8p - 6)

= -p⁴ + 4p³ - (3 + 2)p² + 8p - 6       .......(add like terms)

=  -p⁴ + 4p³ - 5p² + 8p - 6  

Therefore, the required polynomial is -p⁴ + 4p³ - 5p² + 8p - 6  

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Answer:

Step-by-step explanation:

4x - 3 ≤ -7

Add 3 to both sides of the inequality to isolate the term with x on one side:

4x - 3 + 3 ≤ -7 + 3

4x ≤ -4

Divide both sides of the inequality by 4 to solve for x:

4x/4 ≤ -4/4

x ≤ -1

So, the solution to the inequality is x ≤ -1. The largest integer value of x that satisfies this inequality is -1.

Answer:

  A: x +y = 60; y = x +20

  B: 20 minutes on math

  C: no

Step-by-step explanation:

You have some relations and some questions about dance times and math practice times with dance times longer than math practice by 20 minutes.

The given relations can be written as two equations:

  x + y = 60 . . . . . total time is 60 minutes

  y = x + 20 . . . . . dance time is 20 minutes longer than math time

We want the value of x. We can find that by using the second equation to substitute for y in the first equation:

  x + (x +20) = 60

  2x = 40 . . . . . . . . . subtract 20

  x = 20 . . . . . . . . divide by 2

Jordyn practices math 20 minutes every day.

If Jordyn dances for 60 minutes, then she will practice math for 60 -20 = 40 minutes. That brings her total practice time to 60 +40 = 100, which is more than 80.

It is not possible to spend 80 minutes total if she spends 60 minutes dancing.

(She could spend 50 minutes dancing, 30 minutes on math, and have a total practice time of 80 minutes.)

Jordyn spends 20 minutes each day practicing math. However, if her total practice time is 80 minutes, it would not be possible for her to spend 60 minutes practicing dance.

The total time Jordyn spends practicing both dancing and math is 60 minutes. If we establish the time she spends on math as 'x' and the time she spends dancing as 'y', we can establish the following and equations:

To solve for 'x', substitute the first equation into the second to get x + (x + 20) = 60. Simplify to get 2x + 20 = 60. Subtract 20 from each side to get 2x = 40, and finally divide by 2 to get x = 20. Therefore Jordyn spends 20 minutes practicing math each day.

To answer Part C, if Jordyn practices for a total of exactly 80 minutes and dances 20 minutes longer than she does math, it would not be possible for her to spend 60 minutes practicing dance. The most amount of time she could spend dancing is 50 minutes (80 total minutes- 30 minutes for math).

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Answer:

Option (3)

Step-by-step explanation:

Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.

The area of the floor of the igloo is 842.9 m²

We know that the formula for the volume of hemisphere is given by,

V = (2/3) × π × r³

where r is the radius of the hemisphere

Here, a hemisphere igloo has a volume of about 9,202.8 m³

Using above formula of the volume of hemisphere,

V = (2/3) × π × r³

9202.8 = (2/3) × π × r³

r³ = 9202.8 × (3/2π)

r³ = 4394.01

r = 16.38 m

We know that the area of the floor of the igloo is equivalent to the area of circle, as the base of hemisphere is a circle.

So, the area of the floor of the igloo would be,

A = π × r²

A = π × 16.38²

A = 842.9 m²

Therefore, the required area is 842.9 m²

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Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.

The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.

To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.

The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be

V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.

Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.

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2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

To determine whether it would be unlikely to get a box with 31 red pencils based on the Mean Absolute Deviation (MAD) for the given data set, we first need to calculate the MAD.

Step 1: Calculate the mean of the data set

The given data set is: 22, 28, 30, 28, 35, 30, 28

The mean is calculated by adding up all the numbers and dividing by the total number of values:

Mean = (22 + 28 + 30 + 28 + 35 + 30 + 28) / 7 = 201 / 7 = 28.71 (rounded to two decimal places)

Step 2: Calculate the absolute deviations

The absolute deviation for each data point is calculated by finding the absolute difference between the data point and the mean:

|22 - 28.71| = 6.71

|28 - 28.71| = 0.71

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

|35 - 28.71| = 6.29

|30 - 28.71| = 1.29

|28 - 28.71| = 0.71

Step 3: Calculate the MAD

The MAD is the mean of the absolute deviations:

MAD = (6.71 + 0.71 + 1.29 + 0.71 + 6.29 + 1.29 + 0.71) / 7 = 17.71 / 7 = 2.53 (rounded to two decimal places)

Now, to determine whether it would be unlikely to get a box with 31 red pencils, we can compare 31 with the MAD. If the difference between 31 and the mean (28.71) is greater than the MAD (2.53), then it would be unlikely.

Difference = 31 - 28.71 = 2.29

Since 2.29 is less than the MAD of 2.53, it would not be unlikely to get a box with 31 red pencils based on the MAD for the given data set.

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Answer: 350

Step-by-step explanation:

First, 32% divided by 100 becomes a decimal.

     32% / 100 = 0.32

Next, let x be equal to a number.

Then, "of" indicates multiplication and "is" indicates equals.

     0.32x = 112

Lastly, we will divide both sides of the equation by 0.32.

     x = 350

This problem can be represented by turning 32% into a decimal and rewriting it like this: .32x = 112, where x is the unknown number. Dividing both sides of the equation by .32 gives you x = 350, so 32% of 350 is 112

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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Answer:

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

The current volume of the cylinder is:

V = π(12cm)^2(15cm)

V = π(144cm^2)(15cm)

V = 2160π cm^3

If the dimensions of the cylinder are tripled, then the new cylinder will have a radius of 3(12cm) = 36cm and a height of 3(15cm) = 45cm.

The new volume of the cylinder is:

V = π(36cm)^2(45cm)

V = π(1296cm^2)(45cm)

V = 58320π cm^3

Simplifying the expression, we get:

V ≈ 183,124.8 cm^3

Therefore, the volume of the new cylinder, when the dimensions are tripled, is approximately 183,124.8 cm^3.

The answer is C) 183,124.8 cm^3.

Hi,

-The correct answer should be "option 4," 45,781.2 cm ^3.

Let me know if my answer is wrong or not what you were looking for because I would like to help all I can.

If you have any questions let me know and I may be able to help.

I hope that my answer helped you out. :)

Here is the correct figure if anybody needs it. ⇅

The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

The total number of combinations of selecting 5 cards from a deck of 52 cards is 52C5 = 5251504948/120 = 2598960.

The probability of exactly 4 of the 5 cards being Aces is 48*100/2598960 = 0.0018%.

The probability of all 5 of the cards being Spades is 1287*100/2598960 = 0.0495%.

The probability of exactly 4 of the 5 cards being face cards is 49540100/2598960 = 0.7618%.

The probability of exactly 2 Aces and exactly 2 Kings being selected is 1584*100/2598960 = 0.0609%.

The probability of exactly 1 Jack being selected is 4249900100/2598960 = 38.46%.

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Answer:

Less

Step-by-step explanation:

Look at the hundreds number in set L the numbers are greater in Set L than Set K.

slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)

- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4

- slope = 15 / 12 (simplify)

- slope = 5/ 4