A movie theater can seat a maximum of 25 people. Let p represent the total number of people. Which inequality represents p, the number of people the theater can seat?

The number of soda bottles the machine can make per minute is 25

From the question, we have the following parameters that can be used in our computation:

The linear relation

Where we have the points

(2, 50) (6, 150)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = unit rate i.e the required slope

So, we have

2m + c = 50

6m + c = 150

Next, we have

4m = 100

Evaluate

m = 25

So, we have

2 * 25 + c = 50

Evaluate

c  0

So, we have

y = 25x

Hence, the equation of the line in fully simplified slope-intercept form is y = 25x

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Answer:

The probability of rolling any number other than 5 is 5/6.

The total number of grams of baking soda in all 4 samples is given as follows:

B. 16 grams.

The total number of grams of baking soda in all 4 samples is obtained as the sum of the amounts for each sample.

The dot plot shows the number of samples with each amount, hence:

Hence the total amount is given as follows:

2.5 + 3.5 + 2 x 5 = 16 grams.

The problem is given by the image presented at the end of the answer.

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1) Note that when x = 7, then the second coordinate is y =  112.8. (Option d)

2) the approximate value of where x =4 given the function above is 3 (Option a)

A) by logical deduction,  if on the table, x and y values are given, then they retain those positions as coordinates on the graph. Hence, when x = 7, then the second coordinate is y =  112.8.

b) to find the approximate value of y for x = 4, we can use the equation given:

log y = 0.75821x + 0.03442

Substituting x = 4:

log y = 0.75821(4) + 0.03442

Simplifying:

log y = 3.03284 + 0.03442

log y = 3.06726

log y = 3 (Option A)

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The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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The total area of the six-sided composite figure is 45m². (option d)

To find the area of the trapezoid, we use the formula:

Area = (1/2) x height x (base 1 + base 2)

where base 1 and base 2 are the two parallel sides of the trapezoid. In this case, base 1 is 9 meters, and base 2 can be found by subtracting the length of the small portion from the total length of the left vertical line:

base 2 = 4 meters (total length of left vertical line) - 3 meters (small portion) = 1 meter

Therefore, the area of the trapezoid is:

Area = (1/2) x 3 meters x (9 meters + 1 meter) = 15 meters squared

To find the area of the triangle, we use the formula:

Area = (1/2) x base x height

where the base is 3 meters, and the height is also 3 meters. Therefore, the area of the triangle is:

Area = (1/2) x 3 meters x 3 meters = 4.5 meters squared

Finally, we add the area of the trapezoid and the triangle to find the total area of the composite figure:

Total area = area of trapezoid + area of triangle = 25 meters squared + 20 meters squared = 45 meters squared

Hence the correct option is (d).

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The amount that Declan initially invested (present value) in a savings account that pays compound interest at a rate of 8% per annum and that had a balance of £14,685.97 after 14 years was £5,000.

The present value represents the future value discounted to the present or current date at an interest rate.

We can determine the present value using the PV formula or an online finance calculator as follows:

N (# of periods) = 14 years

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = £0

FV (Future Value) = £14,685.97

Results:

Present Value (PV) = £5,000.00

Total Interest = £9,685.97

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The area was approximately 430.365 square meters.

To start, let's recall the formula for finding the area of a triangle. The formula is:

Area of a triangle = (base x height) / 2

To do that, we can use Heron's formula. Heron's formula states that the area of a triangle can be found using its sides, a, b, and c, where s is the semi-perimeter of the triangle (half of the perimeter):

Area of a triangle = √(s(s-a)(s-b)(s-c))

where

s = (a+b+c)/2

Now, let's apply Heron's formula to our problem.

We know that the sides of the triangle are 75.6m, 56.7m, and 52.5m. We can add them together and divide by 2 to get the semi-perimeter:

s = (75.6 + 56.7 + 52.5) / 2

s = 92.4

Next, we can substitute the values of a, b, and c into the formula:

Area of a triangle = √(92.4(92.4-75.6)(92.4-56.7)(92.4-52.5))

Area of a triangle = √(92.4(16.8)(35.7)(39.9))

Area of a triangle = √(185623.66256)

Area of a triangle ≈ 430.365m²

= 99 degrees.

So the area of the triangle with sides measuring 75.6m, 56.7m, and 52.5m, and a height of 42m, is approximately 430.365 square meters.

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The percentage of 6th graders involved in the yearbook club is 25%.

From the sample data given, we know that there are 10 6th graders in the yearbook club, and the total number of 6th graders in the sample is 40 (10 in yearbook + 24 in student council + 6 in jump rope). Therefore, to find the percentage of 6th graders involved in the yearbook club, we can use the following formula:

percentage = (number of 6th graders in yearbook club / total number of 6th graders in sample) x 100

Plugging in the values, we get:

percentage = (10 / 40) x 100

percentage = 0.25 x 100

percentage = 25

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Complete Question:

A random sample from the 6th and 7th grade student population was taken to determine which clubs were the most popular.

6th Grade: Yearbook 10; Student Council 24; Jump Rope 6

7th Grade: Yearbook 18; Student Council 20; Jump Rope 2

What percent of 6th graders are involved in the yearbook club?

The measure of the angles ∠OAT, angle ∠OTA, side AT, and side BT will be 90°, 34.5°, 5.82 units, and 5.82 units, respectively.

Given that:

TA and TB are tangents to O.

OA = 4 and ∠ATB = 69°.

Angle ∠OAT will be 90° because the tangent and radius intersect at a right angle.

Angle ∠OTA is half of the angle ∠ATB. Then we have

∠OTA = ∠ATB/ 2

∠OTA = 69° / 2

∠OTA = 34.5°

The measure of the length AT is calculated as,

tan 34.5° = 4 / AT

AT = 5.82

The measure of the length BT is calculated as,

tan 34.5° = 4 / BT

BT = 5.82

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The amount of money it would cost to recarpet the rectangular hotel room is equal to $1,752.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangular hotel room = 4 × 6

Area of rectangular hotel room = 24 yd²

Now, we can determine the cost as follows;

Cost of recarpet = $73.00 × 24 yd²

Cost of recarpet = $1,752.

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Answer:

Step-by-step explanation:

The probability is given as 7 / 60 for the favorite sport of the person being bicycling

The frequency of bicycling in the table is goven as 7

We have tp add the total of all of the values in order to get the given probability

Hence we would have

2 + 11 + 6 +20 + 7 + 14

= 60

The probability is given as 7 / 60

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Factoring the equation f(x) = 4x^2 - 3x - 10 gives f(x) = (4x - 5)(x + 2)

From the question, we have the following parameters that can be used in our computation:

f(x) = 4x^2 - 3x - 10

Expand the equation

So, we have the following representation

f(x) = 4x^2 + 8x - 5x - 10

Factorize the equation

So, we have the following representation

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

Factor out x + 2 from the equation

So, we have the following representation

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

Hence, the factored exrpression is f(x) = (4x - 5)(x + 2)

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The two different statements are π times radius and π times diameter.

The circumference of a circle is the distance round the circle.

Mathematically, the formula for the circumference of a circle is given as;

C = 2πr, or

C = πD

where;

For this circle, the circumference is calculated as follows;

C = 2π x 6 in

C = 12π in

Thus, the distance round the circle and the circumference are the same.

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The meaning of the number 1125 in the context of this problem is given as follows:

A. the approximate number of feet that sound travels in air in 1 second.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The input and the output variables for this problem are given as follows:

Hence the constant of 1125 represents the distance traveled by the sound each second.

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Answer:

  x/4 = 36/x

Step-by-step explanation:

You want the proportion relating the altitude of the right triangle to the segments of the hypotenuse.

All the triangles in this figure are similar, so the ratios of corresponding sides are the same:

  long leg/short leg = x/4 = 36/x

The proportion of interest is ...

  [tex]\boxed{\dfrac{x}{4}=\dfrac{36}{x}}[/tex]

__

Additional comment

The solution is ...

  x² = 4·36

  x = 2·6 = 12

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Answer: (Maybe) B

Step-by-step explanation:

The answer for this problem would be 42. However, if you take 630 and divide it by 15 (630/15) you'll get 42 as well. I'm not sure if you accidentally typed the hyphen in there (choice B) or if it's supposed to represent a negative sign. But, I believe B would be correct.

Heather's new balance if her APR is 16.2% is, $1773.98

We have to given that;

Heather's statement shows a previous balance of $1413.92, a payment of $40, and new transactions totaling $381.51.

Hence, We have;

Previous balance: 1413.92

payment: 40

new transaction: 381.51

APR: 16.2%

So, We need to divide APR by 12 to get the monthly rate:

16.2% / 12 = 1.35%

⇒ 1413.92 - 40 = $1373.92

And, Interest for month = 1373.92 x 1.35%

                                    = $18.55

Since, We did not include 138 because it still is within the 1 month period and it is not subject to interest.

Only the revolving amount of 1373.92 has interest.

So, Heather's new balance if her APR is 16.2% is,

= 1373.92 + 18.55 + 381.51

= $1773.98

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The sum of the given two polynomials (x²-7x+14) + (x²+10x-4) is 2x² + 3x + 10

To find the sum of the polynomial expression, we need to add the like terms of the two polynomials.

The first polynomial is x²-7x+14 and the second polynomial is x²+10x-4. We can combine the terms with x² to get 2x².

Then, we can combine the x terms to get 3x.

Finally, we can combine the constant terms to get 10.

Therefore, the sum of the two polynomials is:

2x² + 3x + 10

In summary, we can find the sum of two polynomials by adding the like terms of the polynomials. We group the terms with the same degree of x, add them up and simplify the expression by combining the like terms.

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Answer:

Step-by-step explanation:

You want functions for the velocity v(t) and height h(t) of a ball thrown upward at 38 m/s from a height of 1.8 m. The acceleration is -9.8 m/s².

This sort of problem is usually discussed in a physics course. The relation between acceleration, velocity, and position is ...

  velocity is the rate of change of position

  acceleration is the rate of change of velocity

Then the inverse relations are ...

  h(t) = ∫v(t)dt +h(0)

  v(t) = ∫a(t)dt +v(0)

When position is measured in one dimension (up = positive), these have the standard formulas:

  v(t) = g·t + v(0)

  h(t) = 1/2g·t² +v(0)·t +h(0)

Filling in the given values (g = -9.8, v(0) = 38, h(0) = 1.8), we have ...

  v(t) = -9.8t +38 . . . . . . . . . . . . meters per second

  h(t) = -4.9t² +38t +1.8 . . . . . . meters

The value of n is given as follows:

n = 53.3 years.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

The interest rate for this problem is given as follows:

r = 0.03.

Then the amounts are given as follows:

The ratio is given as follows:

A(n + 1)/A(n) = 1.01875.

Hence the value of n is obtained as follows:

(n + 1)/n = 1.01875 (0.03P is simplified as it is common to both expressions)

1.01875n = n + 1

0.01875n = 1

n = 1/0.01875

n = 53.3 years.

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The triangle's third angle has a measure of 73 degrees.

The sum of the angles in a triangle is always 180 degrees. Let's call the third angle x.

So we have:

22 + 85 + x = 180

107 + x = 180

Subtracting 107 from both sides:

x = 73

Therefore, the measure of the third angle of the triangle is 73 degrees.

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The given information shows the number of bullseyes hit by five different teams in a variety of events.

To display & analyze these results, the organizer would want a clear and concise visualization that highlights the performance of each team in which bar graph or a horizontal bar chart would be the most appropriate display to use in this scenario.

On the chart, x-axis would represent the team names and the y-axis would represent the number of bullseyes hit, so, the display would allow for easy comparison of the performance of each team, as well as highlighting any significant differences in performance.

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The length of the base of the right-angle triangle will be 1 / 2 inches.

Since, We know that;

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

So, The area of the right-angle triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the right triangle.

The area of the triangle below is 1/8 square inches. And the length of the perpendicular will be 1/2 inches.

Then the length of the base will be;

A = 1/2 x B x H

1/8 = 1/2 x B x 1/2

1/8 = 1/4 x B

B = 1/2

Thus, The length of the base of the right-angle triangle will be 1/2 inches.

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Answer:

18q + 27

Step-by-step explanation:

9(2q + 3)

9 x 2q = 18q

9 x 3 = 27

18q + 27

: )