Complete the ratio table

Mandy's solution makes sense since it entails multiplying the total number of persons in those entire rows (142) by the number of people in each row (ten).

Similarly, multiplying the total number of people in the remaining seats (142) by the number of people in each row (2) yields the total number of people in the remaining seats. The total number of persons in the theater is calculated by adding these two components.

This is a viable use of multiplication's distributive property, in which we break down a multiplication issue into simpler products and then add them up. As a result, Mandy's approach is a viable method for determining the total number of people in the theater.

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The exponential function in this problem represents a decay, with a percentage rate of 6%.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function is classified as growth or decay as follows:

The function in this problem is defined as follows:

y = 15(0.94)^x.

As |b| = 0.94 < 1, the function is a decay function, and the rate is obtained as follows:

1 - r = 0.94

r = 1 - 0.94

r = 0.06

r = 6%.

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The 3 : 5 ratio of the number of cups of sparkling water to the number of cups of apple juice indicates;

7. a) 12 cups of sparkling water

b) 15 cups of apple juice

c) Please find attached the required graph of the pairs of measurements, which are plotted as points using MS Excel

A ratio expresses the quantitative relationship between two quantities, and it is obtained by dividing the quantity of one by the other.

7. The ratio of the number of cups of sparkling water to the number of cups of apple juice = 3 to 5

a) Where the number of cups of apple juice = 20, we get;

20 = 4 × 5

Therefore, the number of cups of apple juice in the current mixture is 4 times the amount that is mixed with 3 cups of sparkling water

b) 9 cups of sparkling water is 3 times the amount required per 5 cups of apple juice

c) The plot of the points can be presented as follows;

(3, 5), (9, 15), (12, 20)

Please find attached the graph showing the pairs of measurements, plotted as points, created with MS Excel

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Answer:

The second scatterplot does not suggest a linear relationship between x and y.

B) gas mileage decreases with increase of car weight.

The area of the decagon with side length 10 is 769.42 square units

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

side length, l = 10

The area of the decagon is calculated as

Area = 5/2l² * √[5 + 2√5]

Where

l = 10

Substitute the known values in the above equation, so, we have the following representation

Area = 5/2 * 10² * √[5 + 2√5]

Evaluate

Area = 769.42

Hence, the area is 769.42

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The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

We have,

To construct a 96% confidence interval about the population mean(μ) with a sample size of n = 57,

we can use the following formula:

CI = x ± z (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, z is the z-score associated with the desired confidence level (96% in this case), and √n is the square root of the sample size.

The z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or calculator.

For a two-tailed test, the z-score is 1.96.

Substituting the given values, we have:

CI = 19.3 ± 1.96 (4.8/√57)

Calculating the standard error of the mean (s/√n):

s/√n = 4.8/√57 ≈ 0.634

Substituting this value into the formula:

CI = 19.3 ± 1.96*0.634

Calculating the upper and lower bounds of the confidence interval:

lower bound = 19.3 - 1.96*0.634 ≈ 18.06

upper bound = 19.3 + 1.96*0.634 ≈ 20.54

Therefore,

The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

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To construct a 96% confidence interval for the population mean, use the formula x ± z*(s/√n) with z being the z-score for the 96% level, x being the sample mean, s being the sample standard deviation, and n being the sample size. Substituting the given values will give the lower and upper bound of the confidence interval.

The question is asking for the construction of a 96% confidence interval for a population mean u, given a sample size (n) of 57, a sample mean (x) of 19.3 and a sample standard deviation (s) of 4.8.

To find the confidence interval, we need to use the formula: x ± z*(s/√n) where z is the z-score associated with our confidence level. For a 96% confidence interval, the z-score is approximately 2.05 (you can find this from a standard z-table).

Substituting the given values into the formula gives: 19.3 ± 2.05*(4.8/√57)

Calculating the above expression will give the lower and upper bound of the 96% confidence interval.

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The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.

The base angles of isosceles trapezoids are congruent.

In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.

Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.

In the given diagram, we will identify the base angles as follows;

∠TPR ≅ ∠ TAR

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The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

We have,

To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.

a) 1.241 km = 1.241 × 1000 m = 1241 m

b) 6.002 km = 6.002 × 1000 m = 6002 m

c) 5.168 km = 5.168 × 1000 m = 5168 m

d) 3.4 km = 3.4 × 1000 m = 3400 m

e) 21.32 km = 21.32 × 1000 m = 21320 m

f) 0.895 km = 0.895 × 1000 m = 895 m

Therefore,

The distances in meters are:

a) 1241 m

b) 6002 m

c) 5168 m

d) 3400 m

e) 21320 m

f) 895 m

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Answer:

Step-by-step explanation:

The product of two given vectors is 48.

Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.

We know that, |a|·|b|=|a|×|b|×cosθ.

Here, |v|·|w|=8×12×cos60°

= 96× 1/2

= 48

Therefore, the product of two given vectors is 48.

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The statement is false, a triangle can't have two angles of 90°.

Remember that for any triangle, the sum of the 3 interior angles should be equal to 180°.

So if the 3 interior angles are A, B, and C we have.

A + B + C = 180°

In this case we know that two of the angles are of  90°, so let's say that:

A = 90°

B = 90°

Replacing that we will get:

90° + 90° + C = 180°

C = 180° - 90° - 90°

C = 0°

And we can't have a 0° degree angle, so the statement is false, triangles with two 90° don't exist.

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The equation for the translated function is the one in option D:

G(x) = (x - 6)² - 4

We start with the parent quadratic function:

F(x) = x²

We apply two translations, one of 6 units to the right which can be written as:

G(x) = F(x - 6)

And a translation of 4 units down, which is written as:

G(x) = F(x - 6) - 4

Replacing F(x) we will get:

G(x) = (x - 6)² - 4

The correct option is D.

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The measures the angle 3 is given by 45°.

Hence the correct option is (B).

The quadrilateral which has four equal sides and the adjacent sides of which are in perpendicular that is called Square.

The given figure is a Square.

We know that the angle between two adjacent sides = 90°.

We also know that the diagonal of square divides angles into two equal parts of angles.

So here angle 3 is a one equal part of angle between two adjacent sides of  square.

So angle 3 is given by = (1/2)*90° = 45°.

Hence the correct option will be (B).

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The measure of ∠EAC is 25°

It is given that the measure of ∠DAB is 25°

let AD = x and AB = y. Then, AE = 2 x and AC = 2 y, since AE and AC are 2 times longer than AD and AB, respectively.

AB / AC = AD / AE

y / 2 y = x / 2 x

1 / 2 = 1 / 2

We know that if two triangles are similar, then the ratio of its corresponding sides will be equal.

So triangle BAD similar to triangle CAE

So ∠DAB = ∠EAC

∠EAC =25°

Therefore, the measure of ∠EAC is 25°

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Answer:

(x + 1)² + y² = 3

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 1, 0 ) and r = [tex]\sqrt{3}[/tex] , then

(x - (- 1) )² + (y - 0)² = ([tex]\sqrt{3}[/tex] )² , that is

(x + 1)² + y² = 3

When the y-value starts to decrease and the x-value remains constant over time, Y decreases and X increases to a consistent slope.

A consistent slope represents a constant rate of change between two variables, typically represented by the ratio of the change in y to the change in x.

When the y-value starts to decrease and the x-value remains the same over time, the consistent slope represents a negative correlation between y and x.

This means that as the value of y decreases, the value of x remains the same or may increase, depending on the context of the problem.

Therefore, the answer is option B: Y decreases and X increases.

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The requried, there is only 1 possible lineup of 6 songs from a list of 6 songs.

To determine how many different lineups are possible, we can use the formula for combinations, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items being selected, and the exclamation mark denotes the factorial function.

In this case, we have n = 6 (the total number of songs) and k = 6 (the number of songs to be selected). So we can plug these values into the formula:

6C6 = 6! / (6!(6-6)!) = 6! / (6!0!) = 1

Therefore, there is only 1 possible lineup of 6 songs from a list of 6 songs.

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The number of non-working light bulbs that would be expected in the group of 1,000 light bulbs is: 50 bulbs

In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.

We are told that a sample of 40 bulbs were picked from a box of 1000 bulbs and it was discovered that 2 of the bulbs were not working. Thus:

Fraction of bulbs not working = 2/40 = 0.05

Thus, number of bulbs not working in a sample of 1000 bulbs is:

0.05 * 1000 = 50 bulbs

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Answer:

The smaller the coefficient (the number in front of the x), the wider the parabola

Step-by-step explanation:

The quadratic function with roots -9 and 7 is f(x) = x² + 2x - 63

First, recall that a quadratic function has the form:

f(x) = ax² + bx + c

where a, b, and c are constants.

Given the roots of the quadratic function:

-9 and 7
x = -9 and x = 7 are the two distinct solutions to the quadratic equation.

Hence:

x + 9 and x - 7 are the factors of the quadratic equation.

( x + 9 ) ( x - 7 )

Expanding this expression Using FOIL method:

x( x - 7 ) + 9( x - 7 )

x² - 7x + 9x - 63

Collect and add like terms

x² + 2x - 63

Therefore, the function is f(x) = x² + 2x - 63.

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The amount of soil to fill the garden box is V = 1,134 inches³

Given data ,

Let the volume of the first rectangular box be V₁

Let the volume of the second rectangular box be V₂

where Volume of Rectangle = Length x Width x Height

So , V₁ = 21 x 7 x 2

V₁ = 294 inches³

And , V₂ = 12 x 10 x ( 7 )

V₂ = 120 x 7

V₂ = 840 inches³

And , the total soil in the garden box = V₁ + V₂

Amount of soil in garden box = 1,134 inches³

Hence , the volume is V = 1,134 inches³

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The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°

An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are

90° < x < 180°

From the given question, we are to determine the angle which obtuse.

In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.

The angle that is greater than 90° but less than 180° is 120°.

Thus,

The obtuse angle is the angle that measures 120°

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The area of the region in this problem is given as follows:

A = 1 square unit.

The curve represented in this problem is given as follows:

y = sin(x).

The bounds of the region are given as follows:

Hence the area of the region is represented by the definite integral presented as follows:

[tex]\int_{0}^{\frac{\pi}{2}} \sin{x} dx[/tex]

The integral of the sine is the negative cosine, hence the area is:

A = -cos(x), from x = 0 to x = π/2.

Applying the Fundamental Theorem of Calculus, we have that the area is given as follows:

A = -cos(π/2) + cos(0)

A = -0 + 1

A = 1 square unit.

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Answer:

the answer is b

Step-by-step explanation:

The relationship between the mean and variance of the exponential distribution is (c) variance is the square of the mean.

In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate.

The exponential distribution is widely used in various fields such as

For example, it can be used to model the time between machine failures or the time between arrivals of customers at a service facility.

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The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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Based on its second derivative and given initial values, the function is equal to f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4.

In this problem we find the definition of the second derivative of a function, whose form must be dertermined by integration and the use of initial values. First, write the second derivative:

f''(x) = 2 · x + 6 · sin x

Second, determine the first derivative of the function:

f'(x) = x² - 6 · cos x + C

2 = 0² - 6 · cos 0 + C

2 = - 6 + C

C = 8

f'(x) = x² - 6 · cos x + 8

Third, determine the function:

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + C

4 = (1 / 3) · 0³ - 6 · sin 0 + 8 · 0 + C

4 = C

C = 4

f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4

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The trigonometry identity value of sin(A) is -2/5

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

The value of sin(A) has already been given

However, because the angle A is in Quadrant IV, the value of the trigonometry identity would be negative (sine are negative in the 4th quadrants)

So, we have

sin(A) = -2/5

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The y- intercept for both function is 0 and 5.8.

We have First function

y= [tex]9^x[/tex]

Now , the y intercept of the equation is when x = 0

So , when x = 0

y= [tex]9^0[/tex]

y= 0

and, the second function is

y= [tex]9^{0.8[/tex]

y= 5.799

Hence, second function have intercept 5.8.

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