There were 411 people at a play. Admission was $5 for adults and $3.75 for children.
The receipts were $1978.75. How many adults and how many children attended
Thanks so much!

The correct statements about the solids are:

To find which statements are correct:

Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.

The volume of the first triangle is: \(2x^{2} h\)

The volume of the second triangle is: \(x^{2} h\)

Therefore, the correct statements about the solids are:

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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.

A) The bases are congruent.

B) The solids are similar.

C) The ratio of the volumes of the first solid to the second solid is 8:1.

D)The volume of the first solid is twice as much as the volume of the second solid.

E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more

surface area than the second solid.

Answer:

The second one

Step-by-step explanation:

The correct options for the values of a and b in the equation are a = 2 and b = -3/4

We shall use the negative sign before the bracket at the left hand side of the equation to open bracket as follows;

-(-2 + 3/3) = (- × -2) + (- × 3/4)

-(-2 + 3/3) = (+2) +(-3/4)

so the equation becomes;

7/8 -(-2 + 3/3) = (+2) +(-3/4) + 7/8.

Therefore, the correct options for the values of a and b in the equation are a = 2 and b = -3/4

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The potato is in the air for approx. 1.0625 seconds.

The actual cost of manufacturing 24 coffee makers is $1,755.67.

a. To find the time that a potato is in the air, use the quadratic equation formula where a=-16,

b=34, and

c=42. `

t = (-b ± sqrt(b²-4ac))/2a`.

Let's start by finding the discriminant first. `b²-4ac = (34)²-4(-16)(42)

= 1156`.

Substitute the values of a, b, and c into the quadratic formula.

t = (-34 ± sqrt(1156))/-32

= (-34 ± 34)/-32`.

There are two solutions to the quadratic equation. Thus, we need to check if there are any negative values for time.

t = (-34 + 34)/-32

= 0.

t = (-34 - 34)/-32

= 1.0625`.

Therefore, the potato is in the air for 1.0625 seconds.

b. To find the actual cost of manufacturing 24 coffee makers, substitute x=24 into the cost function

C(x) = 155 + 66x + x²/36`.

C(24) = 155 + 66(24) + 24²/36

= 155 + 1584 + 16.67`. `

C(24) = 1755.67`.

Therefore, the actual cost of manufacturing 24 coffee makers is $1,755.67.

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Answer:

x=7

Step-by-step explanation:

5(2x-5) = 10x-25

1) add 25 to both sides

10x+25=10x      6x+3+25=6x+28

10x=6x+28

2) subtract 6x from both sides

10x-6x=4x      6x+28-6x=28

4x=28

3) divide by 4 from both sides

4x/4=x      28/4=7

x=7

Hope this helps, have a great day!!

The value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

According to the given question

We have an equation in one variable

⇒  -5(2x - 5) = 6x + 3

For finding the value of x solve the above equation by adding and subtracting the like terms.

So, -5(2x - 5) = 6x + 3

⇒ -5 x 2x + 5 x 5 = 6x + 3

⇒ -10x + 25 = 6x + 3

⇒  25 - 3 = 6x + 10x

⇒  22 = 16x

⇒ x = 22/16

Hence, the value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

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The given function has an absolute minimum value equal to -2, which is attained at x = 0, and an absolute maximum value equal to -2, which is attained at x = 2.

This is a constant function, and as such, the values it takes don't depend on the input.

The smallest value is -2, and it is attained at x = 0 since it is the only x value in the domain. Any other x values, if they exist, won't affect the output since it will remain -2.

Similarly, the largest value of the function is -2, and it is attained at x = 2 since it is the only x value in the domain.

Let's verify this using the formal definition of absolute maxima and minima:

A function f has an absolute maximum at c if f(c) ≥ f(x) for all x in the domain of f. A function f has an absolute minimum at c if f(c) ≤ f(x) for all x in the domain of f.The domain of f is [0, 2]. The only possible candidates for an absolute maximum and minimum are 0 and 2 since f(0) = f(2) = -2.

If x = 0, f(x) = f(0) = -2 ≤ f(x) for all x in [0, 2]. Hence, f has an absolute minimum at x = 0, and the minimum value is f(0) = -2.If x = 2, f(x) = f(2) = -2 ≥ f(x) for all x in [0, 2]. Hence, f has an absolute maximum at x = 2, and the maximum value is f(2) = -2.

To summarize, the given function has an absolute minimum value equal to -2, which is attained at x = 0, and an absolute maximum value equal to -2, which is attained at x = 2. The formal definition of absolute maxima and minima was used.

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The work done by the force can be found to be 206. 45 foot-pounds.

To find the work done by the force, the formula is:

Work = Force × Distance × cos (θ)

The angle was 55° , the distance was 20 feet and the force was 18 pounds. This is included in the question and so can be used to find the work done to be :

= 18 × 20 × cos ( 55 °)

= 18 × 20 × 0. 573576

= 206. 44568

= 206. 45 foot - pounds

In conclusion, the work done by the force was approximately 206. 45 foot - pounds.

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The work that is done by the force is 280.2 J.

When a force acts on an object and causes it to move a specific distance, the amount of energy that is transmitted is known as the work done. It is described as the result of the amount of force that is exerted on an item and the distance that the object moves in the force's direction.

We have;

W = FdCosθ

W = work done

F = force

d = distance

θ = Angle turned

F = 18 Ib = 80.1 N

d = 20 feet = 6.1 m

θ = 55°

W = 80.1 N * 6.1 m * Cos 55

= 280.2 J

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It is known that the solution to the system of equations is in the interval between x = 0.5 and x = 1 because at x = 0.5, y = -x + 3 is greater than y = 2x + 1, while at x = 1 y = 2x + 1 is greater than y = -x + 3. This means that the two equations intersected in this interval.

The system of equations in this problem is composed by these two equations:

These two are linear functions, meaning that they are continuous and have uniform behavior over their entire domain, that is, they are either increasing or decreasing over their entire domains.

We have that:

Due to the continuity of the linear functions, along with their uniform behavior, this necessarily means that the two functions intersect at a value of x between x = 0.5 and x = 1, meaning that the solution for the system of equations is in this interval.

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The percentage of men getting over 700 on this test in 2005 is 8.85%.

It should be noted that based on the information illustrated, the percentage will be calculated thus:

= P(X - 538/120) > (700 - 538/120)

= P(Z > 1.35)

= 1 - P(Z <= 1.35)

Using normal table

= 1 - 0.9115

= 0.0885

Therefore, the percentage of men getting over 700 on this test in 2005 is 8.85%.

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Answer:

messy... but hope it helps you.

To drive from Kansas City to Des Moines, with a distance of 193.25 miles and an average speed of 65.8 mph, it will take approximately 2 hours and 56 minutes.

To calculate the time it will take to make the drive, we can use the formula: time = distance / speed. Given that the distance is 193.25 miles and the average speed is 65.8 mph, we can substitute these values into the formula.

Dividing the distance by the speed, we get: 193.25 miles / 65.8 mph = 2.94 hours.

Since time is typically expressed in hours and minutes, we need to convert the decimal portion (0.94) of the hours into minutes. Multiplying 0.94 by 60, we find that the decimal portion is equivalent to approximately 56 minutes.

Therefore, the total time it will take to drive from Kansas City to Des Moines is approximately 2 hours and 56 minutes.

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Answer:

1049.682 is 75.3% of 1394 or as a fraction is 1049 341/500

Step-by-step explanation:

1394/x=100/75.3

(1394/x)*x=(100/75.3)*x       - we multiply both sides of the equation by x

1394=1.32802124834*x       - we divide both sides of the equation by (1.32802124834) to get x

1394/1.32802124834=x

1049.682=x

x=1049.682

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{1049.682}}}}}\)

Step-by-step explanation:

\( \sf{75.3\% \: of \: 1394}\)

Convert 75.3 percent into fraction

To convert a percentage to a fraction, divide it by 100

\( \dashrightarrow{ \sf{ \frac{75.3}{100} \times 1394}}\)

Calculate

\( \dashrightarrow{ \boxed{ \sf{1049.682}}}\)

Hope I helped!

Best regards! :D

I can't understand this question write it properly please ok plz

Answer:

[-4, 4]

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

From the graph we see that our x-values span from -4 to 4. Since both are closed dots, they are included in the domain (use brackets):

[-4, 4] or -4 ≤ x ≤ 4

Answer:

539.7

Step-by-step explanation:

Multiply 25.7 to 21 to get the answer.

Answer:

539.7 pounds

Step-by-step explanation:

you have 21 cartons and each one weights 25.7 pounds so you do 21•25.7=539.7

The price of a box of candy will be $1.25.

Expression in math's is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

Tiffany gets $25 and 1 box of candy.

And, Todd gets $20 and 5 boxes of candy.

Now,

Since, Tiffany gets $25 and 1 box of candy.

And, Todd gets $20 and 5 boxes of candy.

Let price of box of candy = x

So, We can formulate;

⇒ $25 + x = $20 + 5x

Solve for x as;

⇒ $25 - $20 = 5x - x

⇒ $5 = 4x

⇒ x = 5/4

⇒ x = $1.25

Thus, The price of a box of candy = $1.25

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A triangle with one angle of 50° cannot be right-angled.

In a right-angled triangle, one of the angles is always equal to 90°. Since we are given that one of the angles in this triangle is 50°, the other two angles must add up to 90° (since the sum of all angles in a triangle is always 180°).

In this case, the other two angles would have to add up to 90° - 50° = 40°. However, it is not possible for one of these angles to be 90° and the other to be 40°, as the sum of these angles would be 130°, which is greater than 180° (which is the total sum of all angles in a triangle).

Therefore, a triangle with one angle of 50° cannot be right-angled.

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In Situation 1, we conducted a hypothesis test to determine if the mean amount of sleep for adults is less than 7 hours per night. Using a significance level of 0.05, we found that there is sufficient evidence to support this claim.

In Situation 2, we conducted a hypothesis test to determine if more than 38.3% of adults in the age range of 35-44 receive at least 7 hours of sleep per night. Using a significance level of 0.01, we found that there is not sufficient evidence to support this claim. In Situation 1, the possible errors that could have occurred are a Type I error or a Type II error. A Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false. To prevent these errors from occurring in future hypothesis tests, we can increase the sample size, use a different significance level, or improve the accuracy of our measurement methods.

In Situation 2, the possible errors that could have occurred are also a Type I error or a Type II error. A Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false. To prevent these errors from occurring in future hypothesis tests, we can increase the sample size, use a different significance level, or improve the accuracy of our measurement methods. Additionally, we can also use a different test statistic or adjust the sample selection criteria to reduce the likelihood of errors.

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Answer:

2 juices

because 32 is 16 multiplied by 2, so to get the answer, you have to multply everything by two, and sense it does't ask for the amount of ounces, you simply say, to juices

hope i helped......

Answer:

12 OUNCES

Step-by-step explanation:

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The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = \(\frac{ (Final value -Initial value)}{ (Initial value)}\)× 100

Percent Change               = \(\frac{(74-60)}{60}\)× 100

…                                     = \(\frac{14}{60}\) × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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Based on the information in the graph, we can infer that the area of the figure is 57 square feet (option C).

To calculate the area of the figure we must calculate the area of two segments of the figure and then add them. First we can calculate the area of the area on the left that is 3 * 4.

Then we must find the area of the area on the right which is 7.5 ft * 6ft.

Finally we must add both areas to find the total area:

Note: This question is incomplete. Here is the complete information:

Image attached.

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Answer:

The optimal, vertex, value will be a minimum

Step-by-step explanation:

The given zeros of the quadratic relation are 3 and 3

The sign of the second differences of the quadratic relation = Positive

Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation

Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;

To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope

By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer:

y - 27 = 0 (x - 21) or y = 27

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(3 - 5)

slope = -6/(-2)

slope = 3

Parallel lines have equal slopes.

Answer: 3

The probability that a vehicle was a light truck, manufactured by u.s. manufacturers, is 0.5661

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

Given that, the automobile industry sold 657,000 vehicles in the United States during January 2009 (The Wall Street Journal, February 4, 2009). This volume was down 37% from January 2008 as economic conditions continued to decline. The Big Three U.S. automakers—General Motors, Ford, and Chrysler—sold 280,500 vehicles, down 48% from January 2008.

We need to find the probability that a vehicle was a light truck, manufactured by u.s. manufacturers,

Probability(Event) = Favorable Outcomes / Total Outcomes

Favorable Outcomes = US manufactured light truck (193.1)

Total Outcomes = Total light trucks manufactured (341.1)

Probability that a vehicle was a light truck, manufactured by u.s. manufacturers =

P(Light Truck & US) = 193.1/341.1 = 0.5661

Hence, the probability that a vehicle was a light truck, manufactured by u.s. manufacturers is 0.5661

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The complete question is

The automobile industry sold 657,000 vehicles in the United States during January 2009 (The Wall Street Journal, February 4, 2009). This volume was down 37% from January 2008 as economic conditions continued to decline. The Big Three U.S. automakers—General Motors, Ford, and Chrysler—sold 280,500 vehicles, down 48% from January 2008. A summary of sales by automobile manufacturer and type of vehicle sold is shown in the following table. Data are in thousands of vehicles. The non-U.S. manufacturers are led by Toyota, Honda, and Nissan. The category Light Truck includes pickup, minivan, SUV, and crossover models.

Type of Vehicle

Car

Light Truck

Total

U.S

87.40

193.10

280.50

Manufacturer

Non-U.S

228.50

148.00

376.50

Total

315.90

341.10

657.00

Answer:

1. x=34

2.x=10

3. x=22

4. x=81

5.x=1

6.x=-8

7.x=-6

8. x=61

9. x=0.8

10. x= 2

11. x=25.2

12.x=-4

13.x=64

14.x=29

15. x=19

Step-by-step explanation:

a)

It is the angle of depression.

Given,

Boy is standing at second floor of the house and sees the dog at the bottom surface.

So,

The angle through which the boy can see the dog at the ground floor will be angle of depression( that is seeing something below the eye level).

b)

Given,

Height = 3m

Angle of depression = 32°

Hence from the trigonometry,

tanФ = perpendicular/base

tan 32 = 3/base

0.6248 = 3/base

base = 4.801 m

Thus the dog is 4.801 m far from the house.

c)

Given,

Base = 7m

Angle of depression = 32°

Again,

tanФ = p/b

tan 32 = p /7

p= 4.3736 m

Thus the height of boy's house is 4.3736m

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Answer:

6

Step-by-step explanation: