An auditorium has a seating capacity of 1500. For an upcoming event community event theater play, tickets cost $4 for adults and $2 for children. At last years play, twice as many children attended as did adults. If the attendance at this year's play has the same ratio, what expression would represent the best estimate of the total amount of money from ticket sales when the auditorium is filled to capacity ?

Answer

whats the question

Step-by-step explanation:

The statistical test would be a Z-test for the difference between the proportions.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

We have:

In a recent poll among 500 students, it was found that 60% of women and 68% of men eat meals on campus at least 3 times a week.

From the above data and the definition of the Z-test, the statistical test would be a Z-test for the difference between the proportions.

Thus, the statistical test would be a Z-test for the difference between the proportions.

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[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times {2}^{3} [/tex]

[tex]v = 33.51 \: {m}^{3} [/tex]

[tex]v = \pi {r}^{2} h[/tex]

[tex]v = \pi \times {2}^{2} \times 6[/tex]

[tex]v = 75.40 \: {m}^{3} [/tex]

[tex]v = 75.40 + 33.51[/tex]

[tex]v = 108.91 \: {m}^{3} [/tex]

Hence, the volume of the given compound shape is 108.91 cubic meters.

sphere:

= 33.51 m^3

cylinder:

= 75.40 m^3

all together:

= 108.91 m^3

Answer:

Question 23: 39

Question 24: 10

Question 25: Airline B

Question 26: 20 to 50

Step-by-step explanation:

Answer:

9. Median: 14

10. Mean: 14.1

11. Mode: No Mode

12. New Median: 14.5

13. New Mean: 14.625

Answer:

143.8 m²

Explanation:

Surface Area of cylinder = 2πr(r + h)

Here given,

Surface Area of cylinder:

⇒ 2π(1.6)(1.6+ 12.7)

⇒ 174.2955 m²

⇒ 143.8 m²        (rounded to nearest 1 decimal place)

Using it's formula, it is found that the accuracy of the test was of 0.85 = 85%.

The accuracy of a test is given by the number of correct results divided by the number of results.

In this problem, there are 80 tests, and of those, 5 + 7 = 12 had incorrect results, hence 68 had correct results.

Hence the accuracy of the test is given by:

a = 68/80 = 0.85 = 85%.

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The volume of the solid that results, when the region enclosed by the curves, is revolved about the x-axis is 3.35 cubic units.

When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.

The function is given below.

y = - x² + 1

y = 0

Then the volume of the solid will be

[tex]\rm Volume = 2\int \pi y^2 dx\\\\\\Volume = 2 \int _0^1 \pi (-x^2 + 1)^2 dx\\\\\\Volume = 2 \pi \int _0^1 (x^4 - 2x^2 + 1)dx\\\\\\Volume = 2 \pi \left [ \dfrac{x^5}{5} - \dfrac{2x^3}{3} + x \right]^1_0\\\\\\[/tex]

On solving further, we have

Volume = 2π [(1/5 - 2/3 + 1) - 0]

Volume = 2π [8/15]

Volume = 3.35

Then the volume of the solid will be 3.35 cubic units.

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Answer:

Getting sum 6 when rolling two dice

Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

Mass is one of the principal quantities, which is related to the matter in the object  

The main mass unit consists of 7 units of other than other units of mass such as quintals, tons, pounds, ounces:  

Kilogram, kg  

Hectogram, hg  

Decagram, dag  

gram, g  

Decigram, dg  

centigram, cg  

milligrams, mg  

Each unit descends then multiplied by 10, and if one unit increases then divided by 10  

Fraction numbers are known as numerator and denominator

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

[tex]\dfrac{a}{b}[/tex]

Mixed fractions consist of integers and ordinary fractions

A mixed number is a combination of a whole number and a fraction

Sara has 14 ounces of vanilla yogurt

Her father's yogurt weighs half of much, so her fathers have yogurt :

= 0.5 x 14 ounces

= 7 ounces

Total ounces of yogurt they buy

= 14 + 7 = 21 ounces

for 1 ounces (oz) the conversion = 0.0625 pounds(lbs)

So for 21 ounces there will be

= 21 x 0.0625

= 1.3125 pounds

if we express as a mixed number , it will be :

[tex]=\dfrac{13125}{10000}[/tex]

[tex]=1\dfrac{5}{16}[/tex]

Hence Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

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7000_1.8%=61.2%this is the answer

The graph represents the function (D) because the graph of the function  is not defined at x = 1 and x = 2 option (D) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function:

If we take the function:

[tex]\rm f(x) = \dfrac{1}{\left(x-1\right)\left(x-2\right)}[/tex]

At x = 1 and x = 2 the function will be not defined, so this region would be hollow and as we can see in the graph of a function.

The function is not defined at x = 1 and x = 2.

Thus, the graph represents the function (D) because the graph of the function is not defined at x = 1 and x = 2.

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The measures for the given angles B and E are 12° .

Triangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.

Like the triangles are similar,  ∠B=∠E. Then,

∠B=∠E

3y=6y-12

3y-6y=-12

-3y=-12

y=4

You can write too:

AC=DF

7a+5=5a+9

7a-5a=9-5

2a=4

a=2

Therefore,

∠B=3y= 3* 4 =12

m∠E=6y-12=6*4-12=21-12=12

AC=7a+5= 7*2+5=14+5=19

DF=5a+9=5*2+9=10+9=19

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It's not hemisphere,It's a complete sphere .

Volume

Volume of each hemisphere.

Answer:

y= ⅓x +2

Step-by-step explanation:

Since the graph is a linear graph, let's use the slope-intercept form to find its equation.

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

The y-intercept is the point at which the graph cuts through the y-axis. In this case, the y-intercept is 2.

Thus, y= mx +2.

Let's find the slope of the graph.

First, identify 2 pairs of coordinates from the graph:

(0, 2) and (3, 3)

Next, substitute these coordinates into the slope formula below:

[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

slope

[tex] = \frac{3 - 2}{3 - 0} [/tex]

[tex] = \frac{1}{3} [/tex]

Thus, the equation of the graph is y= ⅓x +2.

Answer:

[tex] \frac{8}{5} = \frac{2}{m - 3} \\ \\ \implies \: 8(m - 3) = 2 \times 5 \\ \\ \implies \: 8m - 24 = 10 \\ \\ \implies \: 8m = 10 + 24 \\ \\ \implies \: 8m = 34 \\ \\ \implies \: m = \frac{34}{8} \\ \\ \implies \: \boxed{m = 4.25}[/tex]

therefore , second option is correct.

hope helpful ~

Answer:

C = 2(h - 1) + 0.80

Answer:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = [tex]\frac{2}{3}[/tex]x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

[tex]5 \frac{3}{5} \% \: of \: 750[/tex]

[tex]5 \frac{3}{5} = 5.6[/tex]

[tex] \frac{5.6\%}{100} \times \frac{x}{750} [/tex]

[tex] = 42%[/tex]

Answer:

the answer is 11 because there are so many no. repeating so in this case we count total no of terms and say it n if terms are odd then mode

Step-by-step explanation:

mode = n+1÷2

Answer:

a.

Step-by-step explanation:

the area of a whole circle (360°) is

pi×r²

in our case

pi×10² = 100pi

but here we don't need the full circle. we only need a fraction of the whole circle : 128/360

so, the area of the sector is

100pi × 128/360 = 100pi × 16/45 = 20pi × 16/9 =

= 111.7010721... cm² ≈ 111.7 cm²

Answer:

B

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Answer:

36 students.

Step-by-step explanation:

5 + 7 = 12.

So the number of students must be a multiple of 12.

So as the number is  between 25 and 43 it must be 36.

Answer:

Step-by-step explanation:

Comment

There are 9 marbles all together.

The important  fact is that he draws 1 marble to begin with and does not replace it. That means that the next marble is out of 8.

Solution

First marble: Blue = 3/9 = 1/3

Second marble: Green 2/8 = 1/4

The probability of that happening is

P(blue,Green) = 1/3 * 1/4 = 1/12

Answer P(blue, green) = 1/12

its true

they are both already right triangles so if both have acute angles that are congruent then the right triangles are similar

if one of the acute angles of a right triangle is congruent to an acute angle of another right triangle then by angle angle Similarity the triangles are similar

Answer:

4 quarts

Step-by-step explanation:

1 gallon is equal to 4 quarts

s = area = 11.76

p = perimeter = 16.8

r=2*11.76/16.8=23.52/16.8=1.4

r=1.4

a= 90 degrees

b=36.87 degrees

c=53.13 degrees

triangle is in a circle

Circumradius: R = 3.5

Step-by-step explanation:

144 degree is right answer.

Answer:

144°

Step-by-step explanation:

The central angle is 360°. Since it has 5 divisions, the angle of each division is 72°.

From B to D, it requires 2 rotations.

Answer:

See below

Step-by-step explanation:

Expand it a bit to see:

= [tex]\sqrt[5]{ 2^5 * 7 * x^5 * x^5 * x * y^5 * y^3}[/tex]

=[tex]2x^2y \sqrt[5]{7xy^3}[/tex]