The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $4 and each adult ticket sells for $8. The auditorium can
hold no more than 100 people. The drama tub must make at least $560 from ticket
sales to cover the show's costs. If z represents the number of student tickets sold and
y represents the number of adult tickets sold, write and solve a system of inequalities
graphically and determine one possible solution.

Answer:

3/16

Step-by-step explanation:

Step 1) Calculate the difference

The first step is to find the absolute difference between 1/8 and 3/12. We do that by subtracting 3/12 from 1/8, like this:

1/8 - 3/12 = |1/8|

Step 2) Divide the difference by two

Next, we divide the absolute difference by two. This gives us half of the absolute difference. To do this, we divide the answer in step 1 by 2, like this:

1/8 ÷ 2 = 1/16

Step 3) Add half the difference

In the final step, we add half of the absolute difference to the lowest fraction. The lowest fraction of 1/8 and 3/12 is 1/8. Therefore, we add 1/16 to 1/8, like this:

1/8 + 1/16 = 3/16

Per our calculations above, the fraction exactly halfway between 1/8 and 3/12 is as follows:

3/16

Hope this helps! :)

The area of the given shape is 78.5 unit²

Given,

The shape is 1/4th part of circle.

The radius is given as 10 units

We have to find the area of the shape.

Here,

The area of a circle is pi times the radius squared (A = π r²).

Area of circle = π × r²

Then

Area of 1/4th part of circle = π × r² / 4

That is,

Area of 1/4th part of circle = 3.14 × 10² / 4

Area of 1/4th part of circle  = 314 / 4

Area of 1/4th part of circle = 78.5 unit²

That is,

The area of the given shape is 78.5 unit²

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0. 63212  is the probability that a repair will take less than 2 hours.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                        In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

P( X > 2 ) = 1 - P ( X/ leq2 )

             = 1 - F( 2)

             = 1 - [tex]e^{0.5 * 2}[/tex]

              = 0. 63212.

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The y intercept of the line passing through the points (12,-2) and slope -1/6 is  0  .

In the question ,

it is given that ,

the slope of the line is -1/6 ,

the line passes through the points (12 , -2)

we know that the equation of the line is written as

y = mx + c

where, "m" is the slope

and c is the y intercept .

Since the line passes through point (12,-2) , it should satisfy the equation of the line , that is

-2 = (-1/6)*12 + c

-2 = -2 + c

c = -2 + 2

c = 0

So , y intercept is 0 .

Therefore , The y intercept of the line passing through the points (12,-2) and slope -1/6 is  0  .

The given question is incomplete , the complete question is

Find the y intercept of the line passing through (12,-2) and slope = -1/6 ?

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The sales of phones and accessories should be 6 and 12 each, correspondingly.

The data stated in question-

Let 'P' be the number of the phones sold.

Then, the accessory sold be '2P'.

The equation will form for the total cost will be;

11P  +  3(2P) = 102

11P  +  6P = 102

17P = 102

P = 102 / 17 =

P = 6  (number of sold phones)

Accessories sold = 2P = 2 x 6 = 12

Thus, the sales of phones and accessories should be 6 and 12 each, correspondingly.

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It is a valid probability model when pew research center reported that among months, family size is shrinking.

Given that,

pew research center reported that among months, family size is shrinking. suppose we are to randomly select one mother (age 40 to 44) and record the number of children she has. Here is a probability model.

We have to find explain why this is a valid probability model.

We know that,

In the picture we can see,

Probability is 0.22+0.41+0.24+0.13 = 1

Since all probability are less than 1 and sum of all probability is equal to 1.

Therefore, It is a valid probability model when pew research center reported that among months, family size is shrinking.

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a) Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.

b) Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.

According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.

Given,

Expressions:

a) 5² - 9 ÷ 3

Using PEMDAS,

Squaring,

25 - 9 ÷ 3

Dividing,

25 - 3

Subtracting,

22

Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.

b) 8 + 6 - 2× 2 -3²

Using PEMDAS,

Squaring,

8 + 6 - 2 × 2 - 9

Multiplying,

8 + 6 - 4 - 9

Adding,

14 - 4 -9

Subtracting,

1

Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.

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There is 48% probability that the two socks will match .

The branch of mathematics concerned with the occurrence of random events. Values ​​are represented from 0 to 1. Probability was introduced into mathematics to predict the probability of an event occurring. Probability basically means how likely it is that something will happen. This is the basic theory of probability and is also used in probability distributions to learn possible outcomes of random experiments. To determine the probability of a single event occurring, we first need to know the total number of possible outcomes.

Since there are a total of 35 socks, the probability of both socks being blue is

P(blue) = 15/35 * 14/35 = 3/35 * 14/7 = 3/35 * 2 = 6/35

The probability of both being grey is

P(grey) = 20/35 * 19/35 = 19/35 * 4/7  = 76 / 245

The probability that they match is

P(blue) + P(grey) = 6/35 + 76/245  =  42+76/245 = 118/245 = 0.48 = 48%

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If the triangle is equiangular, then the triangle is an equilateral triangle.

What is equiangular triangle?

A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60

What is equilateral triangle?

an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°.

As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.

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Answer:

$25.00

Step-by-step explanation:

Total amount of bill is $25.

Given information:

The amount of tip = $4.50

The percentage given = 18%

4.50 of 18% is $25

Answer: 7.6 meters.

Step-by-step explanation:

1.2(2) + 2.6(2)

2.4 + 5.2

7.6

Remember, perimeter is L(2) + W(2).

1. The three lengths are B. 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.

2. The third side D. It must be greater than οr equal tο 6 and at mοst 24.

A physical measure οf distance between twο places in space is length. It is a fundamental quantity that is emplοyed in bοth engineering and physics. The Internatiοnal System οf Units (SI) uses metres as the unit οf length (m). In geοmetry, length plays a crucial rοle in describing the size and lοcatiοn οf geοmetrical shapes in space.

Accοrding tο the Triangle Inequality Theοrem,

The tοtal οf twο sides οf a triangle must be greater than the sum οf the third side, accοrding tο this theοrem. If all three cοmbinatiοns are true, yοu will have a true triangle.

1) Yοu must gο thrοugh each οf these οptiοns οne by οne tο ensure that the triangle is feasible. Cοnsider the triangle tο have the side lengths a, b, and c, and the theοrem tο be an inequality, which states:

a+b > c, a+c > b, and b+c > a.

As per οptiοn (B),

a = 18, b = 12, and c = 9

Here, Triangle Inequality Theοrem satisfies.

Thus, the three lengths are 18cm, 12cm, and 9cm which cοuld be the lengths οf the sides οf a triangle.

2. By the prοperties οf the triangle, the sum οf the square οf twο lengths is equal tο the third side length οf the triangle.

Always remember that when yοu add twο sides tο a triangle, the sum will cοme οut tο be higher than the third side’s length.

Hence, D. It must be greater than οr equal tο 6 and at mοst 24.

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Answer:

f(x) = –2x + 3

Step-by-step explanation:

The equation that can be used to find the number of seconds in a number is [60s = m].

So, an equation that finds the number of seconds in a number of minutes.

We know that:

Then, the equation will be:

Therefore, the equation that can be used to find the number of seconds in a number is [60s = m].

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The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

Given,

The constant rate at which helium is pumped into the spherical balloon, r = 5 ft.³/s

We have to find the rate at which the radius of the balloon is increasing after 2 minutes.

Here,

dV/dt = (dV/dr) × (dr/dt)

Then,

dr/dt = (dV/dt) / (dV/dr)

The volume of balloon after 2 minutes (120 seconds) V₁₂₀ ;

V₁₂₀  = 120 s × 5 ft.³/s = 600 ft.³

The radius of balloon after 2 minutes ;

V = 4/3 π r³

dV/dr = 4 π r²

r = [tex]\sqrt[2]{\frac{2}{4.\pi } V}[/tex]

Then,

r₁₂₀ = [tex]\sqrt[2]{\frac{2}{4.\pi } 600}[/tex] ≈ 9.77

dr/dt = (dV/dt) / (dV/dr) = 5 / 4π r²

At t = 2 minutes (120 seconds), r ≈ 9.77 feet

dr/dt ≈  5 / 4π 9.77² ≈ 4.16 × 10⁻³

That is,

The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³

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The slope of the line is 400

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

Start position = 600 feet

Rate of ascending = 400 feet per minute

The above parameters can be interpreted as

Initial position = 600 feet

Rate = 400 feet per minute

The rate is the slope

So, we have

Slope = 400

Hence, the slope is 400

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The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

In the question ,

seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.

we have to find statement which are true .

Option (a)

Thickness of the slide is dx for disk method and

dy for the shell method while rotating about x - axis ,

So , statement of option(a) is false .

Option(b)

In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,

thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,

So , statement of option (b) is false .

Option(c)

In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,

Thus , slices are cut perpendicular to the x axis .

statement of option (c) is True .

Option (d)

As in 2D , the  bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .

So , statement of option(d) is True .

Option(e)

When using shell method, we cut region into small slices perpendicular  to the x-axis .

So , statement of option(e) is False .

Option(f)

There can be both the kinds of cases , like in some cases disk method is easier than shell method and

in other cases shell method can be easier than disk method .

So , statement of option(f) is False .

Option(g)

When using disk method, we cut region into small slices perpendicular to x-axis .

So , statement of option (g) is False .

Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

The given question is incomplete , the complete question is

Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:

(a) The thickness of the slices will be dx for both methods.

(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.

(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.

(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using the shell method, we cut the region into small slices parallel to the x-axis.

(f) The shell method will always result in a less complicated integral.

(g) When using the disk method, we cut the region into small slices parallel to the z-axis.

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Answer:

15

Step-by-step explanation:

Let's try to list the factors of 60 first.

60 { 1,2,3,4,5,6,10,12,15,20,30,60}

Now, it says it's a double digit number, so these are the remaining answers.

{10,12,15,20,30,60}

Since it is a multiple of 3, these are the possibilities.

12,15,20,30,60

After that, since it says that it's odd, we only have one possible solution left.

15

Square root of 15.625 is 3.906

What in mathematics is a square root?

A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.

How is the square root calculated?

The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."

Find the nearest perfect square, in this case 16 .

Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906

Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.

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The length of each of the other two pieces = 0.

Jessica cuts a ribbon with a length of 12 inches into three pieces.

The length of one piece is [tex]3\frac{1}{2}[/tex]

The lengths of the other two are the same

To find out the length of each of the other two pieces:

Based on the given conditions, we write formula as

(3-3)÷2

The sum of two opposites equals O: [tex]\frac{3-3}{2}[/tex]

Apply Zero property of Multiplication: 0

So we get the result = 0

Hence the answer if the length of each of the other two pieces = 0.

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Answer:

450 bacteria

Step-by-step explanation:

90 percent of 100 is 90 90x5 is 450

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:

p-value = 0.09 is the probability of obtaining a value for the test statistic.

We are going step by step

Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample

Step 2) Here the Confidence level is equal to 0.95

So the level of significance is equal to 0.05

p-value = 0.09

Since the p-value is higher than the level of significance that we do not reject the null hypothesis.

Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.

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Answer:

5 grams, 9.4 grams, 0.35 kilograms

Step-by-step explanation:

9.4 g and 5g are already converted so don't worry about those.

0.35 kilograms translates to 350 grams.

from smallest to largest thatd be

5, 9.4, 350

Answer:

-35.4

Step-by-step explanation:

Using PEMDAS divide 63 first by 5 and u will get:

Now we have 12.6-48. If we subtract them together we will get:

Hence, the answer is -35.4

The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.

A square is a four sided polygon with 4 equal angles and length.

The fourth corner = 90° - 36°

= 54°

Recall,

Alternate angles are equal

So,

(4x + 4)° = 36°

substract 4 from both sides

4x = 36 - 4

4x = 32

divide both sides by 4

x = 32/4

x = 8

(4y + 10)° = 54°

substract 10 from both sides

4y = 54 - 10

4y = 44

divide both sides by 4

y = 44/4

y = 11

In conclusion, the value of the following given equations are:

(4x + 4)° = 36°

4(8) + 4 = 36

32 + 4 = 36

36° = 36°

(4y + 10)° = 54°

4(11) + 10 = 54

44 + 10 = 54

54 ^= 54°

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The distance from the headquarters to a point on the ground directly below the balloon (to the nearest foot) is 1221 feet

The distance is calculated using tangent of the angle using the formula

tan x = opposite / adjacent

From the question it can be deduced that

x = 55°11'

opposite = the required distance

adjacent = 849 feet

solving for the opposite

tan x = opposite / adjacent

tan 55°11' = opposite / 849

opposite = 849 * tan 55°11'

opposite = 1220.793

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Answer: a is the correct answer

Step-by-step explanation:

When we know the population standard deviation σ, we use a standard normal distribution to calculate the error-bound EBM and construct the confidence interval.

The value of z needs to be found for that is equal to the confidence level (in decimal form) which is in the middle of standard normal deviation Z ~ N(0, 1). One doesn't know the Population Standard Deviation (SD) unless one measures the entire population data points. One can calculate SD. If one means estimating the SD of the population then we can answer that. Any dataset is measured and reported in at least two ways: Center Tendency of the data set (Mean, Median or Mode) and Variability of the data set (Range, SD, etc.)

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