Adult tickets to the fall play cost $8
and student tickets cost $4. The drama class
sold 20 more adult tickets than student tickets
to the fall play. If the class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution is

Answer:  True

Explanation:  Parallel lines are two lines that lie on the same plane and they never intersect.  

The solution values in order from smallest to largest are;

let

(x - 5)-2 = 14

-2x + 10 = 14

-2x = 14 - 10

-2x = 4

x = 4/-2

x = -2

4x - 5 = -8

4x = -8 + 5

4x = -3

x = -3/4

x = -0.75

(x + 3) / 5 = -2

x + 3 = -2(5)

x + 3 = -10

x = -10 - 3

x = -13

1/2x + 4 = -1

1/2x = -1 - 4

1/2x = -5

x = -5 ÷ 1/2

= -5×2/1

x = -10

x + 2 = 6/-4

-4(x + 2) = 6

-4x - 8 = 6

-4x = 6 + 8

-4x = 14

x = 14/-4

x = -3.5

Therefore, the smallest value is -13 and the largest value is -0.75.

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The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.

Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.

Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

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Data collected about a population is not a characteristic of both observational studies and experiments.

Through experiments, two variables' cause and effect relationships are examined. This is where they differ from observations and interviews, which can only assume the existence of contexts and cannot provide evidence for them. The environment of the test subjects is managed in an experiment depending on the issue.

Three things characterize statistical experiments in general:

There are various outcomes that the experiment could produce.

In an experiment, the cause, the independent variable, is changed while the effect, the dependent variable, is measured and any unrelated factors are controlled.

It is possible to anticipate every outcome.

Chance determines how the experiment turns out.

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Answer: 19 and 14

Step-by-step explanation:

19^2+14^2= 557

What I did to start it is I tried 20 and 15 because I know the square roots of those and once I added them I saw that their sum was too big, so then I tried 19 and 14 because 19-14 is 5. It was really just guess and check :)

Answer:

A

Step-by-step explanation:

$30.00 ÷ 5 = $6.00

$6.00 × 3 = $18.00

Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:

p = 3/11 = 0.273 = 27.3%.

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Answer:

road

Step-by-step explanation:

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:

f(n) = a · bⁿ ⁻ ¹    (1)

Where:

If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:

f(12) = 4 · 2¹² ⁻ ¹

f(12) = 4 · 2¹¹

f(12) = 4 · 2,048

f(12) = 4,096

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

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Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

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Answer:

A minimum of 21250 packets per day.

Step-by-step explanation:

If Monday produced 15,000 packets, and Tuesday was closed they produced 15,000 packets in 2 days.

The factory is open 6 days a week.

They need 100,000 packets.

They have 15,000 packets.

6 subtract 2 is 4.

100,000 subtract 15,000 is 85,000.

They need 85,000 packets in 4 days.

That is a minimum of 21250 packets per day.

Answer:

270 uits

Step-by-step explanation:

Answer:

3+37

11+29

17+23

20+20

Step-by-step explanation:

It's 20

(20+20 = 40)

Hope this helps!

Answer:

Step-by-step explanation:

3 things of triangle are given.

2 sides + 1 angle

so, possible triangles = 1 ans

The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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The area of the rectangular field is 468cm².

Step-by-step explanation:

If, length is 18cm; width is unknown( let x represent width). Then,

Perimeter of a rectangle= Length + Width+ Length + Width

88= 18 + x + 18 + x

88= 36 + 2x

88-36 =2x

52= 2x

52/2=2x/2

26=x

•x=26cm

The width of the rectangle is 26cm.

Area of a rectangle= Length × Width

=18cm×26cm

= 468cm².

The simplification of the equation above in words is = Twelve minus thirteen X.

In mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.

The equation given is,

10 - 13x + 2

Arrange the digits without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is Twelve minus thirteen X.

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Answer:

  (b)  (3,-1)

Step-by-step explanation:

One can determine the correct answer by checking to see if it satisfies the equations.

The first equation can be rewritten to ...

  x = 6 +3y . . . . . . . add 3y to both sides

This makes it easier to check answer choices:

  a) -1 = 6 +3(3) . . . . no

  b) 3 = 6 +3(-1) . . . . yes . . . . . (3, -1) is the solution

  c) 1 = 6 +3(-3) . . . . no

  d) -3 = 6 +3(1) . . . . no

__

Additional comment

We can further convince ourselves this is the correct choice by seeing if it satisfies the second equation:

  2x +2y = 4 . . . for (x, y) = (3, -1)

  2(3) +2(-1) = 4 . . . . yes

Using the z-distribution, the 95% confidence interval of the population mean is: (17.5, 24.5).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the other parameters are:

[tex]\overline{x} = 21, \sigma = 26.8, n = 225[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 21 - 1.96\frac{26.8}{\sqrt{225}} = 17.5[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 21 + 1.96\frac{26.8}{\sqrt{225}} = 24.5[/tex]

The interval is: (17.5, 24.5).

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Answer:

-4

Step-by-step explanation:

in order to get from -6 to 24, you need to multiply x by -4 since -6* -4 is 24

The value of bh for b =12 and h = 2 is 24

The expression is given as:

bh

Where

b = 12 and h = 2

So, we have:

bh = 12 * 2

Evaluate

bh = 24

Hence, the value of bh for b =12 and h = 2 is 24

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Answer:

y = 3/2x -15

Step-by-step explanation:

y = mx + b this is the slope intercept form.  We need the slope and the y intercept.  The slope (m) has been given (3/2), we just need the b (y-intercept).  We will use the point given to find b.  The point given is (8,-3).  8 is the x term and -3 is the y term.  We will plug them into y = 3/2x + b to solve for b.

y = mx + b

y = (3/2) x + b   The slope was given

-3 = (3/2)(8) + b  Plugged in the given x and y from the point (8, -3)

-3 = 12 + b  I can make 8 into a fraction by putting a 1 under it.

                   (3/2)(8/1).  I can cross cancel to make the number easier to

                    2 and 8 both share the factor 2 so I will divide both numbers

                   by 2 and I will now have (3/1)(4/1).  3x4 is 12 and 1x1 is 1, so

                   12/1 is  the same as 12.

-15 = b      Subtract both sides by 12.  -3-12 is -15

Now that I have the m and the b, I can write the equation in the slope intercept form.  y =  3/2 + (-15) or y = 3/2 -15    

The answer is 1

10¹ = 10

i hope it was helpful

We know that this ratio is directly because the two magnitudes go up.

In this case we will get the proportionality constant by dividing any term of the second magnitude by the first.

[tex]9 \: \div \: 3 \: = \: \boxed{3}[/tex]

Now that we know that k = 3, we can know how much "y" will be if x = 5.

We just multiply:

[tex]3 \: \times \: 5 \: = \: \boxed{ \bold{ 15}}[/tex]

Answer:

(-oo, -8/3) U (-8/3, oo)

Step-by-step explanation:

Hope this helps.

The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)

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

f(x) = 2/(3x + 1)

The above equation is a rational function

The rule of a function is that

The domain is the set of all input numbers

For the domain, we set the denominator not equal to 0

So, we have

3x + 8 ≠ 0

Evaluate

x ≠ -8/3

When represented as interval notation, we have

Domain = (-∝, -8/3) U (-8/3, ∝)

Hence, the domain is (-∝, -8/3) U (-8/3, ∝)

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Answer:

113°

Step-by-step explanation:

Angles that form a linear pair are supplementary, and thus add to 180°.

Answer:

11

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

Answer:

12.5 inches

Step-by-step explanation:

We use proportion to calculate the scale drawing

27 feet = 5 inches, so

67.5 feet = more inches (we know that it would be bigger than 5 inches)

We then put the bigger number on top and crossmultiply by saying:

67.5 over 27 × 5

Your answer should come out as 12.5 inches.

Answer is slope of 5

Step by step

You can graph the slope as seen on the attached picture. You go up 30, you go right +6. Slope is y/x, so 30/6, equals 5

You can also use the slope formula

(y2-y1) over (x2-x1)

Using points on the graph

(6,0) and (0,-30)

(-30-0 ) over (0-6)

-30 over -6

-30/-6

= 5