50 points

There are 140 people in a theater watching a movie. The number of children present is 3 times the number of adults. How many children are watching the movie?

12 children

35 children

3 children
105 children

The sentence that represents this equation 8 3/4 = 17 - x is B) 8 3/4 is the same as 17 decreased by a number.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, 8 3/4 is the same as 17 decreased by a number will be 8 3/4=17−x.

Therefore, the correct option is B.

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Complete question

What sentence represents this equation?

8 3/4 = 17 - x

A) A number is the same as the difference of 17 and 8 3/4.

B) 8 3/4 is the same as 17 decreased by a number.

C) 17 decreased by 8 3/4 is the same as a number.

D) 8 3/4 is the same as a number decreased by 17.

Answer:

x = 2

Step-by-step explanation:

8x - 6 = 10 ( add 6 to both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Answer:

x = 2

Step-by-step explanation:

8x-6 = 10

8x-6+6 = 10+6

8x = 16

8x/8 = 16/8

x = 2

Answer:

y = 5x + 1

y = 5x + [tex]\frac{-3}{2}[/tex]

When the slopes are the same (5) the equations are parallel.

Step-by-step explanation:

You can look at the graph of the two equaions attached to see that there paralle.

2y - 10x +3 = 0  Add 10 to both sides of the equation

2y -3 = 10x  Add three to both sides of the equation

2y = 10x -3  Divide all the way through by 2

y = 5x + [tex]\frac{-3}{2}[/tex]

The magnitude of the second earthquake, using an logarithmic function, is of:

5.77.

The magnitude of an earthquake is given by the logarithmic rule presented as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

The first earthquake had a magnitude of 3.9, hence it's energy is obtained as follows:

[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]

The logarithm and the base 10 are inverse functions, hence the base 10 is applied to both sides to isolate the energy variable as vollows:

[tex]\frac{E}{E_0} = 10^{5.85}[/tex]

[tex]E = 707945.784E_0[/tex]

For the second earthquake, it's energy was 650 times greater, hence:

[tex]E = 707945.784 \times 650E_0 = 460164760E_0[/tex]

Hence it's magnitude is obtained as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{460164760E_0}{E_0}\right)}[/tex]

M = 5.77.

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The gallons of water and premium antifreeze solution that must be mixed are equal to 60 gallons and 120 gallons respectively.

In order to calculate the gallons of water and premium antifreeze solution, we would assign variables to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:

Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:

x + y = 180      ....equation 1.

0.60y = 0.40(180)    ....equation 2.

From equation 2, we have:

0.60y = 0.40(180)

0.60y = 72

y = 72/0.60

y = 120 gallons of premium antifreeze.

For the gallons of water, we have the following:

x + y = 180

x = 180 - y

x = 180 - 120

x = 60 gallons of water.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~\cfrac{1}{x+8}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{1}{y+8}} \implies y+8=\cfrac{1}{x}\implies {\large \begin{array}{llll} \stackrel{f^{-1}(x)}{y}=\cfrac{1}{x}-8 \end{array}}[/tex]

The amount of the monthly payments is $368.34, and the total interest on the loan is $5,100.

The initial amount of money that we borrow is $17,000. We borrow this amount for a total of five years. The interest charged is 6%. We borrowed the money for the purchase of a car. We need to find the monthly payments and the total interest for the loan.

Let the total amount to be paid and the interest be denoted by the variables "A" and "I", respectively.

I = P*R*T

I = $17,000*0.06*5

I = $5,100

The total amount of money to be paid is the sum of the initial amount and the interest charged.

A = P + I

A = $17,000 + $5,100

A = $22,100

The total number of months in five years is 12*5 = 60.

The amount of the monthly payment is the ratio of the total amount to be paid to the total number of months.

M = $22,100/60

M = $368.34

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Answer:

C= 31in

Step-by-step explanation:

First you must know the circumference equation. The circumference equation is C=2πr, with r being the radius. Since we are given the radius, we will fill in the radius given for r. So then we will fill in and solve:

C=(2)(π)(5in)

C=(10)(π)

C=31.4in...

C=31in

Hope this helps!

The inequality of the scenario is 10000 ≤ l² - 16l < 16000 and the length is 1672 feet

The statements from the question are given as:

Shape = Rectangular park

Minimum perimeter = 5000 square ft

Maximum perimeter = Less than 8000 square ft

Also, we have

Width = 8 less than half the length

This means that

w = 1/2l - 8

The perimeter of a rectangle is

perimeter = 2 * (l + w)

So, we have

P = lw

This gives

P = 2 * (l + 1/2l - 8)

P = 2 * (1.5l - 8)

Open the brackets

P = 3l - 16

Substitute the known values in the above equation So, we have the following equation

5000 ≤ 3l - 16 < 8000

The above represents the inequality

See attachment for the graph

From the graph, we have the solution to be

l = 1672 (approximately)

Recall that:

w = 1/2l - 8

So, we have

w = 1/2 * 1672 - 8

Evaluate

w = 828

Hence, the possible length is 1672 ft

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Based on the given parameters about a carpenter cutting the top section of a window frame, the side pieces of the frame are not parallel.

Parallel lines are lines which are equally distant from one another at all points.

To show that the side pieces of the frame are parallel:

The interior angles are equal in measure and the sum of the interior angles must be equal to 180°

The two given side pieces of the window frame are also equal in measure.

If the sum of both side angles is equal to 180∘, then, the sides are parallel.

37∘ + 50∘ = 87∘

2(37∘ + 50∘)

= 2(87∘)

= 174∘

Hence,

174∘ < 180∘

So therefore, the sides pieces of the window frame cut by the carpenter are not parallel.

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The polynomial of p(x) is  -24 (x² + 15x + 54) with the satisfying's conditions degree 3.

Given,

An nth degree polynomial p meets the requirements listed below:

p is of degree 3.

-9 is a zero, with multiplicity 2, of p.

-6 is a zero, with multiplicity 1, of p.

p(-1) = -960

We have to determine an nth degree polynomial that satisfier the conditions.

Let the polynomial be p(x) whose zero are -9 and -6

a be the coefficient.

p(x) = a (x+9) (x+6)

p(x) = a(x² + 6x + 9x + 54)

p(x) = a(x² + 15x + 54)

Now, take x = -1

p(-1) = a (-1² + 15 x -1 + 54)

-960 = a ( 1 - 15 + 54)

-960 = a x 40

a = -960/40

a = -24

We get,

p(x) = -24 (x+9) (x+6)

p(x)= -24 (x² + 15x + 54)

Therefore, the polynomial of p(x) is  -24 (x² + 15x + 54) with the satisfying's conditions degree 3.

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a) A vertical stretch happens for values of a such that |a| > 1.

b) A vertical compression happens for values of a such that |a| > 0.

c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.

d) A reflection across the x-axis takes place when a < 0.

The definition of the quadratic function is given as follows:

f(x) = a(x - h)² + k.

The transformations to the function are given as follows:

Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:

a < 0.

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Answer:

The answer to your question is,

7

Step-by-step explanation:

The series as represented in the task content is divergent and hence; diverges.

It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.

It is noteworthy to know that;

If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.

Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.

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Answer: 51 ft

Step-by-step explanation:

This is a Similar Triangles problem (geometry)

Draw 2 triangles with the sides correctly labeled.

Set up your ratios

170/6 = x/1.8

Solve for x

28.3 = x/1.8

x = 51 ft (length of shadow cast by the lighthouse)

Answer:

f

Step-by-step explanation:f

a) The number of 12.2 mg chewable tablets would be taken in a week is 53.

b) The liquid antihistamine should a 100-pound person taken in a week is 528ml

An ordered pair of numbers a and b, denoted as a / b, is a ratio if b is not equal to 0. A proportion is an equation that equalizes two ratios.. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls.

Given that a typical dose for a 100-pound person is 23 mg every six hours.

100 pounds person - 23 mg - 6hrs

For  1 day it is 24 hrs

7 days-168hrs

Therefore,

a) For 6 hrs - 23 mg         

168 hrs- ?

X=(23×168)/6

 =644 mg

 For 1 tablet -12.2 mg

 =644/12.2

 = 52.786≈53 tablets

The number of 12.2 mg chewable tablets would be taken in a week is 53.

b) If 12.2 mg equals to 10 ml then

 644mg =(10/12.2)×644 ml

 =527.87 ml≈528ml

The liquid antihistamine should a 100-pound person taken in a week is 528ml

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Answer: I think it’s the first one.

Step-by-step explanation:

The probability that Rebecca's first flight was delayed is 75%.

Probability is the ratio or odds of an expected outcome occurring when there are many possible outcomes.

Probability is always a fractional value lying between 0 and 1.  When the expected outcome is certain, the probability is said to be one.  When it is uncertain, the probability is zero.

Like ratios, probability is depicted as decimals, fractions, or percentages when there is no 100% certainty or uncertainty.

The probability of Rebecca's first flight leaving on time = 0.25

The probability of Rebecca's first flight being delayed = 0.75 (1 - 0.25)

= 75%.

Thus, it is 75% likely that Rebecca's first flight will be delayed.

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Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that Rebecca​'s first flight was​ delayed?

According to the given APR, the monthly interest charge is $47.46

APR

Basically, APR refers the refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors.

Given,

Maxine's credit card has an APR of 21.99%.

Here we have to find the monthly interest charge if her current monthly balance, before interest, is $2,586.50.

While we looking into the given question, we have identified the following,

APR = 21.99%

For one month the APR is calculated as,

APR = 21.99 / 12

APR = 1.8325%

When we convert this into decimal form then we get,

=> APR = 1.8325/100

=> APR = 0.01835

And the current monthly balance is $2,586.50,

So, the interest change for the month is

=>2,586.50 x 0.01835

=> 47.46

Therefore, the monthly interest charge is $47.46.

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Answer:The question is very brief, im not sure if i understand what your asking

Step-by-step explanation:

Answer:

$6

Step-by-step explanation:

5 x 0.20=1

5+1=6

Answer:

[tex]y=-2x-1[/tex]

Step-by-step explanation:

If two lines are parallel, they have the same slope. In this case, it is -2

Using point-slope form, with a slope of -2 going to through point P(0,-1)
We have:

y+1=-2x

y = -2x - 1

:]

1. The journal entries to record the transactions for Kohler Corporation are as follows:

January 2 Debit Treasury Stock $90,0000

Credit Paid-in capital in excess $30,000 Cash $120,000

January 5 Debit Dividend $88,000

Credit Dividend Payable $88,000

January 5 Debit Retained Earnings $88,000

Credit Dividend $88,000

February 28 Debit Dividend Payable $88,000

Credit Cash $88,000

July 6 Debit Cash $72,000

Credit Treasury Stock $45,000

Credit Paid-inn Capital in excess $27,000

August 22 Debit Cash $48,000

Credit Treasury Stock $45,000

Credit Paid-inn Capital in excess $3,000

September 5 Debit Dividend $100,000

Credit Dividend Payable $100,000

September 5 Debit Retained Earnings $100,000

Credit Dividend $100,000

October 28 Debit Dividend Payable $100,000

Credit Cash $100,000

December 31 Debit Income Summary $428,000

Credit Retained Earnings $428,000

2. The preparation of the statement of retained earnings for the current year ended December 31 is as follows:

Kohler Corporation

For the current year ended December 31

Beginning balance     $400,000

Dividends                       (88,000)

Dividends                     (100,000)

Income Summary          428,000

Ending balance          $640,000

The preparation of the stockholder's equity section of the balance sheet as of December 31 of the current year is as follows:

Kohler Corporation

As of December 31 of the current year

Common stock—$15 par value, 100,000 shares authorized

50,000 shares issued and outstanding                   $ 750,000

Paid-in capital in excess of par value, common stock 70,000

Retained earnings                                                        640,000

Total stockholders' equity                                       $1,460,000

January 2 Treasury Stock $90,0000 Paid-in capital in excess $30,000 Cash $120,000

January 5 Dividend $88,000 Dividend Payable $88,000 (50,000 - 6,000 x $2)

January 5 Retained Earnings $88,000 Dividend $88,000

February 28 Dividend Payable $88,000 Cash $88,000

July 6 Cash $72,000 Treasury Stock $45,000 Paid-inn Capital in excess $27,000 (3,000 x $24)

August 22 Cash $48,000 Treasury Stock $45,000 Paid-inn Capital in excess $3,000 (3,000 x $16)

September 5 Dividend $100,000 Dividend Payable $100,000 (50,000 x $2)

September 5 Retained Earnings $100,000 Dividend $100,000

October 28 Dividend Payable $100,000 Cash $100,000

December 31 Income Summary $428,000 Retained Earnings $428,000

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The number of attempts Vonna made is 80.

Given,

Vonna scored 48 goals in her scoccer kicking practice.

Her success to failure rate is 3:2

Vonna scored 48 goals" means that there were 40 successes,

= 48 goals

= 3:2

= 48:3

= 16

x = 6 positive integer

hence let 3x:2x

= 3(16) = 48

= 2(16) = 32

Total attempts = 48+32

= 80

Hence the total number of attempts Vonna made is 80.

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Answer:

Yes i the relationship linear,exponential,or neither

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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Answer:

1.914 %

Step-by-step explanation:

Compounded quarterly means 4 periods per year  = n

   interest in decimal form per period    i = .019/4 = .00475

   Formula    

       annual yield =  ( 1+ i)^n  -1

                   (1+ .00475)^4  -1  = .01914  = ~ 1.914%