Simplify each expression.

2(10m-7a) + (8a-3m)

The marginal cost of producing the next unit of output always affects the average total cost, so the marginal cost curve always intersects the average total cost curve at its lowest point.

The difference in overall production costs caused by creating or producing one more unit is known as the marginal cost.

By producing at the point where marginal cost (MC) equals marginal revenue, a business can optimize its earnings (MR).

Because fixed costs are fixed regardless of output levels, larger production spreads the total fixed cost over more units, resulting in a lower fixed cost per unit.

Production levels affect variable costs, so increasing the number of units will increase those costs.

Companies need to be aware of the situations when expanding production entails step costs as a result of shifting relevant ranges.

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Answer:

see below

Step-by-step explanation:

— 7x — бу = — 15

To find the x intercept set y = 0 and solve for x

-7x - 0 = -15

-7x= -15

Divide by -7

-7x/-7 = -15/-7

x = 15/7

The x intercept is (15/7,0)

To find the y intercept set x = 0 and solve for y

o— бу = — 15

— бу= -15

Divide by -6

— бу/-6= -15/-6

у= 5/2

The y intercept is (0,5/2)

Probabilities are used to determine the chances of an event.

A. Probability of selecting a large flower with a long stem

The total number of flowers is:

\(Total = 10 + 18 + 43 + 29\)

\(Total = 100\)

Large flowers with long stem are 29.

So, the probability is:

\(Pr = \frac{29}{Total}\)

\(Pr = \frac{29}{100}\)

\(Pr = 0.29\)

B. Probability that a large flower has a short stem

The total number of large flowers are

\(Large = 43 + 29\)

\(Large = 72\)

Large flowers with short stem are 43

So, the probability is:

\(Pr = \frac{43}{Large}\)

\(Pr = \frac{43}{72}\)

\(Pr = 0.597\)

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Answer:

△QPS≅△RPK by reason ASA, SAA

PS = PK , AC = BD , m∠ABC=m∠BAD, ΔAOK ≅ ΔBOL are proved.

Congruent triangles are those of the same size and shape. This means that the corresponding sides are equal, as are the corresponding angles. We can determine whether two triangles are congruent without testing all of their sides and angles.

1) in ΔPQR we have ,

             PQ = PR

IN,       ∠PRQ = ∠PQR (Isosceles triangle)

180° - ∠PQR = 180° - ∠PQR

         ∠PQR = ∠PSQ

IN ΔPSQ = PRK

        ∠SPQ = ∠RPK

            ∠Q = ∠R IS GIVEN IN QUESTION SO,

       ∠SPQ = ∠RPQ

so, by ASA congruence  we have ,

     ΔPSQ ≅ ΔPRK

    So, PS = PK

hence proved .

2) There are several ways two triangles can be congruent.

AC = BD congruent by SAS

ABC ≅ BAD congruent by the corresponding theorem

In ΔAOC and ΔBOD, we have the following observations

AO = DO ( O is the midpoint of line segment AD)

BO = CO ( Because O is the midpoint of line segment BC)

∠AOB = ∠COD (vertical angles are congruent)

  ∠AOC = ∠BOD ( vertical angles are congruent)

Using the SAS (side-angle-side) postulate, we have:

AC = BD

Using the corresponding theorem,

ΔABC ≅ ΔBAD

The above congruence equation is true because:

2 sides of both triangles are congruent

1 angle each of both triangles is equal

Corresponding angles are equal

Hence Proved.

3) There are several ways two triangles can be congruent.

ΔAOK ≅ ΔBOK

are congruent by SAS

In ΔAOL and ΔBOK, we have the following observations

AO = BO ( O is the midpoint of line segment AB)

∠AOL = ∠BOK ( vertical angles are congruent)

LO = KO ( O is the midpoint of line segment KL)

Using the SAS (side-angle-side) postulate, we have:

ΔAOK ≅ ΔBOK

The above congruence equation is true because:

2 sides of both triangles are congruent

1 angle each of both triangles is equal

Hence proved

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Answer:

-27

Step-by-step explanation:

The equation -a+7x, when plugged in shows -6+7*(-3).

This gives us -6-21 which is -27.

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Thanks!

The given tax rates are as follows: Drew’s tax due is 4,519.50 and his effective tax rate is 11.6%. Option A is correct.

You will determine your total taxable income based on your tax slab by subtracting all eligible deductions from the gross taxable income. Senior citizens pay a different slab rate.

An income tax system's tax base is referred to as taxable income. That is, the amount of income that was subject to taxation by the government. In most cases, some or all of the income is included, and expenses and other deductions reduce it.

                      Single Taxpayers: Income Brackets

Tax Income                  Rate Bracket             Tax Owed              

0 to 9,525                       10%                     10% of taxable income

9,526 to38,700               12%        $952.50 plus 12% of  38,700 the excess                                                                                        over

$38,701 to 82,500          22 %                $4,453.50 plus 22% of 38,701                                                                                     the excess over

82,501 to 157,500          24%      $14,089.50 plus 24% of the excess over

                                                                                                         157,500

157,501 to  200,000       32%      $ 32089.50  plus 32% of the excess over

200,001 to   500,000     35%      45,689.50 plus 35% of excess over

500,000 >                        37%      $150,689.50 plus 37% of 500,000 of the    

                                                             excess over

The taxable income lies in the tax rate range of   $38,701 to 82,500.

Therefore the tax would be  :

                                  $4,453.50 + 22% of (39,000-38,701=299)

                                           = $4,453.50 + 22% of 299

                                                  =  $4,453.50 + 65.78

                                                  = $ 4519.28

The taxable income lies in the tax rate range of  $38,701 to 82,500. Due and effective tax rate is $4,453.50 plus 22% of 38,701 the excess over.

The calculated tax is $ 4519.28

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Answer:

The exponential model n(t) is \(n(t) = 46(1.1487)^t\)

Step-by-step explanation:

Exponential model of population growth:

An exponential model for population growth has the following model:

\(n(t) = n(0)(1+r)^t\)

In which n(0) is the initial value and r is the growth rate, as a decimal.

Observed to double every 5 hours.

This means that \(n(5) = 2n(0)\)

We use this to find 1 + r. So

\(n(t) = n(0)(1+r)^t\)

\(2n(0) = n(0)(1+r)^5\)

\((1+r)^5 = 2\)

\(\sqrt[5]{(1+r)^5} = \sqrt[5]{2}\)

\(1 + r = 2^{\frac{1}{5}}\)

\(1 + r = 1.1487\)

So

\(n(t) = n(0)(1+r)^t\)

\(n(t) = n(0)(1.1487)^t\)

Initially has 45 bacteria

This means that \(n(0) = 45\). So

\(n(t) = n(0)(1.1487)^t\)

\(n(t) = 46(1.1487)^t\)

The exponential model n(t) is \(n(t) = 46(1.1487)^t\)

Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

P = 0.232

Step-by-step explanation:

In the cooler, we have 12 bottles of apple juice and 18 bottles of orange juice.

This adds up to a total of 30 bottles.

Now we want to find the probability of pulling a bottle of apple juice after you pulled one bottle of apple juice.

The probability of pulling a bottle of apple juice at the beginning is equal to the quotient between the number of apple juice bottles in the cooler and the total number of bottles in the cooler,

This means that 12 out of 30 are apple juice, then the probability of getting first a bottle of apple juice is:

p = 12/30

Now, we want to find the probability of getting another, we will do the same calculation than above, but now the number of bottles of apple juice is 11 (because we took one) and the total number of bottles is 29.

In this case, the probability is:

q = 11/29

The joint probability (the probability of both events happening) is equal to the product of the individual probabilities.

Then the probability of pulling apple juice and then pulling another apple juice is:

P = p*q = (12/30)*(11/29) = 0.232

Answer:

3

Step-by-step explanation:

colinear points mean along the same line

Line m has 3 points labeled

Line n has 3 points labeled

Each line has only 3 points labeled

This is an edit from my previous answer.

Initially I wrote that there were 5 collinear points. My line of reasoning was that A,B,C are on one line (making them collinear), and points D,B,E are on another line (another set of collinear points).

However, if the question is asking how many collinear points are on one particular line, then the answer would be 3 collinear points. You can focus on either line and it's the same number of collinear points.

Definition: The term "collinear" means all points fall on the same straight line.

The volume of the cone is 13 cm³. option D

To determine the volume of the cone, we have that;

The formula for calculating the volume of a cone is expressed as;

Volume = (1/3)πr ²√(L ² - r ²).

Such that;

Substitute the values, we have;

Volume = 1/3 × 3.14 ² × √(25 - 9)

Find the squares, we get;

Volume, V = 1/3 × 9. 86 × √16

Find the square root

Volume, V = 1/3 × 9.86 × 4

Volume, V = 13 cm³

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Answer:

Venus (38.2 million kilometer

explanation=

At their closest, Mars is 55.7 million kilometers (34.6 million miles) from Earth but only 38.2 million kilometers (23.7 million miles) separates Venus and our planet.

Answer is:

Answer is: 

Venus is closer 

Closer by 10,900,000 or 1.09 x 10^7 in scientific notation

Step by step

Earth to Mars = 34,600,000 miles= 3.46 x10^7 miles

Earth to Venus = 23,700,000 miles = 2.37 x 10^7 miles

subtract

34,600,000 - 23,700,000 = 10,900,000 miles

So Venus is closer when it is at its closest orbit with earth. No other planet gets this close. At its furthest orbit from earth it can be as much as 160,000,000 miles from earth.

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

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9514 1404 393

Answer:

  448

Step-by-step explanation:

(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk

That would be 448 fluid ounces per week.

Answer: I believe the answer is 60 square miles.

Step-by-step explanation:
Base = 8, height = 15

A= 15*8/2 = 60

Answer: 11pi/6, choice c

Step-by-step explanation:

Answer can be found on a unit circle. We had to memorize it in my class.

Answer:

6.5 hours per day

$321.75

Step-by-step explanation:

Given Kirsten worked 39 hours in 6 days:

Number of hours worked in one day = 39 ÷ 6 = 6.5 hours

Given Kirsten is paid $8.25 per hour:

Total pay for 39 hours = 39 × 8.25 = $321.75

Answer:

The probability is 0.857

Step-by-step explanation:

We know that:

There is a total of 440 cars

There are 63 cars with defective turn signals

There are 39 with defective tires.

Now we want to find the probability that a randomly selected car does not have defective turn signals.

If all the cars have the same probability of being selected, this probability will be equal to the quotient between the number of cars that do not have defective turn signals and the total number of cars.

We know that the total number of cars is 440

And 63 of these have defective turn signals, then the rest don't.

440 - 63 = 377 cars do not have defective turn signals.

Then the probability is:

P = 377/440 = 0.857

maximum rms velocity formula

Answer:

- 4 ≤ x ≤ 3

Step-by-step explanation:

The line goes from - 4 to 3

The end points are represented by solid circles , indicating that x can be equal to these values.

The inequality representing the line is

= 4 ≤ x ≤ 3

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

y=2/3

Step-by-step explanation:

2y+4y=6-3y

⇔ 2y+4y+3y=6

⇔ 9y=6

⇔ y=6/9=2/3

The answer is:

y = 2/3

Work/explanation:

For now, I focus on the left side and combine the like terms:

\(\bf{2y+4y=6-3y}\)

\(\bf{6y=6-3y}\)

Add 3y to each side

\(\bf{6y+3y=6}\)

Combine like terms

\(\bf{9y=6}\)

Divide each side by 9

\(\bf{y=\dfrac{6}{9}}\)

\(\bf{y=\dfrac{2}{3}}\)

Hence, the answer is 2/3.

Answer:

60 yards

Step-by-step explanation:

300 = 2(30 + w) + 2(w)

300 = 60 +2w + 2w

300 = 60 + 4w

240 = 4w

60 = w

Answer: B 3750

Step-by-step explanation:

Answer:

it is $3750.00

Step-by-step explanation:

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Answer:

y = 1.25x+4

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

Substitute Values for one set of coordinates. I used (0,4) and (4,8)

Once you have derived what m is equal too, put it into your slope intercept form: y=mx+b

y=1.25x+b

b would be equal to 4 in this case (sorry i don't have enough time to explain why, but it is 4)

The final answer is y = 1.25x+4