Read the scenario. 3. Joelle is sewing a new outfit. One pattern piece is 4 in. long. The piece has a seam allowance of in. How long will the piece be after it is sewn? Hint: the seam allowance is how far in from the edge of the piece you sew. It reduces the overall size of the pattern piece. Show the solution to the problem using a horizontal number line. + + 1 O + 2 3. Length of Pattern Piece (in.) 4. 5 Answer:​

Answer:

D. 4a³ + 24ab² - 25b³

Step-by-step explanation:

Simplify the given polynomial expression to find its equivalent as follows:

(2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³)

2a(2a² + 6b²) -3b(2a² + 6b²) + (6a²b + 12ab² - 7b³)

4a³ + 12ab² - 6a²b - 18b³ + 6a²b + 12ab² - 7b³

Collect like terms

4a³ - 6a²b + 6a²b + 12ab² + 12ab² - 18b³ - 7b³

4a³ + 24ab² - 25b³

Therefore, 4a³ + 24ab² - 25b³ is equivalent to the polynomial expression, (2a - 3b)(2a² + 6b²) + (6a²b + 12ab² - 7b³).

Answer:A- 4a³+24ab²-25b³

Step-by-step explanation:

The net profit margin for this shirt is 55%.

What is net profit?

Net profit is the amount of money your business earns after deducting all operating, interest and tax expenses over a period of time. To arrive at this value, you need to know the company's gross profit. If the value of net profit is negative, it is called net loss.

Net profit is another important parameter that determines the financial health of your business. It shows whether the company can earn more than it spends. Net profit helps you decide when and how to expand your business and when to cut costs.

It is important for a business owner to know the difference between profit and profitability. Profit is an absolute number equal to revenues minus expenses. Profitability, on the other hand, is a relative number (percentage) that equals the ratio of profit to revenue.

Profitability is a measure of efficiency and is useful in determining the success or failure of a business.

Given,

Revenue = $12

Cost of goods sold = $3

Operating expenses = 20% of revenue = 20/100 x $12 = $2.4

We know,

Net Profit = Revenue - Cost of goods sold - Operating expenses

\(Net \: Profit = 12 - 3 - 2.4\)

Hence, Net Profit = $6.6

Again,

Net Profit Margin = (Net Profit / Revenue) x 100%

Net Profit Margin \(= ( \frac{6.6}{ 12}) \times 100\%\)

SO, Net Profit Margin = 55%

Therefore, the net profit margin for this shirt is 55%.

So, it is clear that choice A is correct.

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Answer:

[2, ∞)

Explanation:

Given f(x) defined below:

Compare the given quadratic function to the vertex form:

The vertex of the function, (h,k)=(-5,2)

What this means is that the minimum value of f(x) is 2.

Therefore, the range of the quadratic function is:

Answer:

44.84

Step-by-step explanation:

The formula for this is lw + l √(w/2)^2 + h^2 + w * √(l/2)^2 = h^2

After that, you just input the values to get a total of 44.84 inches

Answer:

10: 44.84

11: 149.84

Step-by-step explanation:

(I can't show the angle symbol thing so I'll just say the name)

We have : QPS = TPR
And we have to prove : QPR = TPS

QPR + RPS = QPS
TPS + RPS = TPR

Since QPS = TPR, QRP + RPS = TPS + RPS

Minus both side by RPS :     QRP = TPS

Answer:

Increasing interval

Step-by-step explanation:

Answer:

362,880

Step-by-step explanation:

Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.

Answer:

Caaaaannnnnn''ttttttttt seeeee iiiiiitttttt

Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

The initial speed of the arrow was approximately 46.3 m/s. the arrow is aimed directly at the center of the target, but it hits 52 cmlower.

The initial speed of the arrow was calculated using the horizontal distance and the vertical displacement.

To determine the initial speed of the arrow, we can utilize the principles of projectile motion. Since the arrow was shot horizontally, its initial vertical velocity is zero. The only force acting on the arrow is gravity, which causes it to drop vertically over the given distance.

We are given that the arrow hits the target 52 cm (or 0.52 m) lower than the center. Let's denote the initial speed of the arrow as 'v' and the time it takes to reach the target as 't'. Since there is no initial vertical velocity, the time of flight is the same as the time it takes for the arrow to cover the horizontal distance of 15 m.

Using the equation of motion for vertical displacement, we can calculate the time it takes for the arrow to reach the target:

**Δy = v₀t + (1/2)gt²**

Since Δy is equal to -0.52 m (negative because the arrow hits lower), and the initial vertical velocity is 0, the equation simplifies to:

-0.52 = (1/2)(9.8)t²

Solving for 't', we find:

t ≈ 0.324 s

Now that we know the time of flight, we can determine the initial speed of the arrow by using the equation for horizontal distance traveled:

**Δx = v₀t**

Plugging in the known values:

15 = v(0.324)

Solving for 'v', we get:

v ≈ 46.3 m/s

Therefore, the initial speed of the arrow was approximately 46.3 m/s.

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Using an arithmetic sequence, it is found that the total length of wood required to make 50 rungs is of 34.6875 m.

The nth term of an arithmetic sequence is given by:

\(a_n = a_1 + (n-1)d\)

The sum of the first n terms is given by:

\(S_n = \frac{n(a_1 + a_n)}{2}\)

In this problem:

Then the 50th term is:

\(a_50 = a_1 + (n-1)d = 1 - 0.0125(49) = 0.3875\)

The total length is the sum of the first 50 terms, hence:

\(S_{50} = \frac{50(1 + 0.3875)}{2} = 25(1.3875) = 34.6875\)

The total length of wood required to make 50 rungs is of 34.6875 m.

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Step-by-step explanation:

Number 1

Circumference = 88cm

Circumference = 2πr

2πr = 88

πr = 88/2

πr = 44

22r/7 = 44

22r = (44 × 7)

r = (44 × 7)/22

r = 2 × 7

r = 14cm

Number 2

Length of arc = 44cm

Angle = 45°

L = ∅/360 × 2πr

44 = 45/360 × 2πr

44 = ⅛ × 2πr

44 = ¼ × πr

πr = 44 × 4

22r/7 = (44 × 4)

22r = (44 × 4 × 7)

r = (44 × 4 × 7)/22

r = 2 × 4 × 7

r = 2 × 28

r = 56cm

Perimeter = L + 2r

P = 44cm + 2(56cm)

P = 44cm + 112cm

P = 156cm

The height of the cone that has a volume of 100 cubic inches is calculated to the nearest tenth as: h ≈ 6.0 in.

To find the height of the cone, recall he formula for finding the volume of a cone which is expressed as:

Volume (V) = 1/3πr²h

Given the following:

Volume = 100 in.³

Radius (r) = 8/2 = 4 in.

Plug in the values:

100 = 1/3 * 3.14 * 4² * h

100 = 16.7 * h

Divide both sides by 16.7

100/16.7 = h [Division property of equality][

h ≈ 6.0 in.

The height is approximately 6.0 inches.

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When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.

In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ

where, μ--> population mean,

σ --> population standard deviation and

x --> the raw-score.

Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.

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John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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Answer:

40.3°

Step-by-step explanation:

sin x/ (5.3) = sin 90/ (8.2)

sin x = (5.3 sin 90) / 8.2

= 5.3/8.2

x = arcsin (5.3/8.2)

= 40.3° to 1 dp

The measure of angle x using Trigonometry is 40.263215° or 40.3.

Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.

Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.

From the figure,

Perpendicular = 5.3 m

Hypotenuse = 8.2 m

Using Trigonometry

sin x = P / H

sin x = 5.3/ 8.2

sin x = 0.6463

Using Inverse Trigonometry

x = \(sin^{-1}\)(0.6463)

x= 40.263215°

Thus, the measure of angle x is 40.3.

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Answer:

Step-by-step explanation:

x² + y²

x = - 3 , y = - 2

Substitute the values of x and y into the above expression and solve

That's

( - 3)² + (-2)²

= 9 + 4

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Use the slope formula.

SLOPE:

\(:\Longrightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }\)

\(\sf{\dfrac{-19-1}{0-4}=\dfrac{-20}{-4}=\boxed{\sf{5}}\)

The slope is 5.

I hope this helps. Let me know if you have any questions.

Answer:

Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.

Step-by-step explanation:

The reason for this is because she spent 2 hours on 6 problems and 6 divided by 2 (6/2) equals 3. So if we think about it, she answers the last 12 problems in 3 hours, so when divide 12 by 3 (12/3) we end up getting 4. So in conclusion, she completed the last 12 problems at a rate of 4 problems per hour.

Answer:

Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.

Step-by-step explanation:

Step-by-step explanation:

Answer:

C) 3.5 hours

Step-by-step explanation:

30 minutes is a half of an hour.

So that would be seven halves of an hour.

If we multiply the amount of halves by the amount of day late we get our answer.

0.5 x 7 = 3.5

Or we could simply add 0.5 seven times.

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Answer:

A checking account is a type of bank deposit account that is designed for everyday money transactions. Savings accounts have higher interest rates than checking accounts meaning it is better to let large sums of money sit in savings instead of checking.

Step-by-step explanation:

Answer: I would say the first one

Step-by-step explanation:

Answer:

Best Bet probably the last one

Answer:

c=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

13per mile×1080 mile =140.79

Answer:

B

Step-by-step explanation:

if you at $24.74 * 6 = 148.5

then you take 1083 * .13 = 140.79

then add the two number to get 289.29

From Boston to Kansas City, it takes 20 minutes to get there. When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.

Regardless of an object's beginning or ending position, we can define distance as the amount of ground it has traveled.

given

When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.

Distance = rate*time

864 = 360t,

t = 2.4

In other words, the flight arrived after 2.4 hours. Given that this is longer than two hours, divide the number by sixty to determine the time in minutes:

60 * 2.4 = 144 minutes. Assess the flight's travel time from Kansas City now.

It took 2 hours, 4 minutes, or 124 minutes from the time it departed at 8:30 AM to the time it arrived at 10:34 AM.

According to this, the jet from Kansas City arrived 144 – 124 = 20 minutes earlier than the plane from.

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