5) The line that goes through the points (-1,5) and (3,3)

\( = \frac{140}{3500 } \\ = \frac{1}{25} \\ = 1 : 25\)

hope it helps you ❣❣

The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

Answer: 300

Step-by-step explanation:

please let me know if I'm wrong

Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer:

D. Keep the significance level the same but collect more data

Step-by-step explanation:

The significance level is the probability of rejecting the null hypothesis when it is true.  For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.  This significance level is usually established initially and does not need to be changed.

But, you can collect more data to gain a high standard of evidence for rejecting the null hypothesis.  More data gives more evidence and leads to a result that is not attributed to chance, thus, proving that the result is statistically significant.

The equation that shows the Pythagorean identity is true for 0 = pi/2 is

C. 0² + 1² = 1

The Pythagorean identity is given by sin^2 θ + cos^2 θ = 1 for all values of θ, including θ = 0 and θ = π/2.

When θ = 0, sin 0 = 0 and cos 0 = 1. Thus, plugging in these values into the Pythagorean identity, we get:

sin^2 0 + cos^2 0 = 0^2 + 1^2 = 1

Therefore, the equation that shows that the Pythagorean identity is true for θ = 0 is:

0^2 + 1^2 = 1

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The expression 1/2 + 1/2 can be simplified using simple arithmetic rules and the answer for the expression will be equal to 1.

We have the expression as;

1/2 + 1/2

This can be simplified to 1/1, which is equal to 1.

Now, to solve for x, you need to isolate the variable by performing operations on both sides of the equation in a way that eliminates the other terms and leaves x by itself on one side of the equation. For example, if the equation is 2x + 3 = 7, you can subtract 3 from both sides to get 2x = 4. Then, you can divide both sides by 2 to get x = 2.

The difference between 2/4 and 1/3 is (2/4) - (1/3) = 1/4 - 1/3. To find the difference, you can subtract the fractions by finding a common denominator and expressing both fractions with that denominator. The least common multiple of 4 and 3 is 12, so you can express both fractions with a denominator of 12: (2/4) - (1/3) = (6/12) - (4/12) = 2/12 - 4/12 = -2/12. Simplifying, the difference is -1/6.

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Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

---------------------------------------------------------

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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Answer:

\(a=2\frac{A}{P}\)

Step-by-step explanation:

\(A=\frac{1}{2} ap\)

because you want a, divide both sides by p

\(\frac{A}{p} =\frac{1}{2} a\)

then, because the reciprocal of 1/2 is 2, multiply both sides by 2

\(a=2\frac{A}{P}\)

Answer:

102.95

Step-by-step explanation:

The approximate area of the mulch around the merry-go-round is 126.228 feet².

Diameter of the merry go round = 10.4 feet

Radius is half of the diameter.

Radius of the merry go round = 10.4/2 = 5.2 feet

Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.

Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet

Total area of the merry go round with the mulch is,

Area = π (8.2)² = 67.24π feet²

Area of the merry go round = π (5.2)² = 27.04π feet²

Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²

Hence the required area is 126.228 feet².

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The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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After solving the provided question, Aisha spent 7.9 hours and 9.9 hours, respectively, working last week as a babysitter and a landscaper.

A mathematical statement that has at least two terms, both of which contain variables or equal integers, is defined as an equation.

Aisha is reportedly working two summer jobs, earning $7 an hour for babysitting and $8 an hour for gardening.

Let's say you were to watch the children for x hours.

And y would be the amount of hours spent on landscaping.

Last week, Aisha spent two more hours babysitting than a landscaper, earning a total of $134.

\(y = x + 2\\7x + 8y = 134\\Substitute the value of y = x + 2 in the equation,\\7x + 8(x + 2) = 134\\7x + 8x + 16 = 134\\15x = 134 - 16\\15x = 118\\x = 118/15\\x = 7.9\\Substitute the value of x = 7.9 in the equation y = x + 2 ,\\y = 7.9 + 2\\y = 9.9\\\)

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The lateral area of the pyramid is 512√3 in.

Area is the region bounded by plane shape.

To calculate the area of the pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these value into equation 1

Hence, the right option is D. 512√3 in.

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The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

A-the flour is 4 times as much. b- flour is double sugar

Step One: subtract 4x from both sides

Step Two: divide both sides by -9

There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

chosen at random (purely random, unpredictable). Every person in the demographic being surveyed should have an equal chance of being chosen. She gave an example of a simple representative sample, choosing 25 names at random from a group of 250 employees. The sampling in this case is random since there are 250 of her coworkers in total, and every one has an equal chance of being picked. Researchers select people at random from a population using simple random sampling, which is a type of probability sampling. Every member of the population is given an equal chance at selection.

Given that,

mean(x)=86

standard deviation , σ1 =12

number(n1)=250

y(mean)=85

standard deviation, σ2 =12

number(n2)=300

null,  u1 = u2

alternate, H1: μ1 != u2

level of significance, alpha = 0.05

we got |zo | =0.973  & | z alpha | =1.96

(b) test statistic: 0.97

There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

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Answer:

\(10x + 2y = 2 \\ 2y = - 10x + 2 \\ y = - 5x + 1 \\ \perp \: l \rightarrow\: m = \frac{1}{5} \\ \frac{8 + 7}{1 + 2} = \frac{15}{3} = 5 \\ \frac{4 - 5}{0 + 5} = - \frac{1}{5} \\ \frac{ - 8 + 9}{5 - 0} = \color{yellow} \frac{1}{5} \: \)

so the answer is C

you may check the rest...

Answer:

Step-by-step explanation:

y=2x1-

So this is a very simple question.

First, analyze the problem

It says y=2x-1

The answer is +1 or 1 I believe

Someone pls correct me If I'm wrong.

Answer:

Step-by-step explanation:

ax²+6x+c=0

disc=6²-4×a×c=36-4ac≥0,(∵ it has two real solutions.)

36-4ac≥0

36≥4ac

4ac≤36

ac≤9

Answer:

{x | x is a real number}

Step-by-step explanation:

x can have any real number value.

The three-dimensional shape is formed would be as;  rectangle

Consider the square that has to be rotated about the axis as shown in the picture.

In the attached diagrams this square is black rectangle ABCD.

While rotating each point of the square will describe the circle. The circles with the greatest radii will be circles made by the points from the side that is opposite to the side on the axis of rotation.

We can take that point in any of the two surrounding quadrants. Example, if the point is on the positive x axis, then it can taken as of first quadrant or fourth quadrant.

The formed figure appears to be a rectangle.

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Answer:

\(x -3e^{-x} + C\)

Step-by-step explanation:

Given the integral \(\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx\), we are to evaluate it. Note that sum of integral is equal to the integral of its individual sum as  shown;

\(\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx = \int\limits {\dfrac{e^{x}}{e^x} } \, dx + \int\limits {\dfrac{3}{e^x} } \, dx\)

\(= \int\limits 1\, dx + 3\int\limits {e^{-x} \, dx \\\\\)

\(= x + 3(-e^{-x})\\\\= x -3e^{-x} + C\)

Hence the value of the evaluated integral is \(x -3e^{-x} + C\) where C is the constant of integration.

Answer:

To calculate the accumulated depreciation using the MACRS method, you will need to use Table 17-1 and Table 17-2 from your textbook. Here are the steps:

1. Determine the depreciation rate for the computer system based on its class life. According to Table 17-1, the class life for computers is 5 years. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method (which is used in the first year) is 40%. Therefore, the depreciation rate for the computer system in year 1 is 40%.

2. Calculate the depreciation for year 1 using the depreciation rate and the cost of the asset. The depreciation for year 1 is the cost of the asset multiplied by the depreciation rate, which gives us:

Depreciation for year 1 = $49,500 x 40% = $19,800

3. Determine the depreciation rate for year 2. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 2 is 32%. Therefore, the depreciation rate for the computer system in year 2 is 32%.

4. Calculate the depreciation for year 2 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 1 is the cost of the asset minus the depreciation for year 1, which gives us:

Remaining book value after year 1 = $49,500 - $19,800 = $29,700

Depreciation for year 2 = $29,700 x 32% = $9,504

5. Determine the depreciation rate for year 3. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 3 is 19.2%. Therefore, the depreciation rate for the computer system in year 3 is 19.2%.

6. Calculate the depreciation for year 3 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 2 is the cost of the asset minus the depreciation for year 1 and year 2, which gives us:

Remaining book value after year 2 = $29,700 - $9,504 = $20,196

Depreciation for year 3 = $20,196 x 19.2% = $3,880.35

Answer:

1/9a2

Step-by-step explanation:

I'm not sure if there's supposed to be a list of answers, but 1/9a2 is one. Hope this helps! Let me know if there was supposed to be a list.

Answer:

removing of bracket

Step-by-step explanation:

(3a)-2

3a×(-2)

-6a

If we randomly choose a point on which Federer served and get distracted before seeing his first serve but look up in time to see Federer win the point , then the probability that he missed his first serve given he won the point is (a) 0.3000

To calculate the probability that Federer missed his first serve given that he won the point, we Let , event A is = Federer missed his first serve and

event B is = Federer won the point.

So, probability of Federer missing his first serve = (100-63)% = 37% = 0.37,

probability of Federer winning point given he missed his first serve= 57%.

⇒the probability he first serve and misses point = (0.37)(0.57) = 0.2109  .

The probability of Federer winning the point, regardless of whether he made his first serve or not, can be calculated as

⇒ (0.63)(0.78) + (0.37)(0.57) = 0.7023  .

So , the probability of Federer missing his first serve given that he won the point is 0.2109/0.7023 = 0.300    .

The given question is incomplete , the complete question is

Tennis great Roger Federer made 63% of his first serves in a recent season. When Federer made his first serve, he won 78% of the points. When Federer missed his first serve and had to serve again, he won only 57% of the points. Suppose you randomly choose a point on which Federer served. You get distracted before seeing his first serve but look up in time to see Federer win the point.

What is the probability that he missed his first serve given he won the point?

(a) 0.3000

(b) 0.37

(c) 0.63

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