6a^3 - (1/9 b^4)
If A and B are 3

The complementary angles are angles in which the sum of them is equal to 90º

So: 90º-10º=80º

So, the complementary angle is 80º

The two distributions can be concluded as:

The distributions are similar.

The means-to-MAD ratio is 3.

Options A and C are the correct answer.

The MAD (Mean Absolute Deviation) is a measure of variability similar to standard deviation, but it measures the average absolute difference between each value and the mean, regardless of the direction of the deviation.

The means-to-MAD ratio is a measure of how spread out the data is, relative to the mean.

Since the means-to-MAD ratio for Data Set 1 is 3 and the means-to-MAD ratio for Data Set 2 is 30, Data Set 1 is more spread out than Data Set 2.

However, since the ratio is not extremely different (i.e., not greater than 10), the two distributions can still be considered similar.

Thus,

The two distributions can be concluded as:

The distributions are similar.

The means-to-MAD ratio is 3.

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The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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74.0% of the sandwiches made by the cafeteria on last Wednesday were turkey sandwiches.

On last Wednesday, the cafeteria made a total of 550 sandwiches for lunch.

Out of these sandwiches, 407 were turkey sandwiches. To find the percentage of turkey sandwiches, we can use the following formula:

Percentage of turkey sandwiches = (Number of turkey sandwiches / Total number of sandwiches) × 100

Plugging in the values we have:

Percentage of turkey sandwiches = (407 / 550) × 100

To simplify the calculation, we can divide 407 by 550:

Percentage of turkey sandwiches ≈ 0.740 × 100

Calculating further, we find:

Percentage of turkey sandwiches ≈ 74.0%

Analyzing student preferences and determining the popularity of different sandwich options. 'It can also help in making decisions regarding future lunch menus or adjusting the quantity of sandwich ingredients to meet student demand.

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Answer:

x-14

Step-by-step explanation:

We don't know what this number is so we label it as x or substitute it with x:

14 subtracted from it means, the number minus 14

Therefore our answer is :

x-14

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The resulting shape has an area of 230 sq. units and perimeter of 54 units.

Perimeter is a term used to describe the length of the outer boundaries of a two-dimensional shape. It is found by adding the lengths of all sides of the shape together. Perimeter is also known as the circumference if the shape is a circle. In mathematics, the perimeter of a shape is a measure of the distance around it.

The composed rectangle with one semi circle 14 and 10 is a composite shape made up of a rectangle with dimensions 14 and 10, and a semi circle with a radius of 10. This shape can be thought of as a rectangle with one of its corners cut off to form a semicircle. The resulting shape has an area of 230 sq. units and perimeter of 54 units.

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Answer:

We conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Step-by-step explanation:

We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.

A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.

Let \(\mu_1\) = mean sales per market in Region 1.

\(\mu_2\)  = mean sales per market in Region 2.

So, Null Hypothesis, \(H_0\) : \(\mu_1-\mu_2\) = 0      {means that there is no difference in potential mean sales per market in Region 1 and 2}

Alternate Hypothesis, \(H_A\) : > \(\mu_1-\mu_2\neq\) 0      {means that there is a difference in potential mean sales per market in Region 1 and 2}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                            T.S.  =  \(\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }\)   ~  \(t__n_1_+_n_2_-_2\)

where, \(\bar X_1\) = sample mean sales in Region 1 = 84

\(\bar X_2\) = sample mean sales in Region 2 = 78.3

\(s_1\)  = sample standard deviation of sales in Region 1 = 6.6

\(s_2\)  = sample standard deviation of sales in Region 2 = 8.5

\(n_1\) = sample of supermarkets from Region 1 = 12

\(n_2\) = sample of supermarkets from Region 2 = 17

Also, \(s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }\)  = \(s_p=\sqrt{\frac{(12-1)\times 6.6^{2}+(17-1)\times 8.5^{2} }{12+17-2} }\) = 7.782

So, the test statistics =  \(\frac{(84-78.3)-(0)}{7.782 \times \sqrt{\frac{1}{12}+ {\frac{1}{17}}} }\)  ~   \(t_2_7\)

                                   =  1.943  

The value of t-test statistics is 1.943.

Now, at a 0.02 level of significance, the t table  gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.

From the question given

Past studies have shown that only about 84% of the booked passengers show up

This can be taken as the probability of success (P)

Since we are told to find the probability that if Air-USA books 21 people, not enough people will show up

Then

In this case

We will use the formula below to find the probability that if Air-USA books 21 people, not enough people will show up

since we have the values of P and n

For the B part of the question

let us convert the answer obtained to percentage so we can compare it with 5% probability

Thus,

yes, the probability is low enough so that overbooking is low enough to be a concern.

For the part C of the question

since we have already converted to a percentage, then we will compare to 10%

Since

yes, the probability is low enough so that overbooking is low enough to be a concern.

Answer:19/20

1-20=19

1÷20=0.05

0.05=5%

I hope this is good enough:

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

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Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Answer:

here are 117,600 ways the runners can finish first, second, and third in the race.

Step-by-step explanation:

The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.

The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.

For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.

Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.

To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.

Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.

Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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The first table represents y as a function of x.

If a table represents a function, each of the x-values will have only one possible y-value that corresponds to it, however, two different x-values can have the same y-value.

All the tables, except the first table, have x-values that have more than one y-value assigned to it.

The first table have exactly one y-value that corresponds to each of the x-values. Therefore, the first table represents y as a function of x.

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Answer:

rise, run

Step-by-step explanation:

When finding the slope of a line using a slope triangle, the RISE length is divided by the RUN length. (I think. Sometimes the "divided by" makes me confused about which is on top, but I'm pretty sure this is right.)

Answer:

b=3d-2c

Step-by-step explanation:

Multiply b by 1.

Multiply b by 1.b+2c=3d

Multiply b by 1.b+2c=3dSubtract 2c from both sides of the equation.

Multiply b by 1.b+2c=3dSubtract 2c from both sides of the equation.b=3d−2c

Answer:

b=3d-2c

Step-by-step explanation:

Multiply b by 1.

Multiply b by 1.b+2c=3d

Multiply b by 1.b+2c=3dSubtract 2c from both sides of the equation.

Multiply b by 1.b+2c=3dSubtract 2c from both sides of the equation.b=3d−2c

Answer:

\(\frac{2}{\frac{1}{24} }\)

Step-by-step explanation:

2/x = 48

48x = 2

x = (2)/ (1/24)

\(\frac{2}{\frac{1}{24} }\) = 48

Therefore, in response to the given query, we can state that R(-1)'s inequality possible spectrum is thus: [0, 10]

A connection between two expressions or numbers that is not equivalent in mathematics is referred to as an inequality. Thus, disparity results from inequity. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and disparity are not the same. Use the not equal sign most frequently when two numbers are not identical. (). Values of any size can be contrasted using a variety of disparities. By changing the two sides until only the factors are left, many straightforward inequalities can be answered. However, a number of factors support inequality: Both parts' negative numbers are divided or added. Exchange the left and the right.

The equation can be used to describe the candle's length, R(t):

R(t) = 11 - 1.1t

where t represents how long the light has been burning, in hours.

We must determine t in terms of R in order to determine the negative of R(t):

R = 11 - 1.1 t = (11 - R)/1.1 t = (11 - R)

R(t)'s inverse function is thus:

\(R^{(-1)}(R) = (11 - R)/1.1\)

0 ≤ R ≤ 11

So, R(-1)'s scope is as follows:

[0, 11]

0 ≤ R ≤ 11

Inputting these limits into the equation for R(-1) yields the following results:

\(R^{(-1)}(0) = 11/1.1 = 10\\R^{(-1)}(11) = 0/1.1 = 0\)

R(-1)'s possible spectrum is thus:

[0, 10]

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To find the location of Mac's house, we need to first find the point that is 1/3 of the distance from Nate's house to the park. We can use the midpoint formula to do this:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

where (x1, y1) is the location of Nate's house and (x2, y2) is the location of the park.

Using the formula, we get:

Midpoint = [(-4 + 12)/2, (6 + 4)/2] = [4, 5]

This midpoint is exactly halfway between Nate's house and the park. To find the point that is 1/3 of the distance from Nate's house to the park, we need to go 1/3 of the distance from Nate's house to the midpoint.

The distance between Nate's house and the midpoint can be found using the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) is the location of Nate's house and (x2, y2) is the midpoint.

Using the formula, we get:

Distance = √[(4 - (-4))² + (5 - 6)²] = √128

To find the point that is 1/3 of the distance from Nate's house to the midpoint, we can divide the distance by 3 and move that distance from Nate's house towards the midpoint.

The coordinates of the point that is 1/3 of the distance from Nate's house to the midpoint are:

[(4 - (-4))/3, (5 - 6)/3] = [8/3, -1/3]

To find the location of Mac's house, we need to go 2/3 of the distance from the midpoint to the park, in the opposite direction. The coordinates of Mac's house are:

[(4 + 2/3), (5 - 2/3)] = [22/3, 14/3]

Therefore, the location of Mac's house is (22/3, 14/3).

Answer:

\(Total = \$7800\)

Step-by-step explanation:

Given

\(Cost = \$32.50\) per square yard

\(Length = 432.0ft\)

\(Width = 5.0ft\)

Required

Determine the cost of carpet and installation

First, calculate the area of the carpet

\(Area = Length * Width\)

\(Area = 432.0ft * 5.0ft\)

\(Area = 2160ft^2\)

Convert to square yard

\(Area = \frac{2160yd^2}{9}\)

\(Area = 240yd^2\)

The cost is then calculated as:

\(Total= Area * Unit\ Cost\)

\(Total = 240 * \$32.50\)

\(Total = \$7800\)

We have the following drawing

Note that angle PBR and angle RBM are complementary. That is, their measures add up to 90°. Let x be the measure of angle PBR. So we have the following equation

Then, by subtracting 41 on both sides we get

Then angle PBR has a measure of 49°.

Note that angle PBR is the sum of c and 53. So we have the following equatio

By subtracting 53 on both sides, we get

Thus, the value of C is -4.

Answer:

Radical.

Step-by-step explanation:

To explain;

3√13 is a radical.

The 3 in this expression is known as the index.

The 13 in this expression is known as the radicand.

The √ is considered the radical sign.

The given expression is the radical sign.

The given expression is \(3\sqrt{3}\).

The √ symbol is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol.

Therefore, the given expression is the radical sign.

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Answer:

Just use algebra calculator

Step-by-step explanation:

Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

Given:

Sequence is 55, 44, 33, 22, ...

We need to find the next two terms in the sequence.

According to the question,

Now, calculating the common difference of arithmetic sequence.

d1 = 44  - 55 = -11

d2 = 33 - 44 = -11

Hence, the common difference d is -11.

Now, calculating the next two terms of given sequence.

We know that,

\(a_n = a+ ( n-1) \times d\)

\(a_5 = 55 + ( 4) \times (-11)\\\\a_5 = 55 -44\\\\a_5 = 11\)

\(a_6 = 55 + ( 5) \times (-11)\\\\a_6 = 55 -55\\\\a_6 = 00\)

Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

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