50 Points! Multiple choice algebra question. Expand (x+2y)^3. Photo attached. Thank you!

Answer:

A)

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B)

\(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C)

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D)

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Step-by-step explanation:

A) How many ways can you put all Jellybeans in a row

Total number of Jellybeans = 80

The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans

Therefore the number of ways the Jellybeans can be put in a row is :

\(\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}\)

B) How many ways are there to select a handful of 20 jellybeans

lets assume:

yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d

a + b + c + d = 20

This is the number Non-negative integer solutions

= \(\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}\)

C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3

hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red

= \(\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}\)

D) In this case the value of C ≥ 3 and B ≤ 2

Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange

= \(\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}\)

Answer:

A

Step-by-step explanation:

To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:

First, let's simplify the division 3 11 5 ÷ 3:

3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.

Next, let's subtract 9 5 from the result we obtained:

115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.

Therefore, the simplified expression is 70.

The correct answer is A. 70.

Answer:

Step-by-step explanation:

Answer:

Hey there!

A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.

Let me know if this helps :)

Answer:

0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

11 students means that \(N = 11\)

4 are Sarah, Jamal, Kate, and Mai, so \(k = 4\)

4 are chosen, which means that \(n = 4\)

What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order?

This is P(X = 4). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 4) = h(4,11,4,4) = \frac{C_{4,4}*C_{7,0}}{C_{11,4}} = 0.003\)

0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.

\( \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} \)

\( \\ \)

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

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Let's recall that a complex number in algebraic form is written as \( \sf z = a + ib \) , where a is its real part and b is its imaginary part.

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The modulus of said complex number is calculated as follows:

\( \sf | \sf z| = \sqrt{a^2 + b^2} \)

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Let's identify our values:

\( \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i \)

\( \\ \)

Now, substitute these values into our formula:

\( \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} \)

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While this may be optional, the result can be simplified by using the following property:

\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}\)

\( \\ \)

\( \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} \)

\( \\ \)

\( \hrulefill \)

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Step-by-step explanation:

j. seems to be challenging

Answer:

Step-by-step explanation:

If the larger of 2 consecutive integers is 324, then 324-(2-1) = 323 is the smaller.

If the largest of 89 consecutive integers is 324, then 324 - (89-1) = 236 is the smallest.

Hence, the smallest consecutive integer is \(237\).

What is the smallest consecutive integer?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Here given that,

The largest of \(89\) consecutive integers is \(324\)

So, it is of the form

\(324-89=237\)

Hence, the smallest consecutive integer is \(237\).

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Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

To simplify the expression (sqrt(x - 2))/(sqrt(x - 3)), we can first apply the rule that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. This gives us the simplified expression:

(sqrt(x - 2))/(sqrt(x - 3)) = sqrt((x - 2) / (x - 3))

Next, we can apply the rule that the square root of a product is equal to the product of the square roots of each factor. This gives us:

sqrt((x - 2) / (x - 3)) = sqrt(x - 2) * sqrt(1 / (x - 3))

Finally, we can apply the rule that the square root of a reciprocal is equal to the reciprocal of the square root. This gives us the simplified expression:

sqrt((x - 2) / (x - 3)) = (sqrt(x - 2) * sqrt(1 / (x - 3))) = (1 / sqrt(x - 3)) / sqrt(x - 2)

Therefore, the simplified expression for (sqrt(x - 2))/(sqrt(x - 3)) is (1 / sqrt(x - 3)) / sqrt(x - 2).

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

b. 6

Step-by-step explanation:

The standard deviation is 4.53 approximately 5. The standard deviation  tells how far the data is located from the mean.

The total number of observations= 30

So dividing 30/5 gives  6

Hence 6 intervals or categories used to test the hypothesis for this problem

as each category will have a data point in it .

So the best option is b.

The value of c that satisfies the condition a + b = 10 is 10.

To find the value of c such that the sum of the x- and y-intercepts of any tangent line to the curve √x + √y = √c is equal to 10, we can use the fact that the x-intercept occurs when y = 0, and the y-intercept occurs when x = 0.

First, let's find the x-intercept. When y = 0, we can substitute this value into the equation:

√x + √0 = √c

Simplifying, we have:

√x = √c

Squaring both sides of the equation, we get:

x = c

So, the x-intercept is given by (c, 0).

Next, let's find the y-intercept. When x = 0, we can substitute this value into the equation:

√0 + √y = √c

Simplifying, we have:

√y = √c

Squaring both sides of the equation, we get:

y = c

So, the y-intercept is given by (0, c).

Since we want the sum of the x- and y-intercepts to be equal to 10, we have:

c + 0 = 10

Simplifying, we find:

c = 10

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Answer:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides.

10 cm + 12 cm + 5 cm + 6 cm

= 33 cm

Answer:

chapter 1

Step-by-step explanation:

Answer:

Ok so first he bought the road and pancakes with means he speant 134.85 dollars which mean he out himself in the negatives after he bought the his items

The surface areas of the figures are 336, 82 and 836

From the question, we have the following parameters that can be used in our computation:

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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The length of the side of the square is given as follows:

20 cm.

In the figure, there are two expressions used to give the side length to each square, as follows:

In a square, all the four side lengths have the same length, hence the value of x is obtained as follows:

6x - 1 = 4x + 6

2x = 7

x = 3.5 cm.

Then the side length of the square is obtained as follows:

6(3.5) - 1 = 20 cm.

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0.5236 meters is the length of the given arc.

The formula for the length of an arc is given by:

Arc Length = (θ/360) * 2πr

Where:

In this case, the central angle is 60 degrees and the radius is 1/2 meters.

Plugging the values into the formula, we have:

Arc Length = (60/360) * 2π(1/2)

Arc Length = (1/6) * π

Arc Length = π/6

Therefore, the length of the arc that subtends an angle of 60 degrees at the center of a circle with a radius of 1/2 meters is π/6 meters or approximately 0.5236 meters.

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Answer:

1)

Minimum is a 4th Degree

2)

Positive; Even

3)

\(x=-4, -1\text{ Odd Multiplicity}\\x=3\text{ Even Multiplicity}\)

Step-by-step explanation:

Part 1)

The minimum degree of our function will be 4.

Looking at the graph, we know that the graph crosses the x-axis at -4 and -1. Since it crosses through the x-axis at these two points, these two factors must have an odd multiplicity.

So, it can be anything 1, 3, 5, 7, etc.

However, we will choose the lowest one, 1.

Next, we know that the graph bounces off at 3.

So, it must have an even multiplicity. In other words, 2, 4, 6, 8, etc.

We choose the lowest one, 2.

Therefore, the minimum degree of our function will be 1+1+2 or 4.

Part 2)

The degree of our polynomial is (and will always be) even. Therefore, both ends of the graph will go in the same direction.

Recall the simplest even polynomial, the parent quadratic function. When the leading coefficient is positive, both of the ends go straight up.

This applies to all polynomials with even degrees.

Therefore, since the arms of the graph is going straight up towards positive infinity, the leading coefficient of our graph must be positive.

Part 3)

This is similar to Part 1.

We can see that the graph touches the x-axis at -4, -3, and 1. So, the zeros of the function is: \(x=-4, -1, 3\)

We know that it passes through \(x=-4 \text{ and } x=-1\) . So, these two factors must have an odd multiplicity.

However, since the graph bounces off \(x=3\), this factor must have an even multiplicity.

And we're done!

Answer:

b = 0

Step-by-step explanation:

Because the line passes through x values when y = 0, it means that the line is y = 0. The slope would be 0, and because we are given 2 coordinates we can determine that the y intercept would be at 0.

Answer:

c

Step-by-step explanation:

hope this helps i just had this question on edge 2020

Answer:  $0.27

Step-by-step explanation:

7a + 11b = 1.47

        7a = 1.47 - 11b

          \(a=\dfrac{1.47-11b}{7}\)

Make a table. Choose values for b starting at $0.01 and solve for "a".

The value of "a" must terminate at the hundredths place since we are working with money.

You will discover that a = 0.10 and b = 0.07

The cost of 2 apples and 1 banana is:

  2a + b

= 2(0.10) + (0.07)

=    0.20 + 0.07

=          0.27

9514 1404 393

Answer:

  29)  1/5

  30)  independent; 64/225 ≈ 0.284

Step-by-step explanation:

In general, a "spinner" is considered to be a (mathematically ideal) device that returns one of the values with which it is marked, with a probability according to the area of the sector in which the mark resides. Usually, sectors are presumed to have equal areas. The result of one spin is generally considered to be independent of the result from any other spin. In the real world, an operator familiar with a given spinner can often ensure that the results do not have equal probability and are not independent. We ignore that possibility in math problems.

__

29) Of the numbers 1 to 15, there are three numbers less than 4. The probability of spinning one of them is 3/15 = 1/5.

__

30a) We have defined our spinner so that the events are independent. (See above.)

30b) In the set of numbers 1 to 15, 8 are odd and 7 are even. The probability of getting an odd number on any spin is 8/15. Because the results of successive spins are independent, the probability of any given sequence is the product of the probabilities of the numbers in that sequence.

  P(2 odd) = P(odd)×P(odd) = (8/15)(8/15) = 64/225 ≈ 0.284

Step-by-step explanation:

here's the answer

Hope it helps◉‿◉

The area of the sidewalk is 388 square feet.

To find the area of the sidewalk you can find the area of each individual shape and add them together.

Area of the first triangle T = (1/2) x 6 ft x 11 ft = 33 sq. ft.

Area of the second triangle = (1/2) x 6 ft x 18 ft = 54 sq. ft.

Area of the rectangle = 6 ft x 30 ft = 180 sq. ft.

Area of the square = 11 ft x 11 ft = 121 sq. ft.

Therefore, the total area of the sidewalk is:

33 sq. ft. + 54 sq. ft. + 180 sq. ft. + 121 sq. ft. = 388 sq. ft.

So, the area of the sidewalk is 388 square feet.

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