Choose all of the equations that are equivalent to 8k = 20.

After considering the given data we come to the conclusion that the area to the left of z is 0.982, which is Option D. And the standard deviation of the given data is 87.6, which is Option C.


In order to  calculate the area to the left of z=2.09 we have to  apply the z-table:
1. Search for the row that starts with "2.0" in the leftmost column of the z-table.
2. Then for the column that starts with "0.09" in the top row of the z-table.
3. Here the value at the intersection of this row and column is 0.9821.
4. Finally round this value to three decimal places to get 0.982.
Hence , the area to the left of z=2.09 is 0.982.

Now for the second part of the question
Applying the given data set {10, 26, 84, 48, 250, 56}, we can evaluate the standard deviation as follows:

1. Evaluate the mean:
mean = (10 + 26 + 84 + 48 + 250 + 56) / 6 = 74
2. Applying subtraction of the mean from each data point:
{10 - 74, 26 - 74, 84 - 74, 48 - 74, 250 - 74, 56 - 74}
= {-64, -48, 10, -26, 176, -18}
3. Applying square of the result of step 2:
{(-64)², (-48)², (10)², (-26)², (176)², (-18)²}
= {4096, 2304, 100, 676, 30976, 324}
4. Exercising summation of the result of step 3:
4096 + 2304 + 100 + 676 + 30976 + 324
= 38176
5. Applying division of the result of step 4 by the number of data points (n):
standard deviation = √(38176 / (6 -1))
= √7625.2)
≈ 87.6.
Therefore, the answer is  87.6
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The possible values of V is E. -9, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

To find the possible values of V, we need to consider the maximum and minimum number of pumps in use at the two stations. Let's call the maximum number of pumps used at either station as M, or the minimum number of pumps used as m. Then, the possible values of V would be from -(M-m) to (M-m).

Since each gas station has nine pumps, the maximum number of pumps in use at either station can be 9, and the minimum number of pumps in use at either station can be 0 (if all pumps are idle). Therefore, the possible values of M-m can range from 0 to 9, which means the possible values of V can range from -9 to 9.

The correct answer is E. -9, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

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Answer:

\( - \frac{1}{3} \geqslant - \frac{4}{5} x\)

\( \frac{1}{3} \leqslant \frac{4}{5} x\)

\(5 \leqslant 12x\)

\(12x \geqslant 5\)

\(x \geqslant \frac{5}{12} \)

Answer:

c = 7

d = 5

Step-by-step explanation:

combining coefficient a with the nth root of b: a√ⁿb = √ⁿ((a)ⁿb). This is the reverse of simplifying a radical.

8x³√²7x = √²((8x³)²)√²(7x) = √²(64x⁶)√²(7x) = √²((64x⁶)(7x)) = √²((64 × 7)(x⁶ × x)) = √²((448)(x⁷)) = √²448x⁷ →

√²448x⁷ = √²448xᶜ.

7 → c, √²448x⁷ = √²448x⁷, c = 7.

4x√³9x² = √³((4x)³)√³(9x²) = √³(64x³)√³(9x²) =

√³((64x³)(9x²)) = √³((64 × 9)(x³ × x²)) = √³((576)(x⁵)) = √³576x⁵ →

√³576x⁵ = √³576xᵈ.

5 → d, √³576x⁵ = √³576x⁵, d = 5.

Answer:

9m  +3

Step-by-step explanation:

6m-4+3m+7

Combine like terms

6m+3m    -4+7

9m  +3

Answer:

−3⋅(5m+7)

Step-by-step explanation:

Answer:A

Step-by-step explanation:

The number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is 5/4.

The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.

The number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is

James filled a number of bags with apples when he went apple picking. He recorded the weight of each bag. This line plot shows his results.

In the line plot, in the 6th section, we get the highest value as 5 1/2. Similarly, the lowest value in the line plot is 4 1/4.

The difference between these values is,

\(d=5\dfrac{1}{2}-4\dfrac{1}{4}\\d=\dfrac{5\times2+1}{2}-\dfrac{4\times4+1}{4}\\d=\dfrac{10+1}{2}-\dfrac{16+1}{4}\\d=\dfrac{11}{2}-\dfrac{17}{4}\\d=\dfrac{11\times2-17}{4}\\d=\dfrac{5}{4}\)

Thus, the number of more does one of the heaviest bags weigh than one of the lightest bags filled by James with apples is 5/4.

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We have to expand the expression

Using the binomial theorem. Let us remember what says the Binomial theorem

Let a and b real numbers and n a natural number then we have the next formula:

Now in our particular problem we have to identify the terms in the formula, and then apply it.

Therefore, to find the expansion we have to calculate the combinatorial coefficients, for that, we will use the formula given in the first draw, as follows:

Now, with this terms, we will apply the formula to find:

Where the final line in the last equation is the expansion required.

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

B

Step-by-step explanation:

|-15|/6 + |-7|/3 = 29/6

absolute value of negative number is positive

Answer:

D. 1/6

Step-by-step explanation:

34-49 = -15 so its -15/6

17-24 = -7 so its -7/3

Then find the LCD of the following

LCD = 6

-7/3 x 2 = -14/6

-15/6 + -14/6 = 1/6

Using the concept of profit, it is found that the function is:

\(P(s) = -s^2 + 75s - 2000\)

Profit is revenue subtracted by cost, that is:

\(P(s) = R(s) - C(s)\)

The revenue function is:

\(R(s) = 100s - s^2\)

Fixed cost of $2,000 thus $25 for each sneaker, thus, the cost function is:

\(C(s) = 2000 + 25s\)

Then, the profit function is:

\(P(s) = R(s) - C(s)\)

\(P(s) = 100 - s^2 - (2000 + 25s)\)

\(P(s) = -s^2 + 75s - 2000\)

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a. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. The tennis ball is initially at a height of 126 feet above the ground.

a. The x-coordinate of the vertex is 2. To find the y-coordinate, we substitute this value back into the equation:

h(2) = -14(2)² + 56(2) + 126

h(2) = -14(4) + 112 + 126

h(2) = -56 + 112 + 126

h(2) = 182

Therefore, the vertex of the equation is (2, 182). In this context, the vertex represents the highest point reached by the tennis ball during its trajectory. The x-coordinate of the vertex (2) represents the time it takes for the ball to reach its maximum height, and the y-coordinate (182) represents the maximum height itself.

b. In order to find the y-intercept, we set t equal to zero and evaluate h(t):

h(0) = -14(0)² + 56(0) + 126

h(0) = 126

The y-intercept is 126. In this context, the y-intercept represents the initial height of the ball when it is thrown. Therefore, the tennis ball is initially at a height of 126 feet above the ground.

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Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Answer:

  no

Step-by-step explanation:

If any x-value is repeated, the relation is not a function. Both x=4 and x=9 are repeated values, so this relation is not a function.

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

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Answer:

1. False

2. True

3. False

4. False

5. False

6. True

7. True

8. True

Answer:

139°

Step-by-step explanation:

They would both be 139

Answer:

1/4, 7/8, 7/12, 9/16

LCM of 4,8,12,16 = 48

1/4= 1×12/4×12= 12/48

7/8= 7×6/8×6= 42/48

7/12= 7×4/12×4= 28/48

9/16= 9×3/16×3= 27/48

hence, 7/8 is the largest fraction. I hope it helps ya!!

The largest fraction is 7/8.

Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.

Given fractions,

1/4, 7/8, 7/12, 9/16

LCM of 4,8,12,16 = 48

1/4= 1×12/4×12= 12/48

7/8= 7×6/8×6= 42/48

7/12= 7×4/12×4= 28/48

9/16= 9×3/16×3= 27/48

Since the largest will be the fraction

NUMERATOR > DENOMINATOR

Hence, the largest fraction is 7/8.

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Answer:

plot the table

Step-by-step explanation:

plot the coordinates (1,10) (1.5,30) (2,50) (2.5,70)

Answer:

Step-by-step explanation:

2(y-2x) / (3y-5x)

Answer:

\(3x + 6y = 1200\) is the correct linear equation.

Step-by-step explanation:

Given:

Time taken to manufacture an office chair = 3 hours

Number of office chairs produced = \(x\)

Time taken to manufacture an office desk = 6 hours

Number of office desks produced = \(y\)

Let us calculate, Total Time taken to manufacture \(x\) chairs.

Suppose we manufacture 2 chairs, time taken = 3 hours + 3 hours i.e. = 6 hours

Suppose we manufacture 3 chairs, time taken = 3 hours + 3 hours + 3 hours i.e. = 9 hours

Now, we are manufacturing \(x\) number of chairs so we have to add 3 for \(x\) number of times:

OR

simply multiply 3 with \(x\).

i.e. Total time taken in producing \(x\) chairs = 3\(x\) hours

Similarly Total time taken in producing \(y\) desks = 6\(y\) hours

We have a total of 1200 hours to produce this type of office chairs and desks:

So, 1200 = Total time taken in producing \(x\) chairs + Total time taken in producing \(y\) desks

Putting the values, we get the following:

\(3x+6y=1200\) is the correct linear equation for the situation.

Answer:

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally expressed as a percentage.

Answer:

Step-by-step explanation:

C = 3t - 1 + t^6

D = 2t + 7

2C - 2D

2(3t - 1 + t^6) - 2(2t + 7)

6t -2 + 2t^6 - 4t - 14

2t^6 + 2t - 16

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

C = 3t - 1 + t^6

D = 2t + 7

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

The expression that equals 2C - 2D is

2t - 16 + 2\(t^6\).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

C = 3t - 1 + t^6

D = 2t + 7

Now,

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

Now,

2C - 2D

= 2 ( 3t - 1 + \(t^6\) ) - 2 ( 2t + 7 )

= 6t - 2 + 2\(t^6\) - 4t - 14

= 2t - 16 + 2\(t^6\)

Thus,

C = 3t - 1 + t^6

D = 2t + 7

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

The expression that equals 2C - 2D is

2t - 16 + 2\(t^6\).

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Answer:

354.2

Step-by-step explanation:

Answer:

54*

Step-by-step explanation:

The value of straight line is 180*.So (180*-126*)=54*

Generally:

- Vertical angles are congruent.   An example of vertical angles on the diagram are angles 1 and 4; they are opposite each other on the two intersecting lines.

When two parallel lines are intersected by a transversal:

- Corresponding angles are congruent.   Corresponding angles are angles on the same side of the transversal with corresponding positions, such as angles 2 and 5 in the diagram.

- Alternate interior angles are congruent.   Angles 3 and 5 are an example of alternate interior angles on the diagram.  They are contained within the interior of the two parallel lines, and are on opposite sides of the transversal.

- Alternate exterior angles are congruent.   These angles lie on the outside of the parallel lines and on opposite sides of the transversal.  Angles 1 and 7 are an example of alternate exterior angles.

Looking at the diagram, we can recognize that our given angle of 56° creates a vertical angle pair with angle 7; these angles are congruent.  Additionally, since corresponding angles are congruent, angles 4 and 7 are congruent.  Notice that angle 4 creates a vertical angle pair with angle 1, and that angle 1 also corresponds to the given angle.

The angles which are congruent to the given angle measure are:

∠1, ∠4 and ∠7