Find and interpret the mean absolute deviation of the data.
1.1,7.5,4.9,0.4,2.2,3.3,5.1
The mean absolute deviation is what
The values differ from the mean by an average of what

Answer:

1.430

Step-by-step explanation:

1.430 x 10^-2

The area of the image of the rectangle under the transformation is 10 square units

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

Matrix transformation: [tex]\left[\begin{array}{cc}-7&-2\\6&12\end{array}\right][/tex]

And, we have rectangle plotted on the graph

The transformation is a rigid transformation

This means that the area of the rectangle would be the same before and after the transformation

From the graph, the side lengths of the rectangle are

Length = 2

Width = 5

So, we have

Area = 2 * 5

Evaluate

Area = 10

Hence, the area of the image of the rectangle under the transformation is 10 square units

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Answer:

  276.460 mi²

Step-by-step explanation:

You want the surface area of a cylinder with radius 4 mi and height 7 mi.

The area of a cylinder is given by the formula ...

  A = 2πr(r +h)

  A = 2π(4 mi)(4 mi +7 mi) = 88π mi² ≈ 276.460 mi²

The area of the cylinder is about 276.460 square miles.

__

Additional comment

The surface area is the sum of the areas of the two circular bases and the lateral area. The lateral area is the product of the cylinder height and circumference. These are combined in the formula given.

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The complete table for the linear function y = -2x + 8 is:

x y

1 6

2 4

3 2

4 0

5 -2

The given function is y = -2x + 8, which represents a linear equation in the slope-intercept form. In this form, the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

Comparing the given equation with the slope-intercept form, we can see that the slope of the line is -2, which means that the line goes down by 2 units for every 1 unit it moves to the right. The y-intercept of the line is 8, which means that the line intersects the y-axis at the point (0, 8).

The complete table:

x y

1 6

2 4

3 2

4 0

5 -2

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The complete question:

Complete the following table as per the function y = -2x + 8.

x         y

1

2

3

4

5

There are 35 potential pass codes. The Option B.

A pass code means string of characters used as a password to gain access to a computer or smartphone.

To get number of potential pass codes, we will combinations formula with repetition [tex](n + r - 1)[/tex]  choose r.

n = number of options

r = length of the pass code.

The number of potential pass codes is:

= (5 + 3 - 1) Choose 3

= 7 Choose 3

= (7 x 6 x 5) / (3 x 2 x 1)

= 210 / 6

= 35.

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Answer:

130°

Step-by-step explanation:

<4=<8

180-50=130

Complete sentence is,

The square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16

We have to given that;

Taking the square root of a number technically results in two solutions.

Here, The number is,

⇒ 16

Take square root as;

⇒ √16

⇒ ± 4

Since, 4² = 16

And, (- 4)² = 16

Thus, We get;

the square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16.

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a) The possible pairs of mutually exclusive outcomes are given below:

A and B

A and C

A and D

B and C

B and D

C and D

b) The Three of the outcomes that are said to be all mutually exclusive are:

c) The probability of having B and D is written as P(B or D) = P(B) + P(D)

Mutually exclusive events cannot happen at the same time, like rolling a kick the bucket and getting a 1 and a 2. In this case, there are four conceivable results: A, B, C, and D, a few of which we commonly select.

For example, If A is the outcome, C or D cannot be. To find mutually exclusive pairs, we check which outcomes cannot occur together. A and B are mutually exclusive because they cannot both be true.

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Answer:

f(x)= - [x] + 3

Step-by-step explanation:

because it describes a negative slope and 3 units up from the origin

the volume of the cone to be filled up if it has the same radius and height with is  376. 6 cm³

To determine the volume, we need to know the formula for the volume of a cone.

The formula for the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters are expressed as;

Substitute the values, we have;

Volume = 3.14 × 6² × 10/3

Find the square value

Multiply the value, we have;

Volume = 1130. 4/3

Divide the values

Volume = 376. 6 cm³

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(3) The linear equation is y = 1/3x + 1

(4) The solution to the system is (-1, -1/2)

(5) The factored expression of 45x² + 30x - 40 is 5(3x - 2)(3x + 4)

(6) The factored expression of 4x² - 36 is 4(x - 3)(x + 4)

(7) The surface area is 176

(8) The volume is 144

From the graph, we have the following points

(0, 1) and (-3, 0)

A linear relation is represented as

y = mx + c

So, we have

y = mx + 1

Using the other point, we have

-3m + 1 = 0

m = 1/3

So, we have

y = 1/3x + 1

Next, we solve graphically

To do this, we plot the graphs and write out the point of intersection

In this case, the intersection point is (-1, -1/2)

So, the solution is (-1, -1/2)

Here, we have

45x² + 30x - 40

When factored, we have

45x² + 30x - 40 = 5(3x - 2)(3x + 4)

Also, we have

4x² - 36

When factored, we have

4x² - 36 = 4(x - 3)(x + 4)

For figure (8), we have

Surface area = 2 *(9 * 4 + 4 * 4 + 9 * 4)

Evaluate

Surface area = 176

Also, we have

Volume = 9 * 4 * 4

Evaluate

Volume = 144

Hence, the surface area is 176 and the volume is 144

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[tex] {77.05 \: m}^{2} [/tex]

hope this is correct

The area of the triangle is 18.6 units²

Given data ,

Let the triangle be represented as ΔABC

Now , the sides of the triangle are

We can use the law of cosines to find the length of the third side of the triangle:

c² = a² + b² - 2ab cos(C)

c² = 5² + 8² - 2(5)(8)cos(79°)

c ≈ 9.05

Now, we can use Heron's formula to find the area of the triangle:

s = (5 + 8 + 9.05)/2 = 11.525

A = √(s(s-a)(s-b)(s-c))

A = √(11.525(11.525-5)(11.525-8)(11.525-9.05))

A ≈ 18.6

Hence , the area of the triangle is approximately 18.6 square units

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Answer:

-5,0,1,2,3

Step-by-step explanation:

in a number line the negative numbers are always on your left hand side and as you head to the right they increase thus becoming positive integers

The expected value of the winnings in this game is $1.23.

We have,

The expected value of a random variable is the sum of the products of each possible outcome and its probability.

In this case, the random variable is the winnings from the game and the payout probability distribution specifies the probabilities associated with each possible payout.

The expected value of the winnings is found by multiplying each payout by its probability and summing the products.

Expected value = (0)(0.50) + (1)(0.25) + (2)(0.13) + (4)(0.06) + (8)(0.06)

= 0 + 0.25 + 0.26 + 0.24 + 0.48

= 1.23

Therefore,

The expected value of the winnings in this game is $1.23.

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Answer:

2nd choice. -a^3 - 8ab^2

Step-by-step explanation:

(3a^3b - 4ab^2 + 5ab) - (4a^3b + 4ab^2 + 5ab)

Distribute the minus sign and take out the parenthesis.

3a^3b - 4ab^2 + 5ab - 4a^3b - 4ab^2 - 5ab

Combine like terms.

3a^3b - 4ab^2 -4ab^2 - 4ab^2 + 5ab - 5ab

-1a^3b - 8ab^2

Answer:

-4

Step-by-step explanation:

5x=-13-7

5x=-20

x=-20/5

x=-4

Answer:

5x+7=-13

5x=-13-7

5x=-20

x=-20 divide by 5

x=-4

a) The temperature in Juneau was 23°F lower than in Atlanta.

b) The temperature in Milwaukee at noon would be -3°F.

(a) The temperature difference between Juneau and Atlanta is:

= -3 - (-26)

= 23°F lower in Juneau

Therefore, the 6 a.m. temperature in Juneau was 23°F lower than in Atlanta.

(b) Since the temperature in Milwaukee had risen by 11°F, its temperature at noon would be:

= -14 + 11

= -3°F

Therefore, the temperature in Milwaukee at noon would be -3°F.

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Answer: AE=10, AD=14, x=5, BC=36, DE=52

Step-by-step explanation: finding x

4x-32=2(3x-21) || 4x-32=6x-42 || 10=2x || 5=x

If x represents the number of hats sold, the expression representing Geoff's earnings is 15x.

An algebraic expression is a mathematical statement that combines variables, constants, values, numbers, and other quantities based on mathematical operands but without using equal symbols (=).

The selling price per handknit hat = $15

The total cost of materials (yarn) for making the hats = $45.

Let the number of hats sold = x

Total earnings from the sales = 15x

Total cost = $45

Net earnings = 15x - 45

Thus, the expression that represents Goefft's earnings from the sale of handknit hats is 15x.

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Option C. It t will take approximately 5.923 hours to drive the same distance at 65 miles per hour.

t = k / r

where k is the constant of variation.

First, we need to find the constant of variation, k, using the given information:

t = 7 hours when r = 55 mph

7 = k / 55

To find k, multiply both sides by 55:

k = 7 * 55 = 385

Now that we have the constant of variation, we can find the time it will take to drive the same distance at 65 mph:

t = k / r

t = 385 / 65

t ≈ 5.923 hours

So, it will take approximately 5.923 hours to drive the same distance at 65 miles per hour.

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Check the picture below.

[tex]\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm[/tex]

Make sure your calculator is in Degree mode.

The volume of the prism is 1368 cubic feet.

We have,

The three steps that should be taken to calculate the volume of the prism are:

- Use the formula A = b h to find the area of the base, where b is the length of the base and h is the width of the base.

For a rectangular prism, the base is a rectangle, so the formula is:

A = length x width.

- Use the formula V = B h to find the volume of the prism, where B is the area of the base and h is the height of the prism.

For a rectangular prism, the formula.

V = length x width x height.

- Substitute the given values into the formulas and solve for the volume. For the given rectangular prism with a length of 9 and one-half feet, a width of 24 feet, and a height of 6 feet, we can find the volume by using the formula V = B h.

First, we find the area of the base by using the formula:

A = length x width:

A = (9.5 ft) x (24 ft)

= 228 sq ft

Next, we use the formula V = B h to find the volume:

V = (228 sq ft) x (6 ft)

= 1368 cubic feet

Therefore,

The volume of the prism is 1368 cubic feet.

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The equations has 8 a solution are

x/2 = 16

x/8 = 1

x/2 = 8

x/8 = 1

To check whether 8 is a solution for an equation, we substitute x = 8 into the equation and see if it satisfies the equation. If it does, then 8 is a solution; otherwise, it is not.

Substituting x = 8 into each equation, we get:

1. x + 6 = 8 + 6 = 14 (8 is not a solution)

2. 2x + 2 = 2(8) + 2 = 18 (8 is not a solution)

3. 4x - 2 = 4(8) - 2 = 30 (8 is not a solution)

4. 10 = 10 (8 is not a solution)

5. 2x = 4 (8 is not a solution)

6. 3x = 24 (8 is not a solution)

7. 8/2 = 4 (8 is a solution)

83 8/8 = 1 (8 is a solution)

Therefore, the correct answers are:

x/2 = 16

x/8 = 1

x/2 = 8

x/8 = 1

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a) Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount. b) , the difference in the final payment between choices 1 and 2 is $1,107.60.

a. The cash discount on the printer is calculated as 2% of the list price:

Cash discount = 2% * $860 = $17.20

Using the formula:

Interest = Principal * Rate * Time

Principal = Amount borrowed = List price - Cash discount = $860 - $17.20 = $842.80

Rate = 6% per year = 6%/100 = 0.06

Time = 30 days (since the terms are 2/10, n/30)

To convert the interest to a 360-day basis, we use the formula:

Interest = Principal * Rate * (Time/360)

Interest = $842.80 * 0.06 * (30/360) = $5.60733

Therefore, Janet would save $17.20 - $5.60733 = $11.59 by borrowing the money for the printer at 6% to take advantage of the cash discount.

b. Choice 1 for the computer involves paying $150 per month for 17 months, with the 18th payment paying the remainder of the balance. Choice 2 involves paying 6% interest for 18 months in equal payments.

For choice 1:

Remaining balance = List price - (17 * Monthly payment)

Remaining balance = $4,020 - (17 * $150) = $4,020 - $2,550 = $1,470

For choice 2:

Interest = Principal * Rate * Time

Principal = Amount borrowed = List price = $4,020

Rate = 6% per year = 6%/100 = 0.06

Time = 18 months

To convert the interest to a 12-month basis, we use the formula:

Interest = Principal * Rate * (Time/12)

Interest = $4,020 * 0.06 * (18/12) = $362.40

The final payment difference between choices 1 and 2 is:

Final payment difference = Remaining balance - Interest

Final payment difference = $1,470 - $362.40 = $1,107.60

Therefore, the difference in the final payment between choices 1 and 2 is $1,107.60.

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The values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25

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

The right triangle

The values of sin (A) and sin (B) can be calculated using

sin = opposite/hypotenuse

Using the above as a guide, we have the following:

sin(A) = 14/50

sin(B) = 48/50

Simplify the equations

sin(A) = 7/25

sin(B) = 24/25

Hence, the values of sin (A) and sin (B) are sin(A) = 7/25 and sin(B) = 24/25

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After considering all the given options we conclude that the value of the given formula is y₁ = y₂ - m(x₂ - x₁) which is Option C.

To evaluate for y₁ in the equation m = (y₂ - y₁) / (x₂ - x₁), we can apply algebraic manipulation to isolate y₁.
In the first step, we  multiply both sides of the equation by (x₂ - x₁) to eliminate the denominator. Therefore,
m(x₂ - x₁) = y₂ - y₁
In the second step, we can subtract y₂ from both sides of the equation to isolate y₁.
Therefore,
y₁ = y₂ - m(x₂ - x₁)
So, the solution for y₁ is given by the formula:
y₁ = y₂ - m(x₂ - x₁)
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