The regression equation for change in temperature, y, to amount of rain, r, is given by ŷ = 0.2 − 1.4r. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66. The regression line overpredicts the temperature change.
2.66. The regression line underpredicts the temperature change.
1.94. The regression line underpredicts the temperature change.
−1.94. The regression line overpredicts the temperature change.
−3.02. The regression line underpredicts the temperature change.

Answer:

To graph this line, move one of the points to positive three on the horizontal (side to side) line and negative six on the vertical (up and down) line. To get a slope of negative 1/2 you move down one point and right two points, and you continue until you reach the edge of the graph. Then you do the opposite on the way up (up one and left two).

Hope this helps!

Answer:  Plot the two points (3,-6) and (1, -5). Draw a straight line through those points.

See the graph below.

=============================================

Explanation:

Plot the point (3, -6)

The slope -1/2 means the rise is -1 and the run is 2

If we moved to the right, then we'd drop down 1 and move to the right 2. That would move us from (3,-6) to (5,-7)

We can go in reverse of this. So instead of "move down 1", we move up 1. We're going left instead of right.

-----------

So we start at (3,-6) and move up 1 and to the left 2 to arrive at (1,-5)

Two points on this line are (1, -5) and (3, -6)

Once we have two points, we have enough to graph the line.

See the graph below.

Answer:

Together, they have 12 + 2(12) = 12 + 24 = 36 toys.

Answer:

so in total they have 36 toys

Step-by-step explanation:

The requried cost is $8995 when the two companies charge the same for transporting 20 tons of sugar.

To estimate the amount of sugar for which the two companies charge the same,

4995 + 200.50x = 6500 + 125.25x

Simplifying and solving for x, we get:

74.75x = 1505

x = 20

Therefore, the two companies charge the same when transporting 20 tons of sugar. To estimate the cost at this point, we can substitute x=20 into either equation:

For the first company:

cost = 4995 + 200.50(20) = $8995

For the second company:

cost = 6500 + 125.25(20) = $8995

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First, we'll have to find the radius.

\(\large\boxed{\bold{r= \frac{d}{2}}}\)

\(r= \frac {6}{2}\)

\(r= 3 \ cm\)

Now, we can workout the volume.

Instead of π, we are asked to use 3.

\(\large\boxed{\bold{\red \pi \red = \ \red 3}}\)

\(\large\boxed{\bold{V= \ \frac{4}{3} \pi {r}^{3}}}\)

Now, substitute the values according to the formula.

\(V= \ \frac{4}{3} × 3 × {3}^{3}\)

\(\large\boxed{\bold{V= \ 108 \ {cm}^{3}}}\)

The answer is a whole number so you won't have to round off.

Therefore, the volume of the given sphere is 108 cubic centimeters.

Answer:

24

Step-by-step explanation:

2x3=6

6x4=24

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Answer: Choice A

Explanation:

The phrasing "sum of 8 and 60" means we add those two values. These are placed in the denominator while 50 goes up top.

The correct equation for your test score is 50 divided by the sum of 8 and 60 is,  y = 50 / (8 + 60)

The given condition for write an equation is,

Your test score is 50 divided by the sum of 8 and 60.

Let us assume that, total test score is, y

Hence, It ca be written in mathematical form,

⇒ y = 50 divided by (8 + 60)

⇒ y = 50 ÷ (8 + 60)

⇒ y = 50 / (8 + 60)

Therefore, The correct equation for your test score is 50 divided by the sum of 8 and 60 is,  y = 50 / (8 + 60)

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Answer:

To find the value of the expression 1/2y - x when x = 5 and y = -2, we simply plug these values into the expression and perform the operations:

1/2y - x

= 1/2(-2) - 5

= -1 - 5

= -6

Therefore, the value of the expression when x = 5 and y = -2 is -6.

Answer:

Jenny will have 3 apples

Step-by-step explanation:

5-2=3

Answer:

Chloe would have 2 apples

Step-by-step explanation:

If the question is how many does Chloe have its 2 because that's how many Jenny gave her

Let's say for example you wanted to graph the linear equation \(y = 2x+5\)

At minimum, we'll need 2 points to form this line.

To get any point of the form (x,y), we plug in a number for x to find a corresponding number for y.

For example, replace x with 0 to find that...

\(y = 2x+5\\\\y = 2(0)+5\\\\y = 0+5\\\\y = 5\\\\\)

Therefore, x = 0 leads to y = 5. So the point (0,5) is on the line.

Then we repeat this process for other x values. Let's try x = 1

\(y = 2x+5\\\\y = 2(1)+5\\\\y = 2+5\\\\y = 7\\\\\)

Telling us that (1,7) is also on this line. We have enough to graph this equation. Plot the two points (0,5) and (1,7). Then draw a straight line through them. Extend this line as far as you can to the left and right. The graph is shown below.

We can keep going to get other points like (2,9) and (3,11) and (4,13) and so on. A table is a way to keep track of the xy values.

\(\begin{array}{|c|c|}\cline{1-2}\text{x} & \text{y}\\ \cline{1-2}0 & 5\\ \cline{1-2}1 & 7\\ \cline{1-2}2 & 9\\ \cline{1-2}3 & 11\\ \cline{1-2}4 & 13\\ \cline{1-2}\end{array}\)

Each time x goes up by 1, y goes up by 2. This directly ties to the slope of 2/1 = 2.

The measure of the arc in degrees is 137.50°

An angle is said to have a measure of 1 radian if it is subtended at its center by an arc of lengths 1 unit in a unit circle. "rad" is the sign used to represent the radian unit of measurement.  

Here we have

An arc of a circle that measures 2.4 radians.  

We need to find the measure in degrees  

As we know 1 radian = 180°/π

2.4 radians = [ 180/π ] × 2.4 degrees  

= [57.324] × 2.4

= 137.57°  ( approx)    

Therefore,

The measure of the arc in degrees is 137.50°

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Answer:

Step-by-step explanation:

To find the area, I divided the shape into squares and rectangles. Then, I found the area of the squares and rectangles and added them,

Hence, the area is 163 in.²

a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.

b) The frisbee is in the air for a total of 8 seconds.

To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.

a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:

When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)

When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)

When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)

When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)

When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)

When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)

When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)

When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)

When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)

When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)

b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.

Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:

0 seconds: 5 feet

1 second: 29 feet

2 seconds: 45 feet

3 seconds: 53 feet

4 seconds: 53 feet

5 seconds: 45 feet

6 seconds: 29 feet

7 seconds: 5 feet

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Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

Net profit is the amount of a business earn after deducting all the expenditure over it.

Sam has been running his swimming pool cleaning business now for five years. He is considering enlarging his service area to a 100 mile radius, which would require two new offices in different parts of town.

He would like to take out a business loan to cover the cost of expansion. The profits for Sam's business over the last 5 years are outlined in the table below.

Using the regression graph, the quadratic equation we get for this data as,

\(y=192.4493x^2+3318.1733x+39998.214\)

For the 6 year value,

\(y=192.4493(6)^2+3318.1733(6)+39998.214\\y\approx 66835.43\)

This value is much near to the option b which is $66,933.60.

Thus, the best estimate for Sam to quote as expected profits in the next year in his new business plan is $66,933.60.

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Answer:

1/9

Step-by-step explanation:

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(a) The number of choices with no restriction is 10,000.

(b) The number of choices with no repeated digits is 5,040.

(c) The number of choices with no repeated digits and the third digit as 0 is 648.

(a) With no restriction, there are 10 choices for each digit, ranging from 0 to 9. Since a 4-digit pin code consists of four digits, the total number of choices is 10^4 = 10,000.

(b) When no digit is repeated, the number of choices for the first digit is 10. For the second digit, there are 9 choices remaining (as one digit has been used). Similarly, for the third digit, there are 8 choices remaining, and for the fourth digit, there are 7 choices remaining. Therefore, the total number of choices is 10 × 9 × 8 × 7 = 5,040.

(c) When no digit is repeated and the third digit is fixed as 0, the number of choices for the first digit is 9 (excluding 0). For the second digit, there are 9 choices remaining (as one digit has been used, but 0 is available).

For the fourth digit, there are 8 choices remaining (excluding 0 and the digit used in the second position). Therefore, the total number of choices is 9 × 9 × 8 = 648.

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Answer:

3 - 7x

Step-by-step explanation:

Given ,

=> f(x) = 3 - x / 7

=> y = 3 - x / 7

=> x = 3 - y /7

=> 7x = 3 - y

=> y = 3 - 7x

=> f-¹(x) = 3 - 7x

Answer:

Q1. y = 5 Q2.  (√2 - √3)/2

Step-by-step explanation:

Q1

√12 - √147 + y√3 = 0

Taking -√147 and √12 to the right hand side, we have

y√3 = √147 - √12

y√3 = √(3 × 49) - √(3 × 4)

y√3 = √3 × √49 - √3 × √4

y√3 = √3 × 7 - √3 × 2

y√3 = 7√3 - 2√3

y√3 = 5√3

Dividing both sides by √3, we have

y√3/√3 = 5√3/√3

y = 5

Q2

Sin45° - Cos30°

Since Sin45° = √2/2 and Cos 30° = √3/2

Substituting these values into the equation, we have

Sin45° - Cos30° = √2/2 - √3/2

Taking L.C.M of both factors, we have

Sin45° - Cos30° = (√2 - √3)/2

Answer: $40 can be withdrawn from the account for 7 weeks if she wants to maintain a balance of at least $200.

Step-by-step explanation:

Answer:

qualitative and ordinal.

Step-by-step explanation:

They are both two types of qualitative data under Categorical data.

Nominal and ordinal are the levels of measurement for which data can be qualitative. Therefore, the correct option is option A, D.

A categorization that describes the type of information contained inside the importance attributed to variables is called level of measurement and scale of measure. The most well-known classification was created by psychiatrist Stanley Smith Stevens and included four levels or measurement scales: nominal, ordinal, interval, or ratio.

This system of defining several measurement levels originated within psychology and has drawn heavy criticism from academics in other fields. Additional classifications include those made by Chrisman, Mosteller, and Tukey. Nominal and ordinal are the levels of measurement for which data can be qualitative.

Therefore, the correct option is option A, D.

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There are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

To determine the number of different committees that can be formed, we need to calculate the combination of managers and engineers that can be selected.

The number of ways to select 3 managers from 10 managers can be calculated using the combination formula:

C(n, r) = n! / (r!(n - r)!)

where n is the total number of managers and r is the number of managers to be selected.

In this case, we have n = 10 and r = 3, so the number of ways to select 3 managers from 10 is:

C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

Similarly, the number of ways to select 6 engineers from 20 engineers can be calculated as:

C(20, 6) = 20! / (6!(20 - 6)!) = 20! / (6!14!) = (20 * 19 * 18 * 17 * 16 * 15) / (6 * 5 * 4 * 3 * 2 * 1) = 38,760.

To find the total number of different committees possible, we multiply the number of ways to select managers and engineers:

Total number of committees = C(10, 3) * C(20, 6) = 120 * 38,760 = 4,651,200.

Therefore, there are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

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Answer: 16

Step-by-step explanation:

Answer: it’s the third one

Step-by-step explanation:

Answer:

$85.68 is the final price

Step-by-step explanation:

Add 15% and 33% to get 48%

48% of $178.50 is $85.68

Answer:

Step-by-step explanation:

10(a) (ii)=-10a

10 (b)=10b

n=10b

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

\(m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}\)

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

\(m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}\)

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

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Answer:

8 hours

Step-by-step explanation:

wait what is starting temperature?

Step-by-step explanation:

sin = -3/5     we are told this is between pi/2 and 3pi/2  

                        so Quadrant II  and III  

               of these two quadrants

                         sin is only negative in Q III  where cos is also negative

TRIG IDENTITY:  sin^2 + cos^2 = 1     will show cos = - 4/5

TRIG IDENTITY :   Sin (2Φ) = 2 sinΦ cosΦ

                                            = 2 (-3/5) (-4/5) = 24/25 = .960

The value of g(51) is 91 is obtained by solving linear function.

To find the value of g(51) for a periodic function g with a period of 24, we can use the information given about g(3) and g(8). We know that the function g is periodic with a period of 24, which means that the values of g repeat every 24 units.

We are given that g(3) = 67 and g(8) = 70.

To find g(51), we need to determine how many periods of 24 units have passed from the value g(3) to the value g(51).

Since 51 - 3 = 48, we have 48 units between g(3) and g(51).

Since each period of g is 24 units long, we can divide 48 by 24 to find the number of periods that have passed.

48 / 24 = 2.

So, two periods of 24 units each have passed between g(3) and g(51).

Since the function g is periodic, the value of g(51) will be the same as the value of g at the corresponding position in the first period.

Since g(3) = 67 and the first period starts at g(0), we can add 24 units to g(0) to find the value of g(51).

g(0) + 24 = g(24) = g(51).

Therefore, g(51) = g(24) = g(0) + 24 = g(3) + 24 = 67 + 24 = 91.

So, the value of g(51) is 91.

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