Suppose y varies directly with x. Write a direct variation equation that relates x and y.
y = -10. when x = 2
A. y = -5x
B. y = -1/5x
C. y = 5x
D. y = 1/5x

The interquartile range for the grade 7 data is 9 (30 – 21).

The interquartile range for the grade 8 data is 10 (29 – 19).

The difference of the medians of the two data sets is 6 (21 – 15).

The difference is about 0.67 times the interquartile range of either data set.

It is a measure of the spread of numerical data, which is calculated by subtracting the third quartile (Q3) from the first quartile (Q1). It is used to measure the variability of a data set and is a good indicator of the outliers in the data set.

In the table given, the interquartile range of grade 7 data is 9 and the interquartile range of grade 8 data is 10.

The difference of the medians of the two data sets is 6.

This difference is about 0.67 times the interquartile range of either data set.

This shows that the variability between the two data sets is not significantly different, as the difference between their medians is only two thirds of the IQR of either data set. Thus, the two data sets are relatively similar in terms of their variability.

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Answer:

0.71 weeks

Step-by-step explanation:

To convert 5 days to weeks, we can use the conversion factor:

1 week = 7 days

Therefore, we have:

5 days = 5/7 weeks

Rounding to the nearest hundredth, we get:

5 days ≈ 0.71 weeks

Therefore, 5 days is approximately equal to 0.71 weeks.

The expression √-180  in simplest radical form is 6i√5

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

√-180

Express 180 as product of 36 and 5

So, we have

√-180 = √-(36 * 5)

Rewrite as

√-180 = √(36 * -5)

Take the square root of 36

√-180 = 6√(-5)

The square root of -1 is i

So, we have

√-180 = 6i√5

Hence, the expression in simplest radical form is 6i√5

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Question

Write √-180 in simplest radical form.​

Answer:

3.33  

Step-by-step explanation:

3 1/3 is equal to ((3*3)+1)/3

= 10/3  

= 3.33   ---------> Final answer

Answer:

0

Step-by-step explanation:

Jordan hasn't got enough money to buy any books, as $11.40<$280.

(15) The value of x is -588 (option A).

(16) The value of x makes the expression equal to 0 is -2i. (option B).

The value of x is calculated by solving the equation as follows;

(15) We have the equation:

√x = 14i√3

Squaring both sides, we get:

x = (14i√3)^2

x = -588

(16) Factoring the expression, we get:

x(x⁴ + 6x² + 8)

Setting each factor equal to 0, we get:

x = 0 or x⁴ + 6x² + 8 = 0

Let's solve for the second equation:

Let y = x²

Then we have:

y² + 6y + 8 = 0

Factorizing, we get:

(y + 2)(y + 4) = 0

So y = -2 or y = -4

Since y = x², this means:

x² = -2 or x² = -4

Taking the square root of both sides, we get:

x = ±√(-2) or x = ±√(-4)

Simplifying using imaginary numbers, we get:

x = ±i√(2) or x = ±2i

Thus, for the expression √x is equivalent to 14i√3,  the value of x is -588. And for the expression x⁵ + 6x³ + 8x, x = -2i.

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Exponential smoothing forecast for March is 204.8.

We can use exponential smoothing to forecast the sales for March. Let \(F_t\)be the forecasted value for time t, and \(Y_t\) be the actual value for time t. Then, we can calculate the exponential smoothing forecast as follows:

\(F_t = \alpha Y_t + (1- \alpha ) F_{t-1}\)

where α is the smoothing constant.

We are given that the first forecast value is set to 190, so F_1 = 190. Also, the actual sales data for January, February, and March are 190, 210, and 208, respectively. We are given that α = 0.4.

Using the formula for exponential smoothing, we can calculate the forecast for February as follows:

\(F_2 = 0.4210 + 0.6190 = 202\)

Using the same formula, we can calculate the forecast for March as follows:

\(F_3 = 0.4208 + 0.6202 = 204.8\)

Therefore, the exponential smoothing forecast for March is 204.8.

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The image of the 2 mile markers is missing as well as the options and so i have attached them.

Answer:

> 1.5 hours = 105 miles/speed

> Speed = 105 miles/1.5 hours

> 105 miles = 1.5 hours × speed

Step-by-step explanation:

From the image attached, the distance of the first mile marker is given as 50 miles while the distance of the second mile marker is given as 155 miles.

Thus, difference in distance between the two markers; d = 155 - 50 = 105 miles

Also, we see that the time of first marker is 3 pm while the second marker is 4:30 pm.

Thus, difference in time = 4:30 - 3 = 1 hour 30 minutes or 1.5 hours.

We know that;

Speed = distance/time

Thus;

Speed = 105/1.5

Speed = 70 mph

Thus, the 3 equations that represent this situation from the options are;

> 1.5 hours = 105 miles/speed

> Speed = 105 miles/1.5 hours

> 105 miles = 1.5 hours × speed

Answer:

1.5 hours = 105 miles/speed

Speed = 105 miles/1.5 hours

105 miles = 1.5 hours × speed

Step-by-step explanation:

Answer:

119

Step-by-step explanation:

Given f(x) divided by (x - h) then the value of f(h) is the remainder, thus

f(6) = 2(6)³ - 9(6)² + 11

     = 2(216) - 9(36) + 11

     = 432 - 324 + 11

     = 119 ← remainder

A rule that could represent this dilation of a hexagon on a coordinate grid with the origin as the center is: (x, y) → (kx, ky), where k is the dilation factor (0 < k < 1) for creating a smaller hexagon.

The rule that could represent this dilation is to multiply the coordinates of each vertex of the original hexagon by the scaling factor (the factor by which the hexagon is being dilated) and the distance from the origin. Since the origin is the center of the dilation, the distance from the origin to any point on the hexagon remains constant. Therefore, the rule for dilating a hexagon with the origin as the center of dilation can be written as:
New Vertex = Scaling Factor x Distance from Origin x Old Vertex

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The rule that represents the dilation of the hexagon with the origin as the center of dilation is:
\((x\prime, y\prime) = (xr, yr)\)
r is the ratio of the side lengths of the image to the pre-image, and (x, y) are the coordinates of a point on the pre-image.

A hexagon means to scale it up or down in size while maintaining its shape.

The hexagon will be made smaller.

The center of the dilation is the origin, which means that the hexagon will be scaled equally in all directions from the center.
To find the rule that represents this dilation, we can use the formula for dilation.

The formula for dilation is:
\((x\prime, y\prime) = k(x, y)\)
(x, y) are the coordinates of a point on the pre-image (the original hexagon), \((x\prime, y\prime)\) are the coordinates of the corresponding point on the image (the smaller hexagon), and k is the scale factor.
The center of dilation is the origin, which means that the coordinates of the center of the pre-image and the image are both (0, 0). Since the hexagon is being scaled down, the scale factor k must be less than 1.
To find the value of k, we need to know the ratio of the side length of the image to the side length of the pre-image. Let's say that the side length of the pre-image is s, and the side length of the image is \(s\prime\).

The scale factor k can be found using the formula:
\(k = s\prime / s\)
Since the hexagon is being scaled down, we know that\(s\prime < s.\)

Let's say that the ratio of the side lengths is r, where:
\(r = s\prime / s\)
Then we can rewrite the formula for k as:
\(k = r / 1\)
The center of dilation is the origin, the coordinates of each point on the pre-image are equal to the length of their respective sides.

The vertices of the pre-image using the following coordinates:
A = (0, s)
\(B = (s\sqrt 3/2, s/2)\)
\(C = (s\sqrt 3/2, -s/2)\)
\(D = (0, -s)\)
\(E = (-s\sqrt3/2, -s/2)\)
\(F = (-s\sqrt3/2, s/2)\)
The coordinates of the corresponding vertices on the image, we can substitute these coordinates into the formula for dilation:
\(A\prime = k(0, s) = (0, rs)\)
\(B\prime = k(s\sqrt3/2, s/2) = (s\sqrt3/2 r, s/2 r)\)
\(C\prime = k(s\sqrt3/2, -s/2) = (s\sqrt3/2 r, -s/2 r)\)
\(D\prime = k(0, -s) = (0, -rs)\)
\(E\prime = k(-s\sqrt3/2, -s/2) = (-s\sqrt3/2 r, -s/2 r)\)
\(F\prime = k(-s\sqrt3/2, s/2) = (-s\sqrt3/2 r, s/2 r)\)

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23/14=1.6 square feet per hour

Answer:

Step-by-step explanation:

1. Since we know that Lila wants to use 1 cup of pretzels, we can multiply 1/2 x 1/2, which is 1.

2. Now that we multiplied 1/2 by 1/2, we have to multiply 1 1/4 by 1/2.

So 5/4 x 1/2 is 5/8.

3. Lila will need 5/8 cups of raisins.

At a 98% confidence level, the margin of error for the proportion of college students who buy their books from the bookstore is approximately 1.175.

To find the margin of error for the proportion of college students who buy their books from the bookstore, we can use the formula:

Margin of Error = \(\[Z \times \sqrt{\frac{{\hat{p} \cdot (1 - \hat{p}})}{n}}\]\)

where:

Z is the z-score corresponding to the desired confidence level (98% confidence level corresponds to a z-score of approximately 2.33)

p_hat is the sample proportion

n is the sample size

From the given data, we can count the number of students who buy their books from the bookstore. In this case, it is 17 students out of 40.

p_hat = 17/40 = 0.425

Substituting the values into the formula, we have:

Margin of Error = \(\[2.33 \times \sqrt{\frac{{0.425 \cdot (1 - 0.425)}}{40}}\]\)

Calculating the expression inside the square root:

(0.425 * (1 - 0.425)) / 40 = 0.2551

Taking the square root:

\(\(\sqrt{0.2551} \approx 0.505\)\)

Finally, we calculate the margin of error:

Margin of Error ≈ 2.33 * 0.505 ≈ 1.175

Therefore, at a 98% confidence level, the margin of error for the proportion of college students who buy their books from the bookstore is approximately 1.175.

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Answer:

:)

Step-by-step explanation:

Answer:

Ok

Step-by-step explanation:

Answer: 31

Step-by-step explanation:

Janine has 48 hockey cards in one book and 105 hockey cards in another book. Therefore, the total hockey cards will be:

= 48 + 105

= 153 hockey cards

Since the hockey cards come in packages of 5 cards, the number of packages that she will buy will be:

= 153/5

= 30 3/5

= 31

Therefore, she'll buy 31 packages

Answer:

See Explanation

Step-by-step explanation:

Given

The question is incomplete, as the cylinders are not given.

Required

The cylinder with greater volume

To answer this question, I will assume the following dimensions.

Cylinder 1

\(r = 5\)

\(h = 10\)

Cylinder 2

\(r = 7\)

\(h = 5\)

Volume is calculated as:

\(V = \pi r^2h\)

When the radius is reduced by 2, the formula becomes

\(V = \pi (r - 2)^2h\)

For the first cylinder, we have:

\(V_1 = \pi (r - 2)^2h\)

\(V_1 = 3.14 * (5 - 2)^2 * 10\)

\(V_1 = 3.14 * 3^2 * 10\)

\(V_1 = 3.14 * 9 * 10\\\)

\(V_1 = 282.6\)

For the second cylinder, we have:

\(V_2 = \pi (r - 2)^2h\)

\(V_2 = 3.14 * (7 - 2)^2 * 5\)

\(V_2 = 3.14 * 5^2 * 5\)

\(V_2 = 3.14 * 25 * 5\)

\(V_2 = 392.5\)

Cylinder 2 has a greater volume because 392.5 > 282.6

Note: Irrespective of the dimension of the cylinders, the above step works fine.

Answer:

Step-by-step explanation:

Error 1) It should be divided by 5.

x - 5 = 0

x = 5

Error 2) -3   15   0    -1     5

coefficient of x² is 0 and it is not included

Answer:

Her investment will grow over the years due to the 2 percent interest. Inflation will impact the value of her investment

For the given data. the simple interest will be $100.His investment will grow over the years. Because of the simple interest.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

It is given that, Pardis recently deposited $5,000 in a savings account that pays a return of 2 percent per year.

Principal = $5,000

Rate= 2%

Time= 1 year

SI = (P×R×T)/100

SI = (5000×2×1)/100

SI=100

Thus, for the given data. the simple interest will be $100.His investment will grow over the years. Because of the simple interest.

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Ricardo will be left with $23.92 after 3 hours of Jet ski riding

Ricardo is on vacation so he went jet skiing

The Jet ski has a rental flat rate of $25

They also charge $17.75 per hour

Ricardo had $102.17

The amount spent in 3 hours is

17.75(3) + 25

= 53.25 + 25

= 78.25

The amount left is

= 102.17 - 78.25

= 23.92

Hence Ricardo has $23.92 left after the Jet ski ride

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The CLI option on the MODEL statement of an MLR analysis in PROC GLM produces confidence intervals for the mean response at all predictor combinations in the dataset. b

The CLI option stands for "Confidence Level of Intervals," and it specifies the level of confidence for the confidence intervals produced.

By default, the CLI option is set to 0.95, which means that the confidence intervals produced will have a 95% level of confidence.

These confidence intervals provide a range of values within which the true mean response at a particular combination of predictor values is expected to fall with a specified level of confidence.

They can be useful for assessing the uncertainty associated with the estimated mean response at different combinations of predictor values and for making inferences about the relationships between predictors and the response variable.

The CLI option, which stands for "Confidence Level of Intervals," defines the degree of confidence in the confidence intervals that are generated.

The CLI option's default value of 0.95 designates a 95% degree of confidence for the confidence intervals that are generated.

With a given degree of confidence, these confidence intervals show the range of values within which the real mean response for a specific set of predictor values is anticipated to fall.

They can be helpful for determining the degree of uncertainty surrounding the predicted mean response for various combinations of predictor values and for drawing conclusions on the connections between predictors and the response variable.

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3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

Two or more expressions with an Equal sign is called as Equation.

Rustam has three times as many carrots as Pio

R=3P

Where  is Rustam, P is Pio and C is Claudine.

Rustam has 5 fewer carrots that Claudine.

R=C-5

3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.

Now let us find the number of carrots Pio has when Claudine has 20

3P=20-5

3P=15

Divide both sides by 3

P=5

Pio has 5 carrots when  Claudine has 20.

Now if pio has 10 then the number of carrots with Claudine

3(10)=C-5

30+5=C

35=C

Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and  if pio has 10 then the number of carrots with Claudine are 35

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The number of room that can be painted can be determined as,

Thus, the required number of rooms is 35.

Answer:

A line graph (also known as a line plot or line chart) is a graph which uses lines to connect individual data points that display quantitative values over a specified time interval. Line graphs use data point "markers" that are connected by straight lines to aid in visualization.

Answer:

slope= rise/run= y/x

Step-by-step explanation:

that's the equation of a slope

Answer:

The first term is when n= 1

3(1)+2 = 3+2

= 5

The second term is when n= 2

3(2)+2 = 6+2

= 8

The third term is when n=3

3(3)+2 = 11

Answer:

5, 8, 2

Step-by-step explanation:

.............pi

Answer:

Divide Number by 2

Step-by-step explanation:

To get to 200 from 400, you divide by 2

To get to 100 from 200, you divide by 2, and so on

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Divide by 2.

Step-by-step explanation:

400 ÷ 2

200

200 ÷ 2

100

100 ÷ 2

50

50 ÷ 2

25

Answer:

Function A has a rate of change of 5. Function B has a rate of change of -4.5. so, function A has a greater rate of change

Step-by-step explanation:

When we talk of rate of change of linear equations, we are referring to the slope

For the first function, we can use the equation of the slope

m = y2-y1/x2-x1

We select any two points

m = (25-15)/5.5-3.5 = 10/2 = 5

The general equation of a straight line is;

y = mx + c

where m is the slope

in the case of the second equation, -4.5 is the slope

So we fill in the result as follows;

Function A has a rate of change of 5. Function B has a rate of change of -4.5. so, function A has a greater rate of change

The given inequality holds for the open interval (2.97,3.03)

It is given that

f(x)=6x+7

cL=25

c=3

ε=0.18

We have,

|f(x)−L| = |6x+7−25|

          = |6x−18|

          = |6(x−3)|

          = 6|x−3|

Now,

6|x−3| <0.18  then |x−3|<0.03 ----->−0.03<x-3<0.03---->2.97<x<3.03

the given inequality holds for the open interval (2.97,3.03)

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Although part of your question is missing, you might be referring to this full question: For the given function f(x) and values of L,c, and ϵ0, find the largest open interval about c on which the inequality |f(x)−L|<ϵ holds. Then determine the largest value for δ>0 such that 0<|x−c|<δ→|f(x)−|<ϵ.

f(x)=6x+7,L=25,c=3,ϵ=0.18

.

Answer:

3,165.12 square meters

Step-by-step explanation:

To find the surface area of a cylinder, first separate the shapes you must find the area of. In this case, you need to find the areas of two circles and one rectangle (the height).

The two circles can be found using the equation: a = pi(r^2). r means radius!

12 squared is 144, which, multiplied by pi, is 452.16 square units. Because there are two circles, you can multiply this area by two to get the area of both: 904.32.

The rectangle can be found by multiplying the circumference of the circle by the height of the cylinder. The circumference can be found with the equation: c = 2pi(r). The circumference of this cylinder's base is 75.36, which, multiplied by the height of the cylinder, is 2,260.8.

Now that you have both the area of the circles and the side, you can add them both together and get the surface area.