hi can you do 6 and 7 so i can understand the rest of the questions given to me. also, can you show the check too? so i can understand. thank you!

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

\(\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}\)

For the seniors, the mean is given as,

Mean = (5 x 2 + 35 x 2 + .... + 15 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 5)² + (26 - 5)² + (26 - 15)²] / 10

σ = 14.28

For the juniors, the mean is given as,

Mean = (40 x 2 + 25 x 2 + ....... + 40 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 40)² + (26 - 25)² + (26 - 40)²] / 10

σ = 13.19

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

More about the standard deviation link is given below.

https://brainly.com/question/12402189

#SPJ1

The complete question is given below.

The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= \(\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy\)

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ]\(| \limits^1_0\)

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

learn more about area here

brainly.com/question/27683633

#SPJ4

Answer:

36 Kilograms of Dough in 6 hours

Step-by-step explanation:

Each hour Ken prepares 6 kilograms of dough, and every 2 hours Ken prepare 12 kilograms of dough.

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.

To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:

Help Center to Water Slide #1:

Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)

Toddler area to Concessions:

Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)

Gift Shop to Restrooms:

Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)

Security desk to Water Slide #2:

Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)

Lazy River to Large Whirlpool:

Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5

Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)

Presently, let's calculate the linear equations for each case:

Help Center to Water Slide #1:

The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.

Toddler area to Concessions:

The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:

-7.5 = (-1/3)(1.5) + b

-7.5 = -0.5 + b

b = -7

Gift Shop to Restrooms:

The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.

Security desk to Water Slide #2:

The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.

Lazy River to Large Whirlpool:

The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:

12 = (2/5)(-2) + b

12 = -4/5 + b

b = 61/5

The Linear equations for each case are as follows:

Help Center to Water Slide #1: y = 3

Toddler area to Concessions: y = (-1/3)x - 7

Gift Shop to Restrooms: y = -9

Security desk to Water Slide #2: y = 4

Lazy River to Large Whirlpool: y = (2/5)x + 61/5

Learn more about slope here:

https://brainly.com/question/29044610

#SPJ1

Answer: -10m + 30

Step-by-step explanation:

Given expression

(m - 3) (-10)

Expand parentheses and apply the distributive property

=m · (-10) - 3 · (-10)

Simplify by multiplication

=\(\boxed{-10m+30}\)

Hope this helps!! :)

Please let me know if you have any questions

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer: To solve the rational inequality:

x+1 / x−3 ≤ 0

We can start by finding the critical points of the inequality by setting the numerator and denominator equal to zero:

x + 1 = 0 => x = -1

x - 3 = 0 => x = 3

These critical points divide the number line into three intervals: (-infinity, -1), (-1, 3), and (3, infinity). We can then test each interval to determine whether the inequality is true or false.

Testing the interval (-infinity, -1), we choose a test point x = -2:

(-2 + 1) / (-2 - 3) = -1/5 < 0

Therefore, this interval satisfies the inequality.

Testing the interval (-1, 3), we choose a test point x = 0:

(0 + 1) / (0 - 3) = -1/3 > 0

Therefore, this interval does not satisfy the inequality.

Testing the interval (3, infinity), we choose a test point x = 4:

(4 + 1) / (4 - 3) = 5 > 0

Therefore, this interval satisfies the inequality.

So, the solution to the inequality is:

x ∈ (-∞, -1] ∪ (3, ∞)

In interval notation, this solution is (-∞, -1] U (3, ∞).

Step-by-step explanation:

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

The unit rate of the relationship will be 10/3. The correct option is C.

The given equation is,

y = 10/3x + 8

The general form of an equation of the line is,

y = mx +  c

here, the slope will be 10/3

Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.

The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.

A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.

The unit relationship will be 10/3.

To know more about slope follow

https://brainly.com/question/19131126

#SPJ1

Answer:

  -2

Step-by-step explanation:

Put the given value in the equation and solve for x.

  f(x) = 12

  f(x) = 2(x +8)

  12 = 2(x +8) . . . . . use 12 for f(x)

  6 = x +8 . . . . . . . . divide by 2

  -2 = x . . . . . . . . . . subtract 8

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

360 cm^3

Step-by-step explanation:

Since the height of the block must be 6cm, and the length is 10cm, and the depth is 6cm, the volume must be 6 * 10 * 6 = 360cm^3

Answer:

Step-by-step explanation:

The equation of any line perpendicular to a line with an equation of x= (vertical line) will have the form y= (horizontal line). In this case, since this line passes through the y value of 3, that means that the equation is y=3.

since is an eigenvector of with eigenvalue , we can express the second column of the matrix as . So the matrix is given by:

\($$\begin{bmatrix}\lambda_1 & 0 \\0 & \lambda_2\end{bmatrix}$$\)

This matrix is a diagonal matrix, which is a matrix with all entries except for those on the main diagonal set to zero. In this matrix, the main diagonal elements, which are the elements on the diagonal from the upper left to the lower right, are labelled \(\lambda_1$ and $\lambda_2\)This matrix is symmetric, meaning that the transpose of the matrix is equal to the original matrix. The matrix represents a linear transformation in which the eigenvalues \(\lambda_1$ and $\lambda_2\) represent the scalar factors by which the vectors in the transformed space are scaled. The eigenvalues of this matrix can be used to determine the magnitude of the transformation it performs.

The eigenvalues of this matrix can be calculated by solving the equation

\(\det(\mathbf{A} - \lambda \mathbf{I}) = 0\)

where \(\mathbf{A}\) is the matrix and \(\mathbf{I}\) is the identity matrix.

In this case, we have

\($\det\begin{bmatrix}\lambda_1 - \lambda & 0 \\0 & \lambda_2 - \lambda\end{bmatrix}\)

=\((\lambda_1 - \lambda)(\lambda_2 - \lambda)\) = 0.

Solving this equation for \(\lambda$, we get $\lambda = \lambda_1\) and \(\lambda = \lambda_2\)Therefore, the eigenvalues of this matrix are \(\lambda_1 and \lambda_2\)

the complete question is : use an eigenbasis to determine a matrix consider an matrix such that is an eigenvector of with eigenvalue and is an eigenvector of with eigenvalue . determine the Given an matrix such that is an eigenvector of with eigenvalue and is an eigenvector of with eigenvalue , what is the matrix.

Learn more about matrix here

https://brainly.com/question/29132693

#SPJ4

Considering the volume of a rectangular prism, the capacity of the second sandbox would be of 80 cubic feet.

The volume of a rectangular prism with length l, width w and height h is given by the multiplication of the measures, that is:

V = lwh.

In this problem, the capacity is of 10 cubic feet, that is:

V = lwh = 10.

When each measure is doubled, the volume will be given as follows:

V=  2l x 2w x 2h = (2 x 2 x 2)lwh = 8lwh = 8V = 80 cubic feet.

More can be learned about the volume of a rectangular prism at https://brainly.com/question/17223528

#SPJ1

Answer:

I got a decimal

Step-by-step explanation:

0.857142857

Answer:

Step-by-step explanation:

The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

For more such questions on enrollment,click on

https://brainly.com/question/1101942

#SPJ8

The amounts of each article that should be produced to maximize the profits is given as follows:

The variables for the system of equations are given as follows:

The number of hours is a countable amount, meaning that it cannot assume negative values, hence:

The factory can avail of 80 hours of machine time, hence:

1.5x + 2.5y ≤ 80.

(1.5 hours of machine time for cloth A, 2.5 hours for cloth B, the sum can be at most 80).

The craftsman’s maximum time is of 70 hours, hence:

2x + 1.5y ≤ 70.

The vertex for which the amount is maximized is given as follows:

(11,31).

Meaning that the amounts are of 11 articles from cloth A and 31 articles from cloth B.

More can be learned about linear programming at https://brainly.com/question/13154906

#SPJ1

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

For more such questions on length

https://brainly.com/question/2217700

#SPJ8

The volume of this rectangular prism include the following: 84.375 cubic meters.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 5 × 4 1/2 ×  3 3/4

Volume of rectangular prism = 5 × 4.5 ×  3.75

Volume of rectangular prism = 84.375 cubic meters.

Read more on volume of prism here: brainly.com/question/21012007

#SPJ1

Answer:

i awnsered 4.2^(-3)*5.1^(2)*4.2^(4)*5.1^(3)

Step-by-step explanation:

14491.060542

The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.

Call that angle we're looking for "x" for convenience.

The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.

We now know that 3x, or 3 times x, is the compliment of x.

With this knowledge, we can construct the following equation:

x + 3x = 90°

combining comparable equations;

4x = 90°

x = 22.5°, when both sides are divided by 4.

As a result,

3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.

To know more about complementary visit:

https://brainly.com/question/15592900

#SPJ1

In a case whereby the function is y = -5x + 4, the range of the function of the domain is  {14, 4, -21}

A function's range  serves as one which encompass conceivable values for y. Y = f(x) is the formula to determine a function's range.

We were told to get the range of the function,  which implies that we will be plugging each value in the domain into the given function  so that we can observe the output (y-value) .

When x = -2:

y = -5(-2) + 4 = 1

When x = 0:

y = -5(0) + 4 = 4

When x = 5:

y = -5(5) + 4 = -21

So the range of the function is {14, 4, -21}.Learn more about function at:

https://brainly.com/question/22995209

#SPJ1

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

S(4) = 2

Step-by-step explanation:

S(n) = n(n - 3) / 2

S(4) = 4(4 - 3) / 2

= 4 x 1 / 2

= 4/2

= 2

Answer:

96?

Step-by-step explanation:

The total number of blocks the first time in the day:

14 +34 = 48

Mutiply that by 2 to see how many blocks he does twice a day

48(2)= 96