A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.

What is the volume of the cylinder in terms of
? Show all work.
What is the volume of the cone in terms of
? Show all work.
Estimate the volume of the hemisphere in terms of
by calculating the average of the volumes of the cylinder and cone. Show all work.

When the number of people is multiplied by 4, the number of pizzas is also multiplied by 4. This relationship can be observed by examining the equivalent ratios shown in the table.

Equivalent ratios represent the same proportional relationship between two quantities. In this case, the quantities being compared are the number of people and the number of pizzas. The table displays different combinations of people and pizzas that maintain the same ratio.

Let's consider an example from the table. If we look at the first row, it states that when there are 2 people, there are 1 pizza. If we multiply the number of people by 4 (2 x 4 = 8).

This pattern holds true for all the equivalent ratios in the table. When the number of people is multiplied by 4, the number of pizzas is also multiplied by 4. This demonstrates a consistent and proportional relationship between the two quantities.

The concept of equivalent ratios is fundamental in understanding proportional relationships and scaling. It allows us to make predictions and calculations based on the established ratio.

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(a) The sample mean (x) is 1,275 A.D. and the sample standard deviation (s) is approximately 306.625 A.D.

(b) The critical value for a 90% confidence interval is approximately 1.895.

(c) The maximal margin of error is approximately 204.159.

(d) A 90% confidence interval for the mean of all tree-ring dates from this archaeological site is approximately 1,071 A.D. to 1,479 A.D.

(a) To find the sample mean (x) and sample standard deviation (s), we calculate the following:

Sample mean (x) = (sum of all x values) / (number of values)

= (1,201 + 1,313 + 1,243 + 1,313 + 1,299 + 1,229 + 1,208 + 1,194) / 8

= 10,200 / 8

= 1,275

The sample standard deviation (s):

s = sqrt((sum of (x - x')^2) / (n - 1)), where (x - x') is the deviation of each x value from the mean.

Now, calculate the sum of squared deviations:

Sum of squared deviations = (-74)^2 + 38^2 + (-32)^2 + 38^2 + 24^2 + (-46)^2 + (-67)^2 + (-81)^2

= 547,365 + 1,444 + 1,024 + 1,444 + 576 + 2,116 + 4,489 + 6,561

= 564,109

Finally, calculate the sample standard deviation (s):

s = sqrt(564,109 / (8 - 1))

≈ sqrt(94,018.167)

≈ 306.625

(b) To find the critical value for a 90% confidence interval, we need to determine the value of alpha (α) which is equal to 1 - confidence level. In this case, alpha (α) = 1 - 0.90 = 0.10.

Looking up the critical value for alpha (α) = 0.10 in the t-distribution table with n - 1 degrees of freedom (n = 8 - number of values), we find the critical value to be approximately 1.895.

(c) The maximal margin of error (E) when finding a 90% confidence interval can be calculated using the formula:

E = (critical value) * (standard deviation / sqrt(sample size))

E = 1.895 * (306.625 / sqrt(8))

≈ 1.895 * (306.625 / 2.828)

≈ 204.159

(d) To find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site, we use the formula:

Lower limit = x - E

Upper limit = x + E

Substituting the values, we get:

Lower limit = 1,275 - 204.159 ≈ 1,071

Upper limit = 1,275 + 204.159 ≈ 1,479

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Answer:

immune system

Step-by-step explanation:

it helps fight off bacteria and viruses, which are harmful substances.

Answer:

the immune system? i can explain if needed

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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Answer:

4.5%

Step-by-step explanation:

The total percentage decrease in the investor's stock account was 4.5%. This is calculated by taking the decrease in Company A (3%) and Company B (6%) and adding them together to get a total decrease of 9%. This percentage is then divided by two (since there are two companies) to get 4.5%.

Answer:

30,000​

Step-by-step explanation:

3,000 times 10 is 30,000, therefore 30,000/10=3,000

Answer:

Step-by-step explanation:

3000 of 1/10

3000*0.1=300

Answer: 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/15 = .4666 = 46.66%

Answer:

1.2

Step-by-step explanation:

17 ÷ 20 + 7 ÷ 20

I hope this helps!

Answer:

9 - 3 x = -3 x - 20

Step-by-step explanation:

the equation has one solution

mark me as brainiest if im correct:)

Answer:

There is 160.81 % of increase.

Step-by-step explanation:

Given that,

The average size of a privately owned farm in a particular country was 171 acres.

Now, the average size of a privately owned farm in the country had increased to 446 acres.

We need to find the percent increase.

\(\%=\dfrac{\text{increase}}{\text{original}}\times 100\\\\\%=\dfrac{446-171}{171}\times 100\\\\\%=160.81\%\)

So, there is 160.81 % of increase.

They are parallel, as shown by the graph.

Answer:

33

Step-by-step explanation:

30+9÷(3)

30+3

33

please like and rate and follow

Answer: B. 4/7

Step-by-step explanation:

(3/7)(3/4) = (3/7)*(4/3) = (3*4)/(3*7) = 4/7

Answer:

I need the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sample is the part of the population that somebody wants to study. therefore, the sample is the 100 male students interviewed

The maximum depth of the parabolic dish with a diameter of 12 feet and a focal length of 2 feet  is 4.5 feet deep.

To determine the maximum depth of the parabolic dish with a diameter of 12 feet and a focal length of 2 feet, we can use the formula for a parabola in vertex form:

y = (1/(4f))x²

Here, f is the focal length, and x and y are the coordinates of points on the parabolic surface. The maximum depth of the dish corresponds to the y-value of the vertex, which is the point on the parabolic surface where the x-value is half the diameter (6 feet).

Using the given focal length (f = 2 feet) and x-value (x = 6 feet), we can find the maximum depth (y):

y = (1/(4*2))(6²)
y = (1/8)(36)
y = 4.5

The maximum depth of the parabolic dish is 4.5 feet deep.

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Step-by-step explanation:

X/11+2=4

X+22/11=4 ( LCM of this denominators is 11)..

X+22=4×11

X+22=44

X=44-22

X=22 ANSWER

I guess you're missing some plus signs, so that

\(\vec f(x, y, z) = z \, \vec\imath + y \, \vec\jmath + zx \, \vec k\)

You're also missing the plane that defines the tetrahedron, but no big deal; I'll use the general equation \(ax+by+cz = 1\), where each of a, b, and c are positive. Then S is the boundary of the region R, where

\(R = \left\{ (x, y, z) : 0 \le x \le \dfrac1a \text{ and } 0 \le x \le \dfrac{1-ax}b \text{ and } 0 \le z \le \dfrac{1-ax-by}c \right\}\)

By the divergence theorem, the flux of \(\vec f\) across S is

\(\displaystyle \iint_S \vec f \cdot d\vec s = \iiint_R \mathrm{div}(\vec f) \, dV\)

We have

\(\mathrm{div}(\vec f) = \dfrac{\partial(z)}{\partial x} + \dfrac{\partial(y)}{\partial y} + \dfrac{\partial(zx)}{\partial z} = 1 + x\)

Then the flux is equal to the volume integral,

\(\displaystyle \iiint_R (1 + x) \, dV = \int_0^{1/a} \int_0^{(1-ax)/b} \int_0^{(1 - ax - by)/c} (1 + x) \, dz \, dy \, dx \\\\ = \frac1c \int_0^{1/a} \int_0^{(1-ax)/b} (1 + x) (1 - ax - by) \, dy \, dx \\\\ = \frac1{2bc} \int_0^{1/a} (1 + x) (1 - ax)^2 \, dx \\\\ = \frac1{6abc} \left(\frac1{4a} + 1\right) = \boxed{\frac{1+4a}{24a^2bc}}\)

Answer:

C

Step-by-step explanation:

The surface area of a cylinder is given by the formula:

\(SA=2\pi rh+2\pi r^2\)

Where h is the height and r is the radius of the cylinder.

The given radius is 6 and the height is 24.

We are also using 3.14 for π.

Therefore;

\(SA\approx 2(3.14)(6)(24)+2(3.14)(6)^2\)

Evaluate:

\(SA\approx1130.4\approx 1130\)

The answer is C.

Applying the expression for the circumference of circle, we found the diameter as 16.86 yards

Given Data

Let us apply the expression for the circumference of a circle

Circumference = 2πr----------1

But r = d/2

hence put r = d/2 in the expression above

Circumference = 2πd/2----------2

Circumference = πd

Substitute our given data

53 = 3.142*d

Make d the subject of formula we have

d = 53/3.142

d = 16.86 yards

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Answer:

y=6

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

1. simplify 1/2

 (11 -  (1/2• y)) -  9  = 0  

Circle B will have larger circumference by 3.14 centimeter

The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.

The circumference of the circle is = 2пr where r is radius

According to the information

Circle A has diameter = 9 cm

Radius of circle A = \(\frac{9}{2}\) cm

Circumference of Circle A = 2пr

                                            = 2 × 22/7 × 9/2

                                            = 28.28 centimeter  

Circle B has radius = 5 cm

Circumference of circle B = 2 × 22/7 × 5

                                             = 31.42 centimeter

Circle B will have larger circumference by 3.14 centimeter

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Approximately 44.1% of randomly selected females purchased a compact fuel-powered vehicle, while approximately 26.7% of randomly selected customers purchased an electric vehicle.

a) To compute the probability that a randomly selected female purchased a compact-fuel powered vehicle, we divide the number of females who purchased a compact-fuel powered vehicle (45) by the total number of females (102).

The probability is 45/102, which simplifies to approximately 0.441.

b) To compute the probability that a randomly selected customer purchased an electric vehicle, we divide the number of customers who purchased an electric vehicle (55) by the total number of customers (206).

The probability is 55/206, which simplifies to approximately 0.267.

Therefore, the probability that a randomly selected female purchased a compact-fuel powered vehicle is approximately 0.441, and the probability that a randomly selected customer purchased an electric vehicle is approximately 0.267.

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Answer:

Step-by-step explanation:

not sure 2

The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

What is the Lagrange multiplier?

The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.

To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.

Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.

The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))

The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6

The Lagrange equation is

L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)

To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:

∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0

∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0

∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0

Solving these equations simultaneously will give us the critical points of the function.

We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))

We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)

Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).

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Where are you confused?

The following linear equation gives Johnny's savings w weeks after her opened the account.

S(w) = $95 + $15*w

We know that initially, Johnny deposits an amount of $95, and then he saves $15 per week.

So, after w weeks, the amount in that savings account will be:

S(w) = $95 + $15*w

This linear equation gives the bank account balance w weeks after her opened the account.

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