Using the "opposite operation" to "undo" and isolate the variable
when solving an equation is more commonly called applying the ...

Answer:

[tex]132\pi[/tex]

Step-by-step explanation:

The lateral area is the area of a rectangle. Think of a soup can with the label removed and laid out flat on a table.  The height of the rectangle is the same as the height of the can (cylinder).  Where does the base of the rectangle come from?  It's the circumference of the can "unrolled."

Area of a rectangle = base x height

Circumference of a circle [tex]C=2\pi r[/tex]

Lateral Area [tex]=2\pi r \times h[/tex] [tex]=2 \pi (6)(11) =132\pi[/tex]

Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because i said so

Answer:

x = 5

Step-by-step explanation:

x² -3x -4 = x² - 5x + 6.

-x² - x²

-3x -4 = -5x + 6

+3x + 3x

-4 = -2x +6

-6 -6

-10 = -2x

÷-2 ÷-2

5 = x

Hope this Helps

Answer:

x = 5

Step-by-step explanation:

hope this helps!

Answer:

Estimate = $34.50

Actual charge $33.47

Step-by-step explanation:

To estimate, we round the numbers

9.7 gallons rounds to 10 gallons

10 gallons * 3.45 per gallon =34.50

This is an overestimation

The actual charge

9.7* 3.45 =33.465

We round to the nearest cent

33.47

Answer:

Estimate: $34.5

Actual: $33.465

Step-by-step explanation:

9.7 is approximately 10

Estimate

10 × 3.45 = 34.5

Actual:

9.7 × 3.45 = 33.465

Answer:

Answer A.

Step-by-step explanation:

Recall that [tex]f(x) = \frac{x^2-4}{x-2}[/tex]

we will calculate the lateral limits of f when x approches x=2. Note that

[tex] \lim_{x\to 2^{+}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{+}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]

[tex] \lim_{x\to 2^{-}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{-}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]

We can clasify the discontinuity as follows:

- Removable discontinuity if both lateral limits are equal and finite.

- Jump discontinuity if both lateral limits are finite but different.

- Essential discontinuity if one of the limits is not finite and the other one is finite.

Based on this classification, since both lateral limits are equal, the discontinuity is a removable discontinuity

Answer:

129

Step-by-step explanation:

Answer:

Stephanie runs the fastest per second: 14 feet per second

Step-by-step explanation:

To find the fastest speed, you need to see which person runs the most per second:

Stephanie runs 14 feet per second

Brooke runs 589 feet in 44 seconds.

Find the amount of feet per second by dividing:

[tex]\frac{589}{44} =13.4[/tex]

Brooke runs about 13.4 feet per second

Will runs 1 mile in 454 seconds.

Convert the miles to feet:

There are 5,280 feet in a mile. If Will runs 5,280 feet in 454 seconds, divide to find how much he runs per second:

[tex]\frac{5280}{454}= 11.6[/tex]

Will runs about 11.6 feet per second.

Rob runs 548 feet in a minute.

Convert the minute into seconds. There are 60 seconds in a minute. Divide the feet by the seconds to find how fast he runs per second:

[tex]\frac{548}{60}= 9.1[/tex]

Rob runs about 9.1 feet per second.

Stephanie runs 14 feet per second, the fastest time:

| 14 |, 13.4, 11.6, 9.1

Finito.

We need to calculate a z-score to determine the probability of getting a month with a temperature of 34 degrees or higher, and then subtract that probability from 1 to get the final result.

To solve this problem, we're dealing with a normal distribution. The average maximum monthly temperature in Campinas, Brazil is given as the mean (29.9 degrees). The standard deviation has been given as 2.31 degrees.

We're asked to find the percentage of months that would have a maximum temperature of 34 degrees or higher. This can be interpreted as finding the probability of a temperature being more than 34 degrees. We first need to find the number of standard deviations away from the mean 34 degrees is, which is known as Z-score.

The formula for Z-score is (X - mean) / standard deviation. So, our calculation would be (34 - 29.9) / 2.31. The resultant Z-score would have to be looked up in a standard normal distribution table, which will give us the probability up to that point. As we want the probability of the temperature being higher, we'll subtract the value we get from 1 (as total probability is 1), which would give us the percentage of months with a maximum temperature of 34 degrees or higher.

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Answer:

24 feet

Step-by-step explanation:

sorry I'm so late

Answer:

210.22

Step-by-step explanation:

first you need to divide 3785 divided by 18 which is 210.22222222 then u need to round to the nearest tenth which is equaled to 210.22. I hope this helped

Answer: The surface is (4*n + 2)*L^2

Step-by-step explanation:

The surface of a cube is equal to 6 times the area of one of the sides.

So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2

Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2

But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2

and we have 4 sides, then the total area of the sides is 4*n*L^2

Then the total surface of the tower is:

A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2

Answer:

78,750 pages

Step-by-step explanation:

225 books each with 350 paged

225 x 350

78,750 pages

Answer:

Mean = 2.7

In a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Step-by-step explanation:

We are given that the rate of cancer in children is 37 children in 1 million. So the probability of cancer in a child is P(C) = 0.000037

Poisson distribution is used to approximate the number of cases of diseases and we have to find what will be the mean number of cases for 74,090.

In simple words we have to find the expected number of children with cancer in a group of 74,090 children.

The mean value of expected value can be obtained by multiplying the probability with the sample size. So, in this case multiplying probability of child having a cancer with total group size will give us the expected or mean number of children in the group with cancer.

Mean = E(x) = P(C) * Group size

Mean = 0.000037 x 74090

Mean = 2.7

This means in a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Final answer:

The mean of the Poisson distribution for the number of cancer cases among 74,090 children in Normalville is approximately 2.7413 cases.

Explanation:

To find the mean of the appropriate Poisson distribution for the number of cases in groups of 74,090 children in Normalville, we multiply the probability of the disease by the number of children. Thus, the mean (μ) is:

μ = probability of one child having the disease × total number of children

μ = 0.000037 × 74,090 = approximately 2.7413

The mean of the Poisson distribution, in this case, indicates the average number of children who would have this rare form of cancer in groups of 74,090 children in Normalville.

Answer:

Radius 6.5cm

Diameter  13cm

Step-by-step explanation:

Diameter ia a straight line passing from side to side through the center  a circle or sphere.

Radius formula is simply derived by halving the diameter of the circle

13/2=6.5

Answer:

P(x=2) = 0.2368

Step-by-step explanation:

given data

stocks of local interest N = 20

stocks increased K = 10

stocks decreased =  5

remained unchanged = 5

solution

we take here no of stock that are increased randomly n = 2

so here Hypergeometric random variable can take integer value

{max(0, n+k - N ), min(n,K) } = {0,2}

so here

P(x=2)

so

P(x=k)  = [tex]\frac{(^K_k)\times (^{N-K}_{n-k}) }{(^N_n)}[/tex]      .......................1

P(x=2 ) = [tex]\frac{(^{10}_2)\times (^{20-10}_{2-2}) }{(^{20}_2)}[/tex]    

solve it we get

P(x=2 ) = 0.236842

now we use excel function as

HYPGEOM.DIST (k,n,N.cumulative)   .....................2

so it will be

HYPGEOM.DIST (2,2,10,,false)

we get

HYPGEOM.DIST (2,2,10,,false)  = 0.236842

so

P(x=2) = 0.2368

Answer:

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Step-by-step explanation:

We are given the following information:

We treat people having brown eyes as a success.

P(people have brown eyes) = 41% = 0.41

Then the number of people follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 14

We have to evaluate:

[tex]P(x \geq 12) = P(x = 12) + P(x = 13) + P(X = 14) \\= \binom{14}{12}(0.41)^{12}(1-0.41)^2 + \binom{14}{13}(0.41)^{13}(1-0.41)^1 + \binom{14}{14}(0.41)^{14}(1-0.41)^0\\= 0.0007 + 0.00007 + 0.000003\\= 0.000773[/tex]

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Yes, it is an unusual event due to small probability values.

Answer:

C. 7269108

D. 0689271

E. 7042351

Step-by-step explanation:

If the number is 0,1 or 2, it is a win.

Otherwise, it is a loss.

Each number is a match.

A. 8531905

Two wins(0,1), 5 losses(8,5,3,9,5)

B. 4963184

One win(1), 6 losses(4,9,6,3,8,4)

C. 7269108

Three wins(2,1,0) and four losses (7,6,9,8)

D. 0689271

Three wins (0,2,1) and four losses (6,8,9,7)

E. 7042351

Three wins (0,2,1), four losses (7,4,3,5)

F. 9094562

Two wins (0,2) and five losses (9,9,4,5,6)

Answer:

C.

D.

E.

Step-by-step explanation:

Answer:

-8 and 1

Step-by-step explanation:

the x is going by 5 and the y is going by 2

so add 5 to the x and 2 to the y

hope this help <(*__*)>

Answer:

(-7,1)

Step-by-step explanation:

(1+x/2) = -3     (-3+y/2) = -1

2(1+x/2) = -3(2)    2 (-3+y/2) = -1(2)

multiple each side by two to cancel the two's.

1+x= -6   -3+y= -2

x=-7      y= 1

Answer:(-5,0) , (-6,0)

Y= (0,30)

Step-by-step explanation:

Answer:

9 feet = Perimeter of the triangle.

Step-by-step explanation:

Here, this question is incomplete and lacks essential data. So, still we will try to figure it out. What we can learn from this question.

So, first of all it talks about perimeter. So, let's understand first, what is perimeter and how it can be calculated for a triangle.

What is Perimeter?

So, Perimeter is actually the distance or path covered by a particular 2 dimensional shape. For example, square, triangle, rectangle.

Furthermore,

In this question, we have been given s = 3 feet. We can say that it is a length of one side of a triangle and triangle must be equilateral triangle having all sides equal to one another.

Equilateral Triangle have all sides equal to one another.

Here, we s1 = 3 so, other sides would be s2 = 3 and s3 = 3

Finally, here is the formula for the calculation of Perimeter of a triangle.

P = a + b + c

where, a, b, c represents sides of the triangle.

P = 3 + 3 + 3

P = 9

Hence, the perimeter of the triangle in this question is 9 feet.

Answer:

[tex]47.36\%[/tex]

Step-by-step explanation:

The equation that governs how the insect population dies is

[tex]p' = - \mu p[/tex]

We need to solve this differential equation for p.

We separate variables to get:

[tex] \frac{p'}{p} = - \mu[/tex]

We integrate both sides to get:

[tex] \int\frac{p'}{p} dt = - \mu \int \: dt[/tex]

[tex] ln( |p| ) = - \mu \: t + ln(k) [/tex]

[tex]p = c{e}^{ \ - ut} [/tex]

If 1200 insects hatch, and only 70 remain after 6 days,

Then we have:

[tex]70 = 1200 {e}^{ - 6 \mu} [/tex]

[tex] \frac{70}{1200} = {e}^{ - 6 \mu} [/tex]

[tex] - 6 \mu = ln( \frac{7}{120} ) [/tex]

[tex] \mu = \frac{ln( \frac{7}{120} ) }{ - 6} [/tex]

[tex] \mu = 0.4736[/tex]

[tex]47.36\%[/tex]

Answer:

Expected cost = $6,750

Variance of the cost = $373,500

Step-by-step explanation:

During normal 9 work hours: average number of calls = 7.0

Cost of each call = $50

During 15 off hours:

average number of calls = 4.0

Cost of each call = $60

Let's take U as the number of calls during the normal 9 hours.

I.e, [tex] U = U_1+U_2+U_3+U_4....+ U_9[/tex]

Therefore,

[tex] E(U) = E(U_1)+E(U_2)+E(U_3)+E(U_4)....+E(U_9)[/tex]

= 7+7+7+7+7+7+7+7+7

= 63

In Poisson random variable, Variance= mean, thus:

[tex] Var(U) =Var(U_1)+Var(U_2).....+Var(U_9) [/tex]

= 7+7+7+7+7+7+7+7+7

=63

Let's take V as the number of calls during the day's remaining 15 hours.

E(V) = Var(V)

= 15(4)

=60

The expected cost and the variance of cost associated with the calls received during a 24 hour day:

The expected cost =

$50U + $60V

= $50(63) + $60(60)

= $3150 + $3600

= $6750

The variance of the cost :

= Var(50U + 60V)

= 50²Var(U) + 60²Var(V)

= 2500*63 + 3600*60

= $373,500

Therefore, the expected cost is $6,750 and the variance of the cost is $373,500

Answer:

s would be the dependent variable, and g the independent.

Step-by-step explanation:

Whatever the score is, it would depend on how many goals the team has scored.

Final answer:

The independent variable is typically the one that is manipulated, like the number of goals scored (g), and the dependent variable is the one that responds, like the team's score (S). A scatter plot can reveal patterns, and the correlation coefficient indicates the strength of the relationship. The least-squares line represents a best-fit line through the data.

Explanation:

The independent variable is typically the one that is controlled or manipulated, whereas the dependent variable is the one that responds to changes in the independent variable. In the context of a team's score (S) and the number of goals scored (g), the independent variable is usually the number of goals scored (g) because it can be controlled or affected through the team's actions. The dependent variable is the team's score (S), because it depends on the number of goals scored.

In a broader context, such as analyzing the relationship between the ranking of a state and the area of the state, the independent variable could be the ranking (since it is not influenced by the area), and the dependent variable would be the area of the state (since it could be influenced by a variety of factors, including ranking).

When creating a scatter plot, it is common to place the independent variable on the x-axis and the dependent variable on the y-axis. This scatter plot could reveal correlations or trends between the two variables. The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a number close to 0 indicates a weak relationship. The least-squares line is a regression line that minimizes the sum of the squared differences between the observed values and the values predicted by the line.

Answer:

First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:

       [tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]

Next,  apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:

       [tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]

Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.

Therefore, the final result is:

                                                  [tex]343x^6y^3z^3[/tex]

Explanation:

The expression you have to simplify is:

     [tex](7x^2yz)^3[/tex]

You have to apply two rules:

1. Power of a product

This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:

For instance:

         [tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]

Using this with the expression   [tex](7x^2yz)^3[/tex] it is:

        [tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]

In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.

2. Power of a power:

This rule states that to raise a power to a power, you must multiply the exponents.

For instance:

              [tex](a^n)^m=a^{m\times n}[/tex]

You must apply that rule to the factor [tex](x^2)^3[/tex]

That is:

        [tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]

3. Final result and description using complete sentences:

The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:

       [tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]

The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:

       [tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]

The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.

The final result is: [tex]343x^6y^3z^3[/tex]

Given Information:

Smoothing constant = α = 0.25

Initial forecast salary = F₀ = $55,000

Actual salaries = A = $60,000, $72,000, $84,500, and $96,000

Required Information:

Forecast salaries = F = ?

Answer:

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Step-by-step explanation:

The exponential smoothing model is given by

[tex]F_{n} = \alpha \cdot A_{n - 1} + (1 - \alpha ) F_{n - 1}[/tex]

Where

[tex]F_{n}[/tex] is the forecast salary for nth graduate class

α is the smoothing constant

[tex]A_{n-1}[/tex] is the actual salary of n - 1 graduate class

[tex]F_{n-1}[/tex] is the forecast salary of n - 1 graduate class

For n = 1

[tex]F_{1} = 0.25 \cdot A_0} + (1-0.25) \cdot F_{0}\\F_{1} = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_{1} = 56,250[/tex]

For n = 2

[tex]F_{2} = 0.25 \cdot A_1} + (1-0.25) \cdot F_{1}\\F_{2} = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_{2} = 60,187.5[/tex]

For n = 3

[tex]F_{3} = 0.25 \cdot A_2} + (1-0.25) \cdot F_{2}\\F_{3} = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_{3} = 66,265.625[/tex]

For n = 4

[tex]F_{4} = 0.25 \cdot A_3} + (1-0.25) \cdot F_{3}\\F_{4} = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_{4} = 73,699.218[/tex]

Therefore, the foretasted starting salaries are

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Using an exponential smoothing model with α = 0.25, we sequentially calculate the forecasted starting salary for each year, then use that to estimate the starting salary for the next graduating class.

To predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25 and an initial forecast of $55,000, we follow these steps:

By applying this model, we will obtain the predicted starting salary for the next class after performing these calculations for each given salary data point in sequence.

The ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.

To find the ratio of 3 circles to 4 triangles, we compare the number of circles to the number of triangles.

Given:

Circles = 3

Triangles = 4

The ratio of circles to triangles is expressed as 3:4. This means for every 3 circles, there are 4 triangles.

If we want to express it as a fraction, we can write it as 3/4. This implies that for every set of 3 circles, there are 4 triangles.

To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is still 3:4.

In conclusion, the ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.

The complete question is here:

What is the ratio of 3 circles to 4 triangles?

Answer:

A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Answer: The ice image, bottom left.

Step-by-step explanation:

The albedo values give information about the proportion of radiation that a given object surfaces, for example, if an object has an albedo value of 0.2, this means that the object reflects 0.2*100% = 20% of the radiation.

You usually can see that darker objects have a smaller albedo value, while clearer objects have a bigger albedo value, meaning that as clearer is the color, usually it reflects a bigger proportion of the radiation.

Here we have that the bigger albedo value is in the ice ( 0.55), so the correct image is the ice image, at the bottom left.

Answer:

a) p-hat (sampling distribution of sample proportions)

b) Symmetric

c) σ=0.058

d) Standard error

e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Step-by-step explanation:

a) This distribution is called the sampling distribution of sample proportions (p-hat).

b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.

This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.

c) The variability of this distribution, represented by the standard error, is:

[tex]\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058[/tex]

d) The formal name is Standard error.

e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:

[tex]\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667[/tex]

If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Using the Central Limit Theorem, we get that:

a) Sampling distribution of sample proportions of size 40.

b) Symmetric.

c) 0.0580.

d) Standard error.

e) It would decrease.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard erro .

For a skewed variable, we need n of 30 and greater.

For a proportion p in a sample of size n, we have that:  and standard deviation .

In this problem:

Item a:

We are working proportions, and sample of 40, thus:

Sampling distribution of sample proportions of size 40.

Item b:

Item c:

This is the standard error, thus:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.16(0.84)}{40}} = 0.0580[/tex]

It is of 0.0580.

Item d:

Item e:

The formula is:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

A similar problem is given at https://brainly.com/question/14099217

The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

Now,

Given statement is,  ''9 more than the quotient of 52 divided by 4''

What is Quotient?

A quotient is the answer a division problem. The divisor is the number of parts you divide the dividend by.

Now,

The quotient of 52 divided by 4 is,

52 ÷ 4 = 13

And, 9 more than the quotient of 52 divided by 4 is,

( 52 ÷ 4 )+ 9 = 13 + 9 = 22

Hence, The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

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To solve the expression, divide 52 by 4 to get 13, then add 9 to the quotient, resulting in the final answer of 22.

The question asks to find '9 more than the quotient of 52 divided by 4'.

First, we need to calculate the quotient of 52 divided by 4, which is done by performing the division.

So, 52 ÷ 4 equals 13. Next, we add 9 to this quotient to get the final result.

Adding 9 to 13 gives us 22.

Therefore, 9 more than the quotient of 52 divided by 4 is 22.