In a math class with 28 students, a test was given the same day that an assignment
was due. There were 18 students who passed the test and 23 students who completed
the assignment. There were 16 students who passed the test and also completed the
assignment. What is the probability that a student who passed the test did not
complete the homework?

The calculated depth of the well in feet is 402.5 feet

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

Time, t = 5 seconds

The depth of the well in feet is calculated as

d = 1/2gt²

substitute the known values in the above equation, so, we have the following representation

d = 1/2 * 32.2 * 5²

Evaluate

d = 402.5

Hence, the depth is 402.5 feet

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The solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

To solve the given differential equation y''(t) = 1 - t^17 with the initial condition y(1) = 12, we can integrate the equation twice.

Integrating the equation once will give us y'(t):

y'(t) = ∫(1 - t^17) dt

y'(t) = t - (1/18)t^18 + C₁

Now, we need to apply the initial condition y(1) = 12 to determine the value of the constant C₁:

12 = 1 - (1/18) + C₁

C₁ = 12 + (1/18) - 1

C₁ = 217/18

Next, we integrate y'(t) to find y(t):

y(t) = ∫(t - (1/18)t^18 + 217/18) dt

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + C₂

Finally, we apply the initial condition y(1) = 12 to determine the value of the constant C₂:

12 = (1/2) - (1/342) + (217/18) + C₂

C₂ = 12 - (1/2) + (1/342) - (217/18)

C₂ = (20619 - 1 + 6 - 819)/(342)

C₂ = 19805/342

Therefore, the solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

Answer:

(2x+1) (2x-7)

Step-by-step explanation:

Multiply the coefficient of the first term by the constant   4 • -7 = -28

Find two factors of  -28  whose sum equals the coefficient of the middle term, which is   -12

(  -28    +    1    =    -27  

     -14    +    2    =    -12  )

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  2  

                    4x2 - 14x + 2x - 7

Add up the first 2 terms, pulling out like factors :

                   2x • (2x-7)

             Add up the last 2 terms, pulling out common factors :

                    1 • (2x-7)

Add up the four terms :

                   (2x+1)  •  (2x-7)

The distance of AB is 2√5.

Given that the point A is (2,-1) and point B is (4,3).

The distance formula gives us the shortest distance between the given two points in a plane of two dimensional.

The given points is point A(x₁,y₁)=(2,-1) and point B (x₂,y₂)=(4,3).

Now, we will use the distance formula to calculate the distance that is D=√(x₂-x₁)²+(y₂-y₁)².

Further, we will substitute the given values in the above formula, we get

D=√(4-2)²+(3-(-1))²

D=√2²+(3+1)²

D=√2²+4²

D=√4+16

D=√20

D=2√5

Hence, the distance of AB from the given points point A is (2,-1) and point B is (4,3) is 2√5.

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Answer:

Delaney  solve for X by isolating it,  or getting it by it self

Step-by-step explanation:

5x−2(x+1)=1/4 (distribute the 2)

5x-2x - 2 = 1/4  (subtract 2x from 5x)

3x -2 +2 = 1/4 +2 (add 2 to both sides)

3x = 2_1/4  (put 2 &  1/4 together)

3x = 9/4 (convert 2_1/4 to  9/4)

\(\frac{1}{3}\)*3*x =  \(\frac{1}{3}\)*\(\frac{9}{4}\)  ( mutilply both sides by  1/3)

X = 3/4   (cross multiply )

There you go

X = \(\frac{3}{4}\)

Answer:

\(\huge\boxed{\bf\:x = \frac{3}{4}}\)

Step-by-step explanation:

\(5x - 2(x+1)=\frac{1}{4}\)

Use the distributive property for 2(x + 1).

\(5x - 2x - 2= \frac{1}{4}\)

Subtract 2x from 5x.

\(3x - 2= \frac{1}{4}\)

Bring 2 to the right hand side of the equation .

\(3x = \frac{1}{4} + 2\)

Add 1/4 & 2.

\(3x = \frac{1}{4} + \frac{8}{4} \: \: [LCM = 4]\\3x = \frac{9}{4}\)

Now, bring 3 to the right hand side of the equation .

\(x = \frac{9}{4} \times \frac{1}{3}\\x = \frac{9}{12}\\\boxed{\bf\:x = \frac{3}{4}}\)  

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Based on the statistical analysis, replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections.

To test this hypothesis, we will use a paired t-test, which compares the means of two sets of paired data. The null hypothesis is that there is no significant difference between the mean accident rates before and after installing roundabouts, while the alternative hypothesis is that the mean accident rate after installing roundabouts is significantly lower than before.

Here are the steps to conduct the paired t-test:

Using the given data, the differences between the accident rates before and after installing roundabouts are:

-0.6, 0.2, 0.6, -0.1, 0

The mean of the differences is 0.02, and the standard deviation is 0.43. There are 5 paired observations, so the degrees of freedom are 4.

Using the formula, we get:

t = 0.02 / (0.43 / √(5)) = 0.14

The critical t-value at a 0.05 level of significance and 4 degrees of freedom is 2.776 from a t-distribution table.

Since the calculated t-value (0.14) is less than the critical t-value (2.776), we fail to reject the null hypothesis. Therefore, we can conclude that replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

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Answer:

87

Step-by-step explanation:

Answer:

x=91

Step-by-step explanation:

All angles of a quadrilateral can add up to 360.

360-87=273

273/3=91

x=91

I am not to sure, but I think this is the answer.

Given information: Marginal-cost function is dc/dq = 1/3-1/2√3q, c(0) = 100To find: The cost of producing 300 unit.

To find the cost of producing 300 units, we need to integrate the marginal-cost function.∫dc/dq dq = ∫(1/3 - 1/2√3q)dqOn integrating, we get,c(q) = q/3 - √3q²/4 + C, where C is the constant of integration.To find the value of C, we will use the given condition: c(0) = 100c(0) = 0/3 - √3(0)²/4 + C = 100C = 100So, the cost function is:c(q) = q/3 - √3q²/4 + 100The cost of producing 300 units will be:c(300) = (300/3) - √3(300)²/4 + 100= 100 - 225√3 + 300= 400 - 225√3Therefore, the cost of producing 300 units is 400 - 225√3. Answer: 400 - 225√3.

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The correct answer of the marginal-cost function for a product is cost of producing 300 units is  100.

The marginal-cost function for a product is dc/dq = 1/3-1/2√3q.

Cost of producing 300 unit is to be determined.

The marginal-cost function is given as,dc/dq = 1/3 - (1/2) √3q

Integrate dc/dq to get the cost function c(q),c(q) = ∫dc/dq dqc(q) = ∫(1/3 - (1/2) √3q) dqc(q) = (1/3)q - (1/4) √3q^2 + k

where k is the constant of integration.

To find the value of k, use the given condition that c(0) = 100c(q) = (1/3)q - (1/4) √3q^2 + 100When q = 0,c(0) = (1/3)(0) - (1/4) √3(0)^2 + 100c(0) = 100

Therefore, k = 100

Thus, the cost function isc(q) = (1/3)q - (1/4) √3q^2 + 100

The cost of producing 300 units is

c(300)c(300) = (1/3)(300) - (1/4) √3(300)^2 + 100c(300) = 100

Therefore, the cost of producing 300 units is 100 units.

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A summary of data that shows the number of observations in each of several non-overlapping bins is called a histogram.

A histogram is a graph used to visualize the distribution of a dataset. The x-axis represents the different ranges of the data being observed, which are usually called bins. The y-axis displays the frequency or count of data values that fall into each bin.

The shape of a histogram can provide valuable insights into the underlying data distribution. For example, if a histogram is bell-shaped, it indicates that the data follows a normal distribution, which is a symmetrical distribution with most values clustered around the mean. If a histogram is skewed to the left, the data has a long tail on the left-hand side and is concentrated on the right-hand side. If a histogram is skewed to the right, the data has a long tail on the right-hand side and is concentrated on the left-hand side. In conclusion, a histogram is a useful tool for summarizing data and providing insights into its distribution.

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Answer: 4,322.883

Step-by-step explanation:

Assuming that the interest rate is per year:

4,322.883

By using the formula for variance

\(varX= m*(n*(m-1)/m^n)(1 - n(m-1)/(m^n-1))\)

To compute varX:

we first need to find the expected value of X, denoted as E(X).

We can approach this by using the linearity of expectation, which states that the expected value of the sum of random variables is equal to the sum of their individual expected values.

Let's define a random variable Xi as the number of bins with exactly one ball. Then, we have:

\(X = X1 + X2 + ... + Xm\)

where m is the total number of bins.

By the definition of Xi, we know that Xi can only take on values between 0 and 1, since a bin can either have exactly one ball (Xi = 1) or not (Xi = 0).

To find E(Xi), we can use the probability of Xi being 1. The probability that a specific bin has exactly one ball is given by:

\(P(Xi = 1) = (n choose 1) * ((m-1) choose (n-1)) / (m choose n)\)

The first term (n choose 1) represents the number of ways to choose one ball out of n balls to put into the bin. The second term ((m-1) choose (n-1)) represents the number of ways to choose (n-1) balls out of the remaining (m-1) bins. Dividing by (m choose n) gives us the probability that exactly one bin has one ball.

Therefore, we have:

E(Xi) = P(Xi = 1) * 1 + P(Xi = 0) * 0
     = P(Xi = 1)=\((n choose 1) * ((m-1) choose (n-1)) / (m choose n)\)
Using the linearity of expectation, we can find E(X) as:

E(X) = E(X1) + E(X2) + ... + E(Xm)
    = \(m * (n choose 1) * ((m-1) choose (n-1)) / (m choose n)\)

Now, to find varX, we need to find the variance of Xi and use the formula for variance of a sum of random variables.

The variance of Xi can be found as:

Var(Xi) = E(Xi^2) - (E(Xi))^2

Since Xi can only take on values 0 or 1, we have:

E(Xi^2) =\(0^2 * P(Xi = 0) + 1^2 * P(Xi = 1) = P(Xi = 1)\)

Therefore, we have:

Var(Xi) = P(Xi = 1) - (E(Xi))^2
      = \(m*(n*(m-1)/m^n) + m*(m-1)(n(m-1)/m^n)^2 - (mn(m-1)/m^n)^2\)

Using the formula for variance of a sum of random variables, we have:

varX = Var(X1 + X2 + ... + Xm)
    = Var(X1) + Var(X2) + ... + Var(Xm)      (since Xi's are independent)
    = \(m*(n*(m-1)/m^n)(1 - n(m-1)/(m^n-1))\)

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The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.

It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.

Since the given inequality is;

( 29 / 289z ) < ( 16 / 161 ) z

By cross multiplication; we have;

161 × 29 < ( 16z × 289z )

( 161 × 29 ) / ( 16 × 289 ) < z²

1.00973183 < z²

Therefore;

1.00485413 < z. OR. -1.00485413 > z.

Ultimately, z < - 1.00485413 OR z > 1.00485413.

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The correct answer is C. A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.

Explanation:

The purpose of an equation is to show the equivalence between two mathematical expressions. This implies in the equation "–2 + 4x = y" the value of y should always be the same that -2 + 4x. Additionally, if a table is created with different values of x and y the equivalence should always be true. This occurs only in the third option.

   x                 y

   5                -18    

   0                -2

   3                 10

First row:

-2 + 4 (5) = y  (5 is the value of x which is first multyply by 4)

-2 + 20 = -18 (value of y in the table)

Second row:

-2 + 4 (0) y

-2 + 0 = -2

Third row:

-2 + 4 (3) = y

-2 + 12 = 10

Answer:

it is c

Step-by-step explanation:

Step-by-step explanation:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.

In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.

Solving this equation for x, we get:

(2x-8) + (3x-7) = 180

5x - 15 = 180

5x = 195

x = 39

Substituting this value of x into the expressions for the two interior angles, we find that their measures are:

(2x-8) = (2*39 - 8) = 70 degrees

(3x-7) = (3*39 - 7) = 110 degrees

So, the measure of each of these angles is 70 degrees and 110 degrees.

Answer:

1350m

Step-by-step explanation:

Let the distance ran by Denise, Farah and Elaine be D, F and E meters respectively.

From the given information,

D= ⅔(E +F) -----(1)

E= ½(D +F) -----(2)

Let's get rid of the fraction so the equations are much easier to work with.

From (1):

3D= 2(E +F) (Multiply both sides by 3)

3D= 2E +2F -----(3) (Expand)

From (2):

2E= D +F -----(4)

Substitute (4) into (3):

3D= D +F +2F

3D -D= 3F

2D= 3F

Given that Farah ran 360m, F= 360.

2D= 3(360)

2D= 1080

D= 1080 ÷2

D= 540

2E= D +F

2E= 540 +360

2E= 900

E= 900 ÷2

E= 450

Total distance the 3 girls ran

= D +F +E

= 540 +360 +450

= 1350m

Alternatively, you could start by substituting F= 360 to equations (1) and (2).

Answer:

2.6 m

Step-by-step explanation:

In the attached diagram

Consider Triangle ABC

\(\sin36^\circ =\dfrac{|BC|}{7.8} \\|BC|=7.8*\sin36^\circ\\|BC|=4.5847$ m\)

Our goal is to determine the distance of Jen (at point A) to Holly (at Point D).

In Triangle ABC

\(\cos 36^\circ =\dfrac{|AC|}{7.8} \\|AC|=7.8*\cos36^\circ\\|AC|=6.3103$ m\)

In Triangle BDC

Applying Pythagoras Theorem

\(|BD|^2=|BC|^2+|CD|^2\\5.9^2=4.5847^2+|CD|^2\\|CD|^2=5.9^2-4.5847^2\\|CD|^2=13.7905\\|CD|=\sqrt{13.7905}=3.7136$ m\)

Now, |AC|=|AD|+|DC|

6.3103=|AD|+3.7136

|AD|=6.3103-3.7136

|AD|=2.5967

|AD|=2.6m (correct to the nearest tenth of a metre)

The distance of Jen from Holly is 2.6m.

Answer:

The answer is C

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

-4^2-4(7)(-8) = 240

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Answer:

1/2 of the class

give brainliest if it helps

The function is :\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

To find y as a function of x, we need to solve the differential equation:

\(y′′′ − 17y′′ + 72y′ = 168e^x\)

Step 1: Find the characteristic equation

\(r^3 - 17r^2 + 72r = 0\)

Factor out r:

\(r(r^2 - 17r + 72) = 0\)

Factor the quadratic:

r(r - 8)(r - 9) = 0

So the roots are:

r₁ = 0, r₂ = 8, r₃ = 9

Step 2: Find the general solution

The general solution will be of the form:

\(y(x) = C1 + C2e^8x + C3e^9x + y_p(x)\)

where y_p(x) is a particular solution to the non-homogeneous equation.

Step 3: Find the particular solution

We can use the method of undetermined coefficients to find a particular solution. Since the right-hand side is an exponential function, we can guess that the particular solution is also an exponential function:

\(y_p(x) = A e^x\)

\(y_p′(x) = A e^x\)

\(y_p′′(x) = A e^x\)

\(y_p′′′(x) = A e^x\)

Substituting into the differential equation:

\(A e^x - 17A e^x + 72A e^x = 168 e^x\)

Simplifying:

\(56A e^x = 168 e^x\)

A = 3

So the particular solution is:

\(y_p(x) = 3 e^x\)

Step 4: Find the constants using initial conditions

y(0) = C₁ + C₂ + C₃ + 3 = 16

y′(0) = 8C₂ + 9C₃ + 3 = 23

\(y′′(0) = 8^2 C2 + 9^2 C3 = 24\)

Solving for the constants, we get:

C₁ = 10, C₂ = 7/8, C₃ = 97/72

Step 5: Write the final solution

Substituting the constants and the particular solution into the general solution, we get:

\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

So the function y(x) is:

\(y(x) = 10 + (7/8) e^8x + (97/72) e^9x + 3 e^x\)

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Answer:

-2

Step-by-step explanation:

Answer:For the first one i only know the answer to the division problem i don't know how to do the box things but the division problem is 2,867 divided by 61=47 with no remainder.

           The second one is 3,353 divided by 75 =40 R 4

Answer:

x>2

Step-by-step explanation:

10(1-x) <-2x-6

10-10x<-2x-6

10-10x +2x<-6

-8x<-6-10

-8x<-16 (divide both sides)

x>2

Answer:

x>2

Step-by-step explanation:

1) 10-10x<-2x-6

2)10-10x-10<-2x-6-10

3) -10x<-2x-16

4)-10x+2x<-2x-16+2x

5) -8x<-16

6) (-8x)(-1)>(-16)(-1)

7) 8x>16

8) x>2

Answer:

\( \frac{x + 2}{x {}^{3} + 8} \)

Step-by-step explanation:

\( \frac{ \frac{1}{x} + \frac{2}{x {}^{2} } }{x + \frac{8}{x {}^{2} } } \)

\( \frac{ \frac{x + 2}{x {}^{2} } }{ \frac{x {}^{3} + 8 }{x {}^{2} } } \)

\( \frac{x + 2}{x {}^{3} + 8 } \)

The the 21st, 26th, 65th, and 75th percentiles are 19.45, 21.7, 27.85, and 29.50.

Here, n=8

P21=(21(n+1)100)th value of the observation

=(21⋅9/100)th value of the observation

=1st observation +0.89[2nd-1st]

=15+0.89[20-15

= 19.45

P26 = (26(n+1)100)th value of the observation

=(26⋅9/100)th value of the observation

=2nd observation +0.34[3rd-2nd]

=20+0.34[25-20]

=20+0.34(5)

= 21.7

P65= (65(n+1)100)th value of the observation

=(65⋅9/100)th value of the observation

=5th observation +0.85[6th-5th]

=27+0.85[28-27

= 27.85

P75 = (75(n+1)100)th value of the observation

=(75⋅9/100)th value of the observation

6th observation +0.75[7th-6th]

=28+0.75[30-28]

= 28 + 1.50

= 29.50

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The new man's age would be 525, however the standard deviation would remain the same.

The Standard Deviation measures how evenly distributed numbers are. It has the sign (a Greek letter sigma) and the calculation is simple: it's the variance as a square root.

The average national test score is 500, for a standard deviation = 100.

Each score has been boosted by 25 points.

Let y = x + 25

where x is the old mean & y is the new score

E(x) = 500  and standard deviation (x) = 100 (given)

E(y) = E(x + 25)

     = E(x) + 25

     = 500 + 25

     = 525

Variable (y) = Variable (x + 25)

                  = Variable (x)

As, √variance y = √variance x

standard deviation(y) = standard deviation(x)

                                   = 100

Therefore, the new standard deviation is same as the old one.

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Answer:

x = 3.25 m

Step-by-step explanation:

First, find the height of the triangle using sin31:

sin 31 = h/9 ---> h = 9sin31 = 4.64 m

Next, we can now solve for x using tan55:

tan 55 = h/x --> x = (4.64 m)/(tan 55) = 3.25 m

Answer: (−2,−6) Focus: (−2,−234) Axis of Symmetry: x=−2 Directrix: y=−254x

Step-by-step explanation: it different ways to answer so i just give you all of them

Answer:

9 = -254x

Step-by-step explanation:

I did the test

Hope this helps :)