If the standard deviation of a data set was originally 6, and if each value in the data set was multiplied by 8.5, what would be the standard deviation of the resulting data? o a. 15 ob. 9 o c. 6 od. 51

Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Wanda's guess that the Fermat point $P$ of $\triangle ABC$ is at $P(4, 1)$ is incorrect.

The Fermat point, also known as the Torricelli point, of a triangle is the point at which the sum of its distances from the vertices is minimized. To locate the Fermat point, Wanda needs to consider the angles of the triangle. In this case, she can start by constructing the equilateral triangle $\triangle ABD$ using side $AB$ as the base. Point $D$ will be at $(16, -1)$, forming an equilateral triangle with side lengths equal to $AB$. Next, Wanda should draw the line segments connecting points $C$ and $D$, and $B$ and $C$. The intersection of these line segments will be the Fermat point $P$. By analyzing the angles and distances, Wanda can determine the correct coordinates of the Fermat point.

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The answers for the new work

Generally, using a protractor we see x to be an angle 32 degrees

Hence, we solve

since the angle in point is given by 360 and x=35

Therefore

y=360-x

y=360-32

y=328 degrees

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The measure of angle x would be 35° and the measure of angle y would be 325°

From the question, we are to determine the measures of angle x and angle y.

The measure of angle x can be determined with the aid of a protractor.

From the given diagram, we can observe that angle x is an acute angle. That is, the measure of angle x is less than 90°.

After determining the measure of angle x by using a protractor, for example, let us say the measure of angle x is 35°.

We can determine the measure of angle y by using the sum of angles at a point theorem.

Sum of angles at a point is 360°.

Thus, we can write that

x + y = 360°

Then,

35° + y = 360°

y = 360° - 35°

y = 325°

Hence, the measure of x = 35° and the y = 325°

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The expression -√(7x³)/(5x) can be simplified to -√(7x²)/√(5x), or equivalently, -(√(7x²))/(√(5x)).

To simplify the given expression, we start by simplifying the radical expressions separately.

The square root of 7x³ can be broken down as the square root of 7 multiplied by the square root of x³. The square root of x³ can be further simplified as x√x. Therefore, the expression -√(7x³) becomes -√7 * x√x.

Next, we simplify the denominator radical expression. The square root of 5x can be expressed as the square root of 5 multiplied by the square root of x. Therefore, the expression 5x simplifies to 5 * √x.

Combining the simplified expressions, we get -√7 * x√x / (5 * √x).

To further simplify, we can cancel out one √x term from the numerator and the denominator, resulting in -(√(7x²))/(√(5x)).

Therefore, the simplified form of the expression -√(7x³)/(5x) is -(√(7x²))/(√(5x)).

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Answer:

47 = m - 17

Step-by-step explanation:

I hope this helped!

Answer:

(x (x - 4) (x - 1))/(2 (x + 4))

Step-by-step explanation:

Simplify the following:

((x^2 - 16) (x^3 - 2 x^2 + x))/((2 x + 8) (x^2 + 3 x - 4))

The factors of -4 that sum to 3 are 4 and -1. So, x^2 + 3 x - 4 = (x + 4) (x - 1):

((x^2 - 16) (x^3 - 2 x^2 + x))/((x + 4) (x - 1) (2 x + 8))

Factor 2 out of 2 x + 8:

((x^2 - 16) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

x^2 - 16 = x^2 - 4^2:

((x^2 - 4^2) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):

((x - 4) (x + 4) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor x out of x^3 - 2 x^2 + x:

(x (x^2 - 2 x + 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

The factors of 1 that sum to -2 are -1 and -1. So, x^2 - 2 x + 1 = (x - 1) (x - 1):

(x (x - 1) (x - 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

(x - 1) (x - 1) = (x - 1)^2:

(x (x - 1)^2 (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

((x - 4) (x + 4) x (x - 1)^2)/(2 (x + 4) (x + 4) (x - 1)) = (x + 4)/(x + 4)×((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)):

(x (x - 4) (x - 1)^2)/(2 (x + 4) (x - 1))

Cancel terms. ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^(2 - 1))/(2 (x + 4)):

(x (x - 4) (x - 1)^(2 - 1))/(2 (x + 4))

2 - 1 = 1:

Answer: (x (x - 4) (x - 1))/(2 (x + 4))

Answer:

Step-by-step explanation:

I don't say u must have to mark my and as brainliest but if it has really helped u plz don't forget to thank me ..

Answer:

y=2/3x - 1

Step-by-step explanation:

2x-3y=3

-2x      -2x

-3y= -2x + 3

÷-3     ÷-3   ÷-3

y= -2/3 x  - 1

To find the equation of the tangent line to the graph of the given function at the point (1, 6), we need to determine the slope of the tangent line at that point.

We can find the slope by taking the derivative of the function and evaluating it at x = 1.

First, let's find the derivative of the function y = -4x^3 + 7x^2 - 9x + 12. Taking the derivative of each term, we get:

dy/dx = -12x^2 + 14x - 9

Now, substitute x = 1 into the derivative to find the slope at the point (1, 6):

m = -12(1)^2 + 14(1) - 9 = -7

The slope of the tangent line is -7. Now we can use the point-slope form of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (1, 6) and m = -7, we get:

y - 6 = -7(x - 1)

Simplifying the equation gives:

y - 6 = -7x + 7

Finally, rearranging the equation to the slope-intercept form gives:

y = -7x + 13

Therefore, the equation of the tangent line to the graph of the function at the point (1, 6) is y = -7x + 13.

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The result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

To calculate log4 57 to the nearest thousandth, we can use a scientific calculator or a logarithmic table.

Using a calculator, we can find the logarithm of 57 to the base 4 directly:

log4 57 ≈ 3.682

Therefore, the correct answer is option C: 3.682.

If you prefer to verify the result using logarithmic properties, you can do so as follows:

Let's assume log4 57 = x. This means \(4^x\) = 57.

Taking the logarithm of both sides with base 10:

log (\(4^x\)) = log 57

Using the logarithmic property log (\(a^b\)) = b \(\times\) log a:

x \(\times\) log 4 = log 57

Dividing both sides by log 4:

x = log 57 / log 4

Using a calculator to evaluate the logarithms:

x ≈ 3.682

Thus, the result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

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Answer:

The inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t)

We start by applying partial fraction decomposition to the given expression:

1/(s-1)^2 (s+1) = A/(s-1) + B/(s-1)^2 + C/(s+1)

Multiplying both sides by the denominator, we get:

1 = A(s-1)(s+1) + B(s+1) + C(s-1)^2

Substituting s=1 gives:

1 = 4C

So, C=1/4.

Substituting s=-1 gives:

1 = -4A

So, A=-1/4.

Substituting s=1 and simplifying gives:

B = 1/2.

Thus, we have:

1/(s-1)^2 (s+1) = (-1/4)/(s-1) + (1/2)/(s-1)^2 + (1/4)/(s+1)

Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get:

L^(-1){(-1/4)/(s-1)} = -e^t

L^(-1){(1/2)/(s-1)^2} = te^t

L^(-1){(1/4)/(s+1)} = (1/2)e^(-t)

Hence, the inverse Laplace transform of 1/(s-1)^2 (s+1) is e^t - te^t + e^(-t).

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Answer:

273/1000

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You divide 15 by 3 and get the answer 5

Answer:

5

Step-by-step explanation:

3 divided by 15 = 5 so Dan can buy 5 blackberries in total with his money. Pls brainliest!

Answer:

(1, 2)

(2,2)

Step-by-step explanation:

The inequality Given :

y < 5x + 2

y ≥ One-halfx + 1

We can use the values in the options to see which satisfies the inequality :

(-1, 3) ; X = - 1, y = 3

3 < 5(-1) + 2 ; 3 < - 4 (not true)

(0, 2) ; X = 0 ; y = 2

2 < 5(0) + 2 ; 2 < 2 (nor true)

2 > 1/2(0) + 1

2 > 1 (true)

Using (1, 2).; x = 1 ; y = 2

2 < 5(1) + 2 ; 2 < 7 (true)

2 > 1/2(1) + 1 ; 2 > 1.5 (true)

Using (2, 2)

y < 5x + 2

2 < 10 + 2 ; 2 < 12 (true)

y > 1/2x + 1

2 > 1/2(2) + 1 ; 2

Answer:

12

Step-by-step explanation:

5^2 + b^2 = 13^2

25 + b^2 = 169

169-25= 144

take the square root of 144

answer: 12

A group of 5 students are to be seated in 5 chairs, then the probability that James ends up sitting next to Nancy is 52

Probability:

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

According to the Question:

If everyone could sit in a chair, there are 5! = 120 ways to organize people. Now,

the number of permutations for Person A sitting in Chair 3: 4⋅3⋅1⋅2⋅1=24. And if Mr. D is sitting in chair 1, 1, 2, 3, 4, 1. Also, if Mr. D is sitting on chair 5, 4・3・2・1・1=24.

So,

120−3 24

=120−48 =52

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A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.

Given that,

100-piece batches of canned soup are produced by Company X. They estimate that there are 2% faulty soup cans in circulation.

We have to find how many of the 3%, 8%, 1%, 2%, and 7% defective can percentages in the five batches fell beyond the higher or lower control limits for the percentage of defective soup cans in the batch.

We know that,

LCL= p-3√(p(1-p)/n)

=0.02-3√(0.02(1-0.02)/100)

=-0.022

Since probability can not be negative.

LCL=0

UCL= p-3√(p(1-p)/n)

=0.02-3√(0.02(1-0.02)/100)

=0.062

Therefore. A process is said to be out of control if proportion of defective lies outside the control limits. Since 8% and 7% are outside our upper control limit (UCL) So, 2 batches are defective.

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The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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Answer:

\(sss\)

Step-by-step explanation:

Because

AB = ED ( Side)

BC = EF ( Side )

AC = DF ( Side )

So,

ABC Triangle is congruent to EDF triangle ( SSS)

Please...Can I have the brainliest?

Answer:

y ≥6

Step-by-step explanation:

The probability of getting all heads when flipping a coin four times is 1/16.

(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.

There were 16 total outcomes.

Probability going out of control

HHHH P(A) = P(getting all heads) = 1/16

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Answer:

555.37

Step-by-step explanation:

V = 4/3 πr^3

Answer:

Y = 9

Cause the Sin30 = 0.5

and 9² + x² = 18²

324 - 81 = x²

x² = 243

x = 9 √3

The answer becomes "D"

Yao Ming was 24 inches taller than Earl Boykins, as 7 feet is equal to 84 inches and 5 feet 5 inches is equal to 65 inches. Therefore, 84 - 65 = 19 inches, and Ming was 19 inches taller than Boykins.

Yao Ming, standing at 7'5" (7 feet 5 inches), was significantly taller than Earl Boykins, who was 5'5" (5 feet 5 inches) tall in the NBA in 2003. To calculate the difference in height, first convert their heights to inches: Yao Ming = (7 * 12) + 5 = 89 inches and Earl Boykins = (5 * 12) + 5 = 65 inches. Now subtract Boykins' height from Ming's: 89 - 65 = 24 inches. Yao Ming was 24 inches taller than Earl Boykins.

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Probability of least 2 pupils and no more than 1 teacher and no more than 1 administrator is 0.613

The solution to the given problem is given below. The number of ways of selecting 4 pupils out of 5 = 5C4 = 5The number of ways of selecting 2 pupils out of 5 = 5C2 = 10The number of ways of selecting 1 teacher out of 4 = 4C1 = 4The number of ways of selecting 1 administrator out of 3 = 3C1 = 3

The number of ways of selecting 4 people out of 12 = 12C4 = 495 P(at least 2 pupils and no more than 1 teacher and no more than 1 administrator) = P(2 pupils) + P(3 pupils) + P(4 pupils) = 5C2 * 4C1 * 3C1 * 4C0 + 5C3 * 4C0 * 3C1 * 4C1 + 5C4 * 4C0 * 3C0 * 4C1P(at least 2 pupils and no more than 1 teacher and no more than 1 administrator) = 15*4*3 + 10*3*4 + 1*4*1 = 180 + 120 + 4 = 304P(at least 2 pupils and no more than 1 teacher and no more than 1 administrator) = 304/495P(at least 2 pupils and no more than 1 teacher and no more than 1 administrator) = 0.613

In this way, the probability of the given situation has been calculated.

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The optimization problem for individual A is to maximize their objective function: max {7A(GA1) + 12u(A,G2)}. The Lagrangean for individual A can be written as: L(A) = 7A(GA1) + 12u(A,G2) + λ1(IA1 - DA1) + λ2(IA2 - DA2) + μ1(IA1 - pIA2) + μ2(IA2 - IA1 - IA2).

To solve for individual A's optimality conditions, we take the partial derivatives of the Lagrangean with respect to the decision variables: ∂L(A)/∂GA1 = 0, ∂L(A)/∂GA2 = 0, ∂L(A)/∂IA1 = 0, and ∂L(A)/∂IA2 = 0.

An equilibrium is defined as a set of allocations (GA1, GA2) and prices (p) such that all individuals optimize their objective functions and markets clear, i.e., the total net expenditure on purchasing contracts is zero. The equilibrium conditions that characterize the equilibrium allocations in the market for contracts are: ∑AIA1 + ∑BIB1 = 0, ∑AIA2 + ∑BIB2 = 0, and IA1 + IB1 = IA2 + IB2.

Given the utility function u(e) = ln(c), we can solve for the equilibrium price and allocations by setting the optimality conditions equal to zero and solving the resulting system of equations.

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I think its about 60 dollars