(a) if x is the sample mean young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of x centered, and what is the standard deviation of the x distribution?

Answer:

[tex]x^{2} +10x+24[/tex]

Step-by-step explanation:

Answer:

=(x+1)^2-25

Step-by-step explanation:

=x(x−4)+6(x−4)

=x^2−4x+6x−24

=x^2+2x−24

=x^2+2x+1−25

=(x+1)^2-25

[tex]64^{\text{x}} = (8^2)^{\text{x}} = 8^{2\text{x}}[/tex]

The rule used is that [tex](a^b)^c = a^{bc}[/tex] we multiply the exponents b and c.

Or we could say this

[tex]64^{\text{x}} = (4^3)^{\text{x}} = 4^{3\text{x}}[/tex]

Or,

[tex]64^{\text{x}} = (2^6)^{\text{x}} = 2^{6\text{x}}[/tex]

Therefore, we have multiple possible answers.

Step-by-step explanation:

17, 21, 22, 26, 28, 31, 33, 41, 46, 52

min: 17

Q1: 26

median: 28

Q3: 31

max: 52

Answer:

D 34.8

Step-by-step explanation:

[tex]\frac{31+36+28+52+27}{5}[/tex]

The first five terms of the given arithmetic sequence are:

1/5, 2/5, 3/5, 4/5, 1 (Fourth option)

The arithmetic sequence is given as follows,

f(n) = f(n-1) + 1/5 ............ (1)

Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.

It is already given that f(1) = 1/5 ......... (2)

f(1) is the first term of the sequence.

Now, putting n=2 in equation (1), we get,

f(2) = f(2-1) + 1/5

f(2) = f(1) + 1/5

Substitute f(1) = 1/5 from equation (2)

⇒ f(2) = 1/5 + 1/5

f(2) = 2/5

To find the third term of the arithmetic sequence, put n = 3 in equation (1)

f(3) = f(3-1) + 1/5

f(3) = f(2) + 1/5

⇒ f(3) = 2/5 + 1/5

f(3) = 3/5

Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.

∴ f(4) = f(3) + 1/5

⇒ f(4) = 3/5 + 1/5

f(4) = 4/5

Likewise, f(5) = f(4) + 1/5

⇒f(5) = 4/5 + 1/5

f(5) = 1

Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:

1/5, 2/5, 3/5, 4/5, 1

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The 90% confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

Given,

[tex]N_{1}[/tex] = 731

[tex]N_{2}[/tex] = 644

[tex]P_{1}[/tex] = 0.33

[tex]P_{2}[/tex] = 0.28

z score for 90% confidence interval = 1.645

Here, the confidence interval formula :

( [tex]P_{1} -P_{2}[/tex]) ± z [tex]\sqrt{\frac{P_{1}(1-P_{1}) }{N_{1} }+ \frac{P_{2}(1-P_{2}) }{N_{2} } }[/tex]

Substituting the values, we get

    (0.33 - 0.28) ± 1.645 [tex]\sqrt{\frac{0.33(1-0.33)}{731}+\frac{0.28(1-0.28)}{644} }[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0003024624+0.0003130435}[/tex]

=   0.05 ± 1.645 [tex]\sqrt{0.0006155059}[/tex]

=    0.05 ± 1.645 × 0.0248093914

=    0. 05 ± 0.0408114489

Confidence interval:

- 0.05 - 0.0408114489 = - 0.0908114489 ≈ - 0.0908

- 0.05 + 0.0408114489 = - 0.0091885511 ≈ - 0.0092

The confidence interval for the true difference between the population proportions is [ - 0.0908, - 0.0092]

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Each side of equilateral triangle will have the length equals to 42.7 cm.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

You should find the perimeter of the rectangle.

2P=23+23+41+41= 128 cm

The equilateral triangle will have the same perimeter of the rectangle. An equilateral triangle presents the equal three sides, thus,

128= 3L

L=128/3=42.7 cm

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Answer: 16.63 cm

Step-by-step explanation:

The length of the arc = [tex]\frac{360-130}{360}[/tex] * 2[tex]\pi[/tex]y = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y

The perimeter = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y + y + y = y([tex]\frac{23}{18}[/tex][tex]\pi[/tex] + 1 + 1) = 6.01y = 1 m

y = 16.63 cm

The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

An equation is an expression that shows the relationship between two numbers and variables.

The fact family (number family) is a group of equations that derive from a set of numbers.

Fact Family Triangle are used for Addition, Subtraction, Multiplication and Division

The fact family model that shows the relationship between the numbers 8, 7, and 15 in a triangle means that 15 is 7 more than 8.

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A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

The correlation coefficient exists as the exact measure that quantifies the power of the linear relationship between two variables in a correlation analysis. A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

A negative correlation suggests two variables that tend to move in opposite directions. A correlation coefficient of -0.8 or lower displays a strong negative relationship, while a coefficient of -0.3 or lower signifies a very weak one.

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Answer:

0 and -1

Step-by-step explanation:

Got it right on the test.

2x + 2y = 42

2w + q = 35

2w + v = 29

x + q + y - v = ?

x = 7

y = 14

w = 3

q = 29

v = 23

7 + 29 + 14 - 23 =

The answer is 27

Answer: [tex]\Large\boxed{27}[/tex]

Step-by-step explanation:

Given information converted into a mathematical statement

[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]

[tex]1)~a+b+a+b=42[/tex]

[tex]2)~c+d+c=35[/tex]

[tex]3)~c+c+e=29[/tex]

[tex]4)~a+d+b-e=\mbox{?}[/tex]

Simplify each equation

[tex]1)~2a+2b=42[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Factorize 2 out of the 1) equation

[tex]2a+2b=42[/tex]

[tex]2(a+b)=42[/tex]

Divide 2 on both sides

[tex]2(a+b)\div2=42\div2[/tex]

[tex]a+b=21[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Subtract 3) equation from the 2) equation

[tex](2c +d)-(2c+e)=(35)-(29)[/tex]

Expand the parenthesis

[tex]2c+d-2c-e=35-29[/tex]

Combine like terms

[tex]2c-2c+d-e=6[/tex]

[tex]d-e=6[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~d-e=6[/tex]

[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]

Substitute values into the 3) equation to determine the final value

  [tex](a+b)+(d-e)[/tex]

[tex]=(21)+(6)[/tex]

[tex]\Large\boxed{=27}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is 38cm.

The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).

So,

=2×(12+7)

=2×19

=38cm

The surface area of the larger sphere is equal to 636.365 square centimeters.

In this question we must estimate the surface area of the smaller sphere. By geometry we know that the volume of a sphere is directly proportional to the cube of its radius and the surface area is directly proportional to the square of radius, then the volume to surface area ratio is equal to:

V/A = k · r      (1)

Where:

Then, we can derive the following relationship between the two spheres by eliminating the proportionality constant:

V/(A · r) = V'/(A' · R)     (2)

Where:

First, we need to determine the radii of the spheres:

Larger radius

R = ∛(3 · V' / 4π)

R = ∛(3 · 647 / 4π)

R ≈ 5.365 cm

Smaller sphere

r = ∛(3 · V / 4π)

r = ∛(3 · 87 / 4π)

r ≈ 2.749 cm

Lastly, we find the surface area of the larger sphere:

A · r · V' = A' · R · V

A' = (A · r · V') / (R · V)

A' = (167 · 2.749 · 647) / (5.365 · 87)

A' = 636.365 cm²

The surface area of the larger sphere is equal to 636.365 square centimeters.

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Based on the radius of the being 4 units and the area of the equilateral triangle, the area of the shaded area is 32.85 units².

First, find the area of the triangle.

The center of a triangle divides the median into a 2:1 ratio which means that the radius can be found as:

Radius = 1/3 x Area of Equilateral triangle

4 = 1/3 x (√3/ 2)a

a can be worked out to be:

= 8√3

The area of the triangle is:

= (√3 / 4) x a²

=  (√3 / 4) x (8√3 )²

= 83.14 units ²

The area of the circle is:

= π x radius²

= 22/7 x 4 x 4

= 50.29 units²

The area of the shaded area is therefore:

= 83.14 - 50.29

= 32.85 units²

In conclusion, the area of the shaded area is 32.85 units².

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Answer:

The correct answer is the third option: y = 4x - 20

Step-by-step explanation:

To solve this problem, we should first find two points that are located along our line of best fit. We can see that the points (25,80) and (15, 40) are both located along the line. Next, we can calculate the slope using these two points.

slope = rise/run = Δy/Δx = (80-40)/(25-15) = 40/10 = 4

Therefore, the slope of the line of best fit is 4.

To find the y intercept, we can use our equation for slope and plug in one of our points.

y = mx + b

y = 4x + b

40 = 4(15) + b

40 = 60 + b

b = -20

Therefore, the y intercept is -20.

If we put both our slope and y intercept into one equation, we get:

y = mx + b

y = 4x - 20

The correct answer is the third option.

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A situation where peace is being enforced refers to a peacekeeping mission.

Peacekeeping missions refer to actions by regional and global international bodies to maintain the peace in an area.

For instance, if there has been conflict in an area, a peacekeeping force will work to prevent further violence between the parties in conflict.

An example of such missions include the United Nations Peacekeeping mission to the Democratic Republic of Congo and the African Union Peacekeeping mission to Somalia.

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Answer:

32 mm²

Step-by-step explanation:

perimeter of left rectangle = 2(9 mm + 3 mm) = 24 mm

length of right rectangle = L

perimeter of right rectangle = 2(L + 4 mm) = 2L + 8

perimeter of right rectangle = 24 mm

The perimeter of the right triangle is 2L + 8 and also 24, so 2L + 8 must equal 24. We can solve for L and find the length of the right rectangle.

2L + 8 = 24

2L = 16

L = 8

area of right triangle = length × width

area = 8 mm × 4 mm

area = 32 mm²

**Disclaimer** Hi there! I assumed the purple triangle to be the one on the right. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.

Answer: [tex]\Large\boxed{Area=32~mm^2}[/tex]

Step-by-step explanation:

Given information

Rectangle A:

Rectangle B:

Both rectangles have the same perimeter

Given formula

1) P = 2 (b + h)

2) A = b × h

Substitute values into 1) formula to find the perimeter of rectangle A

P = 2 (b + h)

P = 2 (3 + 9)

Simplify by addition

P = 2 × 12

Simplify by multiplication

P = 24 mm

Substitute values into 1) formula to find the perimeter of rectangle B

P = 2 (b + h)

24 = 2 (4 + h)

Divide 2 on both sides

24 / 2 = 2 (4 + h) / 2

12 = 4 + h

Subtract 4 on both sides

12 - 4 = 4 + h - 4

h = 8 mm

Substitute values into 2) formula

A = b × h

A = 4 × 8

Simplify by multiplication

[tex]\Large\boxed{Area=32~mm^2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x = 2

Step-by-step explanation:

note that 64 = [tex]2^{6}[/tex]

then

[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2

Using the Fundamental Counting Theorem, it is found that 60 different possible student council teams could be elected from these students.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Considering the number of options for president, vice president, treasurer and secretary the parameters are:

n1 = 5, n2 = 2, n3 = 2, n4 = 3.

Hence the number of different teams is:

N = 5 x 2 x 2 x 3 = 60.

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The ticket price which will maximize the student's council is: C. $3.10.

Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about Valley High School student council, we can logically deduce the following data:

Mathematically, the equation which model the profit is given by:

Profit = price × number of tickets sold

P(x) = (2 + 0.2x)(420 - 20x)

P(x) = 840 + 84x - 40x - 4x²

P(x) = -4x² + 44x + 840.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -44/2(-4)

Xmax = -44/-8.

Xmax = 5.5

Ticket price for maximum profit is given by:

Ticket price = 2 + 0.2x

Ticket price = 2 + 0.2(5.5)

Ticket price = $3.10.

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Answer:

14

Step-by-step explanation:

Subtract 3 from both sides to isolate g / make g the subject :

g + 3( -3 ) = 17 (-3)

g = 17-3

g = 14

Substituting this into the equation gives us :

14 + 3  = 17

17 = 17

So our final answer is 14

Hope this helped and have a good day

Answer:

m = -5/4

Step-by-step explanation:

In the slope-intercept form formula, y = mx + b, substitute 4 for x, 7 for y, and b for 12 to solve for m.

y = mx + b

7 = 4m + 12

-5 = 4m

m = -5/4

The inverse maps (x,y) onto (y,x).

Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]

The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:

X = 16:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{16 - 15}{0.4743}[/tex]

Z = 2.11

Z = 2.11 has a p-value of 0.9826.

X = 15:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15 - 15}{0.4743}[/tex]

Z = 0

Z = 0 has a p-value of 0.5.

0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.

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Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

The height of the prism is h = 19 mm

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

A regular pentagonal prism has a volume of 2,850 millimeters³

The pentagonal base has side edge labeled 12 millimeters.

And , Apothem from center to a base edge is labeled 5 millimeters

Area of a regular polygon =  (A x P) / 2

where A = side / (2 * Tan (π / N))

and , N = Number of sides, A = Apothem,  P = Perimeter

h = 2850 / 150

On simplifying , we get

h = 19 mm

Hence , the height is 19 mm

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Answer:

Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.

y'= pY-y(0)

y"=p²Y - py(0)- y'(0)

Substituting these in differential equation :

p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

Y( p²-6p+13) = -3

Y=-3/ p²-6p+13

now looking this up in a table to Laplace transformation we get:

y=-3/2.e³т sin(2t)

for the last one, find the Laplace of t∧2 . which is 2/p³

pY - y(0)+ 5Y= 2/p³

Y= 2/p³(p+5)

Taking partial fractions:

Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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Answer:

The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.

Given:                              y'= pY-y(0)

                                         y"=p²Y - py(0)- y'(0)

Putting y' and y" in differential equation :

                               p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

                                 Y( p²-6p+13) = -3

                                                    Y=-3/ p²-6p+13

by Laplace transform we get:

                                  y=-3/2.e³т sin(2t)

for the last one, find the Laplace transform of t∧2 . which is 2/p³

                                  pY - y(0)+ 5Y= 2/p³

                                                     Y= 2/p³(p+5)

Taking partial fractions:

                                Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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See below for the values of the probabilities

The complete question is added as an attachment

Write down the probability he gets 'Miss a turn'.

From the spinner, we have

Sections = 6

Miss a turn = 1

So, the probability that he gets 'Miss a turn is

P = 1/6

Write down the probability that he gets 'Go back 1 square'.

Here, we have:

Number of rows = 4

'Go back 1 square' = 4

The probability that he gets 'Go back 1 square' is

P = 'Go back 1 square'/Number of rows

This gives

P = 4/4

Evaluate

P = 1

How many of these spins are expected to be 'Go forward 3 squares'?

Here, we have

Spins = 96

From the spinner, the probability of 'Go forward 3 squares' is

P =1/6

So, the expected number is

E(x) = np

This gives

E(x) = 96 * 1/6

Evaluate

E(x) = 16

Hence, 16 spins are expected to be 'Go forward 3 squares'

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Answer:

135 is correct answer of this question

Answer:

x= -3.936 and -0.064

Step-by-step explanation:

I simplified the equation to 40u^2 +16u + 1. Then I just graphed it and found that the zeroes were -3.936 and -0.064.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Let's calculate its discriminant :

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 = 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 41 - 40 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {u}^{2} + 16u + 1 = 0[/tex]

Here, if we equate it with general equation,

[tex]\qquad \sf  \dashrightarrow \: disciminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (4 \times 4 \times 1) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (16) {}^{2} - (16) [/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(16 - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16(15)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 240[/tex]

Now, since discriminant is positive ; it has two real roots ~

The roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - b \pm \sqrt{ d } }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm \sqrt{ 240 } }{2 \times 4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 16\pm 4\sqrt{ 15 } }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ 4(- 4\pm \sqrt{ 15 }) }{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4\pm \sqrt{ 15 } }{2} [/tex]

So, the required roots are :

[tex]\qquad \sf  \dashrightarrow \: u = \dfrac{ - 4 - \sqrt{ 15 } }{2} \: \: and \: \: \dfrac{ - 4 + \sqrt{15} }{2} [/tex]

Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]