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Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let [tex]\mu[/tex] = mean breaking strength of their climbing rope

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi       {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi      {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

                         T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi

            [tex]\sigma[/tex] = population standard devaition = 10 psi

            n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO,  T.S. < -1.645   {then reject null hypothesis}

         [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]

         [tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]

         [tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]

          [tex]-0.27044 \times \sqrt{n}< -1.645[/tex]

               [tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]

                 [tex]\sqrt{n}>6.083[/tex]

                  n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.

Answer:

The slope of AB is

different than the

slope of BC.

Step-by-step explanation:

Answer: You can't. Read explanation.

Step-by-step explanation:

You can't subtract an expression from an equation. If you said something like subtract 8b-ab+7a from 3a-9ab+b that would work, but not here.

Let's just assume You mean it as 8b-ab-7a, then (3a-9ab+b)-(8b-ab-7a) = -8ab + 10a - 7b.

Hope that helped,

-sirswagger21

Answer:

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Given to a woman.

Event B: Masters degree.

21% were master’s degrees

This means that [tex]P(B) = 0.21[/tex]

Women earned 40% of masters

This means that [tex]P(A|B) = 0.4[/tex]

Probability of the degree being given to a women:

52% of 76%, 40% of 21% and 22% of 3%. So

[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]

What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?

[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman

Answer:

2x^2 + 3/2x -5

Step-by-step explanation:

f(x) = x/2 -2

g(x) = 2x^2 +x -3

f(x)+ g(x) =  x/2 -2+ 2x^2 +x -3

Combine like terms

             = 2x^2 + 3/2x -5

Answer:

The recoil velocity of the gun is [tex]0.72\,\,\frac{km}{h}[/tex]  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

[tex]5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}[/tex]

Answer:

5^15

Step-by-step explanation:

(5^10)(5^5)= 5^10+5= 5^15

Answer:

(Missing part of the question is attached)

[tex]L(x)=2x+3[/tex]

Estimates are too large.

Step-by-step explanation:

Suppose the only information we know about the function is:

[tex]f(1)=5[/tex]

where the graph of its derivative is shown in the attachment

If the function [tex]f\\[/tex] is differentiable at point [tex]x=1[/tex] , the tangent line to the graph of [tex]f[/tex] at 1 is given by the equation:

[tex]y=f(1) +f'(1)(x-1)[/tex]

So we call the linear function:

[tex]L(x)=f(1) +f'(1)(x-1)[/tex]

We know the [tex]f(1)=5[/tex] as it is given in the question, and [tex]f'(1)=2[/tex] from the graph attached. Substitute in the equation of [tex]L(x)[/tex].

[tex]L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\[/tex]

At x=1,  [tex]f'(x)[/tex] is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve [tex]f[/tex]. Thus, The estimates are too large.

Answer:

81%

Step-by-step explanation:

22+5=27

22/27

Answer:

Use the quadratic formula:

a =  1  b= -5   c= 2

x = - -5 +-sqr root (25 - 4 * 1 * 2) / 2 * 1

x =  5  +-sqr root (25 - 8) / 2

x =  5  +- sqr root (17) / 2

x1 = 5 +4.1231056256  / 2

x1 = 4.5615528128

x2 = 5 -4.1231056256  / 2

x2 = 4.5615528128

Step-by-step explanation:

Answer:

increase 40

% increase is 40 %

Step-by-step explanation:

Take the new amount and subtract the original amount

140-100 = 40

Divide by the original amount

40/100

.40

Multiply by 100 %

40%

The percent increase is 40%

Answer:

[tex]\frac{\pi x^3}{3}[/tex]

Step-by-step explanation:

[tex]V=\pi r^2h\frac{1}{3}[/tex]

[tex]V=\pi x^2x\frac{1}{3}[/tex]

[tex]V=\pi x^3\frac{1}{3}[/tex]

[tex]V=\frac{\pi x^3}{3}[/tex]

[tex]V=1.047198x^3[/tex]

Answer:

Step-by-step explanation:

1/12 pi x ^3

Question Correction

A circle is inscribed in a regular hexagon with side length 10 feet. What is the area of the shaded region? Recall that in a 30–60–90 triangle, if the shortest leg measures x units, then the longer leg measures [tex]x\sqrt{3}[/tex] units and the hypotenuse measures 2x units.

Answer:

(A)[tex](150\sqrt{3}-75\pi) $ Square Units[/tex]

Step-by-step explanation:

Area of the Shaded region =Area of Hexagon-Area of the Circle

Area of Hexagon

Length of the shorter Leg = x ft

Side Length of the Hexagon =10 feet

Perimeter of the Hexagon = 10*6 =60 feet

Apothem of the Hexagon (Length of the longer leg)

=  [tex]x\sqrt{3}[/tex] feet

[tex]=5\sqrt{3}$ feet[/tex]

[tex]\text{Area of a Regular hexagon}=\dfrac{1}{2} \times $Perimeter \times $Apothem[/tex]

[tex]=\dfrac{1}{2} \times 60 \times 5\sqrt{3}\\=150\sqrt{3}$ Square feet[/tex]

Area of Circle

The radius of the Circle = Apothem of the Hexagon [tex]=5\sqrt{3}$ feet[/tex]

Area of the Circle

[tex]=(5\sqrt{3})^2 \times \pi\\ =25 \times 3 \times \pi\\=75\pi $ Square feet[/tex]

Therefore:

Area of the Shaded region [tex]= (150\sqrt{3}-75\pi) $ Square feet[/tex]

Answer:

it’s A

Step-by-step explanation:

i took the test

Answer:

There are many. Two examples are

[tex]f(x) = x, \\f(x) = x^3[/tex]

Step-by-step explanation:

There are many examples. The simplest is

1 -

[tex]f(x) = x[/tex]

It is trivial that

[tex]\text{if \,\,\,\,} f(x) = f(y) \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]

2 -

[tex]f(x) = x^3[/tex]

That function is injective as well.

[tex]\text{if \,\,\,\,} x^3 = y^3 \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]

An example of a function that is NOT injective is

[tex]f(x) = x^2[/tex]

Notice that

[tex]f(-2) = (-2)^2 = 2^2 = 4[/tex]

Answer:

The answer is around 27.63 seconds.

Step-by-step explanation:

1 km equals 1000 meters so we have to multiply 10,500 and 1,000 which would equal 10,500,000 km. 10,500,000 divided by 380,000 which is around 27.63 seconds.

Answer:

B

The mode is 11 and 3

The Median is 10

The mean is 12

You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x))  your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]

Therefore you answer choice would be B. [tex](x+6)^4[/tex]

Answer:

I think that angles 1 and 2 are complementary

Step-by-step explanation:

option 1

plz mark brainliest!

Answer:a

Step-by-step explanation:

Answer:

176 sweets

Step-by-step explanation:

162 - 30 = 132 this finds the 3/4 before he purchased more sweets.

132 divided by 3 = 44 This finds how many thirds their are. (We do 3 not 4 because 1/4 is already gone and there are only 3rds lefts.)

44 x 4 = 176 This finds the total before he purchased more.

Hope this helps!

Answer:

I think option B

Step-by-step explanation:

Should privately-owned companies be subjected to intrusive governmental regulation and oversight?

This question will produce an unbiased answer either a yes or a no. The question is simple and not too loaded and it is direct without including an inclination to bend to a particular direction. It will produce unbiased responses in that no comment was made about the admittance to large accounting irregularities.

Answer:

The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance

Null hypothesis is accepted at 0.05 level of significance

The population proportion is equal to 0.5

Step-by-step explanation:

Step (i):-

Given random sample size ' n' = 250

Sample proportion 'p'

                                [tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]

Given Population proportion  P = 0.5

                                       Q = 1-P = 1-0.5 =0.5

Null Hypothesis : H₀ : P = 0.5

Alternative Hypothesis : H₁ : P≥ 0.5

Step(ii):-

Test statistic

               [tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]

             [tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]

            Z  = 1.2903

Level of significance α = 0.05

Z₀.₀₅ = 1.96

The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance

Null hypothesis is accepted at 0.05 level of significance

Step(iii):-

P- value

The probability of test statistic

P(Z > 1.2903) = 0.5 - A ( 1.2903)

                      = 0.5 - 0.4015

                      = 0.0985≅ 0.10

i) P- value =0.10 >  α = 0.05

null hypothesis is accepted

Conclusion:-

The population proportion is equal to 0.5

Answer:

a) The equation of Z and C is Z =K C

b) K = 2

Step-by-step explanation:

Explanation :-

Given data Z is directly proportional to C

              ⇒   Z ∝ C

               ⇒  Z = K C

The equation of relating Z and C    

               Z = K C

Given Z = 20 and C =10

              20 = K ( 10)

          ⇒ K = 2

Answer:

The probability that they have a mean height greater than 71.9 inches

P(  x⁻ ≥71.9) =  0.0022

Step-by-step explanation:

Explanation:-

Given mean of the Population μ= 70.9

Standard deviation of the Populationσ = 2.1

Given sample size 'n' =36

let x⁻ be the mean height

given  x⁻ =71.9 inches

[tex]Z=\frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z=\frac{71.9 -70.9}{\frac{2.1}{\sqrt{36} } } = \frac{1}{0.35} = 2.85[/tex]

The probability that they have a mean height greater than 71.9 inches

P(  x⁻ ≥71.9) = P(Z ≥ 2.85)

                    = 1 - P(Z≤ 2.85)

                   =  1 - ( 0.5 + A(2.85)

                   = 0.5 - A( 2.85)

                  = 0.5 - 0.4978

                  = 0.0022

The probability that they have a mean height greater than 71.9 inches

 P(  x⁻ ≥71.9) =  0.0022

Answer:

the answer is 0.0022

Step-by-step explanation:

I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.

Answer:

113.09 hope this helps

Step-by-step explanation:

Answer:

x = ±5

Step-by-step explanation:

x^2 – 9 = 16

Add 9 to each side

x^2 – 9+9 = 16+9

x^2 = 25

Take the square root of each side

sqrt(x^2) = ±sqrt(25)

x = ±5

Answer:

[tex]x = 5 \: \: \: or \: \: x = - 5[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 9 = 16 \\ {x}^{2} = 16 + 9 \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = 5 \\ x = - 5[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = [tex]x^2+7[/tex]

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = [tex]x^2+7[/tex]

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

Answer:The point from which circle is drawn is called center of circle.

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...

Answer:

the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.

Step-by-step explanation:

With the statement we can make a system of 2x2 equations, where:

"x" is the area of the first field

"y" is the area of the second field

However,

x + y = 56 => x = 56 - y

3/4 * x + 2/3 * y = 40

replacing we have:

3/4 * (56 - y) + 2/3 * y = 40

42 - 3/4 * y + 2/3 * y = 40

-0.0833 * y = 40 - 42

y = -2 / -0.0833

y = 24

now for x:

 x = 56 - 24

x = 32

This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.