Solve for X. Round to the nearest tenth of a degree, if necessary.
7.9
4.1
R
S.

Answer:

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Step-by-step explanation:

A manufacturer considers his production process to be out of control when defects exceed 3%.

At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So

[tex]H_0: p \leq 0.03[/tex]

At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So

[tex]H_1: p > 0.03[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis

This means that [tex]\mu = 0.03, \sigma = \sqrt{0.03*0.97}[/tex]

In a random sample of 100 items, the defect rate is 4%.

This means that [tex]n = 100, X = 0.04[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}[/tex]

[tex]z = 0.59[/tex]

P-value of the test

The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.

Looking at the z-table, z = 0.59 has a p-value of 0.7224

1 - 0.7224 = 0.2776

The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.

Answer:

Option a.

Step-by-step explanation:

By looking at the options, we can assume that the function y(x) is something like:

[tex]y = \sqrt{4 + a*x^2}[/tex]

[tex]y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }[/tex]

such that, y(0) = √4 = 2, as expected.

Now, we want to have:

[tex]y' = \frac{x*y}{2 + x^2}[/tex]

replacing y' and y we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

Now we can try to solve this for "a".

[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]

If we multiply both sides by y(x), we get:

[tex]\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}[/tex]

[tex]a*x = \frac{x*(4 + a*x^2)}{2 + x^2}[/tex]

We can remove the x factor in both numerators if we divide both sides by x, so we get:

[tex]a = \frac{4 + a*x^2}{2 + x^2}[/tex]

Now we just need to isolate "a"

[tex]a*(2 + x^2) = 4 + a*x^2[/tex]

[tex]2*a + a*x^2 = 4 + a*x^2[/tex]

Now we can subtract a*x^2 in both sides to get:

[tex]2*a = 4\\a = 4/2 = 2[/tex]

Then the solution is:

[tex]y = \sqrt{4 + 2*x^2}[/tex]

The correct option is option a.

Answer:

13.5 pounds

Step-by-step explanation:

90% of 15 is 13.5 or if you need to round then 14 pounds of lettuce

Answer:

(-2 -3)

Step-by-step explanation:

_____________________

Answer:

10.44cm lon

Step-by-step explanation:

Given data

Height of house= 10cm

Distance of ladder from wall= 3cm

We can apply the Pythagoras theorem to get the length of the ladder

Also, the length of the ladder is the hypothenuse

z^2= x^2+y^2

z^2= 10^2+ 3^2

z^2= 100+9

z^2= 109

square both sides

z= √109

z= 10.44cm

Hence the ladder is 10.44cm long

Answer:

53

Step-by-step explanation:

848 students/16 buses=53 students per bus

Answer:

4p +2

Step-by-step explanation:

(2p + 1)(2)

Distribute

2p * 2 + 1*2

4p +2

Answer:

4p+2

Step-by-step explanation:

See the steps below:)

Answer: 121.5 ft^2

Step-by-step explanation:

Area= L x W

12.8 X 9.5

= 121.6

Answer:

121.50

Step-by-step explanation:

Let x be the earnings

2x+10 = 253

Subtract 10 from each side

2x+10-10 = 253-10

2x = 243

Divide by 2

2x/2 = 243/2

x = 121.50

Answer:

There are 35 of each color.

Step-by-step explanation:

If the number of each color is the same  there are 140 / 4 = 35 balloons of each color.

Answer:

the answer to the question is A.Rs.648.67

Answer:

1/8 miles

Step-by-step explanation:

You have to subtract [tex]\frac{3}{4}- \frac{5}{8}[/tex]  for the answer.

First, you gotta make 3/4 have a common denominator.

To do this multiply 3/4 by 2/2 (2/2 equals one, so value isn't changed.)

and you get 6/8.

Then you can subtract 6/8 - 5/8 to get 1/8 miles.

And there's no need to simplify 1/8.

Answer:

124 students

Step-by-step explanation:

Girls participating in the exercise

4/15 x 285 = 76

Boys participating in the exercise

3/20 x 320 = 48

Total students participating

76 + 48 = 124

Answer:

4

Step-by-step explanation:

go on the x-axis where you see 8

go up until you get to the line

go toward the y-axis to the left and read ( it said 4)

Answer:

B=23.19

Step-by-step explanation:

First, find the last side of the triangle using the Pythagorean theorem.

[tex]a^{2} +b^{2} =c^{2} \\21^{2} +9^{2} =c^{2} \\441+81=c^{2} \\\sqrt[3]{58}=c[/tex]

Then, find the missing angle, lets name it B.

The angle B can be found using the inverse sine function.

B=arcsin(opp/hyp)

[tex]B=arcsin(\frac{9}{\sqrt[3]{58} } )\\B=23.19[/tex]

Answer: hi your question is incomplete below is the complete question

Use the Divergence Theorem to calculate the surface integral S F dS   with F x y z = , , and S is a sphere centered at the origin with a radius of 2. Confirm your answer by computing the surface integral

answer : surface integral = 384/5 π

Step-by-step explanation:

Representing  the vector field as

F ( x, y , z ) = ( a^3 + y^3 ) + ( y^3 + z^3 ) + ( Z^3 + x^3 ) k

assuming the sphere ( s) with radius = 2 be centered at Origin of the vector field.

Hence the divergence will be represented as :

Attached below is the detailed solution

Answer:

B

Step-by-step explanation: Net worth is the total assets minus total liabilities of an individual or entity.

9514 1404 393

Answer:

Step-by-step explanation:

The only given angle is between the two given sides, so the Law of Cosines must be used to find the side opposite the angle. It tells you ...

  e² = d²+f² -2df·cos(E)

  e² = 7² +6² -2·7·6·cos(95°) ≈ 92.321082

  e ≈ 9.608

The remaining angles can be found from the law of sines.

  sin(D)/d = sin(E)/e

  D = arcsin(d/e·sin(E)) ≈ arcsin(7/9.608·sin(95°)) ≈ 46.5°

  F = 180° -95° -46.5° = 38.5°

Answer:

6 3/4 cm³

Step-by-step explanation:

I'm assuming value means volume, so if I'm wrong, let me know ;).

To find volume, you multiply length x height x width. So you multiply 2 1/4 three times.

Convert 2 1/4 to an improper fraction.

2 1/4 = 9/4

9   x   3        27

--        --     =

4   x    1        4

Now convert 27/4 to a mixed fraction.

27/4 = 6 3/4

So the volume of the cube is 6 3/4 cm³.

---

hope it helps

35 is the answer

have a wonderful day

Answer:

The statement is true for any value of x

Step-by-step explanation:

see the steps below:)

Answer:

No solution

Step-by-step explanation:

just trust me

Answer:

Length = 5 feet

Breadth = (5/3) feet

Height(depth) = 2 feet

Volume of the entire tank = Length x Breadth x Height  

                                         = [tex]5 \times \frac{5}{3} \times2 = \frac{50}{3}[/tex]   ----------(1)

Water is filled upto a height of (1/3) feet

Volume of water in the tank = Length x Breadth x Height  

                                           = [tex]5 \times \frac{5}{3} \times \frac{1}{3} = \frac{25}{9}[/tex]     -------------(2)

Volume of space needed to be filled = (1) - (2)

                                                         = [tex]\frac{50}{3} -\frac{25}{9} = \frac{150-25}{9} = \frac{125}{9} cubic feet[/tex]

                                           OR

Height of tank needed to be filled = 2 - (1/3) = (5/3) feet

Volume of space =  Length x Breadth x Height of empty tank

                           =  [tex]5 \times \frac{5}{3} \times \frac{5}{3} = \frac{125}{9} cubic \ feet[/tex]

=======================================

Explanation:

As mentioned earlier (in a previous post) the triangle with sides 2,5,7 is not a right triangle. So we can rule out choice A.

For choice B, we have a = 6, b = 8, c = 10, and that leads to...

a^2+b^2 = c^2

6^2+8^2 = 10^2

36+64 = 100

100 = 100

The true equation at the end means the beginning equation is true as well for those a,b,c values. Therefore, we have a right triangle and the answer is choice B

Choices C and D are similar to choice A. They make a^2+b^2 = c^2 to be false.

Answer:

2.15cm^3

Step-by-step explanation:

V = Mass / Density

21.93g / 10.2 g/cm^3

2.15cm^3

Answer:

A, B, D, E, F

Step-by-step explanation:

48/64 can be simplified into all of them except C

Answer:

Step-by-step explanation:

since they are in continued proportion the ratio will be

3/8=9/x

do cross multiplication

8*9=3*x

72=3x

72/3=x

24=x

therefore x =24

Answer:

ans is 24

Step-by-step explanation:

soln

the 3 8 9 and x are in proportion

so 3/8=9/x

3x=72

x=72/3

x=24