Which exponential function has an x-intercept

The diameters of bearings used in an aircraft landing gear assembly have a standard deviation of ???? = 0.0020 cm. A random samp

vovikov84 [41]

Answer:

(a) We conclude after testing that mean diameter is 8.2500 cm.

(b) P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) 95% confidence interval on the mean diameter = [8.2525 , 8.2545]

Step-by-step explanation:

We are given with the population standard deviation, $\sigma$ = 0.0020 cm

Sample Mean, Xbar = 8.2535 cm and Sample size, n = 15

(a) Let Null Hypothesis, $H_0$ : Mean Diameter, $\mu$ = 8.2500 cm

Alternate Hypothesis, $H_1$ : Mean Diameter, $\mu$ $\neq$ 8.2500 cm{Given two sided}

So, Test Statistics for testing this hypothesis is given by;

$\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ follows Standard Normal distribution

After putting each value, Test Statistics = $\frac{8.2535-8.2500}{\frac{0.0020}{\sqrt{15} } }$ = 6.778

Now we are given with the level of significance of 5% and at this level of significance our z score has a value of 1.96 as it is two sided alternative.

Since our test statistics does not lie in the rejection region{value smaller than 1.96} as 6.778>1.96 so we have sufficient evidence to accept null hypothesis and conclude that the mean diameter is 8.2500 cm.

(b) P-value is the exact % where test statistics lie.

For calculating P-value , our test statistics has a value of 6.778

So, P(Z > 6.778) = Since in the Z table the highest value for test statistics is given as 4.4172 and our test statistics has value higher than this so we conclude that P - value is smaller than 2 x 0.0005% { Here 2 is multiplied with the % value of 4.4172 because of two sided alternative hypothesis}

Hence P-value of test = 2 x 0.0005% = 1 x $10^{-5}$ .

(c) For constructing Two-sided confidence interval we know that:

Probability(-1.96 < N(0,1) < 1.96) = 0.95 { This indicates that at 5% level of significance our Z score will lie between area of -1.96 to 1.96.

P(-1.96 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96\frac{\sigma}{\sqrt{n} }$ < $Xbar - \mu$ < $1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

P( $-Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $-\mu$ < $1.96\frac{\sigma}{\sqrt{n} }-Xbar$ ) = 0.95

P( $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ < $\mu$ < $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ) = 0.95

So, 95% confidence interval for $\mu$ = [ $Xbar-1.96\frac{\sigma}{\sqrt{n} }$ , $Xbar+1.96\frac{\sigma}{\sqrt{n} }$ ]

= [ $8.2535-1.96\frac{0.0020}{\sqrt{15} }$ , $8.2535+1.96\frac{0.0020}{\sqrt{15} }$ ]

= [8.2525 , 8.2545]

Here $\mu$ = mean diameter.

Therefore, 95% two-sided confidence interval on the mean diameter

= [8.2525 , 8.2545] .

6 0

3 years ago

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What is the greatest common factor in this???

Elza [17]

I believe the greatest common factor would be 1 because there are no other multiples that are the same. 1•21=21, and1•40=40

6 0

4 years ago

Complete the following statement of congruence: MON~= .

AlexFokin [52]

Answer:

C. RTS

Step-by-step explanation:

When two triangles are congruent, they will have congruent vertices, like each vertex has a partner.

Take a look at the shape of the triangle.

If you look at the triangle on the right, you can see it is almost like a right triangle.

"R" is at the right angle. "S" is on the short side and "T" is on the long side.

In the triangle on the left, "M" is at the right angle. "N" is on the short side and "O" is on the long side.

Thus, the pairs of congruent angles are:

M ≅ R

O ≅ T

N ≅ S

When you write the statement of congruence between triangles, order the letters by their congruent pair.

MON ≅ RTS

8 0

3 years ago

You are choosing a new cell phone. The screen on your current phone is 10.8 cm high and 6.1 cm wide. The screen on the new phone

Leto [7]

Answer:

19.68 cm^2

Step-by-step explanation:

Area of Current Phone

First, find the area of the current phone. We can assume the screen is rectangular. The area of a rectangle can be found using:

a=l*w

We know the length is 10.8, and the width is 6.1, so we can substitute them in

a=10.8*6.1

a=65.88

Current Phone: 65.88 cm^2

Area of New Phone

Find the area of the new phone.

a=l*w

We know the length is 12.4, and the width is 6.9, so we can substitute them in

a=12.4*6.9

a=85.56

New Phone: 85.56 cm^2

Difference

We want to find how much larger the new phone screen is. To do this, find the difference between the new phone area, and the current phone area.

new phone - current phone

85.56-65.88

19.68

The new phone screen is 19.68 cm^2 larger than the current phone screen

7 0

3 years ago

Read 2 more answers

Please help asap 20 pts

eduard

The discriminant explains how many solutions the quadratic function has. It is found using this formula:

$b^2-4ac$

Using the formula, there are three rules. Let's say the discriminant=d:
d<0 - No solution ø
d=0 -ONLY 1 solution
d>0 -2 solutions

In the following graph, there are no solutions as the graph does not hit the x-axis at any point. Thereafter, the discriminant MUST be less than zero. Let's view the options check which one agrees with our answer.

A - Discriminant is greater than 0, which means two solutions. This is WRONG.
B - Discriminant is less than 0, which means no solutions. CORRECT!
C- Discriminant is equal to 0, which means one solution. WRONG!

Your answer is B.

7 0

3 years ago