Answer with Explanation please! Thank you!

Given Information:

Mean weekly salary = μ = $490

Standard deviation of weekly salary = σ = $45

Required Information:

P(X > $525) = ?

Answer:

P(X > $525) = 21.77%

Step-by-step explanation:

We want to find out the probability that a randomly selected teacher earns more than $525 a week.

[tex]P(X > 525) = 1 - P(X < 525)\\\\P(X > 525) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 525) = 1 - P(Z < \frac{525 - 490}{45} )\\\\P(X > 525) = 1 - P(Z < \frac{35}{45} )\\\\P(X > 525) = 1 - P(Z < 0.78)\\\\[/tex]

The z-score corresponding to 0.78 from the z-table is 0.7823

[tex]P(X > 525) = 1 - 0.7823\\\\P(X > 525) = 0.2177\\\\P(X > 525) = 21.77 \%[/tex]

Therefore, there is 21.77% probability that a randomly selected teacher earns more than $525 a week.

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.7, 2.2, 1.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.78 then go for 0.08 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

Answer:

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{1.9}{\sqrt{4500}} = 0.04[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.

The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

Answer:

A = $ 181,824 rounded

Step-by-step explanation:

A = $ 181,823.93

A = P + I where

P (principal) = $ 69,000.00

I (interest) = $ 112,823.93

Answer:

Step-by-step explanation:

Adding the numbers because that is the only step.  Making it the last operation.

Answer:

[tex]sin\;60 =\frac{\sqrt{3} }{2}[/tex]

Answer:

A 90° counterclockwise rotation about the origin and then a translation 16 units right and 16 units up

Solution -Rotating the triangle 90° counterclockwise will take the triangle to 3rd quadrant and then further moving it 16 steps right will take it to 4th quadrant and followed by 16 steps upward will take it to the desired position which is in 1st quadrant.

Answer:

  -23

Step-by-step explanation:

We note that as x increases by 36 from -72 to 36, y decreases by 24 from 25 to 1.

Increasing x from -36 by another 36 to zero will correspond to a decrease in y by another 24 from 1 to -23.

The y-intercept is -23.

_____

You could go to the trouble to use these observations to compute the slope as -24/36 = -2/3. Then you could pick one of the points and write the equation in point-slope form as ...

  y = -2/3(x +36) +1 . . . point-slope form with m=-2/3, (h, k) = (-36, 1)

  y = -2/3x -24 +1 . . . . . eliminate parentheses

  y = -2/3x -23 . . . . . . . y-intercept is -23

Answer:

Y=2x-9

Step-by-step explanation:

Step-by-step explanation:

There is no question asked here, bit of course it is possible to predict the life expectancies of a lot of things. This takes patience, resistance, and persistence, because working on something that takes time without persistence would result in a painful waste of time.

To predict the life expectancy of an effect is to predict how long it is going to take before it goes extinct, or seize from existence.

Answer:

b) equals 20 hours.

Step-by-step explanation:

The sampling distribution of means refers to the distribution of all the possible sample means, with a certain sample size (in this case, n=100) extracted from the population.

The sampling distribution of the means is equal to the population mean. That does not mean that every sample will result in a mean equal to the population, but that the population of sample means will have an average of 20 hours.

Answer:

Ashley’s backpack is the better buy.

Step-by-step explanation:

You have to calculate the price that was paid for each backpack after the discount was applied.

Ashley’s backpack: $65*0.25= $16.25

Final price= $65-$16.25= $48.75

Robbin's backpack: $75*0.3= $22.5

Final price= $75-$22.5= $52.5

According to this, the backpack that is the better buy is the one that Ashley bought because after the discounts were applied it cost $48.75 and Robbin's backpack cost $52.2 which means that Ashley's backpack was cheaper.

Answer:

He needs four packs.

Step-by-step explanation:

6*4=24 there is 23 so he will need 4 packs in total.

Answer:

4 packs

Step-by-step explanation:

3 packs only gives him 18 and he needs atleast 23. The closest number that meets 23 is 24. It takes 4 packs of 6 to get 24.

Answer:

typically, careers that require higher education levels pay higher salaries than those that require a high school diploma.

Answer:

Step-by-step explanation:

Hello!

The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.

Sample 1: Advanced tennis players

X₁: Force (N) on the hand just after impact on a one- handed backhand drive for an advanced tennis player.

n₁= 6

X[bar]₁= 40.29 N

S₁= 11.29

Sample 2: Intermediate players

X₂: Force (N) on the hand just after impact on a one- handed backhand drive for an intermediate tennis player.

n₂= 8

X[bar]₂= 21.40

S₂= 8.30

Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.

If the force is greater for the advanced players than for the intermediate players, then you'd expect the population mean for the advanced players to be greater than the population mean for the intermediate players:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

α: 0.05

[tex]t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{5*127.51+7*68.92}{6+8-2} }= 9.66[/tex]

[tex]t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62[/tex]

Using the p-value approach, the decision rule is

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.

This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.

I hope this helps!

Answer: 0.0179

Step-by-step explanation:

We know that , the  standard error of the sampling distribution of sample proportion (p) is given by :-

[tex]S.E.=\sqrt{\dfrac{p(1-p)}{n}}[/tex]

where , n= sample size

Let p be the  proportion of households who have incomes in excess of $60,000 .

As per given , we have

p= 20% = 0.20

n= 500

Then,

[tex]S.E.=\sqrt{\dfrac{0.20(1-0.20)}{500}}=\sqrt{\dfrac{0.20\times0.80}{500}}\\\\=\sqrt{0.00032}\\\\=0.01788854382\approx0.0179[/tex]

Hence, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 is 0.0179.

The  standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be 0.0179.

Since  an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000.

So here the standard error should be

[tex]\sqrt (.2\times (1-.2)\div 500) \\\\= 0.0179[/tex]

Hence, the standard error should be 0.0179.

Learn more about sample here: https://brainly.com/question/9222927

Answer:

Step-by-step explanation:

Answer:

yes this right, it depends on what one tho

Step-by-step explanation:

Answer:

C. Independent, 49/1296

Step-by-step explanation:

A jar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.

Total balls = 12+7+10+7

Total balls= 36

Two balls are chosen at random with replacement.

The probability that the both balls are green = probability of the first ball to he green * probability of the second ball to be green

The probability that the both balls are green= 7/36 * 7/36

The probability that the both balls are green= 49/1296

The probability that the both balls are green= 49/1296

Answer:

Step-by-step explanation:

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

Pearson's r is -0.140.

The critical r-value is 0.404.

Since 0.140 < 0.404, we cannot reject the null hypothesis.

Therefore, we cannot conclude that notebook computer use and grades are related.

Pearson's r is -0.140. It means that there is a weak negative relationship between notebook computer use and grades.

The coefficient of determination is 0.020. 2% of the variation in the model is explained.

The relationship is not significant.

Notebook Computer Use Final Grade for Course    

30 86      

23 88      

6 94      

0 56      

24 78      

36 72      

10 80      

0 90      

0 82      

8 60      

12 84      

18 74      

0 78      

32 66      

36 54      

12 98      

8 81      

18 74      

22 70      

38 90      

5 85      

29 93      

26 67      

10 80

r² = 0.020    

r  = -0.140    

Std. Error = 11.996    

n  = 24    

k  = 1

ANOVA table    

Source              SS              df            MS           F             p-value  

Regression    63.6652        1          63.6652   0.44           0.5129  

Residual        3,165.668     22        143.8940    

Total              3,229.333     23  

Answer:

Step-by-step explanation:

Car B, the SUV, obviously holds more fuel after 0 driven miles, 60 gallons, while car A holds 10 gallons after 0 miles.

let's speak about miles with the abbreviation x.

sk at x=0 Car B got more fuel.

Car A gets 60 Miles per gallon, it's consuming 1/60 gallon per mile. The amount of fuel decreases by 1/60 per mile

After each mile, or each x-step, Car A has

This can be expressed mathematically:

A(x) = -1/60*x + 10

The -1/60x is, again, the consumption per mile, the +10 is the full tank at the start.

A(0)= -1/60*0 + 10

=10

For Car B the consumption is 1/2 gallons per mile and the tank holds 60 gallons of fuel, wich ammount is decreases with traveled distance.

B(x) = -1/2*x + 60

See that we could draw these two functions as lines in a coordinate system. (I did it with desmos btw). This step is just to help understand.

After some distance/ amount x of miles, Car A will hold more fuel than car B, because it drives more efficiently.

In the picture we can see that this is after about 100 miles and we could guess the amount of fuel, but I won't. Let's calculate it and then answer the question precisely.

We get the intersection of the two lines by setting them equal, a(x)=b(x)

-1/60x + 10 = -1/2x + 60

Exactly one point lies, equally, on both lines

So let's solve for x

Further on the right, each step is explained. we have to do the same operation on both sides of the equation, just to not break it.

-1/60x + 10 = -1/2x + 60 | -10

-1/60x = -1/2x + 50 | + 1/2x

-1/60x + 1/2x = 50 | *60

-1x + 30x = 3000

29x = 3000 | /29

x = 103.448275862

so after about 103.45 miles, Car B holds less fuel than Car A (and Car A more than Car B), until both are empty. Car B could therefore drive more miles

We can also ask how much fuel is left in both tanks at the intersection point by plugging the x-value we got into one of the equations (doesn't matter which one, since the point is the same)

a(103.4482) = -1/60 * 103.4482 + 10 = 8.28

If you want it to be precise, stay with fractions

a(3000/29) = -1/60 * 3000/29 + 10

= -50/29 +10

= 9 -21/29

= 8 + 8/29

Finding out how far each car could travel would be achieved by setting their fuel-equation equal to 0, because that's the value of it when they run of of fuel. For example 0 = -1/60x+10, then you (just) solve for x.

I did overshoot the given problem to offer offer you understanding that's spans more of the topic you are dealing with

(would really appreciate the brainliest)

Answer:5

Step-by-step explanation:

Answer:

Yo

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the matrix

[tex] A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right] [/tex]

a) To find the characteristic polynomial we calculate [tex]\text{det}(A-\lambda I)=0[/tex] where I is the identity matrix of appropiate size. in this case the characteristic polynomial is

[tex]\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0[/tex]

Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is

[tex](4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0[/tex]

which is the characteristic polynomial of A.

b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are [tex]\lambda=4,3,-1[/tex]

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression [tex]A-\lambda I[/tex] and solve the system [tex](A-\lambda I)x =0[/tex] by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider [tex]\lambda = 4[/tex]. We get the matrix

[tex]\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right] [/tex]

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

[tex](x,y,z) = (5z,5z,z) = z(5,5,1)[/tex]

So, the base for this eigenspace is the vector (5,5,1).

If [tex]\lambda = 3[/tex] then the base is (0,4,3) and if [tex]\lambda = -1[/tex] then the base is (0,0,1)

Answer:

Length = 2.823 in (to 3 decimal places)  

Step-by-step explanation:

assuming that the box is a cubic box:

volume of box = [tex]22\frac{1}{2}[/tex] in³ = 22.5 in³

volume = Length × Length × Length = (Length)³

∴ (Length)³ = 22.5

∴ Length = ∛(22.5)

using the calculator punch ∛(22.5), and the answer is:

∴ Length = 2.823 in (to 3 decimal places)

Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

Hypotheses:

H₀: μ₁ = μ₂

H₁: μ₁ < μ₂  

α: 0.05

Using the following sample information:

Sample 1

n₁= 15

X[bar]₁= 10

S₁= 4

Sample 2

n₂= 27

X[bar]₂= 8

S₂= 7

This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:

[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*16+26*49}{15+27-2} }= \sqrt{\frac{1498}{40} } = 6.119= 6.12[/tex]

[tex]t= \frac{(10-8)-0}{6.12*\sqrt{\frac{1}{15} +\frac{1}{27} } }= 1.01[/tex]

The p-value of this test is 0.1593

To decide using the p-value approach you have to use the following rule:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.

I hope this helps!

Answer:

[tex]scalene \: triangle[/tex]

Step-by-step explanation:

The above given triangle represents the unequal lengths of three sides properties of scalene triangle

Hope this helps you out!!!

Answer:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]

Step-by-step explanation:

Total Number of People on Campus =1000

Let the number of people who have contracted the flu =x(t)

Therefore, the number of people who have not contracted the flu =1000-x(t)

Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.

[tex]\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)][/tex]

Introducing the proportional constant k, we obtain:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)][/tex]

At t=0, there was no infected on the campus, therefore the initial condition is given:

[tex]x(0)=0[/tex]

Therefore, a differential equation for the number of people x(t) who have contracted the flu is:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]