Given A triangle with sides x=6.35 cm and Y=12.25 cm with an angle of 90 degrees between them, find the length of the hypotenuse and the size of the other two angles.

Answer:

E) 0.99

Step-by-step explanation:

100 recruits x 0.4 chance of retiring as police officer = 40 officers

probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers

each new recruit will result in either 0, 1 or 2 new pensions

mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7

σ²  = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81

in order for the total number of pensions (X) that the city has to provide:

the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds

the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9

P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] =  P [(X - 70)/9] ≤ 2.22

z value for 2.22 = 0.9868 ≈ 0.99

Answer:

h = p - l - w

Step-by-step explanation:

p = 4l + 4w + 4h       Divide l, w, and h by 4

p = l + w + h              Set the equation equal to h

h = p - l - w

Answer:

A just did it on edge<3

Answer:

d. 85%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,

Which confidence interval would be the narrowest?

The one with the lowest confidence level. So the answer is d.

Answer:

The probability distribution for x:"number of children per family for this income group" is:

[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]

Step-by-step explanation:

With the information given we have the relative frequencies of each category.

We know:

[tex]\text{P(x=0)}=0.15\\\\\text{P(x=1)}=0.35\\\\\text{P(x=2)}=0.45\\\\\text{P(x=3)}=0.05\\\\[/tex]

Answer:

Hello!

I believe your answer is:

4a(b+2c)

Step-by-step explanation:

I hope this worked for you!  Good luck!

Answer:

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Step-by-step explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Answer:

D.

Step-by-step explanation:

So you know you have to have $62 as the base fee.

If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.

You get C = 62 + 30(g - 2)

Answer:

anwser is d because it is write.

Step-by-step explanation:

Answer:

literally 7.68=7.680

Answer:

The answer is C.

Step-by-step explanation:

For a function, we do a vertical line test. If there is more than one point in one single x-position, it is not a function. Example, the ordered pairs (1, 1) and (1, 2) do NOT describe a function because there are more than one point on x=1.

Answer:

720

Step-by-step explanation:

6!

6x5x4x3x2x1=720

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± [tex]Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

Where  [tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex] is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

Now using the formula you have to clear the sample size:

[tex]d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )[/tex]

[tex]\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p')}{n} }[/tex]

[tex](\frac{d}{Z_{1-\alpha /2}})^2 =\frac{p'(1-p')}{n}[/tex]

[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')[/tex]

[tex]n = p'(1-p')*(\frac{Z_{1-\alpha /2}}{d})^2[/tex]

[tex]n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203[/tex]

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

Answer:

The sample size should be 6157

Step-by-step explanation:

Given that the margin of error (e) = ± 0.01 and the confidence (C) = 95% = 0.95.

Let us assume that the guess p = 0.25 as the value of p.

α = 1 - C = 1 - 0.95 = 0.05

[tex]\frac{\alpha }{2} =\frac{0.05}{2}=0.025[/tex]

The Z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Therefore [tex]Z_\frac{\alpha }{2}=Z_{0.025}=1.96[/tex]

To determine the sample size n, we use the formula:

[tex]Z_{0.025}*\sqrt{\frac{p(1-p)}{n} }\leq e\\Substituting:\\1.96*\sqrt{\frac{0.2(1-0.2)}{n} } \leq 0.01\\\sqrt{\frac{0.2(0.8)}{n} }\leq \frac{1}{196}\\\sqrt{0.16} *196 \leq \sqrt{n}\\78.4\leq \sqrt{n}\\ 6146.56\leq n\\n=6157[/tex]

Answer: LIKLEY

Step-by-step explanation:

Formula : Probability [tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]

A standard cube has six numbers on it (1,2,3,4,5 and 6).

P( NOT 6) =[tex]\dfrac{\text{Numbers that are not 6}}{\text{Total numbers}}[/tex]

[tex]=\dfrac{5}{6}=0.8333[/tex]

We know that when the probability of any event lies between 0.5 and 1then the event is said to be likely to happen.

Since , P(not 6)=0.8333 which lies between 0 and 0.5.

That means, it is likely to happen.

Note :

When probability of having A = 0 , we call A as uncertain event.

When probability of having A = 1 , we call A as certain event.

When probability of having A = 0.5 , we call A as equally likely event.

When probability of having A lies between 0 and 0.5 , we call A as unlikely event.

When probability of having A lies between 0.5 and 1 , we call A as likely event.

Answer:

Can you give the question. Can you post the picture. I can help solve. I will edit this answer once you have given the question/picture.

Answer:

a) 2.84% probability that he is late for his first lecture.

b) 5.112 days

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 16, \sigma = 2.1[/tex]

a. Find the probability that he is late for his first lecture.

This is the probability that he takes more than 20 minutes to walk, which is 1 subtracted by the pvalue of Z when X = 20. So

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

[tex]Z = \frac{20 - 16}{2.1}[/tex]

[tex]Z = 1.905[/tex]

[tex]Z = 1.905[/tex] has a pvalue of 0.9716

1 - 0.9716 = 0.0284

2.84% probability that he is late for his first lecture.

b. Find the number of days per year he is likely to be late for his first lecture.

Each day, 2.84% probability that he is late for his first lecture.

Out of 180

0.0284*180 = 5.112 days

Answer:

His total is $269

Step-by-step explanation:

8x19 = 152

6x19.50 = 117

152+117 = 269

Answer:

[tex]h=\sqrt{1.44}\\h = 1.2[/tex]

Step-by-step explanation:

Base of the triangle on the left = 0.5

Use pythagorean theorem

[tex]a^{2} + b^{2} = c^{2}[/tex]

Substitute

[tex]0.5^{2} + b^{2} = 1.3^{2}[/tex]

[tex]b^{2} = 1.3^2 - 0.5^2[/tex]

[tex]b^2 = 1.44[/tex]

[tex]b = \sqrt{1.44} \\[/tex]

[tex]b = 1.2[/tex]

in this case b is the height

so

[tex]h=\sqrt{1.44}\\h = 1.2[/tex]

Answer:

10ft[tex]{3}[/tex]

Step-by-step explanation:

One face has 15 blocks of 1/3 ft. You can clearly see 2 sets of blocks.

15 x 2 = 30

30 ÷ 3 or 30 x 1/3

= 10 ft cubed

Answer:

1/18

Step-by-step explanation:

First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18

Answer:

1/18

Step-by-step explanation:

plz mark me brainliest.

Answer: f(x)=2-x^2

Step-by-step explanation:

The quadratic equation is

y=ax^2+bx+c

and c is equal to the y-intercept.

in the twi graphs shown both have the same shape but different y-intervepts.

c(the y-intercept) in the first graph is 5 and in the second graph(F) is 2.

On the graphing calculator it says that f(x)=2-x^2 is the correct answer therefore it is correct.

To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.

The equation would be y = 40x + 25

Answer:

The approximate probability that more than six students were born on Christmas day is P=0.105.

Step-by-step explanation:

This can be modeled as a binomial variable, with n=1460 and p=1/365.

The sample size n is the total amount of students and the probability of success p is the probability of each individual of being born on Christmas day.

As the sample size is too large to compute it as a binomial random variable, we approximate it to the normal distribution with the following parameters:

[tex]\mu=n\cdot p=1460\cdot (1/365)=4\\\\\sigma=\sqrt{n\cdot p(1-p)}=\sqrt{1460\cdot(1/365)\cdot(364/365)}=\sqrt{3.989}=1.997[/tex]

We want to calculate the probability that more than 6 students were born on Christmas day. Ww apply the continuity factor and we write the probability as:

[tex]P(X>6.5)[/tex]

We calculate the z-score for X=6.5 and then calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{6.5-4}{1.997}=\dfrac{2.5}{1.997}=1.252\\\\\\P(X>6.5)=P(z>1.252)=0.105[/tex]

Answer:

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Step-by-step explanation:

We can use the future vaue formula for compound interest given by:

[tex] A= P(1+ \frac{r}{n})^{nt}[/tex]

Where P represent the present value, r=0.0675 , n is the number of times that the interest is compounded in a year and t the number of years.

Part a

For this case n = 4. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{4})^{4*10}= 4882.506[/tex]

Part b

For this case n = 365. If we use the future value formula we got:

[tex] A= 2500 (1+ \frac{0.0675}{365})^{365*10}= 4909.776[/tex]

Answer:

In 6 years, Ralph will be only twice as old as Sara

Step-by-step explanation:

Answer:

The answer is C, 3x+4

Step-by-step explanation:

The “in four years” part translates to +4. The 3x translates to 3 times his current age. Hope this helped :)

Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

[tex]P(t) = P(0)(1-r)^{t}[/tex]

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that [tex]P(0) = 750000, P(48) = 250[/tex]

We use this to find r. So

[tex]P(t) = P(0)(1-r)^{t}[/tex]

[tex]250 = 750000(1-r)^{48}[/tex]

[tex](1-r)^{48} = \frac{250}{750000}[/tex]

[tex]\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}[/tex]

[tex]1-r = 0.84637[/tex]

So

[tex]P(t) = 750000(0.84637)^{t}[/tex]

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

[tex]P(56) = 750000(0.84637)^{56} = 65.83[/tex]

Rounding to the nearest number

There will be 66 bacteria in 8 hours.

Answer:

197,488

Step-by-step explanation:

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.

Identify the variables in the formula.

AA0ktA=250=750,000=?=48hours=A0ekt

Substitute the values in the formula.

250=750,000ek⋅48

Solve for k. Divide each side by 750,000.

13,000=e48k

Take the natural log of each side.

ln13,000=lne48k

Use the power property.

ln13,000=48klne

Simplify.

ln13,000=48k

Divide each side by 48.

ln13,00048=k

Approximate the answer.

k≈−0.167

We use this rate of growth to predict the number of bacteria there will be in 8 hours.

AA0ktA=?=750,000=ln13,00048=8hours=A0ekt

Substitute in the values.

A=750,000eln13,00048⋅8

Evaluate.

A≈197,488.16

At this rate of decay, researchers can expect 197,488 bacteria.

Answer:

103

Step-by-step explanation:

[tex]\dfrac{1}{216}^{-2/3}+\dfrac{1}{256}^{-3/4}+\dfrac{1}{243}^{-1/5}= \\\\\\\sqrt[3]{216^2}+\sqrt[4]{256^3}+\sqrt[5]{243}=\\\\\\6^2+4^3+3=\\\\\\36+64+3=\\\\\\103[/tex]

Hope this helps!

Answer:

y = -1/2x - 2

Step-by-step explanation:

If it's parallel, that means that the slope is the opposite of the one in the given equation, meaning that 2 would be flipped and turned negative into -1/2.

Then, fill in the x and y values to get the y-intercept.

1 = -1/2(-6) + b

1 = 3 + b

-2 = b

So your answer is y = -1/2x - 2

Answer:

Step-by-step explanation:

The mean of the reading points is

Mean = (5.8 + 5.9 + 4.9 + 5.2 + 5.0 + 4.9 + 6.2 + 5.1 + 5.7 + 6.1)/10 = 5.48

The process is out of control if the mean salt level of the readings is greater than 5.4

For the null hypothesis,

µ = 5.4

For the alternative hypothesis,

µ > 5.4

This is a right tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 5.4

x = 5.48

σ = 0.3

n = 10

z = (5.48 - 5.4)/(0.3/√10) = 0.84

Looking at the normal distribution table, the probability corresponding to the z score is 0.7996

The probability value to the right of the z score is 1 - 0.7996 = 0.2

Assuming a significance level of 0.05

Since alpha, 0.05 < than the p value, 0.2, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the process is not out of control. If we had rejected the null hypothesis, then our conclusion would be that the process is out of control.

Answer:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]

We are interested on this probability

[tex]P(X>65)[/tex]

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

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

If we find the z score for 65 inches we got:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Answer:

D

Step-by-step explanation:

The volume of pyramid = 1/3 wlh

Where w = width, l = length and h = height

While,

The volume of rectangular prism = wlh

So,

The volume of pyramid = 1/3(the volume of prism)

Answer:

Number of people

6

5

5

6

3

1

Step-by-step explanation:

All you had to do was the count how much numbers there were on the list.

Like there were 6 0s.

Answer:

Hope this helps

Step-by-step explanation:

6 people did 0 sit ups

5 people did 1 sit ups

5 People did 2 sit ups

6 people did 3 sit ups

3 people did 4 sit ups

1 person did 5 sit ups