What is the area & perimeter of this figure?

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:

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:

[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:

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:

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:

r = 1.499619733762 m  There is no such thing a quarter radius!

C = 9.4223886775301 m

A = 7.065 m^2

Step-by-step explanation:

Calculate r and C | Given A

Given the area of a circle calculate the radius and circumference

r = √(A / π)

C = 2πr

Agenda:

r = radius

C = circumference

A = area

π = pi = 3.1415926535898

√ = square root

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:

His total is $269

Step-by-step explanation:

8x19 = 152

6x19.50 = 117

152+117 = 269

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:

8 yds

Step-by-step explanation:

The sides have to have the same length

14 yd = 6yd + ?

Subtract 6 from each side

14-6 = 8

8 yds

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: 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:

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Step-by-step explanation:

(–2x³y² + 4x²y³ – 3xy⁴) – (6x⁴y – 5x²y³ – y⁵)=

–2x³y² + 4x²y³ – 3xy⁴ – 6x⁴y + 5x²y³ + y⁵=

-6x⁴y - 2x³y² + 9x²y³ - 3xy⁴ + y⁵

Answer:

720

Step-by-step explanation:

6!

6x5x4x3x2x1=720

Answer:

Step-by-step explanation:

4x+5x=27

9x=27

x=27/9

x=3

4x3=12

5x3=15

The total number of cats were 12.

Based on the ratio of dogs to cats in the shelter, we know that out of 27 animals, there are 12 cats.

The ratio of cats to dogs is 4:5 which means that there are 5 dogs for every 4 cats.

This means that out of 9 animals, 4 would be cats and 5 would be dogs. If there was 27 animals therefore:

= 4 / 9 x 27

= 108 / 9

= 12 cats

In conclusion, there are 12 cats.

Find out more at https://brainly.com/question/9723361.

Answer:

D :)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Braily please

Answer:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] n_1= 10 , \bar X_1 = 3.5[/tex] for freshmen

[tex] n_2= 20 , \bar X_2 = 2.9[/tex] for sophomores

[tex] n_3= 25 , \bar X_3 = 3.2[/tex] for juniors

[tex] n_4= 15 , \bar X_4 = 3.4[/tex] for seniors

For this case we can use the formula for the sample mean in order to find the total of each group:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]T= \sum_{i=1}^n X_i = n *\bar X[/tex]

And replacing we got:

[tex] T_1 = 10*3.5 = 35[/tex]

[tex] T_2 = 20*2.9 = 58[/tex]

[tex] T_3 = 25*3.2 = 80[/tex]

[tex] T_4 = 15*3.4 = 51[/tex]

And the grand mean would be given by:

[tex] \bar X= \frac{T_1 +T_2 +T_3 +T_4}{10+20+25+15}= \frac{35+58+80+51}{10+20+25+15} = 3.2[/tex]

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:

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:

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:

Step-by-step explanation:

The formula for the area of a triangle is base*height divided by 2. Remember this because itll be important for everything you do in math relating to geometry and calculus. Assuming you go that far

[tex]\frac{base*height}{2} =\frac{14*8}{2} =\frac{112}{2} = 56 units^2[/tex]

Answer:

A =56 units^2

Step-by-step explanation:

The area of a triangle is given by

A =1/2 bh where 14 is the base and 8 is the height

A = 1/2 (14)8

A =56 units^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: 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.

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:

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:

0.8973

Step-by-step explanation:

Relevant data provided in the question as per the question below:

Free throw shooting percentage = 0.906

Free throws = 6

At least = 5

Based on the above information, the probability is

Let us assume the X signifies the number of free throws

So,  Then X ≈ Bin (n = 6, p = 0.906)

[tex]P = (X = x) = $\sum\limits_{x}^6 (0.906)^x (1 - 0.906)^{6-x}, x = 0,1,2,3,.., 6[/tex]

Now

The Required probability = P(X ≥ 5) = P(X = 5) + P(X = 6)

[tex]= $\sum\limits_{5}^6 (0.906)^5 (1 - 0.906)^{6-5} + $\sum\limits_{6}^6 (0.906)^6 (1 - 0.906)^{6-6}[/tex]

= 0.8973

Answer:

For the first question we just plug in the values so we get 5 - 2 * 5 = -5.

Again, for the second one we'll plug in the values and see if it's a true statement. 5 - 2 * 5 = -5 and -5 = -5 so the answer is yes.

Answer:

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

y = 13

Step-by-step explanation:

→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):

-2 + 2y = 24

2y = 26

y = 13

→Then, plug in 13 for y into the other equation:

3x + 2y = 4

3x + 2(13) = 4

3x + 26 = 4

3x = -22

x = -7.33        OR         x = [tex]\frac{-22}{3}[/tex]

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)

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