Find the lateral surface area below given prism:

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Step-by-step explanation:

Let the random variable X be defined as the number of correct answers marked by a student.

It is provided that each question has 5 possible choices, 1 of the which is correct.

Then the probability of marking thee correct option is:

[tex]P(X)=\frac{1}{5}=0.20[/tex]

There are a total of n = 20 questions to be answered.

As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.

All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.

The mean and standard deviation of a Binomial distribution are:

[tex]\mu=np\\\\\sigma=\sqrt{np(1-p)}[/tex]

Compute the mean and standard deviation of the random variable X as follows:

[tex]\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789[/tex]

Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

According to the question,

The probability of making 3 correct options will be:

→ [tex]P(X) = \frac{1}{5}[/tex]

            [tex]= 0.20[/tex]

Total number of questions,

As we know,

The mean will be:

→ [tex]\mu = np[/tex]

By substituting the values, we get

     [tex]= 20\times 0.20[/tex]

     [tex]= 4[/tex]

and,

The standard deviation will be:

→ [tex]\sigma = \sqrt{np(1-p)}[/tex]

      [tex]= \sqrt{20\times 0.20\times (1-0.20)}[/tex]

      [tex]= 1.789[/tex]

Thus the responses above are correct.

Learn more about standard deviation here:

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Answer:

It cost $0.91 10 years ago.

It takes 10.24 years for the cost of bread to double.

Step-by-step explanation:

The equation for the price of bread after t years has the following format:

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

In which P(0) is the current price, and r is the inflation rate, as a decimal.

If we want to find the price for example, 10 years ago, we find P(-10).

Inflation is at a rate of 7% per year. Evan's favorite bread now costs $1.79.

This means that [tex]r = 0.07, P(0) = 1.79[/tex]. So

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

[tex]P(t) = 1.79(1+0.07)^{t}[/tex]

[tex]P(t) = 1.79(1.07)^{t}[/tex]

What did it cost 10 years ago?

[tex]P(-10) = 1.79(1.07)^{-10} = 0.91[/tex]

It cost $0.91 10 years ago.

How long before the cost of the bread doubles?

This is t for which P(t) = 2P(0) = 2*1.79. So

[tex]P(t) = 1.79(1.07)^{t}[/tex]

[tex]2*1.79 = 1.79(1.07)^{t}[/tex]

[tex](1.07)^{t} = 2[/tex]

[tex]\log{(1.07)^{t}} = \log{2}[/tex]

[tex]t\log{1.07} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.07}}[/tex]

[tex]t = 10.24[/tex]

It takes 10.24 years for the cost of bread to double.

Answer:

1/3

Step-by-step explanation:

The total number of marbles

10+4+7 = 21

P(blue) = blue marbles / total marbles

            = 7 / 21

            = 1/3

Answer:

1436.76 m³

Step-by-step explanation:

Volume of sphere= 4/3 π r ³

V= 4/3(3.14)(7)³

V=4/3(3.14)(343)

V= 4310.26 / 3

V= 1436.76 m³

Answer:

a kite

Step-by-step explanation:

Answer:

119000

Step-by-step explanation:

The median is the middle value when placed from smallest to largest

95000, 112000, 126000, 13000

The middle is between 112000 and 126000 so take the average

(112000+126000)/2 =238000/2 =119000

Answer:

0.072

Step-by-step explanation:

Answer:0.072

Step-by-step explanation:

7.2% = 7.2/100

7.2 ➗ 100=0.072

Answer:

  4 square units

Step-by-step explanation:

If corresponding sides have equal lengths, the triangles are congruent by the SSS postulate. They must have equal areas: 4 square units.

ΔDEF has an area of 4 square units.

Answer:

if the corresponding sides are equal the 2 triangles are congruent  ( by SSS) so their areas are the same.

So area of triangle DEF = 4 sq units

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to subtract by adding up 65-39, we need to add -39 to the value of 65. This can be rewritten in this way;

65+(-39)

The equation above is similar to the one given because the product of a minus and a plus sign will still give us back a minus sign.

on solving;

65+(-39) = 26

Answer:

17 i would say it is D

18 i belive it is B

19 it is c

20 A

Answer:

A Type II error happens when the null hypothesis failed to be rejected, although it is false and the alternative hypothesis is true.

In this context, would be that the test does not give enough evidence to support the claim that the new procedure reduces the average cost, although it really does reduces it.

The new procedure is effective, but the sample does not give enough evidence.

Step-by-step explanation:

Answer:

i think its 248m^2

Step-by-step explanation:

Answer:2c^2

Step-by-step explanation:

34c^3 and 2c^5

34c^3=2 x 16 x c x c^2

2c^5=2 x c^2 x c^3

Greatest common factor =2 x c^2

Greatest common factor =2c^2

Answer:

X>-3

Step-by-step explanation:

Hope I helped

Do u want the steps ?

Answer: x > -3

Step-by-step explanation: -5(4x + 7) <25

                                              -20x - 35 < 25

                                              -20x -35 + 35 < 25 + 35

                                              -20x/20 < 60/20

                                              x > -3

Answer:

Define two roughly identical sets.

Reduce the chance of bias.

Step-by-step explanation:

In this experiment, Daniel performs a random assignment in order to stablish two separate groups with roughly equivalent ability to do barbell curls. Two different treatments (verbal encouragement and silence) are then applied in order to verify for a cause and effect relationship. If the groups were not randomly assigned, then the experiment could be biased.

Answer:

[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]  

The p value can be founded with this formula:

[tex]p_v =P(z<-0.936)=0.175[/tex]  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Step-by-step explanation:

Information given

[tex]\bar X_{1}=7.6[/tex] represent the mean for Gibbs products

[tex]\bar X_{2}=8.1[/tex] represent the mean for the competitor

[tex]\sigma_{1}=2.3[/tex] represent the population standard deviation for Gibbs

[tex]\sigma_{2}=2.9[/tex] represent the sample standard deviation for the competitor

[tex]n_{1}=40[/tex] sample size for the group Gibbs

[tex]n_{2}=55[/tex] sample size for the group competitor

[tex]\alpha=0.05[/tex] Significance level provided

z would represent the statistic

Hypothesis to verify

We want to check if babies using the Gibbs brand gained less weight, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}< 0[/tex]  

The statistic would be given by:

[tex]z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{(7.6-8.1)-0}{\sqrt{\frac{2.3^2}{40}+\frac{2.9^2}{55}}}}=-0.936[/tex]  

The p value can be founded with this formula:

[tex]p_v =P(z<-0.936)=0.175[/tex]  

Since the p value is higher than the significance level provided of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean for the Gibbs brand is significantly lower than the true mean for the competitor

Answer:

0.004

Step-by-step explanation:

The probability of rolling any number is 1/6 so that times 3 is 1/216 that as a decimal i 0.004

Answer:

$0.39:1

Step-by-step explanation:

$0.39:1

Dividing the amount by the cost of the bottles.

Answer:

[tex]x=30\\y=68\\z=82[/tex]

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

[tex]y+z=5x[/tex]

The third angle is 14 more than the second

[tex]z=y+14[/tex]

And remember that the sum of these three angles must be equal to 180.

[tex]x+y+z=180[/tex]

Let's take these equations

[tex]y+z=5x\\z=y+14\\x+y+z=180[/tex]

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

[tex]x+y+z=180\\x+(y+z)=180\\x+(5x)=180[/tex]

Distribute the + sign

[tex]x+5x=180[/tex]

Combine like terms;

[tex]6x=180[/tex]

Divide by 6.

[tex]x=\frac{180}{6}\\ x=30[/tex]

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example [tex]z=y+14[/tex]

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

[tex]x+y+z=180\\30+y+(y+14)=180[/tex]

Distribute the + sign and Combine like terms;

[tex]30+y+y+14=180\\44+2y=180\\[/tex]

Subtract 44 to isolate 2y.

[tex]2y=180-44\\2y=136[/tex]

Now divide by 2.

[tex]y=\frac{136}{2}\\ y=68[/tex]

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

[tex]x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82[/tex]

Answer:

C

Step-by-step explanation:

The parallelogram in C has a base of 2 units and a height o 4 units.

Answer:

k=21

Step-by-step explanation:

x=7 X y=3 = 21

7 x 3 = 21

Answer:21

Step-by-step explanation:

xy=k

k=xy x=7 y=3

k=7 x 3

k=21

Answer:

C.  [tex]\frac{\sqrt{5} }{8}[/tex]

Step-by-step explanation:

This expression can be rewritten as [tex]\frac{\sqrt{5} }{\sqrt{64} }[/tex].

Since the square root of 5 is prime and does not have any perfect square factors, it cannot be simplified. However, the square root of 64 is equal to 8, so our final simplified radical expression would be [tex]\frac{\sqrt{5} }{8}[/tex], which is option C.

HOPE THIS HELPED! :)

Answer:

C is the answer

Step-by-step explanation:

You have to rewrite as [tex]\sqrt{5}[/tex]/[tex]\sqrt{64}[/tex]. Then you have to simplify the denominator which is 8. That is how you get your answer.

Hope this helps.

the answer is B

Step-by-step explanation:

and I would love 20 points

Answer:

16

Step-by-step explanation:

distance between point x and z is 8 units

distance between point z and y is 4 units

8 * 4 = 32

formula for area of a triangle (l * w)/2

plugin: (8 * 4)/2 = 16

Answer:150 branliest

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

360/(5+7)=30

30*5=150

Answer:

Denote B(x, y), we have:

-10 + x = 2 x (-16) => x = -22

  8 + y = 2 x 6 => y = 4

=> B(-22, 4)

Hope this helps!

:)

Answer:

The height of the cloud cover is 441.66 meters

Step-by-step explanation:

Distance = 560 m

The height of the cloud cover = h meters

According to the diagram, the worker stands at point R,

Let RT = x

tan 45⁰ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{x}[/tex]

therefore, 1 =  [tex]\frac{h}{x}[/tex], h = x

Then tan 75⁰ = [tex]\frac{h}{560-x}[/tex], substituting x = h, we have

3.732 = [tex]\frac{h}{560-h}[/tex]

3.732(560 - h) =  h

3.732 × 560 = 3.732h + h

2089.92 = 4.732h

h = 441.66 m

The height of the cloud cover is 228.62 meters

The given parameters are:

[tex]\mathbf{\alpha = 75^o}[/tex]

[tex]\mathbf{\theta = 45^o}[/tex]

[tex]\mathbf{d = 560m}[/tex]

See attachment for the image of the cloud cover.

From the attached image, we have the following sine ratios:

[tex]\mathbf{sin(75) = \frac hx}[/tex]

[tex]\mathbf{sin(45) = \frac h{560 - x}}[/tex]

Make h the subject in both equations

[tex]\mathbf{ h = xsin(75)}[/tex]

[tex]\mathbf{ h = (560 - x) sin(45)}[/tex]

So, we have:

[tex]\mathbf{ xsin(75) = (560 - x) sin(45)}[/tex]

Open brackets

[tex]\mathbf{ xsin(75) = 560sin(45) - x sin(45)}[/tex]

Collect like terms

[tex]\mathbf{ xsin(75) + x sin(45)= 560sin(45) }[/tex]

Evaluate sine 45 and 75

[tex]\mathbf{ 0.9659x + 0.7071x= 560 \times 0.7071}[/tex]

[tex]\mathbf{ 1.673x= 395.976}[/tex]

Divide both sides by 1.673

[tex]\mathbf{ x= 236.69}[/tex]

Recall that:

[tex]\mathbf{ h = xsin(75)}[/tex]

So, we have:

[tex]\mathbf{h = 236.69 \times 0.9659}[/tex]

[tex]\mathbf{h = 228.618871}[/tex]

Approximate

[tex]\mathbf{h = 228.62}[/tex]

Hence, the height of the cloud cover is 228.62 meters

Read more at:

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Answer:

both measures show strong growth in CEO

Step-by-step explanation:

350 firms in 2018 was $17.2 million- or $14.0 both show that they have a strong growth in the last  2 years.

Answer:

The answer is B "The annual change in production has exceeded the annual change in the average salary."

Step-by-step explanation:

Yes

Answer:

Option D: 5591.93

Step-by-step explanation:

The best way to understand this question is to apply the formula in an indirect manner;

P - Principle number, Starting Value

T - Time

I - Interest

Let us convert the interest into decimal form, such that 3.8% is shifted two decimal points to the right ⇒ 0.038. Now add 1 to this value to get ⇒ 1.038. By PEDMAS, you would first raise this value to the span of 3 years as such:

(1.038)^3 = 1.118386872.......

The final step would by to multiply the starting value (investment $) $ 5,000 by this continuing value of 1.118386872:

5,000(1.118386872) = 5591.93436 ⇒ Rounded to (About) 5591.93

Answer:D

Step-by-step explanation:

principal=p=$5000

Rate=r=3.8%

Time=n=3 years

amount=a

a=p(1+r/100)^n

a=5000(1+3.8/100)^3

a=5000(1+0.038)^3

a=5000(1.038)^3

a=5000 x 1.038 x 1.038 x 1.038

a=5591.93

a=$5591.93