A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per​ minute, compute the 95​% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.

Answer:

The car's average 18 number of miles per gallon

Step-by-step explanation:

The car has different efficiencies depending if its used on highway or city streets.

The efficiency on a highway is:

[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]

The efficiency for city driving is:

[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]

We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.

Then, we can calculate how many miles makes the car on average as:

[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]

Answer:

Section 1:

a) 7:15 a.m - 19:15

b) 1:05 am - 01:05

c) 2:01 p.m - 14:01

d) 9:22 p.m - 21:22

e) 12:25 am- 24:25

Section 2:

a) 1155 hours - 11:55am

b) 1005 hours -10:05am

c) 1714 hours - 5:14pm

d) 0756 hours - 7:56am

e) 1345 hours- 1:45pm ​

Answer:

12:25 am= 00:25

Step-by-step explanation:

Answer:

x > -4

Step-by-step explanation:

— 3х + 7 < 19

Subtract 7 from each side

— 3х + 7-7 < 19-7

-3x < 12

Divide each side by -3, remembering to flip the inequality

-3x/-3 > 12/-3

x > -4

Just like any of your two-step equations, in this inequality,

start by isolating the x term which in this case is -3x by

subtracting 7 from both sides.

This gives us -3x < 12.

Solving from here, we divide both sides by -3.

However, when solving inequalities, you need to watch out.

When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.

Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.

So we end up with x > -4.

The length of the parametric curve (call it C ) is given by

[tex]\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t[/tex]

[tex]y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t[/tex]

Now,

[tex]\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t[/tex]

so that the arc length integral reduces to

[tex]\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt[/tex]

which has an approximate value of 53.4596.

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]

please see the attached picture for full solution

Hope it helps...

Good luck on your assignment,

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

Answer:

2.5

Step-by-step explanation:

We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.

SMR = observed / expected

therefore if we replace we have:

SMR = 4500/1800

SMR = 2.5

Which means that the standardized mortality ratio (SMR) is 2.5

Answer:

  4 cm

Step-by-step explanation:

The side of the square will be the average of the two sides of the rectangle with the same perimeter.

Formulas for the perimeters are ...

  P = 2(L+W)

  P = 4s

Equating these gives ...

  4s = 2(L+W)

  s = (L +W)/2 . . . . . divide by 4

For the given side lengths, ...

  s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm

The length of one side of the square is 4 cm.

If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.

What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.

Scale factor = new dilated length OB'/(³/₄)

new dilated length OB' = ³/₄ × 4

new dilated length OB' = 3 units

Read more on dilation at; https://brainly.com/question/8532602

Answer:

its 4 units trust just answered it

Step-by-step explanation:

Answer:

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Step-by-step explanation:

Simple interest for any amount p is given by

SI = p*r*t/100

where r is the annual rate rate of interest

t is the time

____________________________________________

Given

p= $500 (loan taken)

r = 8%

t = 1 year

SI = 500*8*1/100 = 40

Thus, $40 is the interest charged in a year.

Total money paid at the end of one year = loan taken  + interest charged

                                                                    = $500 + $40

                                                                    = $540

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Answer:

Step-by-step explanation:

There are no factors outside the parentheses that need to be distributed, so the parentheses can be simply dropped:

  6 -2x +15 -3x

The terms can be rearranged to put like terms next to each other:

  -2x -3x +6 +15

and the like terms can be combined.

  -5x +21 . . . . simplified expression

__

Put the value of x where x is, then do the arithmetic.

  -5(-0.2) +21 = 1 +21 = 22

Answer:

[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]  

The p value would be given by:

[tex]p_v =P(z<20.943)\approx 0[/tex]  

The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81

Step-by-step explanation:

Info given

n=861 represent the random sample

[tex]\hat p=0.53[/tex] estimated proportion of people who responded play on a pc computer

[tex]p_o=0.81[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true proportion decreases from 81%, the system of hypothesis are.:  

Null hypothesis:[tex]p\geq 0.81[/tex]  

Alternative hypothesis:[tex]p < 0.81[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.53 -0.81}{\sqrt{\frac{0.81(1-0.81)}{861}}}=-20.943[/tex]  

The p value would be given by:

[tex]p_v =P(z<20.943)\approx 0[/tex]  

The p value is a very low value compared to the significance level given so then we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.81

Answer:

The probability that either Alex or Bryan get an A is 0.9

Step-by-step explanation:

Before we proceed to answer, we shall be making some important notation;

Let A = event of Alex getting an A

Let B = event of Bryan getting an A

From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1

We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)

We can use the addition theorem here;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)  .......................(i)

Also,

P(A) = P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)   .........................(ii)

We can insert ii into i and we have;

P(A ∪ B) =  P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)  + P(B) - P(A ∩ B) =   P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9

Answer:

it is option A

Step-by-step explanation:

Answer:

a = 13

b = 0

Step-by-step explanation:

Conjugate of -3 + 2i is -3 - 2i

(-3 + 2i) (-3 - 2i)

We need to expand:

9 + 6i + -6i + -4i^2

-4i^2 =(-4)(-1) = 4

9 + 4 = 13

a = 13

b = 0

Answer:

The ratio of the expenses shared by Akmal to Bakri to Cadin is 7 : 4 : 3

Step-by-step explanation:

The 3 of them shares their mother medical expenses which cost RM4200 . There mother medical expenses is RM4200 in total. Cadin pays RM2100 which is half of their mother medical expenses. Then Akmal pays three quarters of Bakri amount.

Let

The amount Bakri pays = a

Akmal pays = 3/4 of a

Akmal pays = 3/4a

Therefore,

a + 3a/4 = 2100

4a + 3a/ 4 = 2100

7a/4 = 2100

cross multiply

7a = 8400

divide both sides by 7

a = 8400/7

a = 1200

Therefore,

Bakri pays =RM 1200

Akmal pays = 3/4 × 1200 =RM 900

The ratio of the expenses shared by AKmal to Bakri to Cadin is expressed as 2100 : 1200 : 900. Divide through by 300

7 : 4 : 3

Answer:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Step-by-step explanation:

Information given

[tex]\bar X=20[/tex] represent the sample mean  

[tex]\sigma=9[/tex] represent the population deviation

[tex]n=36[/tex] sample size  

[tex]\mu_o =25[/tex] represent the value to verify

[tex]\alpha=0.1[/tex] represent the significance level

tzwould represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test the hypothesis that the true mean is lower than 25  and the system of hypothesis are:  

Null hypothesis:[tex]\mu \geq 25[/tex]  

Alternative hypothesis:[tex]\mu < 25[/tex]  

The statistic is given by:

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

Replacing the info given:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Answer:

A) 0.026

B) 0.130

Step-by-step explanation:

Complete Question

A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.

(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.

(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.

Solution

A) This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 4

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.

B) n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 0

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.

Hope this Helps!!!

Answer:

C.

Step-by-step explanation:

Measure of arcURN = 270°

In radians:

270° = 270π/180

270° = 3π/2

Now

Area of sector = 1/2r²∅

= 1/2(10)²(3π/2)

= 50(3π/2)

= 75π

Answer:

The answer is D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

1. More pollination process in the regular corn planted in field A than that of field B.

2. Low pest and insect attack on corn planted in field A compared to that of B.

Step-by-step explanation:

1. Pollination is the process in which a plant becomes fertilized, so as to produced seeds. The process requires some agent which could be; air, human, wind etc.

Therefore more pollination of the corn planted in field A than those in B would lead to more yield (ears of corn harvested) than that of B.

2. Pests and insects are agents which could reduce the yield of the corn after harvest. Comparing the two fields A and B, if the corn planted in field A were not affected by pests or insects, while those planted in B were affected, then more ears of corn would be harvested in field A.

Answer:

a,c, And gg gamer

Step-by-step explanation:

Answer:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

[tex]\bar X= 28.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =4.7[/tex] represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

Learn more about angle of elevation here:

https://brainly.com/question/31006775

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Answer:

See below.

Step-by-step explanation:

The total is 20 friends. This means that we need to make each frequency into a fraction, then simplify to percentage.

1. 10/20 = 50%

2. 3/20 15%

3. 2/20 = 10%

4. 5/20 = 25%

Hope this helps! (Please consider giving brainliest)

Answer:

Bus: 50%

Walk: 15%

Bike: 10%

Car: 25%

Step-by-step explanation:

The total amount of friends is 20.

10 out of 20 is equal to 1/2, which is equal to 50%.

3 out of 20 is equal to 15%.

2 out of 20 is equal to 10%.

And 5 out of 20 is equal to 1/4, which is equal to 25%.

Please mark Brainliest if correct

Complete question:

Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.

a. How much cheese does Mai use per Pizza

b. At this rate how much cheese will she need to make 15 Pizza's

Answer:

a. ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese

b. amount of cheese to make 15 pizzas= 2.5 × 15 = 37.5 ounces of cheese

Step-by-step explanation:

Mai is making a personal pizzas .For 4 pizza she uses 10 ounces of cheese. This means Mai uses 10 ounces of cheese in weight to make just 4 pizzas.

a. How much cheese does Mai use per Pizza

Not she uses 10 ounces of cheese to make 4 pizzas. Therefore,

If 4 pizzas requires  10 ounces of cheese

1 pizza will require ? ounces of cheese

cross multiply

ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese

b. At this rate how much cheese will she need to make 15 Pizza's

Since she requires 2.5 ounces of cheese to make 1 pizza

? ounces of cheese will be required to make 15 pizzas

cross multiply

amount of cheese to make 15 pizzas = 2.5 × 15 = 37.5 ounces of cheese

Answer:

B and F

Step-by-step explanation:

When we'll slice a triangular prism, a square and triangle would be formed

The first differences are 8, 14, 20.

The second differences are 6.

Half of 6 is 3, so the first term of the sequence is 3n^2.

If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.

Therefore your final answer will be 3n^2 - n + 1

Hey there! :)

Answer:

Price per cup: $3.5

Price for 18 cups: $63.

Step-by-step explanation:

To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.

30x = 105

Divide both sides by 30:

x = $3.5.

To find the cost of 18 cups, simply multiply this price by 18:

18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.