I WILL GIVE BRAINLIEST!!! A teacher is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71 *Round your answer to the nearest full value.

Answers

Answer 1

Answer:

The number of students that would have a test score between 61 and 71 are 154 students

Step-by-step explanation:

The given information are;

The mean test score, μ = 61

The standard deviation, σ = 10

The sample size, n = 450

The z score is given as follows;

[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]

We therefore have at x = 61,

[tex]Z=\dfrac{61-61 }{10 } = 0[/tex]

P(x > 61) = P(Z > 0) = 1 - 0.5 = 0.5

For x = 71, we  have;

[tex]Z=\dfrac{71-61 }{10 } = 1[/tex]

P(x < 71) = P(Z < 1) = 0.84134

The probability that the score will be between 61 and 71 is the difference between the two probabilities, which is 0.84134 - 0.5 = 0.34134

Given that the probability is equivalent to  the proportion of the students that would have a test score between 61 and 71, we have;

The number of students that would have a test score between 61 and 71 = 0.34134 × 450 = 153.6 ≈ 154 to the nearest whole number.


Related Questions

Max and Sven bike away from home in the same direction starting at noon. They bike at constant speeds. Max bikes at xmph and he is ymph faster than Sven. By 4pm, how far ahead of Sven would Max be?

Answers

Answer:

Max would be 4y meters ahead by 4pm

Step-by-step explanation:

What we want to calculate here is the difference in the distance they have covered by 4pm given the speed at which they traveled.

Mathematically, distance = speed * time

The time is just the difference between 12 noon and 4pm which is 4 hours

Let’s tackle Max’s

He’s biking at x km/h, so the distance he would have covered by 4pm would be 4 * x = 4x meters

Now let’s tackle Sven

Sven is biking at a speed which is y mph less than Max’s x mph

Thus his speed would be (x-y) mph

His distance covered would be 4(x-y) meters

Now the difference between their bikes distance at 4pm would be;

4x - [4(x-y)]

= 4x -(4x -4y)

4x -4x + 4y

= 4y

Hence, Max would be 4y meters ahead by 4pm

What is the margin of error for 95% confidence for a sample of size 250 where p = 0.45?
A. 0.0541
B. 0.0775
C. 0.0706
D. 0.0617

Answers

Answer:

0.0617

Step-by-step explanation:

so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!

This method applies to any problems with the same basic format. Good luck!

If f ( x) = 4x
2 and g( x) = 5x , what is
g( f (2x)) ?

Answers

Answer: 40x

First, let's find f(2x)

[tex]f(2x)=4(2x)=8x[/tex]

Using this, let's find g(f(2x)):

[tex]g(f(2x))=g(8x)=5(8x)=40x[/tex]

That's the answer. Let me know if you need any clarifications, thanks!

Answer:

80x²

Step-by-step explanation:

f(x) = 4x², g(x) = 5x

f(2x) = 4(2x)² = 16x²

g(f(2x)) = 5(16x²) = 80x²

Solve.
y=x - 7
5+2y=7

Answers

Answer:

[tex]\huge\boxed{x=8;\ y=1\to(8;\ 1)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}[/tex]

[tex]\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}[/tex]

Answer:

(8, 1).

Step-by-step explanation:

y = x - 7

5 + 2y = 7

5 + 2(y) = 7

5 + 2(x - 7) = 7

5 + 2x - 14 = 7

Subtract 5 from both sides

2x - 14 = 2

Add 14 to both sides

2x = 16

Divide both sides by 2

x = 8

Since x = 8...

y = x - 7

y = 8 - 7

y = 1.

To check our work...

5 + 2y = 7

5 + 2 * 1 = 7

5 + 2 = 7

7 = 7

Since it works out, your answer is (8, 1).

Hope this helps!

The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)7 B. 5(7)(0.06) C. 5(1.06)7 D. 5(7)(1.06)

Answers

Complete Question:

The total volume of a tree increases 6% each year. What will its volume be after 7 years if its volume is 5 cubic meters now? A. 5(0.06)^7 B. 5(7)(0.06) C. 5(1.06)^7 D. 5(7)(1.06)

Answer:

C. 5(1.06)^7

Step-by-step explanation:

The volume of a tree increases by 7% every year

The formula we would be using is

V(t) = Vo (1 + r)t

Where V(t) = Volume after t years

Vo = Present of initial volume

r = rate of increase

t = time

From the question,

V(t) = Volume after t years = unknown

Vo = Present of initial volume = 5m³

r = rate of increase = 6% = 0.06

t = time = 7 in years

V(t) = 5 × ( 1 + 0.06)^ 7

V(t) =(5)(1.06)^7

Therefore, its volume be after 7 years if its volume is 5 cubic meters now is

Option C: (5)(1.06)^7

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

Answer:

h(x) = -15.6(x - 3.8)² + 241

Step-by-step explanation:

if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.

or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)

the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.

Which algebraic expression represents the phrase below?
five times the sum of a number and eleven, divided by three times the sum of the number and eight
5(x + 11) + 3(x + 8)
5x+11
3X+8
5(X+11)
3(x+8)
5x + 11 + 3x + 8

Answers

Answer:

[tex] \frac{5x + 11}{3(x + 8)} [/tex]

Step-by-step explanation:

[tex] \frac{5x + 11}{3(x + 8)} [/tex]

Five times the sum of a number and eleven, divided by three times the sum of the number and eight

Five times the sum= 5(_+_)

a number and eleven= x+11

divided= ÷ or /

3 times the sum of= 3(_+_)

the number and eight.

Together it will be

[tex]the \: \: one \: written \: in \: the \: answering \: section[/tex]

Hope this helps ;) ❤❤❤

Find side AC and round your answer to the nearest hundredth, help please.

Answers

Answer:

Step-by-step explanation:

Side AC is the side opposite the reference angle of 70 degrees while side BC is the side adjacent to the reference angle. AB is the hypotenuse since it is across from (or opposite) the right angle. The trig ratio that uses the sides opposite from and adjacent to the reference angle is the tangent. Setting up to solve for AC:

[tex]tan(70)=\frac{?}{3}[/tex] and

3tan(70) = ? so

? = 8.24

If c cars can be parked in each of the four main rows of the parking lot, what is the expression gor the maximum number of cars that can be parked in the parking lot?

Answers

Answer:

4c

Step-by-step explanation:

We can say that the maximum number of cars can be represented as:

Maximum number of cars = Total of rows × Number of cars per row

In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:

Maximum number of cars = 4c

Your sister asks you to pick out one of her CDs to listen to. She has 6 rock, 4 country, and 4 rap CDs. If you pick one at random, what is the probability that you pick a country CD?

Answers

Hey there! I'm happy to help!

We have 6 rock, 4 country, and 4 rap CDs. If we add these all together ,we have 14 total CDs.

Since there are 4 country CDs, we have a 4/14 chance of picking one, which simplifies to 2/7 chance.

Have a wonderful day!

which of the following is the Pythagorean theorem

Answers

Answer:

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

Step-by-step explanation:

The Pythagorean Theorem is used to find a missing side length in a right triangle, and the formula [tex]a^2+b^2=c^2[/tex] is used to find the missing side, assuming a and b are legs, while c is the hypotenuse.

Answer:

in a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length

What the correct answer now fast

Answers

Answer:

y = 12.9

Step-by-step explanation:

To find the value of the side y, simply apply the law of cosines.

y^2 = (14)^2 + (9)^2 - 2(14)(9)cos(64)

y^2 = 196 + 81 - 110.47

y^2 = 166.53

y = 12.9

Therefore, your solution should be y = 12.9

Cheers.

Please help me with this question!!!!!

Answers

Answer:

B. [tex]H(x)=-.008(x-82)^{2}+83[/tex]

Step-by-step explanation:

Well lets graph the following equation first,

H(x) = -.011(x - 82)^2 + 75

Then lets graph all the other equations.

Look at the image below↓

So A.

The purple line does not go farther or higher,

so A. is incorrect

B.

The black line goes higher and farther,

meaning it is correct.

C.

The red line goes farther but not higher.

So it is incorrect

D.

Again the blue line does not go farther of higher.

So its wrong.

Thus,

answer choice B. [tex]H(x)=-.008(x-82)^{2}+83[/tex] is correct.

Hope this helps :)

Ama has a rectangular garden measuring 12m and 25m.He wants to divide it into square plots of equal sizes .What is the largest sized square he can use?

Answers

The largest sized square should be a 12m x 12m square

In a class Vidya ranks 7th from the top. Divya
is 7 ranks ahead of Medha and 3 ranks
behind Vidya. Sushma who is 4th from the
bottom is 32 ranks behind Medha. How many
students are there in the class?​

Answers

Answer:

52 students

Step-by-step explanation:

From the question above, we have the following information:

a) Vidya ranks 7th from the top.

Mathematically,

Vidya = 7th student

b) Divya 3 ranks behind Vidya.

Divya = Vidya + 3

Hence, Mathematically:

Divya = 7 + 3 = 10

Divya = 10th student

c) Also, Divya is 7 ranks ahead of Medha.

Mathematically,

Medha = 10 + 7= 17

Medha= 17th student

d)Sushma is 32 ranks behind Medha

Mathematically,

Sushma = Medha + 32

= 17 + 32 = 49

Sushma is the 49th student

Therefore, since, Sushma is 4th from the bottom, total number of students is:

49 + 3 = 52 students

A student in a statistics class asks students in a long lunch line about their opinions about the school cafeteria. The sample that results is most likely __________________.
A. quota
B. symmetric
C. large
D. biased

Answers

Answer:

The correct option is;

D. Biased

Step-by-step explanation:

A sampling method in which the members of the sample are not representative of the population, such that some members of the population have a higher or lower probability within the sample which is indicative that not all members of the population are sampled

A biased sample is a non random sample and the can lead to misleading data conclusion

In the question, the sampling of student opinion about the school cafeteria among students who are on the lunch line and so prefer the school cafeteria leaves out the portion of the population that get their lunch from alternative sources.

Answer:

biased

Step-by-step explanation:

please heellllpppp ....​

Answers

Answer:

x ≈ 2.3 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos55° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] ( multiply both sides by 4 )

4 × cos55° = x , thus

x ≈ 2.3 cm ( to 1 dec. place )

Brandon mows his lawn once every 4 days. Thomas mows his lawn once every 8 days. Celena mows her lawn once every 6 days. If they are all mowing the lawn today, in how many days will they be mowing their lawns together again? A. 72 B. 24 C. 18 D. 12

Answers

Answer: B

Step-by-step explanation:

4,8 and 6 all go into 24

Sudhir bought an almirah for RS 13600 and spent RS 400 on its transportation . He sold it for RS 16800 . find the his gain percent

Answers

Answer:

His gain percent is 20%

Step-by-step explanation:

In this question, we want to find the percentage gain of the business.

We need the following parameters;

The cost price which is the sum of the amount she bought the goods + the amount spent on transport

Using the values we have in the question;

The cost price will be;

13,600 + 400 = Rs 14,000

The selling price = Rs 16,800

Mathematically the percentage gain will be;

% gain = (selling price- cost price)/selling price * 100%

% gain = (16,800-14,000)/14,000 * 100/1

% gain = 2800/14,000 * 100/1 = 1/5 * 100/1 = 20%

Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice

Answers

Answer:

1/216

Step-by-step explanation:

When a pair of dice is rolled, there are 36 possible different outcomes.

Of those 36 different outcomes, a sum of 3 is obtained in 2 different ways: 1, 2 and 2, 1.

Of those 36 different outcomes, a sum of 10 is possible in 3 different ways: 6, 4; 5, 5; 4, 6.

p(3 followed by 10) = p(3) * p(10) = 2/36 * 3/36 = 1/18 * 1/12 = 1/216

II NEED HELP!!!!!!!! Are the graphs of the lines in the pair parallel? Explain. y = 2/3x– 17 4x – 6y = –6 4x-6y=-6 Yes, since the slopes are the same and the y-intercepts are the same. A )No, since the y-intercepts are different. B)No, since the slopes are different. C)Yes, since the slopes are the same and the y-intercepts are different.

Answers

Answer:

A

Step-by-step explanation:

Can somebody please help me with this & show work ?? :)

Answers

Answer:

s = 116°, q and t are 64°

Step-by-step explanation:

isoceles so r and s are the same and q and t are the same. therefore q and t are 180-116 = 64

HELP please!!!
Jeanie wants a $100 000 mortgage. She arranged payments for the next 15 years. The bank charges 4.8%/a interest, compounded monthly.
a) how much is each monthly payment
b) how much interest is jeanie paying?

Answers

Answer:

in one month : 13676.57/12=1139.71

the interest on 100000 is: 205148.48-100000=105148.48

Step-by-step explanation:

A=P(1+r)^t   (p is the mortgage, t is the time and r is the rate)

p=100000,t=15*12 month,r=4.8%( or 0.048)

A=100000(1+0.048/12)^(12*15)

A=205148.48 (the number rounded to the nearest hundredth)

205128.48 is the amount she has to pay it after 15 years

in one year : 205128.48/15=13676.57 ( rounded to nearest hundredth)

in one month : 13676.57/12=1139.71

the interest on 100000 is: 205148.48-100000=105148.48

MATH PLEASE HELP ME. WILL GIVE BRAINLIEST

Answers

Answer:

The answer is - 17

Step-by-step explanation:

g(x) = 2x³ - 3x + 5

To find g(- 2) substitute the value of - 2 into g(x)

That's

g(- 2) = 2(-2)³ - 3(-2) + 5

= 2(-8) - 3(2) + 5

= - 16 - 6 + 5

= - 17

Hope this helps you

Explain how to get the volume of this figure

Answers

Answer:

350 meters cubed.

Step-by-step explanation:

If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.

The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.

The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.

(5 * 7 * 3) + (7 * 7 * 5)

= (35 * 3) + (49 * 5)

= 105 + 245

= 350

So, the volume of the figure is 350 meters cubed.

Hope this helps!

NEEEED HELPPPPP PLEASEEEEEE Use long division to find the quotient below.
(8x^2 + 4x^2 + 100) - (2x + 5)

Answers

Answer:

[tex]4x^2 - 8x + 20[/tex]

Step-by-step explanation:

The correct equation is:

[tex]8x^3 + 4x^2 + 100[/tex]

We want to divide that by (2x + 5)

To do the long division, divide each term by 2x and then subtract the product of the result and (2x + 5) from the remaining part of the equation.

When you get to 0, you have reached the end of the division.

Whatever term you get from each step of division is part of the quotient.

Go over the steps above carefully while following them below:

Step 1:

Divide [tex]8x^3[/tex] by 2x. You get [tex]4x^2[/tex].

Step 2

Multiply [tex]4x^2[/tex] by (2x + 5)  and subtract from [tex]8x^3 + 4x^2 + 100[/tex]:

[tex]8x^3 + 4x^2 + 100[/tex] - ([tex]8x^3 + 20x^2[/tex]) = [tex]-16x^2 + 100[/tex]

Step 3

Divide [tex]-16x^2[/tex] by 2x. You get [tex]-8x[/tex].

Step 4

Multiply -8x by (2x + 5) and subtract from [tex]-16x^2 + 100[/tex]:

[tex]-16x^2 + 100[/tex] - ([tex]-16x^2 - 40x[/tex]) = 40x + 100

Step 5

Divide 40x by 2x. You get 20.

Step 6

Multiply 20 by (2x + 5) and subtract from 40x + 100:

40x + 100 - (40x + 100) = 0

From the three steps of the division, we got [tex]4x^2[/tex], -8x and 20.

Therefore, the quotient is [tex]4x^2 - 8x + 20[/tex]

Determine the equation for a line perpendicular to y=1/3+4 and has an x-intercept of 2.

Answers

Answer:

y = -3x + 6

Step-by-step explanation:

Any line perpendicular to

y = (1/3)x + 4

has a slope of -1/(1/3) = -3

and equation

y = -3x + b  .................(1)

If the line has an x intercept of 2 at (0,2), then

0 = -3(2) + b

solving

b = 6

By substituting b=6 into (1), the line required

y = -3x + 6

Answer:

y = -3x + 2

Step-by-step explanation:

y= [tex]\frac{1}{3}x +4[/tex]

Slope [tex]m_{1}=\frac{1}{3}[/tex]

slope of the perpendicular line [tex]m_{2}[/tex] = [tex]\frac{-1}{m_{1}}[/tex] = [tex]\frac{-1}{\frac{1}{3}}=-1*\frac{3}{1}=-3\\[/tex]

b= 2

Slope intercept form of required line: y = mx + b

y = -3x + 2

ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.

Answers

Answer:

C

Step-by-step explanation:

Line of symmetry

Can someone please help me?

Answers

Answer:

( - 1 , - 1 )

Option D is the correct option.

Step-by-step explanation:

y = - 2x - 3 → Equation ( i )

y = 3x + 2 → Equation ( ii )

Using elimination method

y + 2x = - 3

y - 3x = 2

---------------------

5x = - 5

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{ - 5}{5} [/tex]

Calculate

[tex]x = - 1[/tex]

Again, Putting the value of x in equation ( ii ) in order t get the value of y

[tex]y = 3x + 2[/tex]

plug the value of x

[tex] = 3 \times ( - 1) + 2[/tex]

Any expression multiplied by ( - 1 ) equals it's opposite

[tex] = - 3 + 2[/tex]

Calculate

[tex] = - 1[/tex]

Therefore, The possible solution of the system is the ordered pair ( x , y )

[tex](x \:, y \: ) = ( - 1 \:, - 1)[/tex]

-----------------------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

[tex] - 1 = - 2 \times ( - 1) - 3[/tex]

[tex] - 1 = 3 \times ( - 1) + 2[/tex]

Simplify the equation

[tex] - 1 = - 1[/tex]

[tex] - 1 = - 1[/tex]

Since all the equalities are true, the ordered pair is the solution of the system.

( x , y ) = ( - 1 , - 1 )

Hope this helps..

Best regards!!

U
480
S
d
T
b
R.
C
P
1549
Q

Answers

Answer:

a = 26°

b = 48°

c = 26°

d = 106°

Other Questions
If y varies inversely with x and y= 17when z = 11when y = 11find y when x=19. The perimeter of a rectangular field is 344m . If the width of the field is 75m, what is its length? Which of the following sentences means "I kick it to you"?A. Te lo pateo.B. Me lo pateas.C. Nos los pateis.D. Se lo pateamos. What is a co-prime number? Please answer as soon as possible Thank you Faustina _____ con los pies. camina. caminas. camine. camino. Which graph represents the solution to this system of inequalities? y 2x-4 Describe in general a process desert plants might need to carry out in order to maintain homeostasis. (4 points) All plants need water; think about how plants in an area without much water might be able to live. Scenario: The Internet Explorer 8 browser is being used to display a web page with an audio player but the audio element displays nothing on the page. Read the following code snippet and select the reason for the incorrect display from the choices below.width="160" height="150">Sparky the Dog (.mov)A. The controls attribute should be controls="yes"B. There are too many source elements.C. The file extension .ogg is incorrect.D. The MIME type values are incorrect. A right triangle has legs with lengths equal to 10 inches and 9x inches. Its hypotenuse measures (x + 10) inches. What is the approximate value of the hypotenuse? 10 inches 10.25 inches 20.25 inches 81 inches Headache?" asked samuel Solve the following rational equation for x.1/4x-3/4=7/x All of the following would be visible on a karyotype exceptaneuploidy.polysomy.trisomy.homologous chromosomes. The increase in Hollywood revenues outside North America reflects which business trend? Multiple Choice strategic alliance globalization cost reduction cultural distance local responsiveness Which statement best summarizes W. W. Jacobs's "The Monkey's Paw"? A.Sergeant-Major Morris warns the family to be careful with the monkey's paw. B.Mr. White receives a monkey's paw that will grant him three wishes. C.A man makes several wishes on a monkey's paw, with tragic consequences. D.Wishing for extravagant things can lead to tragedy. Which of the following accurately represent the protagonist of Araby? Select all that apply. 1. male 2. nameless 3. has moved to Dublin from the countryside 4. decides not to go to the bazaar with Mangan's sister Find the perimeter of an equilateral triangle where area is 72cm. Solve 2x^2 + x - 4 = 0 X2 + The roots of 100x2 20x + 1 = 0 is: Please answer in the form of a number Which word best describes the mood in this excerpt from Little Brother? He slammed his hand down on the desk and then pointed his finger at me. "The problem, Mr Yallow, is that you've been engaged in criminal conspiracy to subvert this school's security system, and you have supplied security countermeasures to your fellow students. You know that we expelled Graciella Uriarte last week for using one of your devices." Uriarte had gotten a bad rap. She'd bought a radiojammer from a headshop near the 16th Street BART station and it had set off the countermeasures in the school hallway. Not my doing, but I felt for her.