uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24

Answers

Answer 1

Answer:

[tex]P(x \le 3.24) = 0.97725[/tex]

Step-by-step explanation:

Given

[tex]\bar x = 2.5[/tex]

[tex]\sigma = 0.37[/tex]

Required

Percentage that is not more than 3.24

The above implies that:

[tex]x = 3.24[/tex]

Calculate z score

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]

[tex]z = \frac{0.74}{0.37}[/tex]

[tex]z = 2[/tex]

So, the probability is represented s:

[tex]P(x \le 3.24) = P(z \le 2)[/tex]

From z probability

[tex]P(z \le 2) = 0.97725[/tex]

Hence:

[tex]P(x \le 3.24) = 0.97725[/tex]


Related Questions

A field is a rectangle with a perimeter of 1100 feet. The length is 300 feet more than the width. Find the width and length of the rectangular field

Answers

Answer:

Step-by-step explanation:

perimeter of rectangle = 1100

let breadth be x

length = 300 + x

perimeter of rectangle = 2(l + b)

1100 = 2(300 + x + x)

1100 = 2(300 + 2x)

1100 = 600 + 4x

1100 - 600 = 4x

500 = 4x

500/4 = x

125 = x

therefore breadth is 125 feet

length = 300 + 125

=425 feet

Answer:

The rectangular field is 425 feet by 125 feet.

Step-by-step explanation:

Let w represent the width of the rectangular field.

Since the length is 300 feet more than the width, the length can be modeled by the expression (w + 300).

The perimeter of a rectangle is given by the formula:

[tex]P=2(w+\ell)[/tex]

Where P is the perimeter and w and l are the width and length, respectively.

We are given that the perimeter is 1,100 feet. Substitute:

[tex]1100=2(w+\ell)[/tex]

Divide both sides by two:

[tex]550=w+\ell[/tex]

We know that l = (w + 300). So:

[tex]550=w+(w+300)[/tex]

Simplify:

[tex]2w=250[/tex]

Divide both sides by two. So, the width is:

[tex]w=125\text{ feet}[/tex]

Since the length is 300 feet more than the width, that means the length is 425 feet.

The rectangular field is 425 feet by 125 feet.

Which of the following is not equal to a ratio of 5 to 2?

A. 25: 10 C.35: 15

B. 35: 14 D. 40:16

Answers

Answer:

C 35:15

Step-by-step explanation:

because 35:15 =5:3 so it is not equal to a ratio of 5 is to 2

Answer:

C

Step-by-step explanation:

If you simplify all the ratios, then you get the following:

A. 25/5 : 10/5 = 5:2

B. 35/7 : 14/7 = 5:2

C. 35/5 : 15/5 = 7:3

D. 40/8 : 16/8 = 5:2

Please help I need help with my hw

Answers

Answer:

a) 2.5 pounds of candy

b) 2.5 pounds of candy

    [tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

    y × 1 = 0.5 × 5

    y = 2.5

Step-by-step explanation:

1 = 5

1/2 = y or 0.5 = y

[tex]\frac{0.5}{1} :\frac{y}{5}[/tex]

y × 1 = 0.5 × 5

y = 2.5

Triangle D E F is shown. Angle E F D is a right angle. The length of E F is 24 and the length of D F is 7.
Which trigonometric ratios are correct for triangle DEF? Select three options.


sin(D) = StartFraction 24 Over 25 EndFraction
cos(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 24 Over 7 EndFraction
sin(E) = StartFraction 7 Over 25 EndFraction
tan(D) = StartFraction 7 Over 24 EndFraction

Answers

Answer:

Sin(E) = 7/25

Sin(D) = 24/25

Tan(D)= 24/7

Step-by-step explanation:

Sin=opp/hyp

Tan=opp/adj

Cos=adj/hyp

The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

How to determine the trigonometric ratios?

The given parameters are:

EF = 24

DF = 7

Start by calculating the length DE using:

DE²= EF² + DF²

So, we have:

DE²= 24² + 7²

Take the square root of both sides

DE= 25

The sine of the angles is calculated using:

sin(Ф) = opp/hyp

So, we have:

sin(E) = 7/25

sin(D) = 24/25

The tangent of the angles is calculated using:

tan(Ф) = opp/adj

So, we have:

tan(D)= 24/7

Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7

Read more about trigonometric ratios at:

https://brainly.com/question/11967894

How many centimeters are there in 3 meters?

A. 100 cm
B. 200 cm
C. 300 cm
D. 400 cm

Answers

Answer:

Step-by-step explanation:

c

Work out the value of 8³

Answers

Answer:

512

Step-by-step explanation:

find the value of 3mm(m+y)​

Answers

Answer:

Step-by-step explanation:

3mn (m+y)

= 3[tex]m^{2}[/tex]n + 3mny

4 x^2+ 4x-14 x=0
Solve this please, you will get brainLiest. Thank you :)

Answers

Answer:

x could be 0 or it could be 5/2

Step-by-step explanation:

Answer:

x= 5/2

Step-by-step explanation:

4x^2 + 4x - 14x = 0

subtract 4x from 14x because they are like terms

4x^2 - 10x=0

4x^2 = 0 + 10x

4x^2 = 10x

x^2/x = 10/4

x=10/4

x=5/2

HELPPPP MEEE

5x-7+3x and 3x-7+5x
equivalent or not equivalent

4y+9+3y and 3y+9+4y
equivalent or not equivalent

6z-2z+4 and 4+2z-6z
equivalent or not equivalent

Answers

Answer: See explanation

Step-by-step explanation:

1. 5x-7+3x and 3x-7+5x

5x - 7 + 3x

Collect like terms

5x + 3x - 7 = 8x - 7

3x-7+5x

Collect like terms

3x + 5x - 7 = 8x - 7

They're equivalent

2. 4y+9+3y and 3y+9+4y

4y + 9 + 3y

Collect like terms

4y + 3y + 9 = 7y + 9

3y + 9 + 4y

Collect like terms

3y + 4y + 9 = 7y + 9

They're equivalent

3. 6z-2z+4 and 4+2z-6z

6z - 2z + 4 = 4z + 4

4 + 2z - 6z = 4 - 4z

They're not equivalent

Will mark Brainlest Help
find the domain and range in each of the following ​

Answers

Step-by-step explanation:

Domain: possible value of x

Range: possible values of y

Domain:

Given in the question

-1smaller or equal to x smaller or equal to 1

Range:

y is greater than 1, smaller than 3

[tex] \sqrt{ \frac{y - 1}{2} } = x \\ [/tex]

y cannot be smaller than 1

when substitute velue of x= 1 or negative 1

we get y=3 and any values between 1 and negative 1 when substitute in x, will give values of y in between 3 and 1.

first list all elements of x and y..

x= -1,0,1

y=2x^2+1

whenx=-1 y=2×-1^2+1=5

similarly, when x=0,y=1

x=1, y=5

therefore, domain=x={-1,0,1}

range=y={1,5}

A railway station measures 200 meters in length. How long is it?


A. 10,000 cm
B. 12,000 cm
C. 15,000 cm
D. 20,000 cm

Answers

D. 20,000. (1 meter = 100 centimeters…200x100=20,000)
The answer is D. 20,000 cm.

36 and 60 as ratio //////// do not mind what I'm going to type on this sidehdshhdsdhdshjhsjdhsdhjd

Answers

36:60

= 18:30

= 9:15

= 3:5

Write the product in simplest form: 1 2/3 x 3 4/5=

Answers

Answer:

19/3

Step-by-step explanation:

1 2/3 = (1*3 + 2)/3 = 5/3

3 4/5 = (5*3 + 4)/5 = (15 + 4)/5 = 19/5

5/3 * 19/5 = 19/3    The 5s cancel.

The simplest form is not obvious to me. I think the answer above is in simplest form, and I will put that below the answer above. But 6 1/3 is also possible.

Answer:

4 1/3

Step-by-step explanation:

1 [tex]\frac{2}{3}[/tex] × 3 [tex]\frac{4}{5}[/tex] =

[tex]\frac{5}{3}[/tex] × [tex]\frac{19}{5}[/tex] =

[tex]\frac{95}{15}[/tex] = 4 [tex]\frac{5}{15}[/tex] = 4 1/3

bcore: 9/ 120 5/17 answered Question 7 You deposit $4000 in an account earning 7% interest compounded monthly. How much will you have in th account in 10 years? Submit Question​

Answers

Answer:

8038.65

Step-by-step explanation:

[tex]4000(1+\frac{.07}{12})^{12*10}=8038.65[/tex]

Can y’all help me on question 20?!

Answers

Answer:

yes I can help you but ???

A. 39 1/2 Meters INCORRECT!

B. 70 Meters CORRECT!

C. 39 Meters INCORRECT!

Suppose that y varies directly with x and inversely with z; y = 27 when
x = 21, and z = 7. Write the equation that models the relationship. Then
find y when x = 25 and z = = 5.

Answers

The value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

What is a proportional relationship?

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have:

y varies directly with x and inversely with z.

y ∝ x/z

Removing the proportional sign.

y = kx/z

k is the constant of proportionality.

Plug y = 27, x = 21, and z = 7 to get the value of k

27 = 21k/7

k = 9

y = 9x/z

Plug x = 25, and z = 5

y = 9(25)/5

y = 45

Thus, the value of y is 45 when x = 25, z = 5 and the value of constant of proportionality is 9, and equation is y = 9x/z

Learn more about the proportional here:

brainly.com/question/14263719

#SPJ1

Help me pleaseeeeeeeee

Answers

Answer:

(f o g)(x) = 4x^4 - 24x^2 + 37

(g o f)(x) = 16x^4 + 8x^2 - 2

Step-by-step explanation:

f(x) = 4x^2 + 1

g(x) = x^2 - 3

(f o g)(x) = f(g(x)) = f(x^2 - 3) = 4(x^2 - 3)^2 + 1 =

= 4(x^4 - 6x^2 + 9) + 1

= 4x^4 - 24x^2 + 37

(g o f)(x) = g(f(x)) = g(4x^2 + 1) = (4x^2 + 1)^2 - 3 =

= 16x^4 + 8x^2 - 2

PLS HELP!! WILL GIVE BRAINLIEST!!! >.<
Write one function for each house to describe the value of the house f(x), in dollars, after x years.

Answers

straightAnswer:

Step-by-step explanation:

The strategy would be to look for the equations of  lines that passes for the points. it can be done but it's a hard work. I prefer to use a calc sheet . You can se that house 2 has a perfect fit to data because it has a [tex]R^2=1[/tex], however house 1 does not have a perfect fit, [tex]r^2=0.99..[/tex] altough it is a very good fit, in the image you can see the corresponding equations

Given: In this figure, `/_AED` and `/_BEC` form a pair of vertical angles. Prove: `/_AED ~= /_ BEC `. Match each statement to its corresponding reason. Drag the items on the left to the correct location on the right.

Answers

Answer:

Step-by-step explanation:

The matched statement to its corresponding reason for the given alternate interior angles as:

Given: Let points A, B, and C form a triangle.

definition: Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Congruent angles: m∠1=m∠4, m∠3 = m∠5

Linear pair theorem: m∠4+m∠2+m∠5 = 180°

As per the shown figure,

Given:

Let points A, B, and C form a triangle.

Defining a parallel line and labeling angles:

Let stackrel(harr)(DE) be a line passing through B, parallel to "bar(AC)", with angles labeled as shown.

Alternate Interior Angles Theorem:

∠1=∠4

∠3 = ∠5

Congruent angles have equal measures:

m∠1=m∠4

m∠3 = m∠5

Definition of a straight angle and angle addition:

m∠4+m∠2+m∠5 = 180°

Substitution:

m∠1 + m∠2 +m ∠3 = 180°

Learn more about Alternate exterior Angles here:

https://brainly.com/question/23134598

#SPJ4

Find the missing length indicated. Hey can someone help me out?

Answers

Answer:

C) 6

by-step explanation:

pls help me do this question but pls don't get it wrong this is my attempt ​

Answers

Answer: (c)

Step-by-step explanation:

Given

The function is [tex]y=-x^2+6x-4[/tex]

Range of a function describes the values y can take

from the graph it is clear that the maximum value of y is 5

[tex]\therefore y\leq5[/tex]

Hence. option (c) is correct.

Given a mean of 21 and a standard deviation of 1.2, what is the z-score of 21?

Answers

zero the z score of the mean is always zero

Natalie just rented an apartment for $900 a month.she was told that the rent will increase 5.5% each year. About how much will her rent be in 7 years

Answers

Answer:

Step-by-step explanation:

the equation you write to solve this should be:

x = 900 (1 + 0.055)^7

x = 900 (1.055)^7

x = 900 (1.454679131133794609375)

x = 1,309.21

*** Note that the answer was rounded to the nearest hundredths digit. ********

Given that ABCD is a rectangle, find the total area of the figure below. Round your answer to the nearest tenth.
Options
18 ft²

20.25 ft²

21.5 ft²

22.5 ft²

Answers

Answer:

C

Step-by-step explanation:

16
The ideal width of a safety belt strap for a certain automobile is4 cm. An actual width can vary by at most 0.3
cm. Write an absolute value inequality for the range of acceptable widths, in centimeters.
IW - 41 303
0214

Answers

Answer:

|x - 4| ≤ 0.3

Step-by-step explanation:

The actual width = 4

Maximum variation, x = 0.3

Hence, the lowest width position based on actual width and possible variation is :

4 - 0.3 ≤ x ≤ 4 + 0.3

3.7 ≤ x ≤ 4.3

The running back for the Bulldogs football team carried the ball 7 times for a total loss of 8 3/4 yards. Find
the average change in field position on each run. Enter the average change as a simplified mixed number.
The average change in field position on each run was
yards.

Answers

Answer:

-1  1/4 yards

Step-by-step explanation:

7 carries

-8.75 yards  total yardage

    -.8.75 / 7  =  -1.25 yards average per carry

In mixed number ?    -1  1/4 yards          

Please answer this, its one of my homework questions

Answers

Answer:

4^4=4^3*4=64*4=256

4^6=4^5*4=1024*4=4096

Step-by-step explanation:

Answer:

4^4 = 256

4^6 = 4,096

Please help me solve this question and steps.Thank you.

Answers

9514 1404 393

Answer:

  no

Step-by-step explanation:

The first step is to understand that the question is asking about the future value of series of payments. An appropriate formula is ...

  P = A(n/r)((1 +r/n)^(nt) -1)

where P is the future value, A is the periodic payment made n times per year for t years. r is the annual interest rate.

The next step is to substitute the given values and do the arithmetic. Using the given values, we have ...

  P = 250(12/0.056)((1 +0.056/12)^(12×2.5) -1) ≈ 8030.32

Shen will have accumulated about $8,030.32, which is not enough to meet his goal.

what is the equation that matches this table?

Answers

Answer:

y = –1 + 3x

Step-by-step explanation:

To know which option is correct, we shall use the equation given in each option to see which will validate the table. This is illustrated below:

Option 1

y = –1x + 3

x = –2

y = –1(–2) + 3

y = 2 + 3

y = 5

This did not give the required value of y (i.e –7) in the table.

Option 2

y = 1 + 3x

x = –2

y = 1 + 3(–2)

y = 1 – 6

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 3

y = –3 + 1x

x = –2

y = –3 + 1(–2)

y = –3 – 2

y = –5

This did not give the required value of y (i.e –7) in the table.

Option 4

y = –1 + 3x

x = –2

y = –1 + 3(–2)

y = –1 – 6

y = –7

This gives the required value of y (i.e –7) in the table.

Thus, the equation that matches the table is:

y = –1 + 3x

An earthquake with a rating of 6.5 is
considered a major earthquake that can
cause damage over a large area.

Answers

Answer:

it is not considered a major earthquake, for it to be considered a major earthquake it has to have a rating of 8.0 or higher

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