Mathematics High School

Assume that the data in each of the following problems is normally distributed. The average salary for a first-year teacher is $35,512 with a standard deviation of $3250.

what salary is two standard deviations above the mean (average) salary?

what is the probability when a first-year teacher makes a salary between $35512 and $38762 ?

what's the probability that a first-year teacher makes a salary between $35,512 and $42,012?

what's salary range accounts for 34% of the salaries below the average salary?

what is the probability of a first-year teacher making more than $42,012

according to the data above, is it likely that a first-year teacher will make more than $46,000? explain your reasoning ​

Answers

Answer 1

Answer:

1) $42,012

2) 0.34134

3) 0.47725

4) $34,173

5) 0.02275

6) Yes, it is likely

Step-by-step explanation:

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = $35,512

σ is the population standard deviation = $3250

1) what salary is two standard deviations above the mean (average) salary?

Two standard deviations above the mean, the formula is given as:

μ + 2σ

$35,512 + 2 × $3250

= $42,012

Therefore, the salary that is two standard deviations above the mean (average) salary is $42,012

2) what is the probability when a first-year teacher makes a salary between $35512 and $38762 ?

For x = $35512

z = 35512 - 35512/3250

z = 0

Probability value from Z-Table:

P(x = 35512) = 0.5

For x = $38762

z = 38762 - 35512/3250

z = 1

Probability value from Z-Table:

P(x = 38762) = 0.84134

Hence, the probability when a first-year teacher makes a salary between $35512 and $38762 is calculated as:

P(x = 38762) - P(x = 35512)

0.84134 - 0.5

= 0.34134

3) what's the probability that a first-year teacher makes a salary between $35,512 and $42,012?

For x = $35512

z = 35512 - 35512/3250

z = 0

Probability value from Z-Table:

P(x = 35512) = 0.5

For x = $42012

z = 42012 - 35512/3250

z = 2

Probability value from Z-Table:

P(x = 42012) = 0.97725

Hence, the probability when a first-year teacher makes a salary between $35512 and $42012 is calculated as:

P(x = 42012) - P(x = 35512)

0.97725 - 0.5

= 0.47725

4) what's salary range accounts for 34% of the salaries below the average salary?

We find the z score of the 34th percentile

= -0.412

x is the raw score = ?

μ is the population mean = $35,512

σ is the population standard deviation = $3250

z = -0.412

Hence:

-0.412 = x - 35512/3250

Cross Multiply

-0.412 × 3250 = x - 35512

+ 1339 = x - 35512

x = 35512 - 1339

x = 34173

Therefore, the salary range accounts for 34% of the salaries below the average salary is $34,173

5) what is the probability of a first-year teacher making more than $42,012

More than = Greater than = >

For x >$42012

z = 42012 - 35512/3250

z = 2

Probability value from Z-Table:

P(x<42012) = 0.97725

P(x>42012) = 1 - P(x<42012)

= 0.02275

6).according to the data above, is it likely that a first-year teacher will make more than $46,000?

More than = Greater than = >

For x > $46,000

z = 46000 - 35512/3250

z = 3.22708

Probability value from Z-Table:

P(x<46000) = 0.99937

P(x>46000) = 1 - P(x<46000)

= 0.00062531

From the above calculations, yes, it is likely

Yes

Related Questions

Find the volume of this shape please!

Answers

I’m pretty sure it’s 160 but don’t put it yet until someone else answers

find the surface area of the prism

Answers

Answer:

         740 m²

Step-by-step explanation:

The surface area of a prism is a sum of areas of all of its faces

2×(¹/₂×16×15) + 2×(17×10) + 16×10 = 240 + 340 + 160 = 740 m²

Factor completely.
25 - 64x2

Answers

Answer:

Factor 25−64x2

−64x2+25

=(8x+5)(−8x+5)

Answer:

(8x+5)(−8x+5)

What is the value of g 6

Answers

Answer:

9.8

Step-by-step explanation:

The answer is going to be 9.8

PLEASE HELP QUICK!!!

A line passes through the points (3, 9) and (0, 3). What is its equation in slope-intercept form?

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

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

Step-by-step explanation:

Given :-

Two points are given to us .The points are (3,9) and (0,3) .

And we need to find the equation in slope intercept form. So here we can find the equation of the line using two point form , as ,

[tex]\implies y - y_1 = \dfrac{ y_2-y_1}{x_2-x_1}( x - x_1) [/tex]

Now plug in the respective values ,

[tex]\implies y - 9 = \dfrac{ 3-9}{0-3}( x - 3) \\\\\implies y - 9 =\dfrac{-6}{-3}( x - 3 ) \\\\\implies y - 9 = 2( x - 3 ) \\\\\implies y - 9 = 2x - 6 \\\\\implies y = 2x - 6 +9 \\\\\implies \boxed{ y = 2x + 3 }[/tex]

Hence the equation in slope intercept form is y = 2x + 3.

Find the area of a circle with radius,
r
= 5.99m.
Give your answer rounded to 2 DP.

Answers

Answer: 112.72

Step-by-step explanation: We know that the formula for area of a circle is pi*r^2. Now we plug in the values. pi*5.99^2. Next we get rid of the exponent. 5.99*5.99 = 35.8801. Now we have pi*35.8801. Now if you are gonna use actual pi for this your answer would be 112.72065857. Round it to 2 decimal points and you have 112.72 . If you do 35.8801*3.14=112.663514 -> Round this and you have 112.66. So any of them would actually work but I would stick with 112.72.

Find m angle dbc in the figur below

Answers

Answer:

It like the once like Line with smaller angle (DBC) measure wouldn't 30* and by the exam the ratio of angle use by subjective by multiplying as large of angle.

oh, by the way I think I hope I'm right so good luck with that?

Yumiko has a drip hose attached to a rain barrel for her garden. The water drains from the rain barrel at a constant rate. What is the change in the volume of water after 1 minute ?​

Answers

The Change after 1 minute is 3/5 gallon but as a fraction hope I helped have a good day :)!!

i need help on number 10!!! plese and thanks

Answers

Answer:

4 5/6

Step-by-step explanation:

4 5/6 = 29/6

5 1/6 = 31/6

29/6 + 31/6 = 60/6 = 10

(please explain clearly, I am very tired) Find the surface area of the composite figure.

Answers

Answer:

644

Step-by-step explanation:

SA=[2×(5×20 + 5×6 + 20×6)] +

[2×(4×12 + 4×6 + 12×6)] -

[ 2× 12×6]

= [2×(250)]+[2×(144)] - [144]

= 500+288-144

= 644 cm²

replace the # symbols in the row 1 function to match the graph below f(x)=(x+5)(x+#)(x-1)(x-#)​

Answers

Answer:

3, 5

Step-by-step explanation:

Looking at the graph, the x-intercepts are -5, -3, 1 and 5.

Hence the graph equation is (x+5)(x+3)(x-1)(x-5)

what fractions are less than 1/2 is it 5/4,1/4 1/5,2/3 2/12,51/100

Answers

Answer:

1/4, 1/5, 2/12

Step-by-step explanation:

these are all lower than 1/2(0.50)

1/4=0.25

1/5=0.20

2/12= about 0.17

PLEASE HELP
I NEED HELP ASAP
Question in photo​

Answers

Answer:

See below

Step-by-step explanation:

ΔABC has been flipped over, so we have a reflexion using line BC

So, the answer to 1.  is line BC

The result is ΔE'F'D'

Now ΔE'F'D' is moved 4 units to the right.  That is the answer to 2.

The result is ΔE"F"D"

Finally ΔE"F"D" is moved 1 unit down.  That is the answer to 3.

The final result is ΔEFD

Ok.  Did that help you?

Can someone do this please asap

Answers

Answer:

f=180-(61+87)

=180-148

=32

e=f=32

e=32

d=180-(87+32)

=61

wish one is bigger 256 cups or 13 gallons

Answers

Answer:

256 cups

Step-by-step explanation:

There are 16 cups in a gallon and 16x13 equals 208, which is less than 256

Help please! No links

Answers

Answer:

Y=x+3

Step-by-step explanation:

Just subtract the x value from the y value and you will always get the right answer... But isn't this iready? A test?

Find the surface area of the figure below.
Round to the nearest tenth. Do not
use commas in your answer or units of
measures. Only use numbers and decimals.

Answers

Answer:

2167.7 sq yds

Step-by-step explanation:

SA(cone) = πr² + πrs     ('s' = slant height)

= π(15)² + π(15)(31)

= 225π + 465π

= 690π

= 2167.7

Refer to the figure to complete the following item.

Given: PB tangent PV, PU secants

angle1=30 and mSTarc= 20, then mVUarc=___​

Answers

Answer:

Answer: 80°

Step-by-step explanation:

Since, If two secants intersect outside the circle, then the measure of the angle formed is one half of the difference  of the measures of the intercepted arcs.

In the given diagram,

Chord VS and chord UT are intersecting externally,

Also, ∠SPT is the angle formed by the intersection of these chords.

Thus, by the above property,

⇒ Measurement of the arc VU= 80°.

Answer:

80 is the correct answer

Step-by-step explanation:



Find the area of a square with side lengths of 2/5 inch

Answers

The area of the square would be 4/25 here is the work:

Area of an 2d shape: length * width

For a square it is 2/5 * 2/5

You multiply the two numbers and you should get 4/25.


If helped mark me the brainiest!!

PLEASE HELP QUICK. The Hiking Club plans to go camping in a State park where the probability of rain on
any given day is 4/5. What is the probability that it will rain on exactly six of the six
days they are there? Round your answer to the nearest thousandth.

Answers

Answer:0.013

Step-by-step explanation:

(DOK 2)
Find the area of each triangle. Round to the nearest tenth.
5
40°
3

Answers

4.82
hope this helped <3

Answer:

D

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ab sinC ( a, b are the sides and C the angle between them ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × 3 × sin40° = 7.5 × sin40° ≈ 4.8 units² ( to nearest tenth )

Help please
Nowwwww

Answers

Answer:

ab+ac

Step-by-step explanation:

The area of the figure is the length multiplied by the width, which is (a+b)c. By the commutative property, this is equal to c(a+b), and by the distributive property, it is also equal to ac+bc. It is not equal to ab+ac.

Answer:

c(a+b)

Step-by-step explanation:

A bag contains 6 white marbles, 5 red
marbles, 19 marbles of other colors. Find the probability of choosing a white marble and then a red marble if you replace the first marble before choosing the second marble.

Answers

Answer:

1/30

Step-by-step explanation:

      6 white marbles

      5 red marbles

+    19 marbles of other colors

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

     30 marbles in total

First drawing:

p(white) = (number of white marbles)/(total number of marbles)

p(white) = 6/30 = 1/5

Second drawing:

Since the first marble is replaced, there are still 30 marbles in the bag.

p(red) = (number of red marbles)/(total number of marbles)

p(red) = 5/30 = 1/6

The two drawings are independent events, so the overall probability of the two events is the product of the individual probabilities.

p(white then red) = p(white) × p(red)

p(white then red) = 1/5 × 1/6

p(white then red) = 1/30

The percentage difference from 239,900 to 251,895

Answers

Answer:

4.87805%

Step-by-step explanation:

yuh yw

Answer:

= 4.87805% difference

Solution:

Calculate percentage difference

between V1 = 239900 and V2 = 251895

|V1−V2|[(V1+V2)2]×100=?

=|239900−251895|[(239900+251895)2]×100

=|−11995|[4917952]×100

=11995245897.5×100

=0.0487805×100

=4.87805%difference

8/15(-2/3) whats the answer?

Answers

Answer:

-0.8 is the correct answer of this question

Answer:

-16/45

Step-by-step explanation:

When you mulitply these two fractions together it's best to muliteply them by the number across so therefore 8x-2= -16 and 15x3= 45 which you end up with -16/45

What is the height ? Please help, I need it! Urgent !

Answers

Answer:

207.24 inch^2

Step-by-step explanation:

A=2*3.14*9+2.3.14*3*8

=56.52+150.72

=207.24 square inches

Ahmed works 6 days daily from 9 am to 5pm at a local bank at a rate of 30 dollars per hour . how much he earns daily from his job​

Answers

IIIIIIIIIIIIIOOIIIOOOIOWPWKDNRBKRRPJWBWOepejejwldnkwoqjddnbdbdbdbd

Answer:

$240

Step-by-step explanation:

the working hours per day =

5pm - 9am = 17-9 = 8 hours

so, he earns daily = 8×30

= $240

Help mee…pleasseeessss

Answers

The answer would be: 63 < 2j (im so sorry if I’m wrong)

If w÷3=3(w-1)-1 find the value of w

​

Answers

Answer:

3/2

Step-by-step explanation:

w/3=3(w-1)-1

w=9w-9-3

-8w=-12

w=3/2

y=5x-9
-2x-3y=-7
Please show
work!

Answers

Answer:

hmm... thats a good question

Step-by-step explanation:

as you can see i'm Petty

Answer:

JK

Step-by-step explanation:

HAHA it's so funny don't do it to other people like u did to me bacause if u don't know it don't awnser it

Other Questions
35/49 - 3/7 in it's simplest form What is the value of the expression below when z = 5 2. Find the values of the six trigonometric functions for angle 0, when AC = 10 and BC = 8. similarities of business correspondence and the other types of communication You pay 5.65% on the first 110,000 of income and 1.45% in excess of $110,000. Calculate the FICA tax for an employee who earns 60,000 a year Which of the following organizations was created by the Allied Forces to prevent futurewars, protect human rights, and keep the peace in the world after WWII ended? 4. More people die each year in the U.S. as a result ofa. Alcohol.b. Tobacco.c. Marijuana.d. Cocaine.e. Heroin. In a class, we have 61 students of different majors. There are 23 chemistry majors (C), 12 math majors (M), 9 engineering majors (E), and 17 students who are undecided (U). Of these students, 4 of them have declared both math and engineering majors. A student will randomly be chosen to win a scholarship.Suppose that we decide to award three scholarships. What is the probability that the first winner is a chemistry major, the second winner is a chemistry major, and the third winner is an undecided major? (A student cannot win more than one scholarship). a. 0.3096.b. 1.0319.c. 0.0398.d. 0.9604. Whats 4.87 rounded to the nearest tenths Help pls pls help pls find the area of each circle This year, a construction company had expenses of $850 million, which was $75 million more than the expenses fromlast yearHow much were last year's expenses? In the compound NaCl (table salt) the metal sodium (Na) has a -1 ionic charge. What is the dynamics, harmony, texture of the song Mercy by Shawn Mendes Can someone please help me ? MARKING BRAINLIEST..yes yes What is the measure of arc FGD?DHGEF 34 Simplify the algebraic expression:2(y + 5) + 3y - 4 Sorry the image is blurry, please help me. Each bar includes the left-end value but not the right-end value. For example, the first barincludes dogs that weigh 60 pounds and 68 pounds but not 80 pounds.