MATHEMATICS
COLLEGE

Answer:

Answer:

Critical value for the rejection region if the level of significance is 5% = 1.645

We conclude that the average starting salary of graduates is more than 85,000$.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 85,000$

Sample mean, = 88,000$

Sample size, n = 64

Alpha, α = 0.05

Population standard deviation, σ = 10,000

First, we design the null and the alternate hypothesis

85,000\text{ dollars}" alt="H_{0}: \mu = 85,000\text{ dollars}\\H_A: \mu > 85,000\text{ dollars}" align="absmiddle" class="latex-formula">

We use One-tailed(right) z test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,

z_{critical}" alt="z_{stat} > z_{critical}" align="absmiddle" class="latex-formula">

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the average starting salary of graduates is more than 85,000$.

HIGH SCHOOL

The measure of one of the acute angles in right triangle is 56.what is the measure of the other acute angle

Answer: 54 degrees

Step-by-step explanation:

right triangle so a degree has to be 90

90+56=146

180-146=54

MIDDLE SCHOOL

What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4? 7ab3

6a4b

42a5b4

77a8b7

6x(10x2 + 8x + 2)

12x(5x2 + 4x + 2)

Answer:

the answer is 77a8b7

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I took the test

HIGH SCHOOL

Joan and Carl both worked 19 hours this week and each sold $2000 worth of meals. Their hourly wages are $10.50 and $9.00, respectively. In addition, Joan's percent of tips was 12% while Carl's was 23%. Who made the most money this week between Joan and Carl?

Answer:

Carl

Step-by-step explanation:

The money each made is ...

(19 hours)(hourly rate) +($2000)(tip rate)

For Joan, this is ...

(19 h)($10.50/h) +($2000)(0.12) = $199.50 +240 = $439.50

For Carl, this is ...

(19 h)(9.00/h) +($2000)(0.23) = $171.00 +460 = $631.00

Carl's take for the week was $191.50 more than Joan's.

_____

You can also compare the difference in wages of 1.50/h × 19 h = $28.50 to the difference in tips of 11% × $2000 = $220. Carl's additional tips more than made up for his lower wages.

Answer:

Carl

Step-by-step explanation:

Joan and Carl both worked 19 hours this week and each sold $2000 worth of meals. Their hourly wages are $10.50 and $9.00, respectively. In addition, Joan's percent of tips was 12% while Carl's was 23%. Therefore, Carl made the most money this week.

MIDDLE SCHOOL

If a submarine surfaced after a dive of 20 fathoms, how far was the round trip

The submarine dove 20 fathoms of water, and one fathom of water is equivalent to 6 feet of water. Thus, the submarine descended 20 * 6 feet

= 120 feet

The submarine then traveled the same distance to return to the surface. Therefore, covered 120 feet again.

The submarine thus traveled 120 + 120 =

240 feet in the round trip

= 120 feet

The submarine then traveled the same distance to return to the surface. Therefore, covered 120 feet again.

The submarine thus traveled 120 + 120 =

240 feet in the round trip

HIGH SCHOOL

Determine the slope of the line that contains the given points T(4,6) a V(8,7) A) -1/2

B) 4

C) 1/4

D) -4

Finding the slope using two points:

The formula for slope is

In this case...

^^^Plug these numbers into the formula for slope...

C)

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

The answer is C. 1/4

HIGH SCHOOL

What is y? 2(-3y-6)+4(5y-8)=92

I got 9.5 but when I checked it, I couldn't seem to get the right one.

2(-3y - 6) + 4(5y - 8) = 92 |use distributive property: a(b - c) = ab - ac

-6y - 12 + 20y - 32 = 92

14y - 44 = 92 |add 44 to both sides

14y = 136 |divide both sides by 14

y = 136/14

y = 68/7

y = 9 5/7

-6y - 12 + 20y - 32 = 92

14y - 44 = 92 |add 44 to both sides

14y = 136 |divide both sides by 14

y = 136/14

y = 68/7

y = 9 5/7

COLLEGE

There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. A county healthy office inoculates 83 people. What is the probability that exactly 10 of them will get the disease at some point in their lives?

Let be a random variable denoting the number of inoculated people in a population of size that contract this disease. is said to be binomially distributed with probability , or .

So the probability that exactly 10 of 83 people get the disease, despite inoculation against it, is

So the probability that exactly 10 of 83 people get the disease, despite inoculation against it, is

MIDDLE SCHOOL

Lori buys a $459 certificate of deposit (CD) that earns 5.6% interest that compounds monthly. How much will the CD be worth in 6 years? (Express your answer rounded correctly to the nearest cent!)

According to the question:

Principal,

Rate of interest,

Time,

Compounded Monthly.

According to the formula of Compound Interest, the worth of certificate of deposit in 6 years will be:

i.e.,

i.e.,

i.e.,

i.e.,

i.e.,

MIDDLE SCHOOL

What is 3/5 times 20

First make 20 into a fraction, then solve; 3/5 · 20/1. 60/5 = 12. Hope that helps!

Answer:

your answer should be 12