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konstantin123 [22]
2 years ago
5

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the

mean income is found to be $23.7 for a random sample of 4825 people. Assume the population standard deviation is known to be $11.2. Construct the 90% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Mathematics
1 answer:
Arisa [49]2 years ago
5 0
The answer is 50%...
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Calculate the angle of depression, x, if the boat is 850 ft. away from the lighthouse and the lighthouse is 250 ft. high. Round
trapecia [35]

Firstly , we can draw diagram

we can see that

adjacent = 850

opposite =250

so, we can use tan formula

tan(x)=\frac{250}{850}

x=tan^{-1}(\frac{250}{850})

16.38

x=16.38

so,

angle of depression is 16.38 degree........Answer

6 0
3 years ago
Tisha and her academic team are working to go to state finals. They must have a certain number of points to advance. They have h
kolbaska11 [484]

Answer:

b=\frac{T-a-c-d}{3}

b = (T - a - c - d) / 3

Step-by-step explanation:

Let T be the total number of points required to advance.

a, c and d are points scored in the local matches, and b is the number of points scored in the district match. If b is worth 3 times as much as the other matches, the total number of points is given by:

T=a+c+d+3b

Isolate b in order to find out how many points they need in the district match:

T=a+c+d+3b\\3b=T-a-c-d\\b=\frac{T-a-c-d}{3}

They need to score (T - a - c - d)/3, in the district match in order to win.

4 0
3 years ago
Hi can someone please help me on my homework
Murrr4er [49]

Answer:

8. yes, ASA

9. yes, SAS

10. yes, AAS

11. no

12. no

13. yes, SSS

Step-by-step explanation:

4 0
3 years ago
A train leaves Philadelphia at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train t
polet [3.4K]

Answer: First train speed shall be 42 mi/hr

Second train speed shall be 84 mi/hr

Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.

Step-by-step explanation:

What is the 1st train's head start in miles?

Let +s+ = the speed of the 1st train in mi/hr

From 2PM to 4PM is 2 hrs

+d%5B1%5D+=+s%2A2+

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

Let +d+ = distance the 2nd train travels until

it overtakes the 1st train

From 4PM to 6PM is 2 hrs

Start time when the 2nd train leaves

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

Equation for 1st train:

(1) +d+-+2s+=+s%2A2+

Equation for 2nd train:

(2) +d+=+%28+s%2B42+%29%2A2+

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

Substitute (2) into (1)

(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+

(1) +2s+%2B+84+-+2s+=+2s+

(1) +2s+=+84+

(1) +s+=+42+

and

+s%2B+42+=+42+%2B+42+

+s+%2B+42+=+84+

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

The 1st train's speed is 42 mi/hr

The 2nd train's speed is 84 mi/hr

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

check:

(2) +d+=+%28+s%2B42+%29%2A2+

(2) +d+=84%2A2+

(2) +d+=+168+

and

(1) +d+-+2s+=+s%2A2+

(1) +d+-+2%2A42+=+42%2A2+

(1) +d+=+84+%2B+84+

(1) +d+=+168+

8 0
2 years ago
Mr. Wilson invested money in two accounts. His total investment was $20,000. If one account pays 5% in interest and the other pa
blagie [28]

a = amount invested at 5%

b = amount invested at 2%

now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.

a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}

now, we know the total of earned interest is 550 bucks, so then

0.05a~~ + ~~0.02(20000-a)~~ = ~~550\implies 0.05a+400-0.02a=550 \\\\\\ 0.03a+400=550\implies 0.03a=150\implies a=\cfrac{150}{0.03}\implies a=5000 \\\\\\ ~\hspace{24em}\stackrel{20000~~ - ~~5000}{b=15000}

5 0
1 year ago
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