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3 years ago

PLEASSSSSE HELPPPPPP This is my third post of this! I really need help

Mathematics

1 answer:

Nesterboy [21]3 years ago

6 0

Answer: x=25

solution:

we know that
The triangle external angle theorem states that: An exterior angle of a triangle is equal to the sum of the opposite interior angles

In this problem:
m∠9=m∠7+m∠8

substitute the given values:
(6x-20)°=30°+4x°

now solve for x:
6x-4x=30+20
2x=50
x=25 which is the final answer:)

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Could -free, automatic faucets actually be housing more bacteris than the old fashioned, manual kind The concern is that decreas

Volgvan

Answer:

Not enough evidence to reject Null hypothesis

Step-by-step explanation:

Solution:-

- A comparative study for bacterial growth in manual and electronic faucets is made.

- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.

- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.

- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.

- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.

- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:

Null Hypothesis: P = 0.15

Alternate hypothesis: P > 0.15

- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.

- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.

- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:

X ~ Bin ( 20 , 0.15 )

- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).

- The pmf for a binomially distributed random variable X is given below:

$P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)$

Where,

p ( success ) = 0.15

p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85

- Use the pmf to determine the required test statistics:

$P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\$

$P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003$

- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003

- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.

- Assuming normality of the population, the Z-statistics would be:

$Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109$

- If we were to test the claim to 90% level of confidence:

significance level (α) = 1 - CI = 1 - 0.9 = 0.1

- The rejection region Z-critical is defined by a right-tail:

$Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28$

- Compare the test statistics with the rejection criteria defined by the Z-critical:

Z-test < Z-critical

-1.84 < 1.28

Conclusion:

There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.

3 0

4 years ago

(Optional topic) Should the government help the poor? In the 2014 General Social Survey, 32% of those sampled thought of themsel

alina1380 [7]

Answer:

0.71875

Step-by-step explanation:

Probability that a person thinks of himself as Democrat = P(A)= 0.32

Probability that a person agress that the govt. in Washington should do everything possible to improve the standard of living of poor= P(B)

Probability that a Democrat agress that the govt. in Washington should do everything possible to improve the standard of living of poor P(A ∩ B) = 0.23

P(B/A) = P(B∩A)/ P(A)

P(B/A)= 0.23/0.32

P(B/A) = 0.71875

8 0

3 years ago

Please help me how to solve and what it asks me to do

Anna007 [38]

<span> Higher Order Thinking problems require you to think about the facts that are given to you in any problem and do something with those facts. This involves understanding them, infer from them, connect them to other facts and concepts, categorize them, manipulate them, put them together and apply them to find new solutions.
<span>
For example the first problem which asks to evaluate the expression 0.1(3.7). This can also mean that 1/10*3.7 = 0.37.

I hope it helps, Regards.</span></span>

6 0

4 years ago

Henry is purchasing a number of magnets. He wants some idea of how many he can buy. On a coordinate plane, the points (3, 1), (6

GaryK [48]

Step 1: Find the slope

Every 3 magnets that you buy, you need to pay 1 more dollar. Therefore, if you have 9 magnets, the cost will be 3 dollars. Also, if you have 6 magnets, the cost will be 2 dollars. Finally, if you have 3 magnets, the cost will be 1 dollar. So... the correct options are Options B, E, F

Answer options: B,E,F

4 0

3 years ago

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Simplify the expression: (2n + 3)(–2)

bonufazy [111]

Answer:

(2n+3)(−2)

=(2n+3)(−2)

=(2n)(−2)+(3)(−2)

=−4n−6

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3 years ago

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