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4 years ago

Marina is heating a solution in her chemistry lab. The temperature of the

Mathematics

1 answer:

vodka [1.7K]4 years ago

4 0

Answer:

Don’t really have a step by step explanation, I guessed and got (4,32)

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Sixty percent of U.S. adults trust national newspapers to present the news fairly and accurately. You randomly select nine U.S.

Pavel [41]

Answer:

a) 0.251

b) 0.483

c) 0.0994

Step-by-step explanation:

We are given the following information:

We treat adult adults trusting national newspapers to present the news fairly and accurately as a success.

P(Adult trust) = 60% = 0.6

Then the number of adults follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 9

a) exactly five

$P(x = 15) = \binom{9}{5}(0.6)^{5}(1-0.6)^{9-5} = 0.2508 \approx 0.251$

b) at least six

We have to evaluate

$P(x \geq 6) = P(x = 6) + P(x = 7) + P(x=8) + P(x=9) \\= \binom{9}{6}(0.6)^6(1-0.6)^3 + \binom{9}{7}(0.6)^7(1-0.6)^2 + \binom{9}{8}(0.6)^8(1-0.6)^1 +\binom{9}{9}(0.6)^9(1-0.6)^0\\= 0.482609 \approx 0.483$

c) less than four

We have to evaluate

$P(x < 4) = P(x = 0) + P(x = 1) + P(x=2) + P(x=3) \\= \binom{9}{0}(0.6)^0(1-0.6)^9 + \binom{9}{1}(0.6)^1(1-0.6)^8 + \binom{9}{2}(0.6)^2(1-0.6)^7 +\binom{9}{3}(0.6)^3(1-0.6)^6\\= 0.099352 \approx 0.0994$

3 0

3 years ago

Which expressions are equivalent to the one below? Check all that apply.<br> log 2 - log 8

blagie [28]

Answer:

$\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=-\log 4$

Step-by-step explanation:

$\log 2-\log 8=\log\frac{2}{8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=\log 1-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \log 1=0$

8 0

3 years ago

Choose the table that represents g(x) = −2⋅f(x) when f(x) = x + 4.

grigory [225]

Answer: THIRD OPTION.

Step-by-step explanation:

Since $g(x) = -2f(x)$ , then $g(x)$ is:

$g(x)=-2( x + 4)\\\\g(x)=-2x-8$

In order to find which table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ , you can follow these steps:

1. Substitute $x=1$ into the function $g(x)=-2x-8$ :

$g(1)=-2(1)-8\\\\g(1)=-10$

2. Substitute $x=2$ into the function $g(x)=-2x-8$ :

$g(2)=-2(2)-8\\\\g(2)=-12$

3. Substitute $x=3$ into the function $g(x)=-2x-8$ :

$g(3)=-2(3)-8\\\\g(3)=-14$

Notice that those ouput values (for $x=1,\ x=2$ and $x=3$ ) matches with the table provided in the third option. That table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ :

6 0

3 years ago

Read 2 more answers

Voting rates in presidential elections from 1996-2012 are modeled below

Ray Of Light [21]

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3 0

3 years ago

Is the following true or false? The 12th derivative of sin(x) = cos(x).

pogonyaev

False ? I pretty sure that’s the answer

8 0

3 years ago