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2 years ago

What is the mean of the values in the dot plot? Enter your answer in the box.

Mathematics

1 answer:

ziro4ka [17]2 years ago

4 0

Answer:

The mean is 19.5

Step-by-step explanation:

You have to add all of the numbers up then divide by how many numbers there are.

Ex: 5, 5, 6, 7

add them up and you get 23

Divide 23 by how many numbers you have, which in this case, is 4

The answer to this example would be 5.75

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A certain virus infects one in every 200 people. a test used to detect the virus in a person is positive 70% of the time when t

V125BC [204]

We're told that

$P(A)=\dfrac1{200}=0.005\implies P(A^C)=0.995$

$P(B\mid A)=0.7$

$P(B\mid A^C)=0.05$

a. We want to find $P(A\mid B)$ . By definition of conditional probability,

$P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}$

By the law of total probability,

$P(B)=P(B\cap A)+P(B\cap A^C)=P(B\mid A)P(A)+P(B\mid A^C)P(A^C)$

Then

$P(A\mid B)=\dfrac{P(B\mid A)P(A)}{P(B\mid A)P(A)+P(B\mid A^C)P(A^C)}\approx0.0657$

(the first equality is Bayes' theorem)

b. We want to find $P(A^C\mid B^C)$ .

$P(A^C\mid B^C)=\dfrac{P(A^C\cap B^C)}{P(B^C)}=\dfrac{P(B^C\mid A^C)P(A^C)}{1-P(B)}\approx0.9984$

since $P(B^C\mid A^C)=1-P(B\mid A^C)$ .

4 0

3 years ago

What is the average rate of change of the function over the interval x = 0 to x = 8?

salantis [7]

Ans: The average rate of change of function = $\frac{1}{102}$ (in fraction)

Explanation:
The average rate of change of function = $\frac{f(b) - f(a)}{b - a}$

Where
b = 8 (x's upper bound)
a = 0 (x's lower bound)

$f(b) = f(8) = \frac{2*8-2}{5*8-6} = \frac{7}{17} \\ f(a) = f(0) = \frac{2*0-2}{5*0-6} = \frac{1}{3} \\ \frac{f(b) - f(a)}{b-a} = \frac{ \frac{7}{17} - \frac{1}{3}}{8} = \frac{1}{102}$

Hence the average rate of change of function = $\frac{1}{102}$ (in fraction)

5 0

3 years ago

What is the tangent ratio for

kirill115 [55]

Answer:

The answer to your question is letter A (2/3)

Step-by-step explanation:

Formula

tangent Ф = $\frac{opposite side}{adjacent side}$

For A

opposite side = 2

adjacent side = 3

Substitution

tan Ф = $\frac{2}{3}$

Result

tan Ф = $\frac{2}{3}$

3 0

3 years ago

Read 2 more answers

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Amy's grandmother gave her 3 identical chocolate chip cookies and 4 identical sugar cookies. In how many different orders can Am

Dmitrij [34]

Answer:

chocolate chip cookie first: 15 ways

chocolate chip cookie last: 15 ways

chocolate chip cookie first and last: 5 ways

Step-by-step explanation:

There is a total of 7 cookies.

Is she eats a chocolate cookie first, she will have 2 chocolate cookies and 4 sugar cookies (6 in total).

So, to find the number of different orders that Amy can eat the remaining cookies, we just need to calculate a combination of 6 choose 2 (that is, the number of ways we can put the 2 chocolate cookies among the 6 cookies) or a combination of 6 choose 4 (same thing, but for the sugar cookies):

C(6,2) = 6! / (2! * 4!) = 6 * 5 / 2 = 15 ways

Is she eats a chocolate cookie last, she will have 2 chocolate cookies and 4 sugar cookies (6 in total), so the problem is solved again with a combination of 6 choose 2:

C(6,2) = 15 ways

Is she eats a chocolate cookie first and last, she will have just 1 chocolate cookie left and 4 sugar cookies (5 in total), so the problem is solved with a combination of 5 choose 1 or a combination of 5 choose 4:

C(5,1) = 5! / (1! * 4!) = 5 ways

6 0

2 years ago