Ask question

Ask question

All categories

3 years ago

14

John wants to spend the Saturday outside with his kids and their friends, but he can't decide what to do. He asks his kids and t

heir buddies to see what they are interested in. 10 children want to go to the beach, 8 want to stay at the pool, and 15 want to go to the water-park. 4 of those children want to go to the pool and the water-park. 6 want to go to the water-park and the beach, and 2 want to go to the pool and the beach. 1 child wants to fit in all three. How many children does John plan to spend the day with?

1 answer:

solmaris [256]3 years ago

7 0

John will spend time with about 8 kids all together, if you just subtract the amount of kids from each section. you will get it

You might be interested in

Larry fills his bathtub at a constant rate. The amount of water in his tub is proportional to the amount of time he spends filli

Kryger [21]

Answer:

7 but im not sure

Step-by-step explanation:

8 0

2 years ago

There is strong believe that language skills of Political science students are greater than students who study Finance. Research

BaLLatris [955]

Answer:

a

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

b

$p-value = 0.232$

c

The decision rule is

Fail to reject the null hypothesis

Step-by-step explanation:

From the question we are told that

The value given is

S/N

1 7 5

2 4 3

3 8 7

4 8 8

5 7 9

6 7 5

7 6 5

Generally the sample mean for the first sample is mathematically represented as

$\= x _1 = \frac{\sum x_i }{n}$

=> $\= x _1 = \frac{7 +4 + \cdots + 6}{7}$

=> $\= x _1 = 6.714$

Generally the sample mean for the second sample is mathematically represented as

$\= x _2 = \frac{\sum x_i }{n}$

=> $\= x _2 = \frac{5 + 3+ \cdots + 5}{7}$

=> $\= x _2 = 6$

Generally the sample standard deviation for the first sample is mathematically represented as

$s_1 = \sqrt{\frac{\sum (x_i - \= x_1)^2 }{n-1 } }$

=> $s_1 = \sqrt{\frac{ (7 - 6.714 )^2 +(4 - 6.714 )^2 + \cdots + (6 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 1.905$

Generally the sample standard deviation for the second sample is mathematically represented as

$s_2 = \sqrt{\frac{\sum (x_i - \= x_2)^2 }{n-1 } }$

=> $s_2 = \sqrt{\frac{ (5 - 6.714 )^2 +(3 - 6.714 )^2 + \cdots + (5 - 6.714 )^2 }{7-1 } }$

=> $s_1 = 4.33$

Generally the pooled standard deviation is

$s = \sqrt{\frac{(n_1 - 1 )s_1^2 + (n_2 - 1 )s_2^2}{n_1 + n_2 -2 } }$

=> $s = \sqrt{\frac{(7 - 1 )1.905^2 + (7 - 1 )4.333^2}{7 + 7 -2 } }$

=> $s = 1.766$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x _1 - \= x_2 }{s * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}} }$

=> $t = \frac{6.714 - 6 }{1.766 * \sqrt{\frac{1}{7} + \frac{1}{7}} }$

=> $t = 0.757$

Generally the degree of freedom is mathematically represented as

$df = n_1 + n_2 - 2$

=> $df = 7 + 7 - 2$

=> $df = 12$

From the t distribution table the probability of $t = 0.757$ at a degree of freedom of $df = 12$ is

$t_{ 0.757 , 12} = 0.232$

Generally the p-value is

$p-value = t_{ 0.757 , 12} = 0.232$

From the values obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

8 0

2 years ago

Bayes' theorem provides a way to transform prior probabilities into posterior probabilities. Group of answer choices True False

Dvinal [7]

Answer:

True

Step-by-step explanation:

Bayes' theorem is indeed a way of transforming prior probabilities into posterior probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

The prior probability in this theorem is the present understanding we possess about the possible outcome of an event based on the current understanding we have about the subject. Posterior probability on the other hand is the new understanding we have of the subject matter based on an experiment that has just been performed on it. Bayes' Theorem finds widespread application which includes the fields of science and finance. In the finance world, for example, Bayes' theorem is used to determine the probability of a debt being repaid by a debtor.

6 0

2 years ago

Given that α and β are the roots of the quadratic equation <img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20%2B6x-7%3Dp" id="Tex

siniylev [52]

Answer:

$\large \boxed{\sf \ \ \ p=-11 \ \ \ }$

Step-by-step explanation:

Hello,

$\alpha \text{ and } \beta \text{ are the roots of the following equation}$

$2x^2+6x-7=p$

It means that

$2\alpha^2+6\alpha-7=p \\\\2\beta ^2+6\beta -7=p \\\\$

And we know that

$\alpha= 2\cdot \beta$

So we got two equations

$2(2\beta)^2+6\cdot 2 \cdot \beta -7=p \\\\8\beta^2+12\beta -7=p\\\\ and \ 2\beta ^2+6\beta -7=p \ So \\\\\\8\beta^2+12\beta -7 = 2\beta ^2+6\beta -7\\\\6\beta^2+6\beta =0\\\\\beta(\beta+1)=0\\\\ \beta =0 \ or \ \beta=-1$

For $\beta =0, \ \ \alpha =0, \ \ p = -7$

For $\beta =-1, \ \ \alpha =-2, \ \ p= 2-6-7=-11, \ p=2*4-12-7=-11$

I assume that we are after two different roots so the solution for p is p=-11

b) $\alpha +2 =-2+2=0 \ and \ \beta+2=-1+2=1$

So a quadratic equation with the expected roots is

$x(x-1)=x^2-x$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

3 0

2 years ago

a dental company has rolls of floss that are 1872 in long they want to put the distance in the yard on their label what is the d

statuscvo [17]

Copy and paste ur answer onto internet it will tell u

4 0

2 years ago