ECCOTHES

In a set of five consecutive integers, the smallest integer is more than $\frac23$ the largest. What is the smallest possible va

Goryan [66]

Answer:

55

Step-by-step explanation:

Let x represent the middle integer. Then the smallest is x-2 and the largest is x+2. Your requirement is that ...

(x-2)/(x+2) > 2/3

3x -6 > 2x +4 . . . . cross multiply

x > 10 . . . . . . . . . . .add 6-2x

The smallest integer satisfying this requirement is x=11. The sum of the 5 integers is 5x = 55.

The smallest sum is 55.

4 0

2 years ago

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Last year Victoria paid £354 for her car insurance

Fed [463]

Answer:

the price decreased by 7.06 percent

Step-by-step explanation:

100/354x329=92.93785311

100-92.93785311=7.06

3 0

2 years ago

The domain of a function is

never [62]

The domain of a function is the set of all possible inputs for the function.

3 0

3 years ago

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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

The top walking of a ship is 480 feet long. This is only 6 sevenths of the ship. How long is the ship?

GarryVolchara [31]

480/6<span> = 80ft </span>7<span> x 80 = 560ft.</span>

7 0

2 years ago

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