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3 years ago

Which set of side lengths can form a triangle?

Mathematics

1 answer:

emmainna [20.7K]3 years ago

4 0

Answer:

C:4 cm, 8 cm, 5 cm

Step-by-step explanation:

sum of length of any two sides of a triangle will be larger than the third side.

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From a random sample of 87 us adults with no more than a high school education that mean weekly income is 678 with a sample stan

evablogger [386]

Answer:

So on this case the 95% confidence interval would be given by $-1235.756 \leq \mu_1 -\mu_2 \leq -1072.245$ . So we can conclude that we have a significant difference, with the mean of population two higher than the mean for the population 1, because the interval just contains negative values.

Step-by-step explanation:

Notation and previous concepts

$n_1 =87$ represent the sample of us adults with no more than a high school education

$n_2 =73$ represent the sample of us adults with no more than a bachelor's degree

$\bar x_1 =678$ represent the mean sample of us adults with no more than a high school education

$\bar x_2 =1837$ represent the mean sample of us adults with no more than a bachelor's degree

$s_1 =197$ represent the sample deviation of us adults with no more than a high school education

$s_2 =328$ represent the sample deviation of us adults with no more than a bachelor's degree

$\alpha=0.05$ represent the significance level

Confidence =95% or 0.95

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{(\frac{s^2_1}{n_s}+\frac{s^2_2}{n_s})}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =678-1837=-1159$

The appropiate degrees of freedom are $df=n_1+ n_2 -2=158$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,158)".And we see that $t_{\alpha/2}=1.98$

The standard error is given by the following formula:

$SE=\sqrt{(\frac{s^2_1}{n_s}+\frac{s^2_2}{n_s})}$

And replacing we have:

$SE=\sqrt{(\frac{197^2}{87}+\frac{328^2}{73})}=43.816$

Confidence interval

Now we have everything in order to replace into formula (1):

$-1159-1.98\sqrt{(\frac{197^2}{87}+\frac{328^2}{73})}=-1235.756$

$-1159+1.98\sqrt{(\frac{197^2}{87}+\frac{328^2}{73})}=-1072.245$

So on this case the 95% confidence interval would be given by $-1235.756 \leq \mu_1 -\mu_2 \leq -1072.245$ . So we can conclude that we have a significant difference with the mean of population two higher than the mean for the population 1, because the interval contains just negative values.

4 0

3 years ago

Is y= 5 3 a solution of 6y+10=12y?

Arturiano [62]

$6y + 10 = 12y \\ 10 = 12y - 6y \\ 10 = 6y \\ y = \frac{10}{6} \\ y = \frac{5}{3}$
The answer is 5/3 so it's true

7 0

3 years ago

1. 11 1/6 =? 2. 2 9/10 =? 3. - 4/12 =? Please help me

Jobisdone [24]

Answer:

1.Exact Form: 67/6

Decimal Form: 11.167

Mixed Number Form: 11 1/6

2. 2 9/10

3. Exact Form: −1/3

Decimal Form: −0.3333

4 0

4 years ago

Given the two functions f(x)=x2 - 4x +1 and g(t)=1- t<br><br> Find & Simplify f(g(t))

Nikolay [14]

Answer:

Step-by-step explanation:

Given the two functions f(x)=x² - 4x +1 and g(t)=1-t

To simplify the composite function f(g(t)), we will replace x with (1-t) in f(x) as shown:

f(g(t)) = f(1-t)

f(1-t) = (1-t)²-4(1-t)+1

Expand the parenthesis

f(1-t) = 1-2t+t²-4+4t+1

f(1-t) = t²-2t+4t+1+1-4

f(1-t) = t²+2t-2

Hence the simplified form of f(g(t)) is t²+2t-2

3 0

4 years ago

What is the correct unit rate?And what is Jessie's likely error?

s2008m [1.1K]

Answer:

Step-by-step explanation:

1 $\frac{1}{2} / \frac{1}{8} = \frac{1}{2} * \frac{8}{1} = \frac{8}{2} = 4$

she forget that fraction will reverse if it move below or up side, I think

6 0

3 years ago