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3 years ago

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A cable is attached to the top of a 28-foot utility pole. The cable is fastened to the ground at a point 21 feet from the base o

f the pole. Find the length of the cable.

1 answer:

Elenna [48]3 years ago

4 0

Answer:

Length of the cable (H) = 35 foot

Step-by-step explanation:

Given:

Height of the pole (P) = 28 Foot

Distance from the pole (B) = 21 Foot

Find:

Length of the cable (H) = ?

Computation:

According to the Pythagoras theorem:

$H = \sqrt{P^2+B^2}$

$Length\ of\ the\ cable = \sqrt{(Height\ of\ the\ pole)^2+(Distance\ from\ the\ pole)^2}$

$Length\ of\ the\ cable =\sqrt{28^2+21^2}\\\\ Length\ of\ the\ cable =\sqrt{784+441}\\\\Length\ of\ the\ cable=\sqrt{1,225} \\\\Length\ of\ the\ cable = 35$

Length of the cable (H) = 35 foot

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An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

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3 years ago

One tenth the value of 2 in 8.524

Romashka [77]

85.25 would be one thenth of 8.524

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3 years ago

Read 2 more answers

50 students were asked what they did last night. 16 said they read a book, 41 said they watched TV, 7 said they did neither, how

Kamila [148]

Answer:

14 students

Step-by-step explanation:

Given

Let:

$b \to$ read a book

$t \to$ watched TV

So, we have:

$n = 50$ -- total

$b = 16$

$t = 41$

$none = 7$

Required

Students that did both (x)

This is calculated using:

$Total = Books\ only + TV\ only + Both + None$

So, we have:

$n = (b - x) + (t - x) + x + none$

This gives:

$50 = (16 - x) + (41 - x) + x + 7$

Open brackets

$50 = 16 - x + 41 - x + x + 7$

$50 = 16 - x + 41 +7$

Collect like terms

$x = 16 - 50 + 41 +7$

$x = 14$

<em>Hence, 14 students did both</em>

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3 years ago

If you know the radius, r, of a circle, what do you multiply rby to get the circle's CIRCUMFERENCE?

KengaRu [80]

Answer:

C=2 x pi x radius

Step-by-step explanation:

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3 years ago

Mary scored 28 points, which is twice as many points as Lashawna scored. Let L represent the points Lashawna scored.

Basile [38]

Answer: Lashawna scored 14 points

Step-by-step explanation:

Let M = Mary's score

L = Lashawna score

M = 28 points

And M is twice as much as L score

M= 2L

L= M/2

L= 28/2

M = 14.

Lashawna score was 14 points

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