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2 years ago

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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a=7 feet and b=7 feet, what i

s c? if necessary, round to the nearest tenth.

1 answer:

V125BC [204]2 years ago

4 0

The length of hypotenuse when the value of legs of a right angled triangle are 7 and 7 feet is 9.9 feet.

Given that a and b are legs and c is the hypotenuse. length of legs of a right angled triangle are 7 feet and 7 feet.

We have to find the value of c in the right angled triangle.

In this we have to apply pythagoras theorem because it says tat the square of hypotenuse is equal to the sum of squares of base and perpendicular of that right angled triangle.

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

H=c

P=7 feet

B=7 feet.

Put the values in the above rule:

$c^{2} =7^{2} +7^{2}$

$c^{2}$ =49+49

$c^{2}$ =98

c=9.899

After rounding off to nearest tenth we will get c=9.9.

Hence the value of c is 9.9 which is the length of hypotenuse.

Learn more about pythagoras theorem at brainly.com/question/343682

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Giving 100 points.

Nitella [24]

Answer:

1. <u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>: 10 + x

<u>Average number of customers</u>: 16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130. Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

2 years ago

Someone help plz

Lilit [14]

Hope this helps !!!!

7 0

3 years ago

The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Pr

aniked [119]

Answer:

(a) $E(X) = 0.383$

The expected number in the sample that treats hazardous waste on-site is 0.383.

(b) $P(x = 4) = 0.000169$

There is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

Step-by-step explanation:

Professional Geographer (Feb. 2000) reported the hazardous waste generation and disposal characteristics of 209 facilities.

N = 209

Only eight of these facilities treated hazardous waste on-site.

r = 8

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treats hazardous waste on-site?

n = 10

The expected number in the sample that treats hazardous waste on-site is given by

$E(X) = \frac{n \times r}{N}$

$E(X) = \frac{10 \times 8}{209}$

$E(X) = \frac{80}{209}$

$E(X) = 0.383$

Therefore, the expected number in the sample that treats hazardous waste on-site is 0.383.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site

The probability is given by

$P(x = 4) = \frac{\binom{r}{x} \binom{N - r}{n - x}}{\binom{N}{n}}$

For the given case, we have

N = 209

n = 10

r = 8

x = 4

$P(x = 4) = \frac{\binom{8}{4} \binom{209 - 8}{10 - 4}}{\binom{209}{10}}$

$P(x = 4) = \frac{\binom{8}{4} \binom{201}{6}}{\binom{209}{10}}$

$$ P(x = 4) = \frac{70 \times 84944276340}{35216131179263320}$

$P(x = 4) = 0.000169$

Therefore, there is a 0.000169 probability that 4 of the 10 selected facilities treat hazardous waste on-site.

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3 years ago

What fraction is equal to 3/5? 12/20 16/25 20/30 26/40

Debora [2.8K]

12/20 is equivalent to 3/5. <span />

6 0

3 years ago

What is the area of the rectangle, in square feet?<br>9 ft<br>20 ft

goblinko [34]

Answer:

180 Square Feet

Step-by-step explanation:

For Rectangle:

l = 9 ft

b = 20 ft

Area of Rectangle

$= l \times b \\ = 9 \times 20 \\ = 180 \:square \: feet$

3 0

3 years ago