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2 years ago

Which number is a solution of the inequality 8 – 14b ≥ 27?

Mathematics

1 answer:

AysviL [449]2 years ago

3 0

Answer:

8 - 14b ≥ 27 ⇒ subtract 8 from both sides
- 14b ≥ 27 -8
- 14b ≥ 19 ⇒ divide both sides by 14
- b ≥ 19/14 ⇒ multiply both sides by -1
b ≤ - 19/14 ⇒ multiplication by a negative changes the

inequality sign to opposite one

b ≤ - 19/14 and the answer choices B, C and D are all correct as are less than -19/14

A. 140 is the only one incorrect

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The production department has installed a new spray machine to paint automobile doors. As is common with most spray guns, unsigh

Nesterboy [21]

Answer:

The numbers of doors that will have no blemishes will be about 6065 doors

Step-by-step explanation:

Let the number of counts by the worker of each blemishes on the door be (X)

The distribution of blemishes followed the Poisson distribution with parameter $\lambda =0.5$ / door

The probability mass function on of a poisson distribution Is:

$P(X=x) = \dfrac{e^{- \lambda } \lambda ^x}{x!}$

$P(X=x) = \dfrac{e^{- \ 0.5 }( 0.5)^ x}{x!}$

The probability that no blemishes occur is :

$P(X=0) = \dfrac{e^{- \ 0.5 }( 0.5)^ 0}{0!}$

$P(X=0) = 0.60653$

P(X=0) = 0.6065

Assume the number of paints on the door by q = 10000

Hence; the number of doors that have no blemishes is = qp

=10,000(0.6065)

= 6065

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2 years ago

The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches.

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35 squared + 35 squared
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2 years ago

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Triangle A B C is shown. Angle A C B is a right angle. The length of hypotenuse A B is 12 centimeters, the length of C B is 9.8

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Step-by-step explanation:

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A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. After a storm, the linear dimensions of th

QveST [7]

we know that

the volume of a cone is equal to

$V= \frac{1}{3} \pi r^{2}h$

in this problem

the radius is equal to

$r= \frac{112}{2}= 56ft$

1) Find the height of the cone before the storm

Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) Find the volume before the storm

$V= \frac{1}{3}*\pi* 56^{2}*33$

$V=34,496\pi\ ft^{3}$

3) Find the volume after the storm

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

r=(56/3) ft

h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

$V= 1,277.63\pi\ ft^{3}$

4) Find how this change affect the volume of the pile

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

the answer part a) is

The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

Part b) Estimate the number of lane miles that were covered with salt

5) Find the amount of salt that was used during the storm

$=34,496 \pi - 1,277.63 \pi \\= 33.218.37 \pi \\= 104,358.59\ ft^{3}$

6) Find the pounds of road salt used

$104,358.59*80=8,348,687.2\ pounds$

7) Find the number of lane miles that were covered with salt

$8,348,687.2/350=23,853.39 \ lane\ miles$

therefore

the answer part b) is

the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

Part c) How many lane miles can be covered with the remaining salt? Round your answer to the nearest lane mile

the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) Find the pounds of road salt

$4,013.79*80=321,103.20\ pounds$

9) Find the number of lane miles

$321,103.20/350=917.44 \ lane\ miles$

therefore

the answer part c) is

the number of lane miles is $917 \ lane\ miles$

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2 years ago

What is the surface area of this right rectangular prism? Enter your answer in the box.

antoniya [11.8K]

Answer:

The surface area is 22m

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2 years ago