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1 year ago

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Mathematics

1 answer:

Alecsey [184]1 year ago

6 0

The area that the dog can wander based on the information provided will be 931π.

<h3>How to calculate the area?</h3>

From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.

In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.

The area that the dog can wander will be:

= 3/4(π35²) + 1/4(π(35 - 28)²)

= 3/4π(35)² + 1/4π(7)²

= (3/4 × 1225)π + (1/4 × 49)π

= 918.75π + 12.25π

= 931π

Therefore, the area that the dog can wander based on the information provided will be 931π.

Learn more about area on:

brainly.com/question/25292087

#SPJ1

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Zen spent $255 on a bag and a belt. She wanted to buy another

Galina-37 [17]

Answer:

A)$ 45

B) $105

Step-by-step explanation:

Bag and a belt cost $255

Let bag = x

Let belt = y

X+y= 255 equation 1

Let total money be z first

Remaining money= z-255

X-30 = z-255

Y +15 = z-255

Equating the left side of the equation

X+30 = y+15

X-y= 45 equation 2

Solving simultaneously

X+y= 255

X-y= 45

2x = 300

X= 150

If x= 150

150-y= 45

150-45= y

105=y

Bag = $150

Belt = $105

Bag Is 150-105 more than the belt

150-105= $45

8 0

3 years ago

An art history professor assigns letter grades on a test according to the following scheme.A: Top 5% of scoresB: Scores below th

adoni [48]

Answer:

Grade B score:

$76 \leq x \leq 89$

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 73.3

Standard Deviation, σ = 9.7

We are given that the distribution of score on test is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

B: Scores below the top 5% and above the bottom 62%

We have to find the value of x such that the probability is 0.62

$P( X > x) = P( z > \displaystyle\frac{x - 73.3}{9.7})=0.62$

$= 1 -P( z \leq \displaystyle\frac{x - 73.3}{9.7})=0.62$

$=P( z \leq \displaystyle\frac{x - 73.3}{9.7})=0.38$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 73.3}{9.7} = 0.305\\\\x = 76.26$

We have to find the value of x such that the probability is 0.05

$P(X < 0.95) = \\\\P( X < x) = P( z < \displaystyle\frac{x - 73.3}{9.7})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 73.3}{9.7} = 1.645\\\\x = 89.26$

Thus, the numerical value of score to achieve grade B is

$76 \leq x \leq 89$

7 0

3 years ago

Cheryl painted her living room walls with two different colors. She painted part of the room yellow and another part green. If t

kramer

Answer:

Total percent of the room did she paint green = 60%

Step-by-step explanation:

Given - Cheryl painted her living room walls with two different colors. She painted part of the room yellow and another part green. If the surface area of the walls in her room is 720 ft² and she painted 288 ft² yellow.

To find - What percent of the room did she paint green ?

Proof -

Given that,

The surface area of the walls in her room = 720 ft²

Total area painted in yellow color = 288 ft²

So,

Total area painted in green color would be = 720 - 288 = 432 ft²

Now,

Let the total percent green color painted = x

So,

720 × x% = 432

⇒ $720*\frac{x}{100} = 432$

⇒ x = $\frac{432*100}{720}$ = 60

∴ we get

Total percent of the room did she paint green = 60%

7 0

3 years ago

A farm has 75 acres of wheat. The farmer can only harvest 12 acres per day. How many days will all of the fields be harvested?

eduard

7 days because 12 per day 12×6=72 but you need 3 more acres so it would be another day for it to be 7

3 0

3 years ago

A train goes at a constant speed. If it covers 150 miles in 2 1 2 hours, What distance would it cover in 3 hours?

Rus_ich [418]

The answer is 4.24 I just multiplied

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3 years ago