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In-s [12.5K]
3 years ago
12

A path through the middle of a circular garden is 14 feet long. [a] What is the distance around the outside of this garden? [b]

What is the area of the garden? Use 3.14 for π.
Mathematics
1 answer:
Neko [114]3 years ago
7 0

Answer:

a. 43.96 feet

b.153.86 square feet

Step-by-step explanation:

Hi, the path through the middle of the circular garden is the diameter.

Since the diameter is equal to:

Diameter = 2 radius (r)

Solving for r

14 =2r

14/2 = r

r = 7 feet

The distance around the outside of this garden is the perimeter.

Perimeter of a circle (P) = 2 π r

Replacing with the values given:

P = 2 (3.14) 7 = 43.96 feet

b. area of the circle-

Area of a circle (A)= π r²

Replacing with the values given:

A = 3.14 (7²) =153.86 square feet

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<h3>Answers are: sine, tangent, cosecant, cotangent</h3>

Explanation:

On the unit circle we have some point (x,y) such that x = cos(theta) and y = sin(theta). The sine corresponds to the y coordinate of the point on the circle. Quadrant IV is below the x axis which explains why sine is negative here, since y < 0 here.

Since sine is negative, so is cosecant as this is the reciprocal of sine

csc = 1/sin

In quadrant IV, cosine is positive as x > 0 here. So the ratio tan = sin/cos is going to be negative. We have a negative over a positive when we divide.

Because tangent is negative, so is cotangent.

The only positive functions in Q4 are cosine and secant, which is because sec = 1/cos.

7 0
3 years ago
A 20 foot ladder is leaning against the side of a building. The bottom of the ladder is 4 feet from the wall. How many feet abov
Semenov [28]
It form a right triangle
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distance up wall is other leg
a^2+b^2=c^2
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4^2+b^2=20^2
16+b^2=400
minus 16 both sides
b^2=384
sqrt both sides
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aprox
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6 0
3 years ago
F the simple interest on ​$4000 for 6 years is ​$1440​, then what is the interest​ rate?
Alborosie

Answer:

Step-by-step explanation:

rate=\frac{interest \times 100}{principle \times time } \\=\frac{1440 \times 100}{4000 \times 6 } \\=6 \%

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Sheila plans to row across the lake from point A to point B as shown below. to determine how far she will have to row, she has c
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3 years ago
At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 111 keypads is analyzed. Find
Serggg [28]

Answer:

The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 \mu_{\hat p}=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

Let <em>p</em> = the proportion of keypads that pass inspection at a cell phone assembly plant.

The probability that a randomly selected cell phone keypad passes the inspection is, <em>p</em> = 0.77.

A random sample of <em>n</em> = 111 keypads is analyzed.

Then the sampling distribution of \hat p is:

\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})\\\Rightarrow \hat p\sim N (0.77, 0.04)

Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:

P(0.72

                             =P(-1.25

Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

8 0
3 years ago
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