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3 years ago

Can someone please answer. There is one problem. There is a picture. Thank you!

Mathematics

1 answer:

jonny [76]3 years ago

5 0

SA=4pir^2
78.54km^2=SA
78.54=4pir^2
divide both sides by 4
19.635=pir^2
aprox pi=3.14 so divide both sides by 3.14
6.25318=r^2
sqrt both sides
2.50063=r
round
radius=2.5km

this question is flawed in that it gives the wrong units

answer is the option with 2.5 in it
2nd one

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Determine the value of x. A. 4√2 B. 2/√2 C. 2√2 D. 2

ZanzabumX [31]

Answer:

$\huge\boxed{\sf C.}$

Step-by-step explanation:

sin 45 = opposite / hypotenuse

Where opposite = x , hypotenuse = 4

sin 45 = x / 4

$\sf \frac{\sqrt{2} }{2 } = \frac{x}{4} \\\\x = \frac{4\sqrt{2} }{2} \\\\x = 2\sqrt{2} \\\\\rule[225]{225}{2}$

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3 0

3 years ago

The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 mi

Orlov [11]

Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 51200, \sigma = 8200$

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{65000 - 51200}{8200}$

$Z = 1.68$

$Z = 1.68$ has a pvalue of 0.954

X = 55000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55000 - 51200}{8200}$

$Z = 0.46$

$Z = 0.46$ has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{48000 - 51200}{8200}$

$Z = -0.39$

$Z = -0.39$ has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41000 - 51200}{8200}$

$Z = -1.24$

$Z = -1.24$ has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{61200 - 51200}{8200}$

$Z = 1.22$

$Z = 1.22$ has a pvalue of 0.889

X = 41200

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{41200 - 51200}{8200}$

$Z = -1.22$

$Z = -1.22$ has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

4 0

3 years ago

3-2i/1+4i include each step necessary in simplifying

Likurg_2 [28]

Answer:

$\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i$

Step-by-step explanation:

$\frac{3-2i}{1+4i}$ <-- Given

$\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i}$ <-- Multiply by the conjugate of the denominator as a factor of 1

$\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}$

$\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)}$ <-- Use the Distributive Property and FOIL

$\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}$

$\frac{3-10i-8i^2}{1-16i^2}$

$\frac{3-10i-8(-1)}{1-16(-1)}$ <-- Rewrite $i^2$ as $-1$

$\frac{3-10i+8}{1+16}$

$\frac{11-10i}{17}$

$\frac{11}{17}-\frac{10}{17}i$ <-- Rewrite in $a\pm bi$ form

8 0

3 years ago

The gazebo in the park is an octagon. Each side of the gazebo is 4 feet long. What is the perimeter of the gazebo?

pychu [463]

The answer is A because an octagon has 8 sides and if each side is 4 feet you would multiply 4 times 8 and get 32.

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3 years ago

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Anderson has $50 in his savings account. He deposits $5 every week. His father also deposits $20 into the account every time And

vodomira [7]

50 + 5w + 20m
The constant is 50.
A coefficient is 5 and another is 20.
A variable is w and another is m.

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