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3 years ago

What is the equation for a line parallel to y=-4x-9 that passes through the point 0,8

Mathematics

1 answer:

Afina-wow [57]3 years ago

8 0

Parallel = same slope
Y = -4x + b
(0,8) y intercept; plug in
Solution: y = -4x + 8

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Carmen deposits $700 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in t

VLD [36.1K]

First we need to find what 3% of 700 is. We know 10% is 70, 5% is 35, so we need to find out what 3% is. If you don't know how to calculate percentages of a number, I recommend starting with 10%. This way you know 10% of the number is 70, so you will also know that 1% of the number is 7. 7 x 3 = 21. So 3% of 700 is 21. Since it was over 6 years, we multiply 21 x 6. That gives us 126. She will be paid $126 in interest in the first six years.

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3 years ago

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Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who

zmey [24]

Answer:

18.7939 m

Step-by-step explanation:

-Let x be the distance between John and clock tower.

-Let y be the vertical distance from the eyes of the two men standing to the top of the clock tower.

#Taking the right triangle ACD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5$

#Taking the right triangle ABD:

$\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5$

#We equate the two yo solve for x and y;

$(x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939$

Hence, John's distance from the tower's base is 18.7939 m

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3 years ago

A random sample of 100 observations from a quantitative population produced a sample mean of 22.8 and a sample standard deviatio

natima [27]

Answer:

We conclude that the population mean is 24.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 24

Sample mean, $\bar{x}$ = 22.8

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 8.3

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 24\\H_A: \mu \neq 24$

We use Two-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{22.8 - 24}{\frac{8.3}{\sqrt{100}} } = -1.44$

We calculate the p-value with the help of standard z table.

P-value = 0.1498

Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.

Now, $z_{critical} \text{ at 0.05 level of significance } = \pm 1.96$

Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.

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3 years ago

Which is the best estimate of 162% of 79? O 112 O 119 O 128 O 136

sladkih [1.3K]

Answer:

128

Step-by-step explanation:

You would multiply 79 by 1.62 to get the answer.

This would give you 127.98 which you would round up to 128.

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3 years ago

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How many more people in the world speak Chinese than speak English?

Lelechka [254]

Answer:

The answer is 912 million

Step-by-step explanation:

912 million people speak Chinese in the world than they do English.

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3 years ago