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3 years ago

What is an equation of the line that is parallel to y=4x-10 and passes through (1,13)?

Mathematics

1 answer:

bija089 [108]3 years ago

3 0

Answer:

y = 4x + 9

Step-by-step explanation:

Parallel lines have the same slope. If the line y = 4x - 10 is parallel to it then the slope for both lines is 4.

To write the equation, substitute m = 1 into the point slope form with (1,13).

$y - y_1 = m(x-x_1)\\y -13 = 4(x-1)\\y - 13= 4x - 4\\y = 4x +9$

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During two years, the population of birds of an island became 7 times more than before. If the first year increase in the popula

nordsb [41]

Answer:

The percent increase of the second year is 400%.

Step-by-step explanation:

Consider the provided information.

Let the population of birds was x.

After 2 years the population becomes 7 times more than before.

Therefore, after 2 years population is 7x.

In first year increase in the population was 40%.

Population after 1st year = x + 40% of x

Population after 1st year = x + 0.40x

Population after 1st year = 1.4x

The population increase from 1st year to 2nd year is: 7x-1.4x=5.6x

Thus the percentage increase is:

$\% increase=\frac{5.6x}{1.4x}\times100=400\%$

Hence, in second year the population of birds increase by 400%.

6 0

3 years ago

A plane covers 2,160 miles in 5.5 hours. what is the average speed of the plane to the nearest tenth?

pantera1 [17]

2160 divided by 5.5 = 392.7 hopefully this is right!

8 0

3 years ago

Read 2 more answers

What percent of $90 = $45

Lynna [10]

45 is exactly half of 90
that means 45 is 50% of 90.

8 0

3 years ago

In a given year, the average annual salary of a NFL football player was $189,000 with a standard deviation of $20,500. If a samp

nika2105 [10]

Answer:

15.15% probability that the sample mean will be $192,000 or more.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 189000, \sigma = 20500, n = 50, s = \frac{20500}{\sqrt{50}} = 2899.14$

The probability that the sample mean will be $192,000 or more is

This is 1 subtracted by the pvalue of z when X = 192000. So

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

By the Central Limit Theorem

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

$Z = \frac{192000 - 189000}{2899.14}$

$Z = 1.03$

$Z = 1.03$ has a pvalue of 0.8485.

1-0.8485 = 0.1515

15.15% probability that the sample mean will be $192,000 or more.

7 0

3 years ago

Find the values of the sine, cosine, and tangent for ZA C A 36ft B 24ft

Reptile [31]

<h2>Question:</h2>

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = $\frac{\sqrt{13} }{2}$ , cos A = $\frac{\sqrt{13} }{3}$ , tan A = $\frac{2 }{3}$

b. sin A = $3\frac{\sqrt{13} }{13}$ , cos A = $2\frac{\sqrt{13} }{13}$ , tan A = $\frac{3}{2}$

c. sin A = $\frac{\sqrt{13} }{3}$ , cos A = $\frac{\sqrt{13} }{2}$ , tan A = $\frac{3}{2}$

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Answer:</h2>

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Step-by-step explanation:</h2>

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = $\sqrt{1872}$

⇒ AB = $12\sqrt{13}$ ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of $12\sqrt{13}$ ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = $\frac{opposite}{hypotenuse}$ -------------(i)