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2 years ago

Describe the rays of an angle that measures 1/2 turn

Mathematics

2 answers:

d1i1m1o1n [39]2 years ago

6 0

Since a circle i 360 deegrees half of 360 degrees would be 180 degrees so half kf a 1/2 turn would be 180

topjm [15]2 years ago

5 0

Angles are measures of turn. A complete turn is called a perigon angle or full angle which measures 360°. A half (1/2) turn is called a straight angle, because it looks like a straight line with a dot (the vertex) in the middle, its measure is 180°. The rays are the two halves of a line and they point in opposite directions.

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Write the equation of the line for the following table of values.

Luda [366]

Answer:

We conclude that the equation of the line is:

$y = 5x + 1$

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the slope

b is the y-intercept

Given the data table

x -3 -5 -7 -9 -11

y -16 -26 -36 -46 -56

From the table taking two points

(-3, -16)

(-5, -26)

Determining the slope between (-3, -16) and (-5, -26)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)$

$m=\frac{-26-\left(-16\right)}{-5-\left(-3\right)}$

$m=5$

Thus, the slope of the line is: m = 5

substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation to determine the y-intercept b

$y = mx+b$

-16 = 5(-3) + b

-16 = -15 + b

b = -16+15

b = 1

Thus, the y-intercept b = 1

now substituting m = 5 and b = 1 in the slope-intercept form of the line equation

$y = mx+b$

$y = 5x + 1$

Therefore, we conclude that the equation of the line is:

$y = 5x + 1$

5 0

2 years ago

On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter

andrezito [222]

Answer:

1) The common ratio = 1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio = 1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0

2 years ago

Sally’s parents deposited $15,000 into a college savings account on her third birthday. The account had an interest rate of 9.6%

oee [108]

Rule of 72 says to divide 72 by the rate of return and that will be the number of years an investment will double
so 72 / 9.6 = 7.5 years to double

7.5 * 2 = 15 years

18-3 = 15

the answer is: <span>Yes, the $15,000 will double each 7.5 years. In 15 years, it will double twice.</span>

5 0

2 years ago

Read 2 more answers

After Mia gave 1/4 of her milk to Dante, Dante had twice the amount of milk as Mia. What was the ratio of the amount of milk Mia

krok68 [10]

Answer:

4:5

Step-by-step explanation:

You start with the equation:

2(3/4m)=D+1/4m

Simplify it to solve:

5/4m=D

5 0

2 years ago

Read 2 more answers

The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of,"

svetlana [45]

Answer:

At least 202.44 mm in the top 15%.

Step-by-step explanation:

When the distribution is normal, we use 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:

$\mu = 134, \sigma = 66$