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2 years ago

Write an equation for the nth term of the given arithmetic sequence:15, 29, 43, 57, ....

Mathematics

1 answer:

VARVARA [1.3K]2 years ago

7 0

Answer :

an = 15 + (9-1) 14

an = 15 + (8) 14

an = 15 + 112

an = 127 is the answer

Hope it helped

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4. The length of a rectangle is one more than twice the width. The area is 105 in?.

Zanzabum

9514 1404 393

Answer:

7 in

Step-by-step explanation:

For width w in inches, the length is given as 2w+1. The area is the product of length and width, so we have ...

A = LW

105 = (2w +1)w

2w^2 +w -105 = 0

To factor this, we're looking for factors of -210 that have a difference of 1.

-210 = -1(210) = -2(105) = -3(70) = -5(42) = -6(35) = -7(30) = -10(21) = -14(15)

So, the factorization is ...

(2w +15)(w -7) = 0

Solutions are values of w that make the factors zero:

w = -15/2, +7 . . . . . negative dimensions are irrelevant

The width of the rectangle is 7 inches.

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2 years ago

Suppose that you buy a bond with face value $1,000 that was originally issued 18 months ago. The maturity date is 4 years from t

ziro4ka [17]

Answer:

Step-by-step explanation:

Interest earned during the rest of 2 years and 6 months

40 + 40 + 40 = 120

he will be getting 1000 at the time of maturity ie after 2.5 years .

Total receipt = 1000 + 120 = 1120

investment made = 820

total receipt earned = 1120

profit made = 300

time = 2.5 years

profit = investment x rate of intt x time / 100

300 = 820 x r x 2.5 / 100 where r is rate of interest

r = 30000 / 820 x 2.5

= 14.63 % .

4 0

2 years ago

Lonna uses 8.2 pints of blue paint and white paint to paint her bedroom walls. 2 5 of this amount is blue paint, and the rest is

vova2212 [387]

Answer:

the number of pints of blue paint did she use for painting her bedroom walls is 1.875 pints

Step-by-step explanation:

The computation of the number of pints of blue paint did she use for painting her bedroom walls is shown below:

= Total pint × blue paint

= 7.5 × (1 - 3 ÷ 4)

= 7.5 × 1 ÷ 4

= 1.875 pints

Hence, the number of pints of blue paint did she use for painting her bedroom walls is 1.875 pints

5 0

3 years ago

The 2010 General Social Survey reported a sample where about 48% of US residents thought marijuana should be made legal. If we w

Sati [7]

Answer:

The sample size is $n = 600$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The margin of error is $MOE = 0.04$

Given that the confidence level is 95% the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the values is

$Z_{\frac{\alpha }{2} } = 1.96$

The reason we are obtaining critical value of $\frac{\alpha }{2}$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

$MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }$

substituting values

$0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }$

$0.02041 = \sqrt{ \frac{0.48(52 )}{n} }$

$0.02041 = \sqrt{ \frac{ 0.2496}{n} }$

$0.02041^2 = \frac{ 0.2496}{n}$

$0.0004166 = \frac{ 0.2496}{n}$

=> $n = 600$

5 0

3 years ago

How much sales tax would you pay on a dirt bike that cost $215 with a 5.3%<br> sales tax?

Archy [21]

Answer:

11.40

Step-by-step explanation:

215×0.053=11.395 rounded up to $11.40

7 0

3 years ago