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3 years ago

the first term of an arithmetic sequence is 20 and the common difference is 15. Find the fifth term of the sequence

Mathematics

1 answer:

grandymaker [24]3 years ago

5 0

Solution

The 1st term = 20

Common difference (d) = 15

5th term = a + d(n-1)

= 20 + 15(5- 1) [Here n = 5)

= 20 + 15(4)

5th term = 20 + 60 = 80

The answer is 80.

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Can 15x-10 be factored

Anna [14]

Yes because removing the common factor is important. There are a few steps, then you can factor by regrouping. Hope this helps.

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4 years ago

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An English professor assigns letter grades on a test according to the following scheme. A: Top 15% of scores B: Scores below the

lisabon 2012 [21]

Answer:

59 to 66

Step-by-step explanation:

Mean test scores = u = 74.2

Standard Deviation = $\sigma$ = 9.6

According to the given data, following is the range of grades:

Grade A: 85% to 100%

Grade B: 55% to 85%

Grade C: 19% to 55%

Grade D: 6% to 19%

Grade F: 0% to 6%

So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.

6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)

The formula for z score is:

$z=\frac{x-u}{\sigma}$

For z = -1.56, we get:

$-1.56=\frac{x-74.2}{9.6}\\\\ x = 59$

For z = -0.88, we get:

$-0.88=\frac{x-74.2}{9.6}\\\\ x = 66$

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)

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4 years ago

The measure of one acute angle in this right triangle is 45°.

maks197457 [2]

Answer:

45°

Step-by-step explanation:

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How much do I pay for the loan

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3 years ago

A painter starts with a blank 24-inch by 12-inch piece of rice paper. The painter wants to leave a uniform border x inches wide

ddd [48]

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

In this scenario, 'x' represents the width of the border. A "uniform border" means that the border has the same width all around.

The area of the paper that can be painted does not include the border. Since the border is on the original rice paper (not added to it), you subtract 'x' from each side of the rice paper.

The area of a rectangle is A = lw (Area is length times width). <u>Each length and width is reduced by 'x'.</u>

If the original rice paper's area is: 24 X 12, then,

the Area that can be painted is:

A = (24 - x) (12 - x)

A polynomial in standard form means the most expanded version of an expression, ordering the terms (numbers) from greatest to least degree. (The degree of a term is the value of its exponent).

Expand the expression. Multiply the numbers from each bracket in the order FOIL (first, outside, inside last):

A = (24 - x) (12 - x)

= 288 - 24x - 12x + x² Collect like terms (-24x - 12x = -36x)

= 288 - 36x + x² Rearrange ordering greatest to least exponent value

= x² - 36x + 288 Standard form polynomial

The width of the margin is the same thing as the width of the border. Since 'x' is the width of the border,

x = 2

Using either the expanded or factored equation for area of that can be painted, substitute 'x' for 2.

I will use the factored form.

A = (24 - x) (12 - x) Substitute x for 2

= (24 - 2) (12 - 2) Solve inside each bracket first by subtracting

= (22) (10) Multiply

= 220 Area that can be painted

Remember to include the units: 220 in²

Therefore if the margin is 2 inches wide, then the area that can be painted in 220 square inches.

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3 years ago