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4 years ago

Factor the algebraic expression 27a+21

1 answer:

3 0

We know that we can do
ab+ac=a(b+c)
so find common factor

factor them
27a=a times 3 times 3 times 3
21=3 times 7
common factor=3
3=a
27a/3=9a
21/3=7

so now we have
(3)9a+(3)7=3(9a+7)

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Step-by-step explanation:

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3 years ago

1. A company uses a computer to identify their 600 most loyal customers

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Answer:

A blood bank needs 6 people to help with a blood drive. 11 people have volunteered. Find how many different groups of 6 can be formed from the 11 volunteers.

Step-by-step explanation:

A blood bank needs 6 people to help with a blood drive. 11 people have volunteered. Find how many different groups of 6 can be formed from the 11 volunteers.

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3 years ago

The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. Th

e-lub [12.9K]

Answer:

95% of monthly food expenditures are between $110 and $190.

Step-by-step explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side, $\bar{x}-2\sigma$

To the right side, $\bar{x}+2\sigma$

We have given,

The sample mean $\bar{x}=\$150$

The standard deviation $\sigma=\$20$

Substitute in the formula,

$\bar{x}-2\sigma$

$=150-2(20)$

$=150-40$

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$=150+2(20)$

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6 0

3 years ago

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

nikitadnepr [17]

Answer:

* sin Ф = -15/17 * cos Ф = 8/17 * tan Ф = -15/8

* csc Ф = -17/15 * sec Ф = 17/8 * cot Ф = -8/15

Step-by-step explanation:

Lets revise the trigonometric function of angle Ф

- Angle θ is in standard position

- Point (8, -15) is on the terminal ray of angle θ

- That means the terminal is the hypotenuse of a right triangle x and y

are its legs

∵ x-coordinate is positive and y-coordinate is negative

∴ angle Ф lies in the 4th quadrant

- The opposite side of angle Ф is the y-coordinate of the point on the

terminal ray of angle Ф and the adjacent side to angle Ф is the

x-coordinate of that point

∵ The length of the hypotenuse (h) = √(x² + y²)

∴ h = √[(8)² + (-15)²] = √[64 + 225] = √[289] = 17

∴ The length of the hypotenuse is 17

- Lets find sin Ф

∵ sin Ф = opposite/hypotenuse

∵ The opposite is y = -15

∵ The hypotenuse = 17

∴ sin Ф = -15/17

- Lets find cos Ф

∵ cos Ф = adjacent/hypotenuse

∵ The adjacent is x = 8

∵ The hypotenuse = 17

∴ cos Ф = 8/17

- Lets find tan Ф

∵ tan Ф = opposite/adjacent

∵ The opposite is y = -15

∵ The adjacent = 8

∴ tan Ф = -15/8

- Remember csc Ф is the reciprocal of sin Ф

∵ csc Ф = 1/sin Ф

∵ sin Ф = -15/17

∴ csc Ф = -17/15

- Remember sec Ф is the reciprocal of cos Ф

∵ sec Ф = 1/ cos Ф

∵ cos Ф = 8/17

∴ sec Ф = 17/8

- Remember cot Ф is the reciprocal of tan Ф

∵ cot Ф = 1/tan Ф

∵ tan Ф = -15/8

∴ cot Ф = -8/15

5 0

3 years ago