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andrey2020 [161]

2 years ago

15

Use the two-way frequency table to calculate the probability that the person is a democrat, given the fact that the person suppo

rts the issue,
P(democrat supports the issue)

1 answer:

Slav-nsk [51]2 years ago

8 0

Answer:

23/58

Step-by-step explanation:

number of people that support the issue. (58)

start with that first because it is given

now find the number of democrats that are in that column which is 23

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According to the Ruler Postulate, what does the set of points on any line correspond to?

S_A_V [24]

The correct answer is real numbers

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4 years ago

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Solve the following equations for x,

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(i) 3 csc²(<em>x</em>) - 4 = 0

3 csc²(<em>x</em>) = 4

csc²(<em>x</em>) = 4/3

sin²(<em>x</em>) = 3/4

sin(<em>x</em>) = ± √3/2

<em>x</em> = arcsin(√3/2) + 2<em>nπ</em> <u>or</u> <em>x</em> = arcsin(-√3/2) + 2<em>nπ</em>

<em>x</em> = <em>π</em>/3 + 2<em>nπ</em> <u>or</u> <em>x</em> = -<em>π</em>/3 + 2<em>nπ</em>

where <em>n</em> is any integer. The general result follows from the fact that sin(<em>x</em>) is 2<em>π</em>-periodic.

In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, the first family of solutions gives <em>x</em> = <em>π</em>/3 and <em>x</em> = 4<em>π</em>/3 for <em>n</em> = 0 and <em>n</em> = 1, respectively; the second family gives <em>x</em> = 2<em>π</em>/3 and <em>x</em> = 5<em>π</em>/3 for <em>n</em> = 1 and <em>n</em> = 2.

(ii) 4 cos²(<em>x</em>) + 2 cos(<em>x</em>) - 2 = 0

2 cos²(<em>x</em>) + cos(<em>x</em>) - 1 = 0

(2 cos(<em>x</em>) - 1) (cos(<em>x</em>) + 1) = 0

2 cos(<em>x</em>) - 1 = 0 <u>or</u> cos(<em>x</em>) + 1 = 0

2 cos(<em>x</em>) = 1 <u>or</u> cos(<em>x</em>) = -1

cos(<em>x</em>) = 1/2 <u>or</u> cos(<em>x</em>) = -1

[<em>x</em> = arccos(1/2) + 2<em>nπ</em> <u>or</u> <em>x</em> = 2<em>π</em> - arccos(1/2) + 2<em>nπ</em>] <u>or</u> <em>x</em> = arccos(-1) + 2<em>nπ</em>

[<em>x</em> = <em>π</em>/3 + 2<em>nπ</em> <u>or</u> <em>x</em> = 5<em>π</em>/3 + 2<em>nπ</em>] <u>or</u> <em>x</em> = <em>π</em> + 2<em>nπ</em>

For 0 ≤ <em>x</em> ≤ 2<em>π</em>, the solutions are <em>x</em> = <em>π</em>/3, <em>x</em> = 5<em>π</em>/3, and <em>x</em> = <em>π</em>.

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3 years ago

Find the student’s error in solving the following inequality. 31 < –5x + 6 25 < –5x –5 < x

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Answer:

He subtracted -5 from both sides, not -6

Step-by-step explanation:

The inequality that we have to solve in this problem is

$31$

To solve the inequality, we proceed as follows:

1)

First, we isolate the term in x. To do that, we add -6 on both sides of the inequality, and we find:

$31-6$

So, this is now the new inequality.

2)

Then, we divide both sides of the equation by 5; we get:

$\frac{25}{5}$

3)

Finally, we change sign to the inequality, so we get:

$x$

So, the student's error is that he subtracted -5 from both sides, not -6.

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Answer:

Total amount paid for the Car=$24,832

Finance Charge=$2,382

Step-by-step explanation:

Down payment on the Car=$2800

Number of Monthly Installments=36

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Total Monthly Installment Paid=36*$612=$22032

Therefore, the Total Amount Paid for the Car=Down Payment+Total Installmental Payment=2800+22032=$24,832

Next, we determine the finance charge.

Finance Charge=Total Amount Paid for the Car - Delivered Price of the Car

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Therefore:

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4 years ago