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3 years ago

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Mathematics

1 answer:

Nonamiya [84]3 years ago

3 0

The only point outside of the line is (2, 0)

In order to find if a point is outside, inside or on the line, you simply have to put the number into the equation. If the result is both sides are equal, then it is on the line. If the left side is bigger than the right side, then it is outside of the line. If the right side is bigger than the left, then it is inside of the line. So lets plug in and see where (2, 0) falls.

(x - 2)^2 + (y + 3)^2 = 4

(2 - 2)^2 + (0 + 3)^2 = 4

0^2 + 3^2 = 4

0 + 9 = 4

9 = 4

Since the left side is bigger than the right, we know it is outside of the line.

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4 years ago

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3 years ago

An education researcher claims that 58% of college students work year-round. In a random sample of 400 college students, 232

Hatshy [7]

Answer:

The proportion of college students who work year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58% of college students work year-round.

A random sample of 400 college students, 232 say they work year-round.

To test the researcher's claim use a one-proportion z-test.

The hypothesis can be defined as follows:

H₀: The proportion of college students who work year-round is 58%, i.e. p = 0.58.

Hₐ: The proportion of college students who work year-round is 58%, i.e. p ≠ 0.58. C

Compute the sample proportion as follows:

$\hat p=\frac{232}{400}=0.58$

Compute the test statistic value as follows:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0$

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

$p-value=2\times P(z$

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work year-round is 58%.

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4 years ago

Which expression is equivalent to 1.5 raised to the fifth power divided by 0.7 raised to the fourth power, all raised to the thi

harina [27]

The expression which is equivalent to the given expression as in the task content is; 1.5 raised to the fifteenth power divided by 0.7 raised to the twelfth power.

<h3>What is the expression which is equivalent to the given expression?</h3>

According to the task content, it follows that the expression given is;

(1.5⁵/0.7⁴)³

= 1.5^(3×5) /0.7^(4×3)

= 1.5¹⁵/0.7¹².

Hence, the expression which is equivalent is; 1.5 raised to the fifteenth power divided by 0.7 raised to the twelfth power.