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3 years ago

Write the domain and range as inequalities.

Mathematics

1 answer:

Andrews [41]3 years ago

6 0

Answer:

domain: -∞ < x < ∞
range: -2 ≤ y < ∞

Step-by-step explanation:

Domain

The domain is the horizontal extent of the function, the set of input values for which it is defined. A parabola that opens up or down is defined for all x values, so its domain is ...

-∞ < x < ∞ . . . . . . (-∞, ∞) in interval notation

Range

The range is the vertical extent of the function, the set of output values it produces. The vertex of the parabola is one extreme of the range. Depending on the direction it opens, the other extreme will be +∞ or -∞. The range includes the y-value of the vertex. Here, the range is ...

-2 ≤ y < ∞ . . . . . . [-2, ∞) in interval notation

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The temperature is 15°F and is expected to fall 2°F each hour during the night.expression

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Answer:

I think the answer might be 15 - 2h. I am not sure.

The “h” represents each hours.

Step-by-step explanation:

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2 years ago

What is the answer to 7/12 plus 1/3

viva [34]

Answer: 11/12

Step-by-step explanation: Notice that 7/12 and 1/3 are unlike fractions. Our first step when adding unlike fractions is to get a common denominator.

The common denominator of 12 and 3 will be the least common multiple of 12 and 3 which is 12.

The fraction 7/12 already has a 12 in the denominator so we leave it alone.

To get a 12 in the denominator of 1/3, we multiply both the numerator and the denominator by 4 and we get the equivalent fraction 4/12.

Now we are adding like fractions.

To add like fractions, we simply add across the numerators.

7/12 + 4/12 = 11/12

Therefore, 7/12 + 1/3 = 11/12.

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2 years ago

Lee Jenkins worked the following hours as a manager for a local Pizza Hut: 82,61,7

emmainna [20.7K]

Answer:

223 hours

Step-by-step explanation:

Total hours worked by Lee = sum of all the hours worked

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82 + 61 + 7 + 73 = 223 hours

Therefore, Lee worked 223 hours as manager for the local Pizza Hut

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3 years ago

Determined that intercepts of the line.

hjlf

Answer:

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Step-by-step explanation:

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2 years ago

1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,

gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

$\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988$

The combined proportion is:

$\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989$

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78$

Compute the p-value as follows:

$p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075$

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\$

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

6 0

3 years ago