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3 years ago

15

Mackenzie had 2 inches of snow on her lawn. It then began to snow at a rate of 2.5 inches per hour. Which of the variables below

is the dependent variable

1 answer:

S_A_V [24]3 years ago

5 0

Answer: per hour

Step-by-step explanation:

That is dependent. It is by itself

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Which of the following best defines an output

Finger [1]

The answer is the 3rd option im pretty sure :)

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3 years ago

Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))

Softa [21]

Answer:

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Step-by-step explanation:

tan(sin⁻¹x + cos⁻¹y)

Use angle sum formula:

[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]

To evaluate these expressions, I suggest drawing right triangles.

For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1. Therefore:

sin θ = x/1

θ = sin⁻¹x

Using Pythagorean theorem, the adjacent side is √(1−x²). Therefore:

tan θ = x / √(1−x²)

tan(sin⁻¹x) = x / √(1−x²)

Draw a new triangle. This time we'll make y the adjacent side to angle θ.

cos θ = y/1

θ = cos⁻¹y

Using Pythagorean theorem, the opposite side is √(1−y²). Therefore:

tan θ = √(1−y²) / y

tan(cos⁻¹y) = √(1−y²) / y

Substituting:

[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]

Multiply top and bottom by √(1−x²).

[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]

Multiply top and bottom by y.

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

3 0

3 years ago

3x+2>5x-8<br><br> Can some one help me with this problem

Andre45 [30]

Answer:

5 > x

Step-by-step explanation:

3x+2>5x-8 rewrite the inequality by exporting like terms to the same side

2+8 > 5x - 3x now add/subtract like terms

10 > 2x divide both sides by 2

5 > x

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3 years ago

Please help! ILL GIVE BRAINLIST

Andru [333]

Answer: the answer is 36

Step-by-step explanation: You add all the sides together

8 0

3 years ago

Read 2 more answers

A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard d

bagirrra123 [75]

The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

<h3>
How to find the confidence interval for population mean from large samples (sample size > 30)?</h3>

Suppose that we have:

Sample size n > 30
Sample mean = $\overline{x}$
Sample standard deviation = s
Population standard deviation = $\sigma$
Level of significance = $\alpha$

Then the confidence interval is obtained as

Case 1: Population standard deviation is known

$\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}$

Case 2: Population standard deviation is unknown.

$\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}$

For this case, we're given that:

Sample size n = 90 > 30
Sample mean = $\overline{x}$ = 138
Sample standard deviation = s = 34
Level of significance = $\alpha$ = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).

At this level of significance, the critical value of Z is: $Z_{0.1/2}$ = ±1.645

Thus, we get:

$CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]$

Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]

Learn more about confidence interval for population mean from large samples here:

brainly.com/question/13770164

3 0

2 years ago