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3 years ago

Evaluate and simplify sin (-15º).

Mathematics

1 answer:

olga55 [171]3 years ago

7 0

Note:

sin(-θ) = -sinθ

sin(-15°) = -sin15° Use a calculator

sin(-15°) = -sin15° = -0.2588

sin(-15°) = -0.2588

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Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a norm

Artemon [7]

Answer:

a) 0.5.

b) 0.8413

c) 0.8413

d) 0.6826

e) 0.9332

f) 1

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 6, \sigma = 0.2$

(a) P(x > 6) =

This is 1 subtracted by the pvalue of Z when X = 6. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6-6}{0.2}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

1 - 0.5 = 0.5.

(b) P(x < 6.2)=

This is the pvalue of Z when X = 6.2. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6.2-6}{0.2}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

(c) P(x ≤ 6.2) =

In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.

(d) P(5.8 < x < 6.2) =

This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X 5.8.

X = 6.2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6.2-6}{0.2}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 5.8

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5.8-6}{0.2}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

(e) P(x > 5.7) =

This is 1 subtracted by the pvalue of Z when X = 5.7.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5.8-6}{0.2}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

1 - 0.0668 = 0.9332

(f) P(x > 5) =

This is 1 subtracted by the pvalue of Z when X = 5.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5-6}{0.2}$

$Z = -5$

$Z = -5$ has a pvalue of 0.

1 - 0 = 1

5 0

3 years ago

A rectangular vegetable garden will have a width that is 4 feet less than the length and an area of 140 square feet if x represe

k0ka [10]

X times parentheses x minus 4 equals 140

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3 years ago

3. Write the equation. Slope: riset Run y intercept: equation: y=mx+b;

larisa [96]

Answer: y = 1/4 x – 4

OR y = x/4 –4

m is the slope. b is the y-intercept.

Without numbers on the x and y axis, it may not be correct. But assuming a normal scale, the slope is positive 1/4 and the y-intercept is -4

Step-by-step explanation: To find the slope, m, determine "rise over run"

Look for places where the graphed line crosses the grid at intersections. There seems to be such places at (–4,–5), (0,–4) and (4,–3)

The "rise" is the difference in y-values. Here, they increase by 1.

The "run" is the difference in x-values. Here they increase by 4.

So the slope is 1/4. Put that in place of m.

The graphed line crosses the y-axis at –4

That is the y-intercept. Use -4 in the place of b

Keep the y and x; substitute the values for m and b we found.

y = 1/4 x – 4

y = x/4 – 4 This makes it clear that x is not in the denominator of the fraction, 1/4, and in calculations with given coordinates, the value of x will be divided by 4.

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3 years ago

Lines m and n are parallel. What is the measure of angle 5 Pls help

Nonamiya [84]

Answer:

Step-by-step explanation:

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4 years ago

PLEASE ANSWER

statuscvo [17]

Answer: B) 2

Detailed Answer:

The degree of a polynomial is the highest power in the polynomial. Here the highest power is 2 hence the degree is 2. Polynomials with the degree 2 are also called quadratic polynomials.

8 0

2 years ago