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3 years ago

I can’t figure out the next smallest non negative solution. Can you please help me?

Mathematics

1 answer:

nlexa [21]3 years ago

3 0

Let w = cos(x)

The given equation turns into -5w^2 + 4w + 1 = 0. Use the quadratic formula to find that the two solutions, in terms of w, are:

w = -1/5 = -0.2
w = 1

The solution w = 1 leads to cos(x) = 1 which then becomes x = 0, x = 2pi, x = 4pi, etc. The general way to write this is x = 2pi*n where n is any integer. These angles are in radian mode.

The solution w = -0.2 leads to cos(x) = -0.2 which becomes x = arccos(-0.2) = 1.77215 approximately assuming your teacher wants the angle in radian mode. Unfortunately, I don't know the exact value of x here. There may not be an exact value, or finding this exact value may be well beyond the scope of this course.

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The following mapping statements describe the transformation of the vertices of △ABC to the vertices of its image, △A′B′C′. A(0,

victus00 [196]

Answer:

C. a reflection in the y-axis

Step-by-step explanation:

The mapping statement for the transformation of the vertices of the triangle ABC is given as following:

A(0,2)→A'(0,2)

B(2,9)→B'(-2,9)

C(4,2)→C'(-4,2)

To find the correct transformation for the given statement.

Solution:

From the given statements, the general transformation statement for the the vertices of the triangle can be given as:

$(x,y)\rightarrow (-x,y)$

The above transformation shows a reflection in the y-axis as the transformation in y-axis changes the sign of the x-coordinate of the point.

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n200080 [17]

I would go with A, but I'm not positive.

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3 years ago

Please help me<br><br> You travel 224 miles in 4 hours. Find the unit rate.

Tpy6a [65]

Answer:

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Step-by-step explanation:

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5 0

3 years ago

Read 2 more answers

Estimate the answer.

azamat

Answer:

The correct answer is B.

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3 years ago

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Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this

BigorU [14]

Answer:

a. 0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.

b. 0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.

c. 0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.

d. An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 27 dollars and a standard deviation of 9 dollars.

This means that $\mu = 27, \sigma = 9$

A. What proportion of the bank's Visa cardholders pay more than 29 dollars in interest?

This is 1 subtracted by the p-value of Z when X = 29, so:

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

$Z = \frac{29 - 27}{9}$

$Z = 0.22$

$Z = 0.22$ has a p-value of 0.5871.

1 - 0.5871 = 0.4129

0.4129 = 41.29% of the bank's Visa cardholders pay more than 29 dollars in interest.

B. What proportion of the bank's Visa cardholders pay more than 35 dollars in interest?

This is 1 subtracted by the p-value of Z when X = 35, so:

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

$Z = \frac{35 - 27}{9}$

$Z = 0.89$

$Z = 0.89$ has a p-value of 0.8133.

1 - 0.8133 = 0.1867

0.1867 = 18.67% of the bank's Visa cardholders pay more than 35 dollars in interest.

C. What proportion of the bank's Visa cardholders pay less than 14 dollars in interest?

This is the p-value of Z when X = 14. So

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

$Z = \frac{14 - 27}{9}$

$Z = -1.445$

$Z = -1.445$ has a p-value of 0.0742.

0.0742 = 7.42% of the bank's Visa cardholders pay less than 14 dollars in interest.

D. What interest payment is exceeded by only 18% of the bank's Visa cardholders?

This is the 100 - 18 = 82nd percentile, which is X when Z has a p-value of 0.82, so X when Z = 0.915.

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

$0.915 = \frac{X - 27}{9}$

$X - 27 = 0.915*9$

$X = 35.2$

An interest payment of $35.2 is exceeded by only 18% of the bank's Visa cardholders.

7 0

3 years ago