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3 years ago

Write an equation in slope-intercept form for a line that is (a) parallel (b) perpendicular to

Mathematics

1 answer:

ollegr [7]3 years ago

4 0

Answer:

A) parallel

It has the same slope.

y-intercept is 6.

So,

m = -5

b = + 6

y = -5x + 6

B) perpendicular

It has a negative reciprocal of the slope.

-5 = 1/5

y-intercept is 6

m = 1/5

b = + 6

y = 1/5x + 6

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Solve for t in scientific formula d=rt

yarga [219]

The problem is: d=rt
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d=rt
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t t

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d/t=r or r=d/t

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If the first step of solving a system of equations by subsistution is to solve one equations for one of the variables, how do ch

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Solve the initial-value problem y' = x^4 - \frac{1}{x}y, y(1) = 1.

natta225 [31]

The ODE is linear:

$y'=x^4-\dfrac yx$

$y'+\dfrac yx=x^4$

Multiplying both sides by $x$ gives

$xy'+y=x^5$

Notice that the left side can be condensed as the derivative of a product:

$(xy)'=x^5$

Integrating both sides with respect to $x$ yields

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Since $y(1)=1$ ,

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$\boxed{y(x)=\dfrac{x^5}6+\dfrac5{6x}}$

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3 years ago

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 201.9-cm and a standard dev

Nesterboy [21]

Answer:

There is a 0.08% probability that the average length of a randomly selected bundle of steel rods is greater than 204.1-cm.

Step-by-step explanation:

Problems of normally distributed samples can be 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:

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 201.9-cm and a standard deviation of 2.1-cm. This means that $\mu = 201.9, \sigma = 2.1$ .

For shipment, 9 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is greater than 204.1-cm.

By the Central Limit Theorem, since we are using the mean of the sample, we have to use the standard deviation of the sample in the Z formula. That is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{9}} = 0.7$

This probability is 1 subtracted by the pvalue of Z when $X = 204.1$ .

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

$Z = \frac{204.1 - 201.9}{0.7}$

$Z = 3.14$

$Z = 3.14$ has a pvalue of 0.9992. This means that there is a 1-0.9992 = 0.0008 = 0.08% probability that the average length of a randomly selected bundle of steel rods is greater than 204.1-cm.

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If the vertex of a parabola is (2,-9) and another point on the curve is (5,18), what is the coefficient of the squared expressio

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