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3 years ago

Given f(x) = 5x, find each of the following:

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

4 0

Answer:

Given f(x) = 5x, find each of the following:

f(3) = 15

f(-2) = -10

f(-1) = -5

f(8) = 40

f(-4) = -16

Step-by-step explanation:

When you have a value of x, it shows up inside the parenthesis.

For example: f(3) means x = 3.

Once you know what x is, you just have to plug in it's value into the original function.

So f(x) = 5x where f(3) means (5*3) or 15.

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I can Multiply a 4x4 matrix by a 4x3 matrix. The resulting matrix will be a?

hodyreva [135]

Answer:

Step-by-step explanation:

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3 years ago

The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amou

lions [1.4K]

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = <u><em>the amount spent on daily transportation</em></u>

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = average annual amount American households spend on daily transportation = $6,312

$\sigma$ = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

P(X < $1,000) = 0.05

P( $\frac{X-\mu}{\sigma}$ < $\frac{\$1000-\$6312}{\sigma}$ ) = 0.05

P(Z < $\frac{\$1000-\$6312}{\sigma}$ ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

$\frac{\$1000-\$6312}{\sigma}=-1.645$

$\sigma=\frac{-\$5312}{-1.645}$ = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

P($4000 < X < $6000) = P(X < $6000) - P(X $\leq$ $4000)

P(X < $6000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{\$6000-\$6312}{\$3229.18}$ ) = P(Z < -0.09) = 1 - P(Z $\leq$ 0.09)

= 1 - 0.5359 = 0.4641

P(X $\leq$ $4000) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{\$4000-\$6312}{\$3229.18}$ ) = P(Z $\leq$ -0.72) = 1 - P(Z < 0.72)

= 1 - 0.7642 = 0.2358

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

P(X > x) = 0.03 {where x is the required range}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-\$6312}{3229.18}$ ) = 0.03

P(Z > $\frac{x-\$6312}{3229.18}$ ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

$\frac{x-\$6312}{3229.18}=1.88$

${x-\$6312}=1.88\times 3229.18$

x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

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4 years ago

Need help fast please

nalin [4]

B, because they said increasing and most people would say D but it isn’t because they mean increasing in how much money she transfers out so it’s B.

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4 years ago

Nick needs 65 yards of wire for a project. if the wire is only sold on spools which hold 6 feet of wire, how many spools will he

Vladimir [108]

Answer:

Step-by-step explanation:

I would first convert the spools into the yard equivalent so 6 ft spools are equal to 2 yard spools now you take 65 divided by 2 which would give you the answer and the answer is 32.5 unless they refuse to sell a partial spool then you would by 33 spools of wire and you would have enough yards of wire with one yard left over

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3 years ago

Perpendicular to 3x-6y=-2 containing points (-3,-8)

vovangra [49]

Answer:

Step-by-step explanation:

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m\ -\ \text{slope}\\b\ -\ \text{y-intercept}$

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2$

$\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope intercept from:}\\\\3x-6y=-2\qquad\text{subtract }\ 3x\ \text{from both sides}\\\\-6y=-3x-2\qquad\text{divide both sides by (-6)}\\\\y=\dfrac{-3}{-6}x+\dfrac{-2}{-6}\\\\y=\dfrac{1}{2}x+\dfrac{1}{3}\to m_1=\dfrac{1}{2}$

$\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-1\cdot\dfrac{2}{1}=-2.\\\\\text{Put the value of a slope and the coordinates of the point (-3, -8)}\\\text{ to the equation of a line:}\\\\-8=-2(-3)+b\\\\-8=6+b\qquad\text{subtract 6 from both sides}\\\\-14=b\to b=-14\\\\\text{Finally:}\\\\y=-2x-14$

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3 years ago