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3 years ago

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The line segment joining A(6, 3) to B(–1, –4) is doubled in length by having half its length added to each end. Find the coordin

ates of the new ends.

1 answer:

mr Goodwill [35]3 years ago

4 0

Answer:

(9.5, 6.5) and (-4.5, -7.5)

Step-by-step explanation:

Let the extended points be A' and B' and add the point M as midpoint of AB

<u>Coordinates of M are:</u>

((6 - 1)/2, (3-4)/2) = (2.5, -0.5)

Now point A is midpoint of A'M and point B is midpoint of MB'

<u>Finding the coordinates using midpoint formula:</u>

A' = ((2*6 - 2.5),(2*3 - (-0.5)) = (9.5, 6.5)
B' = ((2*(-1) - 2.5), (2*(-4) - (-0.5)) = (-4.5, -7.5)

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What is he reciprocal of 3

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1/3 because reciprocal is the opposite

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3 years ago

Read 2 more answers

Multiple Representations:Question 1

alexdok [17]

Answer:

y = 27.1

Step-by-step explanation:

We have the value of x:

x = 12

and we need to find the value of y in the expression:

y = x + 15.1

as we can see by the equation, the value of y depends on the value of x.

thus, we substitute x = 12 on the previous equation:

y = 12 + 15.1

y = 27.1

the value of y is 27.1

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3 years ago

The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees°

Schach [20]

Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 98.6, \sigma = 0.6, n = 36, s = \frac{0.6}{\sqrt{36}} = 0.1$

If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.

This is 1 subtracted by the pvalue of Z when X = 98.4. So

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

By the Central Limit Theorem

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

$Z = \frac{98.4 - 98.6}{0.1}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228

1 - 0.0228 = 0.9772

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

6 0

3 years ago

What is the present value of $3,000 per year for 9 years discounted back to the present at 10 percent?

Studentka2010 [4]

Answer:

$17,277.07

Step-by-step explanation:

Present value of annuity is the present worth of cash flow that is to be received in the future, if future value is known, rate of interest is r and time is n then PV of annuity is

PV of annuity = $\frac{P[1-(1+r)^{-n}]}{r}$

= $\frac{3000[1-(1+0.10)^{-9}]}{0.10}$

= $\frac{3000[1-(1.10)^{-9}]}{0.10}$

= $\frac{3000[1-0.4240976184]}{0.10}$

= $\frac{3000(0.5759023816)}{0.10}$

= $\frac{1,727.7071448}{0.10}$

= 17,277.071448 ≈ $17,277.07

3 0

3 years ago

Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate mrs s gets a loan payoff of 60 months how much interest would s

Artist 52 [7]

Answer:

$\$4701.80$

Step-by-step explanation:

Mrs. Siebenaller bought a bus for 25,000 with a 7% interest rate and she gets a loan payoff of 60 months,

We know that,

$\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right]$

Where,

PV = Present value of annuity = 25000,

r = rate of interest of each period = $\dfrac{7}{12}$ % monthly

n = number of periods = 60 months,

Putting the values,

$\Rightarrow 25000=P\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]$

$\Rightarrow P=\dfrac{25000}{\left[\dfrac{1-(1+\frac{0.07}{12})^{-60}}{\frac{0.07}{12}}\right]}$

$\Rightarrow P=\$495.03$

Hence total amount paid is,

$=495.03\times 60=\$29,701.80$

Therefore interest amount is,

$=29,701.80-25,000=\$4701.80$

4 0

3 years ago