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3 years ago

What is the slope of the line that contains the points (-1, 8) and (2, -4)?

Mathematics

2 answers:

vovikov84 [41]3 years ago

7 0

Answer:

-4

Step-by-step explanation:

Use the equation for slope.

$m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{-4 - 8 }{2-(-1) }\\m=\frac{-4 - 8 }{2+1 }\\m=\frac{-12}{3}\\ m=-4$

The slop is -4.

trapecia [35]3 years ago

4 0

Answer:

-4

Step-by-step explanation:

The slope of a line given two points is given by

m = (y2-y1)/(x2-x1)

= (-4-8)/(2 - -1)

= (-4-8)/(2+1)

= -12/3

= -4

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In studies for a medication, 3 percent of patients gained weight as a side effect. Suppose 643 patients are randomly selected.

timofeeve [1]

Part a)

It was given that 3% of patients gained weight as a side effect.

This means

$p = 0.03$

$q = 1 - 0.03 = 0.97$

The mean is

$\mu = np$

$\mu = 643 \times 0.03 = 19.29$

The standard deviation is

$\sigma = \sqrt{npq}$

$\sigma = \sqrt{643 \times 0.03 \times 0.97}$

$\sigma =4.33$

We want to find the probability that exactly 24 patients will gain weight as side effect.

P(X=24)

We apply the Continuity Correction Factor(CCF)

P(24-0.5<X<24+0.5)=P(23.5<X<24.5)

We convert to z-scores.

$P(23.5 \: < \: X \: < \: 24.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 1.20) \\ = 0.051$

Part b) We want to find the probability that 24 or fewer patients will gain weight as a side effect.

P(X≤24)

We apply the continuity correction factor to get;

P(X<24+0.5)=P(X<24.5)

We convert to z-scores to get:

$P(X \: < \: 24.5) = P(z \: < \: \frac{24.5 - 19.29}{4.33} ) \\ = P(z \: < \: 1.20) \\ = 0.8849$

Part c)

We want to find the probability that

11 or more patients will gain weight as a side effect.

P(X≥11)

Apply correction factor to get:

P(X>11-0.5)=P(X>10.5)

We convert to z-scores:

$P(X \: > \: 10.5) = P(z \: > \: \frac{10.5 - 19.29}{4.33} ) \\ = P(z \: > \: - 2.03)$

$= 0.9788$

Part d)

We want to find the probability that:

between 24 and 28, inclusive, will gain weight as a side effect.

P(24≤X≤28)=

P(23.5≤X≤28.5)

Convert to z-scores:

$P(23.5 \: < \: X \: < \: 28.5) = P( \frac{23.5 - 19.29}{4.33} \: < \: z \: < \: \frac{28.5 - 19.29}{4.33} ) \\ = P( 0.97\: < \: z \: < \: 2.13) \\ = 0.1494$

3 0

3 years ago

Eric and Frank want to equally share 4/3 feet of rope. what length of rope should each friend get? explain how to use a drawing

blondinia [14]

The rope is 1 and 1/3 long,1 is the same as saying 3/3,
this means that the rope is 3/3 + 1/3 long,so it is 4/3 foot long,
you now want to get half of this number so that each person has an equal length of rope,so multiply the length of rope by a half,
4/3 x 1/2 = 4/6 , which if simplified = 2/3, this means that each friend gets 2/3 foot of rope.

You can draw this in a diagram by drawing the 1 foot of rope, and then dividing it up into 3 sections. Then add the 1/3 foot of rope into the drawing. It should then be easy to see that altogether there are 4 separate sections of rope and that if each friend has two sections then they will be sharing equal amounts, so consequently each friend has two of the thirds of rope, 2/3

4 0

3 years ago

What's the gcf of 47 and 17

ElenaW [278]

Answer:

The GCF of 47 and 17 is 1

Step-by-step explanation:

6 0

2 years ago

4x+3y=-5 -2x+2y=6 elimination method

Semenov [28]

X=-6.5
Y=7

Hope this helps

4 0

3 years ago

Factor to write an equivalent expression.(What is the Greatest Common Factor?).<br><br> −9x+15y

KengaRu [80]

Answer:

GCF is 3

Step-by-step explanation:

Given the expression -9x + 15y

First, we need to find ther individual factors

-9x = -3 *3 * x

15y = 3 * 5 * y

Since 3 is common to both factors

−9x+15y = 3(-3x+5y)

Hence the GCF is 3

3 0

3 years ago