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Empirical rule (statistics)Help please!!!

emmasim [6.3K]

The empirical rule you're referring to is the 68-95-99.7 rule, which asserts that for a normal (bell-shaped) distribution, approximately 68% of the distribution lies within 1 standard deviation of the mean; 95% lies within 2 standard deviations of the mean; and 99.7% lies within 3 standard deviations of the mean.

Let $X$ be the random variable denoting vehicle speeds along this highway. We want to find $P(61$ . To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.

Notice that $61=70-9=70-3\cdot3$ , and $79=70+9=70+3\cdot3$ . In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so $P(61$ .

8 0

3 years ago

Solve. the square root of 44-2x = x-10

Anuta_ua [19.1K]

44-2x=x-10 subtract 44 from both sides -2x= x-54 subtract x from both sides -3x= -54 divide by -3 x= 18 square root of 18= 4.24 in radical form 3 square root of 2 hope this helps

5 0

3 years ago

Read 2 more answers

Which equation is represented by the graph shown in the image? A. y + 2= x B. y + 1= x C. y - 1= x D. y - 2= x Please show ALL w

olasank [31]

Answer:

A. y + 2= x

Step-by-step explanation:

Which equation is represented by the graph shown in the image?

A. y + 2= x

B. y + 1= x

C. y - 1= x

D. y - 2= x

Please show ALL work! <3

The graph shown has a slope of +1 and a y intercept of -2.

All given answer choices have a slope of +1, so that's not the problem.

We need one that has a y-intercept of -2, or the equation should be

y = x-2, or equivalently y+2 = x

which corresponds to answer choice A.

6 0

3 years ago

Pls solve the simultaneous equation in the attachment.

siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

$\frac{x}{2}-\frac{y}{5}=1$ ----> equation A

$y-\frac{x}{3}=8$ ----> equation B

Multiply equation A by 10 both sides to remove the fractions

$5x-2y=10$ ----> equation C

isolate the variable y in equation B

$y=\frac{x}{3}+8$ ----> equation D

we have the system of equations

$5x-2y=10$ ----> equation C

$y=\frac{x}{3}+8$ ----> equation D

Solve the system by substitution

substitute equation D in equation C

$5x-2(\frac{x}{3}+8)=10$

solve for x

$5x-\frac{2x}{3}-16=10$

Multiply by 3 both sides

$15x-2x-48=30$

$15x-2x=48+30$

Combine like terms

$13x=78$

$x=6$

<em>Find the value of y</em>

$y=\frac{x}{3}+8$

$y=\frac{6}{3}+8$

$y=10$

The solution is the ordered pair (6,10)

Part b) we have

$xy=21$ ---> equation A

$x+5y=22$ ----> equation B

isolate the variable x in the equation B

$x=22-5y$ ----> equation C

substitute equation C in equation A

$(22-5y)y=21$

solve for y

$22y-5y^2=21$

$5y^2-22y+21=0$

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

<em>Find the values of x</em>

For y=1.4

$x=22-5(1.4)=15$

For y=3

$x=22-5(3)=7$

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

3 0

3 years ago

Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the equation of the line con

almond37 [142]

Answer:

$y=-x+r$

Step-by-step explanation:

we know that

The tangency point on the x-axis is (r,0)

The tangency point on the y-axis is (0,r)

Find the slope of the line containing the points of tangency

$m=\frac{0-r}{r-0}=-1$

Remember that the equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have

$m=-1$

$b=r$

substitute

$y=-x+r$

4 0

3 years ago