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2 years ago

The endpoints of EF are E(xE , yE) and F(xF , yF). What are the coordinates of the midpoint of EF?

Mathematics

2 answers:

tatyana61 [14]2 years ago

7 0

Answer:

The coordinates of the midpoint of EF is equal to

$(\frac{xE+xF}{2},\frac{yE+yF}{2})$

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

In this problem we have

$(x1,y1)=(xE,yE)$

$(x2,y2)=(xF,yF)$

Substitute the values in the formula

$M=(\frac{xE+xF}{2},\frac{yE+yF}{2})$

baherus [9]2 years ago

7 0

I guess you are looking for a general way of writing a midpoint in coordinate system.
we have the following:
E(xe, ye) and F(xf,yf)
then mind point is as follows
((xe+xf)/2, (ye+yf)/2)

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In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute

Vera_Pavlovna [14]

Answer:

a) 1.88% percent of the runners have heart rates above 130.

b) 50% percent of the nomrunners have heart rates above 130.

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.

(a) What percent of the runners have heart rates above 130?

In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104,12.5) distribution. This means that $\mu = 104, \sigma = 12.5$ .

This percentage is 1 subtracted by the pvalue of Z when $X = 130$ .

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

$Z = \frac{130 - 104}{12.5}$

$Z = 2.08$

$Z = 2.08$ has a pvalue of 0.9812.

This means that 1-0.9812 = 0.0188 = 1.88% percent of the runners have heart rates above 130.

(b) What percent of the nonrunners have heart rates above 130?

The heart rates for male nonrunners after the same exercise have the N(130, 17) distribution. This means that $\mu = 130, \sigma = 17$ .

This percentage is 1 subtracted by the pvalue of Z when $X = 130$ .

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

$Z = \frac{130 - 130}{17}$

$Z = 0.00$

$Z = 0.00$ has a pvalue of 0.5000.

This means that 1-0.50 = 0.50 = 50% percent of the nomrunners have heart rates above 130.

4 0

2 years ago

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e0

nikitadnepr [17]

Answer:

$8\ years$

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$t=?\ years\\ P=\$100\\A=\$150\\ r=0.05$

substitute in the formula above

$150=100(e)^{0.05*t}$

$1.5=(e)^{0.05*t}$

Applying ln both sides

$ln(1.5)=(0.05t)ln(e)$

$ln(1.5)=(0.05t)$

$t=ln(1.5)/(0.05)$

$t=8\ years$

8 0

1 year ago

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An Internet service provider sampled 540 customers, and finds that 75 of them experienced an interruption in high-speed service

Nastasia [14]

Answer:

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Step-by-step explanation:

7 0

1 year ago

Yumi wants to make 12 cups of party mix using candies and nuts her budget require the party mix to cost her $1 29 per cup. The c

kifflom [539]

Answer:

Acording to the question,

Cost per cup = $1.29

Total number of cups = 12

Total cost of cups = 12 x 1.2 = $15.48

Cost of candies = $2.49 per cup

Total number of candies = x

Cost of nuts = $0.69 per cup

Total number of nuts = y

Equations :

x + y = 12 (because total cups of nuts and candies will be equal to 12)

2.49x + 0.69y = 15.48 (Total cost of the 12 cups should be 15.48)

<u>Step 1 : Find x in terms of y</u>

x = 12 - y

<u>Step 2 : substitute x in terms of y from step 1 in the second equation</u>

2.49x + 0.69y = 15.48

2.49 ( 12 - y) + 0.69y = 15.48

29.88 - 2.49y + 0.69y = 15.48

-1.8y = -14.4

y = 14.4/1.8

y = 8

Step 3 : Find x

x + y = 12

x = 12 - y

x = 12- 8

x = 4

Thus,Yumi should use 4 cups of candies and 8 cups of nuts.

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2 years ago

A student is deriving the quadratic formula. Her first two steps are shown. Step 1: –c = ax2 + bx Step 2: -c = a[x^2+b/ax] Which

marta [7]

Given choices:

(1) division property of equality

(2) factoring the binomial

(3)completing the square

(4)subtraction property of equality

Answer : (2) factoring the binomial

Step 1: $-c = ax^2 + bx$

Step 2: $-c = a[x^2+\frac{b}{a} x]$

In step 2, 'a' is taken out from $ax^2 + bx$ . when we take out 'a' we divide each term by 'a'. so it becomes $a[x^2+\frac{b}{a} x]$

'a' is factored out in step 2. we call it as factoring a binomial.

6 0

1 year ago

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