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2 years ago

Mara ran 3km north and then 4km east. She will finish her run by running directly home. What was the total distance of her run?

Mathematics

2 answers:

Vilka [71]2 years ago

7 0

Answer:

its option C

Step-by-step explanation:

Reil [10]2 years ago

5 0

So we need to find the length of the hypotenuse of a right triangle with sides of 3 and 4, then add that distance to 3 and 4.

By the Pythagorean Theorme, the hypotenuse squared is equal to the sum of the sides squared...

d^2=3^2+4^2

d^2=9+16

d^2=25

d=√25

d=5

So the total distance of her run is 5+4+3=12 km

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2 years ago

Trevor Ariza is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next on

vivado [14]

Answer:

Probability of making none of next 5 free throws = 0.00243

Step-by-step explanation:

"Making or missing free throws doesn't change the probability that he will make his next one"

So the probability of making none of next 5 free throws

= Probability of missing next 5 free throws

= Probability of missing 1 free throw^5

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2 years ago

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Avon Edwards worked 45.5 hours at $5 per hour. He made $100 in tips but no bonuses. Anything over 40 hours is paid time-and-a-ha

posledela

Answer:

1. D

2. B

Step-by-step explanation:

Question 1:

We can get Avon's earnings using the equation $W=HR+1.5VR+B+T$

Where W is his earnings

HR is the regular hours (40 hours in this case)

V is overtime hours (hours over 40, 45.5 - 40 = 5.5 hours)

B is bonus (no bonus)

T is tips ( $100 tips, given)

and R is the rate (which is $5 per hour)

Substituting the given info into the equation, we get:

$W=HR+1.5VR+B+T\\W=(40)(5)+1.5(5.5)(5)+0+100\\W=341.25$

So avon's earnings are $341.25

Answer choice D is right.

Question 2:

The other employee needs to work $x$ hours @ $15 per hour to equate or surpass $428. So we can set up the equation shown below and solve for x:

$(15)(x)=428\\x=\frac{428}{15}\\x=28.53$

Rounded to 1 decimal place, this is about 28.5 hours

Answer choice B is right.

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2 years ago

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PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

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