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2 years ago

Solve the following 5 3/4 + (6 2/3 - 4 5/6) =

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

4 0

Answer:

7 5/12

Step-by-step explanation:

first, subtract 4 5/6 from 6 2/3 by converting 6 2/3 to 6 4/6

5 3/4 + (6 4/6 - 4 5/6) = 5 3/4 + 1 4/6

* I borrowed 6/6 or '1' from the 6 and made 4/6 into 10/6

5 3/4 equals 5 9/12 and 1 4/6 equals 1 8/12

adding them gives you:

6 17/12 which is the same as 6 + 1 5/12, or 7 5/12

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In △ E F G △EFG, K K is the centroid. If K J = 7 KJ=7, find F K FK. E J G I F H K

VladimirAG [237]

The answer is 50 degrees
You get this by subtracting 180-130

8 0

2 years ago

A class survey in a large class for first-year college students asked, “About how many minutes do you study on a typical weeknig

Anika [276]

Answer: (110.22, 125.78)

Step-by-step explanation:

The confidence interval for the population mean is given by :-

$\mu\ \pm z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size = 463

$\mu=118\text{ minutes}$

$\sigma=65\text{ minutes}$

Significance level : $\alpha=1-0.99=0.01$

Critical value : $z_{\alpha/2}=z_{0.005}=\pm2.576$

We assume that the population is normally distributed.

Now, the 90% confidence interval for the population mean will be :-

$118\ \pm\ 2.576\times\dfrac{65}{\sqrt{463}} \\\\\approx118\pm7.78=(118-7.78\ ,\ 118+7.78)=(110.22,\ 125.78)$

Hence, 99% confidence interval for the mean study time of all first-year students = (110.22, 125.78)

3 0

3 years ago

Alex was biking along a 48 mile trail. First half of the time he was biking twice as fast as the second half of the time. If he

nydimaria [60]

Answer:

The speed in the first part is 16 mph.

Step-by-step explanation:

The total distance is 48 miles. The total time is 4 hours.

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.

In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part of trip:

48 - d = 2s * 2

d + 4s = 48 Equation 1

Second part of the trip:

d = s * 2

d = 2s Equation 2

Equations 1 and 2 form a system of equations in two unknowns, d and s.

d + 4s = 48

d = 2s

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48

s = 8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) = 16.

The speed in the first part is 16 mph.

Check:

d = 2s = 2(8) = 16

48 - d = 48 - 16 = 32

The second part is 16 miles. The first part is 32 miles.

16 miles at 8 mph takes 2 hours.

32 miles at 16 mph takes 2 hours.

2 hours + 2 hours = 4 hours.

Our answer is correct.

Answer: The speed in the first part is 16 mph.

7 0

3 years ago

Three more than a number is 15

podryga [215]

Answer:

The number is 12

Step-by-step explanation:

If 15 is three more than the number is three less so you do, 15 - 3 which is 12.

I hope this helps

7 0

2 years ago

Two triangles are similar.The the smaller triangle has side 10,20 and 15 units the larger triangles longest side is 52 units.Wha

Oliga [24]

Answer: The perimeter of the largest triangle = 117 units.

Step-by-step explanation:

Sides of smaller triangle = 10,20 and 15 units

Longest side = 20 units

Longest side of larger triangle = 52 units

Sides of two similar triangles are proportional.

Let k be proportionality constant.

$k=\dfrac{\text{Length in larger triangle}}{\text{Length in smaller triangle}}$

$k=\dfrac{52}{20}\\\\\Rightarrow\ k=\dfrac{13}{5}$

Length of other two sides,

$10\times\dfrac{13}{5}, 15\times\dfrac{13}{5}\ i.e.\ 26\text{ units}, 39\text{ units.}$

So sides of larger triangle = 52 units, 26 units , 39 units

Perimeter of largest triangle = 52 +26+39 = 117 units

Hence, the perimeter of the largest triangle = 117 units.

4 0

3 years ago