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Nata [24]
3 years ago
6

14. A plane traveled from California and back. It took one hour longer on the way out than it did on the way back. The plane's a

verage
speed out was 300 mph. The average speed on the way back was 350 mph. How many hours did the trip out take?
A. 13 hours
B. 8 hours
C. 7 hours
D. 6 hours
Mathematics
1 answer:
kow [346]3 years ago
8 0

Answer:

  C.  7 hours

Step-by-step explanation:

Let the time for the trip out be represented by t. Then the time for the return trip is t-1. The distance was the same for both trips, so we have ...

  distance = speed × time

  300t = 350(t -1)

  300t = 350t -350 . . . . eliminate parentheses

  350 = 50t . . . . . . . . . . add 350-300t

  7 = t . . . . . . divide by 50

The trip out took 7 hours.

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(20 points)Solve the equation cos x = sin (x + 22)
Law Incorporation [45]

Answer:

\bold{x = 34^\circ}

Step-by-step explanation:

Given:

cos x = sin (x + 22^\circ)

To solve:

The given equation.

Solution:

First of all, let us consider an important property of sine and cosine.

sin(90^\circ-\theta )=cos\theta

OR

cos(90^\circ-\theta )=sin\theta

We can apply above property to solve for x as per given equation.

cos x = sin (x + 22^\circ)

Changing cosx to sine form:

cosx=sin(90^\circ-x)

cosx=sin(90^\circ-x) = sin(x+22^\circ)

\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}

So, solution to the equation cos x = sin (x + 22^\circ) is:

\bold{x = 34^\circ}

7 0
3 years ago
Guys help please again
Anon25 [30]
The answer is c and a
8 0
3 years ago
From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. Wha
Ede4ka [16]

Answer:

D. 2/7

Step-by-step explanation:

The probability is calculate as a division between the number of ways in which Andrew will be selected and karen will not and the total ways in which they can select 4 people from a group of 8 volunteers.

The number of ways in which they can select 4 people from a group of 8 volunteers can be calculated using:

nCk=\frac{n!}{k!(n-k)!}

Where nCk give as the number of ways in which we can form groups of k elements from a group of n elements.

So, if we replace n by 8 and k by 4, we get:

8C4=\frac{8!}{4!(8-4)!}=70

Then, there are 70 ways to select 4 people from a group of 8 volunteers.

At the same way, the number of ways in which Andrew will be selected and karen will not can be calculate replacing n by 6 and k by 3 in the same equation as:

6C3=\frac{6!}{3!(6-3)!}=20

We replace n by 6 because from the 8 volunteers, Andrew is going to be selected and Karen will not, so, the people that affect the result are just the 6 remaining volunteers. Also, k is equal to 3 because Andrew is already selected and we just need to select 3 more people.

Finally, the probability is:

P=\frac{20}{70} = \frac{2}{7}

4 0
3 years ago
one teaspoon equals 0.5 centimeters. how many liters equals 50 teaspoons? Round the answer to the nearest hundredth.
alukav5142 [94]

50 teaspoons would equal 50*0.5 = 25 centimeters

1 cm = 0.001 liter

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3 years ago
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brilliants [131]
This problem basically already gives you X, you just have to simplify.

To complete this problem all you have to do is divide 11 by 9.6

11 / 9.6 = 1.15

So X = 1.15
5 0
3 years ago
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