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Korolek [52]
2 years ago
11

a bird leaves its nest and travels 20 miles per hour downwind for xx hours. on the return trip, the bird travels 4 miles per hou

r slower and has 6 miles left after xx hours.a. what is the distance of the entire trip? b. how long does the entire trip take?
Mathematics
2 answers:
Rudik [331]2 years ago
3 0
A. if the return trip is the same then the bird traveled 40miles
b. the time of the trip is x hours + 6/x-4
allochka39001 [22]2 years ago
3 0

The <em><u>correct answers</u></em> are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours.

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denpristay [2]

Answer: g(x) is the image of f(x)


Step-by-step explanation:

multiplying the x value by -1 means you reflect that point across y-axis, therefore, g(x) is the reflection of f(x) across y-axis.

4 0
1 year ago
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For the level 3 course, exam hours cost twice as much as workshop hours, workshop hours cost twice as much as lecture hours. How
natulia [17]
<h2>Answer</h2>

Cost of lectures = $7.33 per hour

<h2>Explanation</h2>

Let e the cost of the exam hours

Let w be the cost of the workshop hours

Let l be the cost of the lecture hours.

We know from our problem that exam hours cost twice as much as workshop, so:

e=2w equation (1)

We also know that workshop hours cost twice as much as lecture hours, so:

w=2l equation (2)

Finally, we also know that 3hr exams 24hr workshops  and 12hr lectures cost $528, so:

3e+24w+12l=528 equation (1)

Now, lets find the value of l:

Step 1.  Solve for l in equation (3)

3e+24w+12l=528

12l=528-3e-24w equation (4)

Step 2. Replace equation (1) in equation (4) and simplify

12l=528-3e-24w

12l=528-3(2w)-24w

12l=528-6w-24w

12l=528-30w equation (5)

Step 3. Replace equation (2) in equation (5) and solve for l

12l=528-30w

12l=528-30(2l)

12l=528-60l

72l=528

l=\frac{528}{72}

l=\frac{22}{3}

l=7.33

Cost of lectures  = $7.33 per hour



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1 year ago
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Let X represent the amount of time until the next student will arrive in the library parking lot at the university. If we know t
Ber [7]

Answer:

The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

Step-by-step explanation:

The random variable <em>X</em> is defined as the amount of time until the next student will arrive in the library parking lot at the university.

The random variable <em>X</em> follows an Exponential distribution with mean, <em>μ</em> = 4 minutes.

The probability density function of <em>X</em> is:

f_{X}(x)=\lambda e^{\lambda x};\ x\geq 0, \lambda >0

The parameter of the exponential distribution is:

\lambda=\frac{1}{\mu}=\frac{1}{4}=0.25

Compute the value of P (X > 10) as follows:

P(X>10)=\int\limits^{\infty}_{10}{0.25e^{-0.25x}}\, dx

                 =0.25\times \int\limits^{\infty}_{10}{e^{-0.25x}}\, dx\\=0.25\times |\frac{e^{0.25x}}{-0.25}|^{\infty}_{10}\\=(e^{-0.25\times \infty})-(e^{-0.25\times 10})\\=0.0821

Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.

3 0
1 year ago
A. One day Annie weighed 24 ounces more than Benjie, and Benjie weighed 3 1/4 pounds less than Carmen. How did Annie’s and Carme
Debora [2.8K]
<h2>Answer:</h2>

A.

Let Annie's weight be = a

Let Benjie's weighs = b

Let Carmen's weight be = c

One day Annie weighed 24 ounces more than Benjie, equation forms:

a=b+24        ......(1)

Benjie weighed 3 1/4 pounds less than Carmen.  

In ounces:

1 pound = 16 ounces

\frac{13}{4} pounds = \frac{13}{4}\times16=52 ounces

b=c-52  or

c=b+52    ......(2)

Now adding (1) and (2), we get

a+b=b+24+c-52

=> a=c-28

This gives  Annie weighs 28 ounces less than Carmen.

B.

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Lesechka [4]
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