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ExtremeBDS
1 month ago
10

Hector is competing in a 42 mile bicycle race. He has already completed 18 miles of the race and is traveling at a constant spee

d of 12 miles per hour when Wanda starts the race. Wanda is traveling at a constant speed of 16 miles per hour. Write and solve an equation to find when Wanda will catch up to Hector. Will Wanda catch up to Hector before the race is complete? Explain. At what constant speed would Wanda travel to catch up with Hector at the finish line? Explain.

Mathematics
1 answer:
lawyer [12.5K]1 month ago
7 0
Wanda encounters Hector after 4.5 hours. Wanda will not be able to reach Hector before the end of the race because at his current pace (16m/h), he would finish when both reach mile 72, while the race is only 42 miles.
To catch up with Hector at the finish line, Wanda must raise her speed to 21m/h. I have included the answers.

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The bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Fr
Svet_ta [12734]

Answer:

66\frac{2}{3} \%

Step-by-step explanation:

Refer to the attached bar graph.

The bar graph illustrates the count of reserved campsites at a campground across a week.

Consequently, the total number of reserved campsites on Friday and Saturday will amount to (26 + 30) = 56.

Now, calculating the total reservations from Monday to Sunday gives us (5 + 3 + 4 + 7 + 26 + 30 + 9) = 84.

Therefore, the percentage of bookings for Friday and Saturday will be

\frac{56}{84} \times 100\% = \frac{200}{3}\% = 66\frac{2}{3}\%. (Answer)

8 0
2 months ago
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so th
lawyer [12517]
The response is a3.
6 0
1 month ago
Read 2 more answers
A nationwide survey of 100 boys and 50 girls in the first grade found that the daily average number of boys who are absent from
Leona [12618]
The formula to calculate the difference between two standard deviations of populations n1 and n2 is:
sigma (difference)=√(sigma1/n1 + sigma2/n2). For this scenario:

sigma(d)= √(49/100 + 36/50)

Thus, the calculated standard deviation of the difference equals 1.1.

6 0
2 months ago
Read 2 more answers
What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (
Inessa [12570]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format y/x=k or y=kx

For this question, we have

the point (5,12) lies on the direct variation line

therefore

Determine the constant of proportionality k

y/x=k-------> substitute ------> k=12/5

The equation is

y=\frac{12}{5}x

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point (0,0)

x=0\ y=0

Insert the values of x and y into the direct variation equation

0=\frac{12}{5}*0

0=0 -------> is valid

thus

the point (0,0) lies on the direct variation line

case B) point (2.5,6)

x=2.5\ y=6

Insert the values of x and y into the direct variation equation

6=\frac{12}{5}*2.5

6=6 -------> is valid

thus

the point (2.5,6) lies on the direct variation line

case C) point (3,10)

x=3\ y=10

Insert the values of x and y into the direct variation equation

10=\frac{12}{5}*3

10=7.2 -------> is not valid

thus

the point (3,10) does not lie on the direct variation line

case D) point (7.5,18)

x=7.5\ y=18

Insert the values of x and y into the direct variation equation

18=\frac{12}{5}*7.5

18=18 -------> is valid

thus

the point (7.5,18) lies on the direct variation line

case E) point (12.5,24)

x=12.5\ y=24

Insert the values of x and y into the direct variation equation

24=\frac{12}{5}*12.5

18=30 -------> is not valid

thus

the point (12.5,24) does not lie on the direct variation line

case F) point (15,36)

x=15\ y=36

Insert the values of x and y into the direct variation equation

36=\frac{12}{5}*15

36=36 -------> is valid

thus

the point (15,36) lies on the direct variation line

ultimately

the solution is

(0,0)

(2.5,6)

(7.5,18)

(15,36)


5 0
2 months ago
Read 2 more answers
1. X^4(dy/dx) +x^3y =- sec (xy)<br><br>Integral by separation of variables? <br>​
PIT_PIT [12445]

Answer:

Step-by-step explanation:

Considering the differential equation x^4(dy/dx) + x^3y = -sec(xy). We will solve it employing the method of separation of variables;

x^{4} \frac{dy}{dx} +x^{3}y = -sec(xy)\\x^{3}(x\frac{dy}{dx} + y) = -sec(xy)\\let \ v=xy\\\frac{dv}{dx} = x\frac{dy}{dx} + y(implicit \ in\ nature)\\

By substituting v and dv/dx into the previous equation, we acquire;

x^{3}\frac{dv}{dx} = -secv

We then separate the variables:

-\frac{dv}{secv} = \frac{dx}{x^{3} }

-cosvdv = x^{-3}dx\\ integrating\ both\ sides\\-\int\limits {cosv} \, dv = \int\limits {x^{-3} } \, dx\\-sinv = \frac{x^{-2} }{-2} + C\\since\ v = xy\\-sinxy = \frac{x^{-2} }{-2} + C\\2sin(xy) = x^{-2} -2C\\2 sin(xy) = \frac{1}{x^{2} } -K (where\ K = 2C)\\

The end expression provides the solution to the differential equation.

8 0
2 months ago
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