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A class of 165 students went on a field trip. They

navik [9.2K]

answer

the number of buses is 3

the number of cars is 6

Step-by-step explanation:

total number of the students=165

total number of the vehicles=9

let x represent the number of cars

let y represent the number of buses

x+y=9...........equation 1

(the number of the cars plus the number of the buses= to the number of vehicles )

5x + 45y=165.......equation 2

(the number of student the car can hold plus the number of student the bus can hold= to the total number of the student in a class)

x+y=9.......eqn 1

5x +45y=165....eqn 2

make x the subject of the formula in eqn 1

x+y=9

x= 9-y

substitute for x= 9-y in eqn 2

5(9-y)+45y=165

45-5y+45y=165

-5y+45y=165-45

40y=120

divide both sides by 40

40y÷40=120÷40

y=3

since y represent number of buses,the numbet of bus is 3

Also,substitute for y=3 in eqn 1

eqn 1 is x+y=9

x+3=9

x=9-3

x=6

therefore,the number of cars is 6.

3 0

3 years ago

The table below shows the distance Chris is located from his school at different times. Time (minutes) Distance (miles) 0 20 3 1

telo118 [61]

Answer:

20 minutes

Step-by-step explanation:

x is 0 in the graph and y is 20

so 20 is your answer if 0 is x

3 0

3 years ago

Justin is running a 10-mi. race on Saturday. If he runs at a steady pace, what rate of speed must he maintain to finish the race

attashe74 [19]

Answer:

5 MPH

Step-by-step explanation:

10 miles at what speed , in MPH ? at 5 MPH he would cover 10 miles in 2 hours... does that make sense?

6 0

3 years ago

Read 2 more answers

In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that c

Stella [2.4K]

Answer:

this explanation is false

4 0

3 years ago

Be sure to answer all parts. List the evaluation points corresponding to the midpoint of each subinterval to three decimal place

gayaneshka [121]

Answer:

The Riemann Sum for $\int\limits^5_4 {x^2+4} \, dx$ with n = 4 using midpoints is about 24.328125.

Step-by-step explanation:

We want to find the Riemann Sum for $\int\limits^5_4 {x^2+4} \, dx$ with n = 4 using midpoints.

The Midpoint Sum uses the midpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f\left(\frac{x_0+x_1}{2}\right)+f\left(\frac{x_1+x_2}{2}\right)+f\left(\frac{x_2+x_3}{2}\right)+...+f\left(\frac{x_{n-2}+x_{n-1}}{2}\right)+f\left(\frac{x_{n-1}+x_{n}}{2}\right)\right)$

where $\Delta{x}=\frac{b-a}{n}$

We know that a = 4, b = 5, n = 4.

Therefore, $\Delta{x}=\frac{5-4}{4}=\frac{1}{4}$

Divide the interval [4, 5] into n = 4 sub-intervals of length $\Delta{x}=\frac{1}{4}$

$\left[4, \frac{17}{4}\right], \left[\frac{17}{4}, \frac{9}{2}\right], \left[\frac{9}{2}, \frac{19}{4}\right], \left[\frac{19}{4}, 5\right]$

Now, we just evaluate the function at the midpoints:

$f\left(\frac{x_{0}+x_{1}}{2}\right)=f\left(\frac{\left(4\right)+\left(\frac{17}{4}\right)}{2}\right)=f\left(\frac{33}{8}\right)=\frac{1345}{64}=21.015625$

$f\left(\frac{x_{1}+x_{2}}{2}\right)=f\left(\frac{\left(\frac{17}{4}\right)+\left(\frac{9}{2}\right)}{2}\right)=f\left(\frac{35}{8}\right)=\frac{1481}{64}=23.140625$

$f\left(\frac{x_{2}+x_{3}}{2}\right)=f\left(\frac{\left(\frac{9}{2}\right)+\left(\frac{19}{4}\right)}{2}\right)=f\left(\frac{37}{8}\right)=\frac{1625}{64}=25.390625$

$f\left(\frac{x_{3}+x_{4}}{2}\right)=f\left(\frac{\left(\frac{19}{4}\right)+\left(5\right)}{2}\right)=f\left(\frac{39}{8}\right)=\frac{1777}{64}=27.765625$

Finally, use the Midpoint Sum formula

$\frac{1}{4}(21.015625+23.140625+25.390625+27.765625)=24.328125$

This is the sketch of the function and the approximating rectangles.

5 0

4 years ago