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3 years ago

What is the next number in the pattern? 7,11,10,14,13

Mathematics

1 answer:

nikdorinn [45]3 years ago

6 0

I think the answer is 17 because the pattern adds 4 then takes away 1 so 14-1=13 13+4=17

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Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 38 ve

Oxana [17]

Answer:

C. 19 cars; 19 motorcycles

Step-by-step explanation:

Let c represent the number of cars and m represent the number of motorcycles that participated this year.

This year a total of 38 vehicles participated. So, we can write the equation as:

c + m = 38 (Equation 1)

Each car has 4 tires, so number of tires in c cars will be 4c.

Each motorcycle has 2 tires, so number of tires in m motorcycles will be 2m.

In total there were 114 tires, so we can set up the equation as:

4c + 2m = 114 (Equation 2)

From equation 1, m = 38 - c. Using this value in Equation 2, we get:

4c + 2(38 - c) = 114

4c + 76 - 2c = 114

2c = 114 - 76

2c = 38

c = 19

Using this value in equation 1, we get:

19 + m = 38

m = 19

Thus, 19 cars and 19 motorcycles participated in the ride.

4 0

3 years ago

Read 2 more answers

In 1992, the population of Seoul. South Korea was 17,334,000. In 1995, the population of Seoul was 19,065,000. Find the average

gizmo_the_mogwai [7]

577,000, there is an average change of 577,000 people per year.

To find the average rate of change of the population of people per year, we first need to find the population change per any amount of time, and then divide by how much time that is (in this case, three years). We can find the population change by <u>subtracting </u>the values 17,334,000 and 19,065,000. Subtracting them, we get a change of 1,731,000 in three years. Now, to find the average rate of change of the population in people per year, we divide by three, which gives us our answer of 577,000 people, on average, per year.

3 0

3 years ago

Please help me with this question!!

Mama L [17]

Answer:

$=\pi$

Step-by-step explanation:

$\int _0^{2\pi }\sin ^2\left(x\right)-\cos ^3\left(x\right)dx$

compute the indefinite integral

$\int \sin ^2\left(x\right)-\cos ^3\left(x\right)dx=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)+C\\\int \sin ^2\left(x\right)-\cos ^3\left(x\right)dx\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\int \sin ^2\left(x\right)dx=\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)\\\int \cos ^3\left(x\right)dx=\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}$

$=\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)-\left(\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}\right)\\\mathrm{Simplify\:}\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)-\left(\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}\right):\quad \frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)\\=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)\\Add\:a\:constant\:to\:the\:solution$

$=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)+C\\\mathrm{Compute\:the\:boundaries}:\quad \int _0^{2\pi }\sin ^2\left(x\right)-\cos ^3\left(x\right)dx=\pi -0\\=\pi -0\\\mathrm{Simplify}\\=\pi$

7 0

3 years ago

The volume of fuel in a tank changes at a rate given by the equation V'\left(t\right)=\frac{4t}{\sqrt[3]{t^2+3}},\:t\ge0 V ′ ( t

Ksju [112]

$V'(t)=\dfrac{4t}{\sqrt[3]{t^2+3}}$

The volume of fuel in the tank after 9 hours is given by

$\displaystyle\int_0^9V'(t)\,\mathrm dt=\int_0^9\dfrac{4t}{(t^2+3)^{1/3}}\,\mathrm dt$

To compute the integral, substitute $u=t^2+3$ , so that $\mathrm du=2t\,\mathrm dt$ . Then when $t=0$ , $u=0^2+3=3$ ; when $t=9$ , $u=9^2+3=84$ .

$\displaystyle\int_0^9V'(t)\,\mathrm dt=2\int_{t=0}^{t=9}\frac{2t}{(t^2+3)^{1/3}}\,\mathrm dt=2\int_{u=3}^{u=84}u^{-1/3}\,\mathrm du$
$=2\cdot\dfrac32u^{2/3}\bigg|_{u=3}^{u=84}=3(84^{2/3}-3^{2/3})\approx51.3$

So the volume of fuel after 9 hours is about 51.3 gallons.

8 0

4 years ago

What is the greatest possible whole number remainder when you divide a number by 75? Explain.

adoni [48]

74. When dividing by 75, you can have a remainder anywhere from 0 to 74. For example 149/75 is 1 remainder 74, and then 150/75 is 2.

3 0

3 years ago