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3 years ago

5

A survey showed that 25% of students chose cola as their favorite soda; 40% chose orange; and the other 35% chose grape. If you

survey 32 students from the same group, how many will choose cola?
16 people
8 people
12 people
25 people

1 answer:

Anastasy [175]3 years ago

5 0

A survey showed that 25% of students chose cola as their favorite soda;
40% chose orange
and the other 35% chose grape.
There are 32 students fromthe same group that took the survey. Let's find out how many will choose cola.
=> 32 * 0.25 = 8 Therefore, there are 8 people that chooses soda as their favorite drink.

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Round 218 to the nearest hundred

Sergio [31]

When rounding to the nearest hundred, if the number in the tens place is less than 5, you should round downwards (keep the same number shown in the hundreds place). However, if the number in the tens place is 5 or greater, than you have to round up, which means adding one to the number currently in the hundreds place. So, for this problem, the digit 1 is in the tens place. Because 1 is less than 5, we know that we have to round down. Thus, 218 rounded to the nearest hundred is 200. Hope this helps!!

7 0

3 years ago

Carlos finds the absolute value of -3.8, and then finds the opposite of his answer. Jason finds the opposite of -3.8, and then f

DENIUS [597]

Carlos finds |-3.8| = 3.8. Then he finds the opposite, which is of -3.8. Jason finds the opposite of -3.8, which is of 3.8. Then he finds the absolute value, which is 3.8. Therefore, Jason has a greater final value.

<h3>Absolute value and opposite of a number</h3>

The absolute value and the opposite of a number are given as follows:

Absolute value: number without the signal.

Opposite: number with the signal exchanged.

Hence:

The absolute value of -3.8 is of |-3.8| = 3.8.

The opposite of 3.8 is -3.8. (Carlos number).

The opposite of -3.8 is of 3.8.

The absolute value of 3.8 is 3.8. (Jason number).

Hence Jason has the greater number.

More can be learned about absolute value at brainly.com/question/17795998

#SPJ4

8 0

1 year ago

Solve the initial value problem 2ty" + 10ty' + 8y = 0, for t > 0, y(1) = 1, y'(1) = 0.

Eva8 [605]

I think you meant to write

$2t^2y''+10ty'+8y=0$

which is an ODE of Cauchy-Euler type. Let $y=t^m$ . Then

$y'=mt^{m-1}$

$y''=m(m-1)t^{m-2}$

Substituting $y$ and its derivatives into the ODE gives

$2m(m-1)t^m+10mt^m+8t^m=0$

Divide through by $t^m$ , which we can do because $t\neq0$ :

$2m(m-1)+10m+8=2m^2+8m+8=2(m+2)^2=0\implies m=-2$

Since this root has multiplicity 2, we get the characteristic solution

$y_c=C_1t^{-2}+C_2t^{-2}\ln t$

If you're not sure where the logarithm comes from, scroll to the bottom for a bit more in-depth explanation.

With the given initial values, we find

$y(1)=1\implies1=C_1$

$y'(1)=0\implies0=-2C_1+C_2\implies C_2=2$

so that the particular solution is

$\boxed{y(t)=t^{-2}+2t^{-2}\ln t}$

# # #

Under the hood, we're actually substituting $t=e^u$ , so that $u=\ln t$ . When we do this, we need to account for the derivative of $y$ wrt the new variable $u$ . By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dt}=\dfrac{\mathrm dy}{\mathrm du}\dfrac{\mathrm du}{\mathrm dt}=\dfrac1t\dfrac{\mathrm dy}{\mathrm du}$

Since $\frac{\mathrm dy}{\mathrm dt}$ is a function of $t$ , we can treat $\frac{\mathrm dy}{\mathrm du}$ in the same way, so denote this by $f(t)$ . By the quotient rule,

$\dfrac{\mathrm d^2y}{\mathrm dt^2}=\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac ft\right]=\dfrac{t\frac{\mathrm df}{\mathrm dt}-f}{t^2}$

and by the chain rule,

$\dfrac{\mathrm df}{\mathrm dt}=\dfrac{\mathrm df}{\mathrm du}\dfrac{\mathrm du}{\mathrm dt}=\dfrac1t\dfrac{\mathrm df}{\mathrm du}$

where

$\dfrac{\mathrm df}{\mathrm du}=\dfrac{\mathrm d}{\mathrm du}\left[\dfrac{\mathrm dy}{\mathrm du}\right]=\dfrac{\mathrm d^2y}{\mathrm du^2}$

so that

$\dfrac{\mathrm d^2y}{\mathrm dt^2}=\dfrac{\frac{\mathrm d^2y}{\mathrm du^2}-\frac{\mathrm dy}{\mathrm du}}{t^2}=\dfrac1{t^2}\left(\dfrac{\mathrm d^2y}{\mathrm du^2}-\dfrac{\mathrm dy}{\mathrm du}\right)$

Plug all this into the original ODE to get a new one that is linear in $u$ with constant coefficients:

$2t^2\left(\dfrac{\frac{\mathrm d^2y}{\mathrm du^2}-\frac{\mathrm d y}{\mathrm du}}{t^2}\right)+10t\left(\dfrac{\frac{\mathrm dy}{\mathrm du}}t\right)+8y=0$

$2y''+8y'+8y=0$

which has characteristic equation

$2r^2+8r+8=2(r+2)^2=0$

and admits the characteristic solution

$y_c(u)=C_1e^{-2u}+C_2ue^{-2u}$

Finally replace $u=\ln t$ to get the solution we found earlier,

$y_c(t)=C_1t^{-2}+C_2t^{-2}\ln t$

4 0

4 years ago

6 miles to feet<br><br> 24 centimeter to inches<br><br> 4 gallons of water to ounces

Monica [59]

Answer:

6 miles = 31,680 feet

24 centimeters = 9.44 inches

4 gallons = 512 fluid ounces

Step-by-step explanation:

For every mile there is approximately 5,280 feet

For every inch there is approximately 2.54 centimeters

For ever gallon there is approximately 128 fluid ounces.

3 0

3 years ago

Read 2 more answers

Solve for X 6 48 4 2

romanna [79]

Answer:

6

Step-by-step explanation:

By the property of intersecting secants outside of a circle. We have:

$x \times 8 = 4 \times (4+8) \\ \\ 8x = 48 \\ \\ x = \frac{48}{8} \\ \\ x = 6$

7 0

4 years ago