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2 years ago

13

Ally has 30 quaters. The ratio if her quarters to dimes is 2:3 and the ratio of her dimes to nickels is 5:3. How many nickles do

es ally have

1 answer:

ryzh [129]2 years ago

6 0

She has 27 nickels.
30/2*3 = 45
45/5*3 =27

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A high school has 1,500 students. In a random sample of 50 students, 32 own one or more pets. Predict the number of students at

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I wanna say 32 because it repeats it in the question

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2 years ago

Find the equation of the plane through the point (2,5,7) that is parallel to the line r=(3i+2j−2k)+t(i+2j+9k) and perpendicular

insens350 [35]

The plane we want to find has general equation

$a(x-2)+b(y-5)+c(z-7)=0$

with $a,b,c$ not equal to 0, and has normal vector

$\vec n=a\,\vec\imath+b\,\vec\jmath+c\,\vec k$

$\vec n$ is perpendicular to both the normal vector of the other plane, which is $4\,\vec\imath+5\,\vec\jmath+6\,\vec k$ , as well as the tangent vector to the line $\vec r(t)$ , which is $\vec\imath+2\,\vec\jmath+9\,\vec k$ .

This means the dot product of $\vec n$ with either vector is 0, giving us

$\begin{cases}4a+5b+6c=0\\a+2b+9c=0\end{cases}$

Suppose we fix $c=1$ . Then the system reduces to

$\begin{cases}4a+5b=-6\\a+2b=-9\end{cases}$

and we get

$(4a+5b)-4(a+2b)=-6-4(-9)\implies-3b=30\implies b=-10$

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Then one equation for the plane could be

$\boxed{11(x-2)-10(y-5)+(z-7)=0}$

or in standard form,

$\boxed{11x-10y+z=-21}$

The solution is unique up to non-zero scalar multiplication, which is to say that any equation $(11x-10y+z)k=-21k$ would be a valid answer. For example, suppose we instead let $c=2$ ; then we would have found $a=22$ and $b=-20$ , but clearly dividing both sides of the equation

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by 2 gives the same equation as before.

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2 years ago

The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the

german

Answer:

3 gallons

Step-by-step explanation:

Given

Seconds Spent ----- Gallons of Gas

0 ---------------------------- 3

12 -------------------------- 5

24 ------------------------- 7

36 ------------------------- 9

48 ------------------------ 11

Required

Determine the output of the initial value

From the given parameters, we have that:

Gallon of gas is a function of time spent

This means:

The input is the time spent while the output is the gallon of gas

From the table above,

Initial Value = 0 seconds

The corresponding output of this is 3 gallons

Hence;

<em>Option C answers the question.</em>

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2 years ago

Read 2 more answers

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zubka84 [21]

Answer:

C. $\dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3$

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The volume of the ball with radius R can be calculated using formula

$V=\dfrac{4}{3}\pi R^3$

A basketball has a diameter of 9.5 cm, so its radius is

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$V=\dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3$

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A department store paint mixer contains 4 pints of equal amounts of yellow and red paint. The shade of red that you want require

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Answer:

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Step-by-step explanation:

The ratio of red to yellow needs to be ...

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For the 4 pins of yellow paint in the mixer, a total of 12 pints of red paint are needed. There are already 4 pints in the mixer, so ...

8 pints of red paint need to be added.

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2 years ago