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Nana76 [90]
2 years ago
10

Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.

Mathematics
1 answer:
lesantik [10]2 years ago
8 0

Answer:

e none is the answer

Step-by-step explanation:

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The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 7 feet, represented by a ve
xenn [34]

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at x=4, the equation will contain a (x-4)^2 term.

If we start with y=-(x-4)^2 we have a parabola, concave down, with vertex at x=4 and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be (4, 7)

We have

y = -(x-4)+7

Now we only have to fix the fact that this parabola doesn't land at (8,0), because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

y = a(x-4)^2+7

such that:

  • a
  • when we plug x=8, we have y=0

Plugging these values gets us

0 = a(8-4)^2+7 \iff 16a+7=0 \iff a = -\dfrac{7}{16}

As you can see in the attached figure, the parabola we get satisfies all the requests.

3 0
3 years ago
If Julie needs 3 and 1/4 cups of oatmeal how many 1/4 cups of oatmeal will she use
Effectus [21]

Answer:

She will use 13 quarter cups of oatmeal

Step-by-step explanation:

3 1/4 = 13/4

x/4 = 13/4

4(x/4) = 4(13/4)

x = 13

3 0
3 years ago
Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =
irga5000 [103]

Answer:  The required solution is y=50e^{0.1386t}.

Step-by-step explanation:

We are given to solve the following differential equation :

\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

\dfrac{dy}{y}=kdt.

Integrating both sides, we get

\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]

Also, the conditions are

y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50

and

y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.

Thus, the required solution is y=50e^{0.1386t}.

8 0
3 years ago
Read 2 more answers
What is the 30°-60°-right triangle theorem?
kondaur [170]
<span>the 30°-60°-right triangle theorem states that the 
</span>In a right triangle, the hypotenuse is twice as long as a leg if and only if the measure of the
<span>angle opposite that leg is 30°
so the option C is correct from above all
</span>see the figure
hope it helps

4 0
2 years ago
How do you measure the diameter of four steel rods and than compare the measurement? Thank you!
enyata [817]
The answer is B. 0.25 inch. Lets multiply all of them by the same factor. Since A. and B. have 3 decimals, lets divide all numbers by 1000: A. 0.026 * 1000 = 26, B. 0.25 * 1000 = 250, C. 0.24 * 1000 = 240, D. 0.025 * 1000 = 25. So, by comparing the whole numbers, it can be concluded that the biggest steel rod is B. 0.25 inch.
7 0
3 years ago
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