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3 years ago

13

the length of a rectangle is one inch less than three times its width. if the perimeter of the rectangle is 118 inches, find the

dimensions of the rectangle

1 answer:

Aneli [31]3 years ago

4 0

The picture above has the work and answer for you

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An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 1 of 2: Su

AVprozaik [17]

Answer:

0.249 is the required proportion.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 822

Number of people who preferred foreign cars over domestic, x = 205

We have to find the proportion of new car buyers who prefer foreign cars.

Formula:

$\hat{p} = \dfrac{x}{n}$

Putting values, we get,

$\hat{p} = \dfrac{205}{822}\\\\\hat{p} = 0.249$

Thus, 0.249 is the proportion of the new car buyers who preferred foreign over domestic cars..

3 0

3 years ago

This year, benny is 12 years old, and his mom is 48 years old. In how many years will benny be 50% of his mom's age

Dahasolnce [82]

It will take 12 years for Benny to reach his moms height.

Benny’s mom: 48
Benny: 12

Half of 48 is 24, so Benny will have to turn 24.

24 - 12= 12

7 0

2 years ago

What is the midpoint between 0.13 and 0.14

weqwewe [10]

0.13 + 0.14= 0.27 0.27 ÷ 2 = 0.135 Therefore the midpt. Is 0.135

3 0

3 years ago

The sum of 5.75 and half a number is -5. What is the number? Please help!

barxatty [35]

Answer:

$5.75 + \frac{x}{2} = - 5 \\ \frac{x}{2} = - 5 - 5.75 \\ \frac{x}{2} = - 10.75 \\ x = - 21.5$

4 0

2 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function <em>f</em>, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to <em>x</em> :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

7 0

2 years ago