A monthly budget with expenses is shown.

Julie is constructing a scale model of her room.The rectangular room is 10 1/4 inches by 8 inches.If 1 inch represents 2 feet of

zlopas [31]

The way to determine this is to know that 1 foot is 12 inches (so 2 is 24)
Now the ration that would determine the scale factor of the room is 1:24 (1 inch for every 24 inches)
So the scale factor is 1:24
Now to determine the area we multiply the numbers we have by 2 and change the inches to feet (I hope that makes sense to you, it does to me, I'll show you)
10.25 * 2 = 20.5 ft.
8 * 2 = 16 ft.
now we know the dimensions of the room so we need to find the area.
A=B*H
20.5 * 16 = 328
so the area of the room is 328 ft.²

6 0

3 years ago

Read 2 more answers

Six times the reciprocal of a number equals 3 times the reciprocal of 2. Find the number

Aleonysh [2.5K]

3=x as the answer would be the reciprocal

6 0

3 years ago

The number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Alchen [17]

Answer:

Probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is 0.89435.

Step-by-step explanation:

We are given that the number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Also, sample of 49 adults is given.

Let X = number of hours spent per week on household chores

So, assuming data follows normal distribution; X ~ N( $\mu=28,\sigma^{2}=7^{2}$ )

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean hours = 28

$\sigma$ = standard deviation = 7 hours

n = sample of adults = 49

Let $\bar X$ = sample mean hours spent per week on household chores

So, probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is given by =P( $\bar X$ > 26.75 hours)

P( $\bar X$ > 26.75 hours) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{26.75-28}{\frac{7}{\sqrt{49} } }$ ) = P(Z > -1.25) = P(Z < 1.25)

= 0.89435 {using z table}

Therefore, probability that the mean hours spent per week on household chores is more than 26.75 is 0.89435.

4 0

2 years ago

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You must fast before having bloodwork done for your insurance company. The last time you had something to eat was at 9:30 pm. At

luda_lava [24]

10 hours 45 minutes :)

3 0

2 years ago

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes

ArbitrLikvidat [17]

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for $x = 3$ and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?

Answer:

The generally expression for the slope of $y = 2x^2 + 4x$ is $y' = 4x +4$

The graph is shown on the first uploaded image

The generally expression for the slope of $y=2x^2+4$ is $y' = 4x$

Step-by-step explanation:

From the question we are told that

The equation of the curve is $y = 2x^2 + 4x$

First we differentiate the equation

So

$y' = 4x +4$

Therefore the generally expression for the slope tangent to the curve $y=2x^2+4x$ is $y' = 4x +4$

The next step is to substitute for x = 3 and x = 0.5

So for $x_1 = 3$

$y' = 4(3) +4$

$y' =m_1= 16$

And for $x_2 = 0.5$

$y' = 4(0.5) +4$

$y' =m_2= 6$

Here m_1 and m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So at $x_1 = 3$

$y_1 = 2(3)^2 + 4(3)$

$y_1 = 21$

So the coordinate for the first tangent line is

$(x_1 , y_1 ) = (3 , 21)$

At $x_2 = 0.5$

$y_2 = 2(0.5)^2 + 4(0.5)$

=> $y_2 = 2.5$

So the coordinate for the second tangent line is

$(x_2 , y_2 ) = (0.5 , 2.5)$

Next we obtain the equation for the tangent lines

So generally the slope is mathematically represented as

$m = \frac{y - y_1 }{x-x_1}$

For $(x_1 , y_1 ) = (-3 , 21)$ and $y' =m_1= 16$

$16 = \frac{y -21 }{x-3)}$

=> $y = 16x - 27$

For $(x_2 , y_2 ) = (0.5 , 2.5)$ and $y' =m_2= 6$

$6 = \frac{y -2.5 }{x-0.5}$

$y = 6x -0.5$

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows

$y' = 4x$

7 0

2 years ago