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2 years ago

10

A heated piece of metal cools according to the function c(x) = (.5)x − 11, where x is measured in hours. A device is added that

aids in cooling according to the function h(x) = −x − 3. What will be the temperature of the metal after five hours? (1 point)
−8° Celsius
26° Celsius
32° Celsius
56° CelsiusWhat is the answer?

1 answer:

ruslelena [56]2 years ago

8 0

The answer is -8 degrees Celsius

You might be interested in

normally distributed with mean 24.6 seconds and standard deviation 0.64 seconds;the lower finishing time, the better. If the qua

marshall27 [118]

Answer:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the finishing time of a population, and for this case we know the distribution for X is given by:

$X \sim N(24.6,0.64)$

Where $\mu=24.6$ and $\sigma=0.64$

Solution to the problem

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.15$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

3 0

3 years ago

4 is 1/4 of what number? Plzzzzzz help

WARRIOR [948]

Answer:

16

Step-by-step explanation:

to reverse the division meaning the fraction, we multiply 4 by 4:

4 times 4=16

to check, divide:

16/4=4

i hope this helps u pls give a brainliest and a thx ;)

8 0

3 years ago

Pls help It’s due tomorrow question is in the picture

Slav-nsk [51]

Answer:

C

Step-by-step explanation:

Let's find the area of each of the two circles.

First Circle:

The first circle has a diameter of 10 inches. That means the radius is 5 inches. So, its area is:

$A=\pi r^2\\A=\pi (5)^2\\A=25\pi$

Second Circle:

The second circle has a diameter twice that of the first. So, the diameter is 20 inches. This means that the radius is 10 inches. Find the area:

$A=\pi r^2\\A=\pi (10)^2\\A=100\pi$

Now, find the ratio between them by dividing:

$\frac{\text{Smaller}}{\text{Larger}}=\frac{25\pi}{100\pi}$

Simplify:

$\frac{\text{Smaller}}{\text{Larger}}=\frac{1}{4}$

1/4 is the same as 1:4

So, our answer is C :)

5 0

3 years ago

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and

egoroff_w [7]

Answer:

a) $P(140$

$P(0.036$

$P(0.036$

b) $P(140< \bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(139,28.1)$

Where $\mu=139$ and $\sigma=28.1$

We are interested on this probability

$P(140$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(140$

And we can find this probability like this:

$P(0.036$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(0.036$

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)$

And the new z score would be:

$Z=\frac{\bar X -\mu}{\sigma_{\bar x}}$

$P(140< \bar X$

$P(140< \bar X$

5 0

3 years ago

A total of $12,000 is invested at an annual interest rate of 9%. Find the balance

sineoko [7]

Answer:

$18,726.11

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

<em />

First lets change 9% into a decimal:

9% -> $\frac{9}{100}$ -> 0.09

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

$A=12,000(1+\frac{0.09}{4})^{4(5)}$

$A=18,726.11$

<u>The balance after 5 years is $18,726.11</u>

6 0

3 years ago