Which of the following is a graph of the function k(x) = 3x6

The parallelogram shown below has an area of 35 units^2 2 squared. Find the missing height. h =h=h, equals units

Anit [1.1K]

Answer:

h = 5 units

Step-by-step explanation:

Given that,

The area of the parallelogram, A = 35 unit²

In the attached figure, we can see that the base is 7 unit.

We know that,

Area of a parallelogram, A = b × h

So,

$h=\dfrac{A}{b}\\\\h=\dfrac{35}{7}\\\\h=5\ units$

So, the value of h is equal to 5 units.

4 0

3 years ago

Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 75 hours and a

shepuryov [24]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

c) $z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

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 life of a particular brand of a population, and for this case we know the distribution for X is given by:

$X \sim N(75,10)$

Where $\mu=75$ and $\sigma=10$

Part a

We are interested on this probability

$P(X$

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:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

$P(X>77)=P(\frac{X-\mu}{\sigma}>\frac{77-\mu}{\sigma})=P(Z>\frac{77-75}{10})=P(z>0.2)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.2)=1-P(Z$

Part c

For this case we select a sample size of n =16. and we want this probability:

$P(70 < \bar X$

We know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we can find the z scores for the limits like this:

$z = \frac{70-75}{\frac{10}{\sqrt{16}}}= -2$

$z = \frac{80-75}{\frac{10}{\sqrt{16}}}= 2$

And we can find this probability with this difference:

$P(-2$

6 0

4 years ago

Can someone help me solve this Please

Dafna1 [17]

9514 1404 393

Answer:

523 grams
52 grams

Step-by-step explanation:

To find the initial amount, put 0 where t is in the formula and do the arithmetic.

A(0) = 523(1/2)^0 = 523(1) = 523

The initial amount is 523 grams.

__

To find the amount remaining after 100 years, put 100 where t is in the formula and do the arithmetic.

A(100) = 523(1/2)^(100/30) ≈ 523(0.0992123) ≈ 52

About 52 grams will remain after 100 years.

8 0

3 years ago

A gallon of gasoline costs $2.96. Your car has a 25-gallon gas tank and can travel 28.8 miles on each gallon of gasoline. You ta

Andreas93 [3]

Answer:

$70.56

Step-by-step explanation:

Lets convert the mixed number (trip length) to decimal.

We know 3/5 (by long division) is 0.6, so 705 3/5th = 705.60 miles

Now, let's come to the problem:

1 gallon = 28.8 miles (mileage)

or

$2.96 = 28.8 miles

To find cost per mile, we divide:

$\frac{2.96}{28.8}=0.10$

That means, it costs $0.10 per mile

Since we want to travel 705.60 miles, we multiply to find the cost:

$0.10 per mile * 705.60 miles = $70.56

6 0

4 years ago

HELP ME PLEASE!!! i cant do this and it is due in 10 minutes.

SpyIntel [72]

Answer:

12 classrooms

Step-by-step explanation:

25% of classrooms is 3, find 100%

25% ⇒ 3
100% ⇒ x

Since 100% is 4 times 25%, the corresponding number will also be 4 times greater:

x = 4*3 = 12

6 0

2 years ago

Which of the following is a graph of the function k(x) = 3x6 - 4?