Find the square root of (3√5-3)³

What is the scale factor of a cube with a volume of 512m^3 to a cube with a volume of 3,375m^3

GalinKa [24]

8:15 will be your answer.

7 0

3 years ago

Find the lengths of the sides of the rectangle if it is known that one of them is 14cm bigger than the other, and the diagonal o

slega [8]

Let's call the smaller side $s$ . This means that the other side of the rectangle is $s + 14$ .

In this problem, we are trying to find the lengths of the sides. The problem gives us someinformation about the sides, but that's really it. However, the problem also let's us know that the diagonal of the rectangle (the line connecting opposite corners of the rectangle) is 34 cm long.

This fact is very important, because we can actually make a triangle, with the smaller side, bigger side, and the diagonal of the rectangle. Additionally, since we are working with rectangles, we know that the sides form a right angle. Since we are constructing a triangle with the sides as the legs, we know that we are going to be constructing a right triangle, which means that we can work with Pythagorean's Theorem.

Remember that Pythaogrean's Theorem is:

$a^2 + b^2 = c^2$

$a$ and $b$ are the lengths of the legs of the triangle
$c$ is the length of the hypotenuse

Applying the Pythagorean Theorem to this problem, we get:

$s^2 + (s + 14)^2 = 34^2$

Let's simplify and solve for $s$ :

$s^2 + (s + 14)^2 = 34^2$

Set up

$s^2 + (s^2 + 28s + 196) = 1156$

Simplify left hand side and evalutate $34^2$

$2s^2 + 28s -962 = 0$

Subtract 1156 from both sides of the equation and combine like terms

$(s + 30)(s - 16) = 0$

Factor

$s = -30, 16$

Apply the Zero Product Property to solve for $s$

$s = 16$

$s = -30$ is an extraneous solution because you can't have a negative side length

We have now found that the smaller side is 16 cm long. Since the larger side is 14 cm longer, it can be found as shown:

$16 \,\textrm{cm} + 14 \,\textrm{cm} = 30 \,\textrm{cm}$

The sides are length 16 cm and 30 cm.

4 0

3 years ago

You have a standard deck of 52 playing cards (13 of each suit). You draw a hand of the top 17 of them. Spades are one of the fou

Vadim26 [7]

Answer:

The expected value of the number of spades are = 4.25

Step-by-step explanation:

As per the question,

W know that in a standard deck of 52 playing card, there are 4 suits, and each suit have 13 playing card.

Since, we know that

$Probability\ of\ a \ event\ = \frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}$

Therefore,

Probability of any random card being a spade is

$=\ \frac{13}{52}$

$=\ \frac{1}{4}$

So the expected number of spades we draw are

$=\ \frac{1}{4} \times 17$

$=\ 4.25$

Hence, the expected value of the number of spades are = 4.25

7 0

3 years ago

2. The average score of all golfers for a particular course has a mean of 75 and a standard deviation of 4.5. Suppose we going t

stiv31 [10]

Answer:

$P(\bar X>76)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 76 we got:

$z =\frac{76-75}{\frac{4.5}{\sqrt{81}}}= 2$

And if we use the complement rule and the normal standard distribution or excel we got:

$P(Z>2) = 1-P(Z$

And we can find this using the ti 84 with the following code:

1-normalcdf(-1000, 76, 75, 0.5 )

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Let X the random variable who represent the score of golfers. We select a sampel size of 81.

From the central limit theorem 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 want to find this probability:

$P(\bar X>76)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 76 we got:

$z =\frac{76-75}{\frac{4.5}{\sqrt{81}}}= 2$

And if we use the complement rule and the normal standard distribution or excel we got:

$P(Z>2) = 1-P(Z$

And we can find this using the ti 84 with the following code:

1-normalcdf(-1000, 76, 75, 0.5 )

6 0

3 years ago

Write how many hundred thousands, ten thousands, and thousands there are in the numbers of acres of Land Big Bend National Park

sveta [45]

To solve this problem, we must remember our place values. 100,000 represents hundred thousands, 10,000 represents ten thousands, and 1,000 represents thousands similarly to how 100 represents hundreds, 10 represents tens, and 1 represents ones. Using this knowledge, we know that the number 8 is in the hundred thousands place, the number 0 is in the ten thousands place, and the number 1 is in the thousands place.

This means that there are 8 hundred thousands, 0 ten thousands, and 1 thousand in the number of acres of land the National Park owns.

Hope this helps!

4 0

3 years ago