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3 years ago

14

Jeremy baked 9 cakes for the bake sale. he shifted 2 cups of powdered sugar evenly on the tops of the cakes. how much powdered s

ugar is on each cake. __ of a __ cup

1 answer:

Ira Lisetskai [31]3 years ago

6 0

9 cakes of a 2 cups equals 18 cups

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Find the h.c.f by prime factorization method 27, 30

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Find the length of a rectangle with a diagonal of 10 and a height of 8.

Dmitry_Shevchenko [17]

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

<em>EXTRA:</em>

<em>If</em><em> you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.</em>

<em>Instead of 5, a diagonal of 10 is given (factor of 2 bigger).</em>

<em>Instead of 4, the height of 8 is given (factor of 2 bigger</em><em>)</em><em>.</em><em> </em><em>By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?</em>

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

<em>EXTRA</em><em>:</em>

<em>You</em><em> can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.</em>

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

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3 years ago

Plz will gave a brain who ever answer this will get a brain

inessss [21]

Energy in the form of HEAT

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3 years ago

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that $\mu = 8, \sigma = 1.1$

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

$n = 5$ means that $s = \frac{1.1}{\sqrt{5}} = 0.4919$

This probability is the pvalue of Z when X = 9.3. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{9.3 - 8}{0.4919}$

$Z = 2.64$

$Z = 2.64$ has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

$n = 6$ means that $s = \frac{1.1}{\sqrt{6}} = 0.4491$

This probability is 1 subtracted by the pvalue of Z when X = 9. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{9 - 8}{0.4491}$

$Z = 2.23$

$Z = 2.23$ has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0

3 years ago