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2 years ago

Ending time 6:30, elapsed time 37 minutes

Mathematics

1 answer:

Nastasia [14]2 years ago

6 0

Answer:

5:53

Step-by-step explanation:

The original time would be 37 minutes before 6:30 so you would subtract 37 minutes from 6;30. So 6:30 minus 30 would be 6 and you would have 7 left over so 6:00 minus 7 minutes would be 5:53

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Express 96 as the product of prime factors need it asap plzz write the method too

Murrr4er [49]

Given:

The given number is:

$96$

To find:

The product of prime factors of given number.

Solution:

We have,

$96$

The prime factors of given number are:

2 | 96

2 | 48

2 | 24

2 | 12

2 | 6

3 | 3

| 1

So, 96 can be written as:

$96=2\times 2\times 2\times 2\times 2\times 3$

Therefore, the 96 as the product of prime factors is $96=2\times 2\times 2\times 2\times 2\times 3$ .

3 0

2 years ago

Suppose the heights of a population of people are normally distributed with a mean of 65.5 inches and a standard deviation of 2.

kupik [55]

Answer:

a) $P(64.2$

b) 69.764

Step-by-step explanation:

1) 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".

2) Part a

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

$X \sim N(65.5,2.6)$

Where $\mu=65.5$ and $\sigma=2.6$

We are interested on this probability

$P(64.2$

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:

$P(64.2$

And we can find this probability on this way:

$P(-0.50$

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

$P(-0.50$

3) Part b

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

$P(X>a)=0.05$ (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 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

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:

$z=1.64$

And if we solve for a we got

$a=65.5 +1.64*2.6=69.764$

So the value of height that separates the bottom 95% of data from the top 5% is 69.764.

5 0

3 years ago

Given 6(x) = (x+41, what is b(-10)?

prisoha [69]

The value of $b(-10)$ is 31

Explanation:

The given expression is $b(x)=x+41$

We need to determine the value of $b(-10)$

The value of $b(-10)$ can be determined by substituting $x=-10$ in the expression $b(x)=x+41$

Thus, we have,

$b(-10)=-10+41$

Adding the terms, we have,

$b(-10)=31$

Thus, the value is 31.

Therefore, the simplified value of the expression by substituting $x=-10$ in the expression $b(x)=x+41$ is 31.

7 0

2 years ago

Find the volume of the figure below.

Nana76 [90]

This is something I’ve never seen before I think you have to add the numbers.

4 0

2 years ago

RoseWind [281]

Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.

Therefore, even if $\Delta ABC$ is dilated to $\Delta JKL$ by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle $\Delta ABC$ will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.

Please note that this is true for all two dimensional geometric shapes.

5 0

3 years ago