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2 years ago

For what value of x is P|| BC? A. 5 B. 6 C. 7 D. 8

Mathematics

1 answer:

77julia77 [94]2 years ago

4 0

Answer:

Option C. x=7

Step-by-step explanation:

we know that

If PQ is parallel to BC

then

triangles APQ and ABC are similar

Remember that

If two figures are similar them the ratio of its corresponding sides is proportional

$\frac{AP}{AB}=\frac{AQ}{AC}$

substitute the values

$\frac{x}{x+7+x}=\frac{x-3}{x-3+x+1}$

Solve for x

$\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units$

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1) How is unit rate related to slope or rise over run?

quester [9]

The unit rate is a ratio of change in y and into the change on x. It can also be the rise to run or the slope.

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3 years ago

The function h(x)=x^2+3 and g(x)=x^2-6. if g(x)=h(x)+k, what us the value of k

lutik1710 [3]

Answer:

The value of k is -9

Step-by-step explanation:

Subsitute

g(x)=h(x)+k

$(x^2-6)=(x^2+3)+k$

$x^2-6=x^2+3+k$

subtract $x^2+3$ from both sides (or add $-x^2-3$ to both sides)

$-9=k$

$k=-9$

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3 years ago

which of the following ordered pairs could be placed in the table below and still have the relation qualify as a linear function

mr_godi [17]

(1,31)
Subtract 2 from x, add 8 to y

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3 years ago

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with

Ratling [72]

Answer:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

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

$P(z>1.61)=1-P(z$

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

$X \sim N(10.5,0.3)$

Where $\mu=10.5$ and $\sigma=0.3$

We are interested on this probability

$P(X>10.983)$

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:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

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

$P(z>1.61)=1-P(z$

8 0

3 years ago

What is the difference between discrete vs continuous data

Sergeeva-Olga [200]

With continuous data, it is possible to find the midpoint of any two distinct values. For instance, if h = height of tree, then its possible to find the middle height of h = 10 and h = 7 (which in this case is h = 8.5)

On the other hand, discrete data can't be treated the same way (eg: if n = number of people, then there is no midpoint between n = 3 and n = 4).

-------------------------------------

With that in mind, we have the following answers

1) Continuous data. Time values are always continuous. Any two distinct time values can be averaged to find the midpoint

2) Continuous data. Like time values, temperatures can be averaged as well.

3) Discrete data. Place locations in a race or competition are finite and we can't have midpoints. We can't have a midpoint between 9th and 10th place for instance.

4) Continuous data. We can find the midpoint and it makes sense to do so when it comes to speeds.

5) Discrete data. This is a finite number and countable. We cannot have 20.5 freshman for instance.

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3 years ago