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3 years ago

Can someone solve the system of equations?

Mathematics

1 answer:

kogti [31]3 years ago

5 0

Y=x^2-5

y=2x-5
y+5=2x
x=(y+5)/2

y=((y+5)/2)^2-5
y=(y^2+10y+25)/4-5
4y=y^2+10y+25-20
0=y^2+6y+5
0=(y+5)(y+1)
y= -5 or -1

y=2x-5 (y= -5 doesn't work for this one so use -1)
-1=2x-5
2x=4
x=2

Using these answers, you can choose answer D with reasonable certainty.

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State whether the following statements are true or false, with reasoning:

zmey [24]

Answer:

Attached is the complete working. Hope it helps.

3 0

3 years ago

Assume that foot lengths of women are normally distributed with a mean of 9.6 in and a standard deviation of 0.5 in.a. Find the

Makovka662 [10]

Answer:

a) 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b) 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c) 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

Problems of normally distributed samples 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.

In this problem, we have that:

$\mu = 9.6, \sigma = 0.5$ .

a. Find the probability that a randomly selected woman has a foot length less than 10.0 in

This probability is the pvalue of Z when $X = 10$ .

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

$Z = \frac{10 - 9.6}{0.5}$

$Z = 0.8$

$Z = 0.8$ has a pvalue of 0.7881.

So there is a 78.81% probability that a randomly selected woman has a foot length less than 10.0 in.

b. Find the probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 8.

When X = 10, Z has a pvalue of 0.7881.

For X = 8:

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

$Z = \frac{8 - 9.6}{0.5}$

$Z = -3.2$

$Z = -3.2$ has a pvalue of 0.0007.

So there is a 0.7881 - 0.0007 = 0.7874 = 78.74% probability that a randomly selected woman has a foot length between 8.0 in and 10.0 in.

c. Find the probability that 25 women have foot lengths with a mean greater than 9.8 in.

Now we have $n = 25, s = \frac{0.5}{\sqrt{25}} = 0.1$ .

This probability is 1 subtracted by the pvalue of Z when $X = 9.8$ . So:

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

$Z = \frac{9.8 - 9.6}{0.1}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772.

There is a 1-0.9772 = 0.0228 = 2.28% probability that 25 women have foot lengths with a mean greater than 9.8 in.

5 0

4 years ago

How can you find the unit rate on a graph that goes through the origin?

Andrew [12]

Answer:

In an equation in the form , the unit rate is the number represented by the . If a graph of a line passes through the origin and contains the point , representing the unit rate, then the relationship is proportional.

Step-by-step explanation:

7 0

3 years ago

What is the next term in the geometric sequence? 7,14,28, __

aleksandr82 [10.1K]

We have to look for the pattern in the numbers, so we can figure out what the next term in the sequence is !

It looks like, each number is multiplied by 2!

7 × 2 = 14

14 × 2 = 28

So, what's next?

28 × 2 = ?

The next term in the geometric sequence is ... 56!

I hope I helped :)

Comment if you have any confusion !

7 0

3 years ago

Read 2 more answers

Find all real zeros of the function y=2x-4

Ber [7]

For this case we have the following linear function:
$y = 2x-4
$
What we must do is equal the function to zero or equivalently, substitute the value of y = 0 in the given function.
We have then:
$2x - 4 = 0
$
From here, we clear the value of x.
We have then:
$2x = 4

x = 4/2

x = 2$
Answer:
all real zeros of the function y = 2x-4 are:
x = 2

5 0

3 years ago