All categories

3 years ago

Describe the solution to the system of equations below. HALP

Mathematics

1 answer:

guajiro [1.7K]3 years ago

6 0

Solve for
y
y in
5
x
−
y
=
8
5x−y=8.
y
=
5
x
−
8
y=5x−8

2 Substitute
y
=
5
x
−
8
y=5x−8 into
2
0
x
−
4
y
=
2
4
20x−4y=24.
3
2
=
2
4
32=24

3 Since
3
2
=
2
4
32=24 is not true, this is an inconsistent system.

You might be interested in

Find the area of a triangle with legs that are 9mm 6mm and 12mm

Sidana [21]

Here we are given the three sides of the triangle.

So we have Heron's formula to find its area.

Heron's formula is given by :

$A= \sqrt{S(S-A)(S-B)(S-C)}$

where A, B and C are sides of triangle and S is semi perimeter which is given by,

$S= \frac{A+B+C}{2}$

plugging values of A, B and C to find S

$S= \frac{9+6+12}{2}$

S=13.5

Now plugging values of A, B , C and S in Heron's formula

$A= \sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}$

A=26.14 mm²

Answer: Area of triangle is 26.14 mm².

6 0

3 years ago

Assume the hold time of callers to a cable company is normally distributed with a mean of 5.5 minutes and a standard deviation o

Ierofanga [76]

Answer:

The percent of callers are 37.21 who are on hold.

Step-by-step explanation:

Given:

A normally distributed data.

Mean of the data, $\mu$ = 5.5 mins

Standard deviation, $\sigma$ = 0.4 mins

We have to find the callers percentage who are on hold between 5.4 and 5.8 mins.

Lets find z-score on each raw score.

⇒ $z_1=\frac{x_1-\mu}{\sigma}$ ...raw score, $x_1$ = $5.4$

⇒ Plugging the values.

⇒ $z_1=\frac{5.4-5.5}{0.4}$

⇒ $z_1=-0.25$

For raw score 5.5 the z score is.

⇒ $z_2=\frac{5.8-5.5}{0.4}$

⇒ $z_2=0.75$

Now we have to look upon the values from Z score table and arrange them in probability terms then convert it into percentages.

We have to work with P(5.4<z<5.8).

⇒ $P(5.4$

⇒ $P(-0.25$

⇒ $P(z$

⇒ $z(1.5)=0.7734$ and $z(-0.25)=0.4013$ .<em>..from z -score table.</em>

⇒ $0.7734-0.4013$

⇒ $0.3721$

To find the percentage we have to multiply with 100.

⇒ $0.3721\times 100$

⇒ $37.21$ %

The percent of callers who are on hold between 5.4 minutes to 5.8 minutes is 37.21

4 0

3 years ago

An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

3 years ago

Graph the given inequality. y ≤ 4 – | x |

Brilliant_brown [7]

Answer:

The graph is included in the attached pictures

Step-by-step explanation:

The graph for y=4-|x| is shown in the attached picture, the inequality tell us that the region is located below that particular graph including the function, hence you have the second attached picture

6 0

3 years ago

4x^2 + 3 ( 3 - 3x^2)

AnnyKZ [126]

-5x^2(small two at top ) +9

6 0

3 years ago