I need the fully simplified slope-intercept form

Un boligrafo cuesta 30 ptas mas que un lapiz. Un muchacho ha comprado 8 boligrafos y 15 lapices. En total le han costado 700 pta

Firdavs [7]

Por un sistema de ecuaciones, tiene-se que:

Cada lapiz cuesta 20 ptas.
Cada boligrafo cuesta 50 ptas.

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Considera-se un sistema de ecuaciones, con cada boligrafo custando x y cada lapiz custando y.

Boligrafo cuesta 30 mas que un lapiz, o sea, $x = 30 + y$
8 boligrafos y 15 lapices cuesta 700, o sea, $8x + 15y = 700$

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Aplicando el primer ecuación en la segunda, tiene-se el cuesto de cada lapiz:

$8x + 15y = 700$

$8(30 + y) + 15y = 700$

$240 + 8y + 15y = 700$

$23y = 460$

$y = \frac{460}{23}$

$y = 20$

Cada lapiz cuesta 20 ptas.

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Por fin, el cuesto de cada boligrafo es dado por:

$x = 30 + y = 30 + 20 = 50$

Cada boligrafo cuesta 50 ptas.

Un problema similar es dado en brainly.com/question/24637096

4 0

3 years ago

Describe how the graph of y= x^2 can be transformed to the graph of the given equation.

AnnyKZ [126]

Answer:

We conclude that the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.

Hence, option D is true.

Please check the attached graph.

Step-by-step explanation:

Given the parent function

y = x²

Given the transformed function

y = (x - 12)²

Horizontal Translation:

The horizontal translation of y = x² is of the form

f(x-h)

so y = y = (x - 12)² means y = x² is shifted 12 right.

Vertical Translation:

y = x²

Then y = x² + b is a vertical translation of y = x²

if b > 0, then y = x² + b is the graph of y = x² 'b' units up.

if b < 0, then y = x² + b is the graph of y = x² 'b' units down.

Thus, y = x² + 3 means the graph y = x² is vertically shifted up by 2 units.

Please check the attached graph.

The blue graph is representing the graph of y = x².

The red graph is representing the graph of y = (x - 12)²+3

Therefore, the graph y = x² can be transformed into the graph of the given equation y = (x - 12)²+3 by shifting the graph of y = x² right 12 units and then up 3 units.

Hence, option D is true.

6 0

3 years ago

Read 2 more answers

The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms. Statistical analysis of the o

Ugo [173]

Answer:

a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Step-by-step explanation:

Question a:

The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.

At the null hypothesis, we test if this is the average resistance, that is:

$H_0: \mu = 0.15$

We are interested in testing the hypothesis that the resistors conform to the specifications.

At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:

$H_1: \mu \neq 0.15$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.15 is tested at the null hypothesis:

This means that $\mu = 0.15$

Sample mean of 0.152, sample of 10, population standard deviation of 0.005.

This means that $X = 0.152, n = 10, \sigma = 0.005$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}$

$z = 1.26$

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.

Looking at the z-table, z = -1.26 has a p-value of 0.1038.

2*0.1038 = 0.2076

The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

Question b:

We have to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a p-value of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{0.005}{\sqrt{10}} = 0.003$

The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.

The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.

The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

8 0

3 years ago

Spencer is going snowboarding. He rode the ski lift to the top of the mountain,

Marina CMI [18]

Not sure but good luck 25•

5 0

3 years ago

On a number line, there are two numbers, 535 and -8, how far are these two from each other? plz, answer ILL GIVE BRAINLIEST!!!!!

Luden [163]

Answer:

543

Step-by-step explanation:

From 0 to 535 is a distance of 535 to the right

From 0 to - 8 is a distance of 8 to the left

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535 + 8 = 543

8 0

3 years ago

Read 2 more answers