Find two consecutive even integers such that the square of the first decreased by 11 equals 5 times the second.

Compare the line passing through the points (–2, –9) and (4, 6) to the line given by the equation y = 25x – 4.

elena-s [515]

Answer:

D. They have the same y-intercep

Step-by-step explanation:

Before the comparison will be efficient, let's determine the equation of the two points and the x intercept .

(–2, –9) and (4, 6)

Gradient= (6--9)/(4--2)

Gradient= (6+9)/(4+2)

Gradient= 15/6

Gradient= 5/2

Choosing (–2, –9)

The equation of the line

(Y+9)= 5/2(x+2)

2(y+9)= 5(x+2)

2y +18 = 5x +10

2y =5x -8

Y= 5/2x -4

Choosing (4, 6)

The equation of line

(Y-6)= 5/2(x-4)

2(y-6) = 5(x-4)

2y -12 = 5x -20

2y = 5x-8

Y= 5/2x -4

From the above solution it's clear that the only thing the both equation have in common to the given equation is -4 which is the y intercept

4 0

3 years ago

What is the equation of a horizontal line that passes through the point (3,-5)?

Kryger [21]

your answer for this question is y=c hope this helps

5 0

2 years ago

A person breathes 2.5 x 10^-4 in about cubic meters of air per second. How long does it take to breathe in 2.5 cubic meters of a

Ipatiy [6.2K]

Answer:

10⁴ seconds

Step-by-step explanation:

Given that,

A person breathes $2.5\times 10^{-4}$ in about cubic meters of air per second.

We need to find time taken to breathe 2.5 cubic meters of air.

In 1 sec = $2.5\times 10^{-4}$ m³ of air breathe

Let in x seconds, 2.5 m³ of air taken by the person.

$x=\dfrac{2.5}{2.5\times 10^{-4}}\\\\x=10^4\ s$

Hence, in 10⁴ seconds 2.5 m³ of air is taken by the person.

5 0

3 years ago

For every 10 flowers,there are 36 butterflies resting on the flower with the same number on each flower .How many butterflies ar

Gemiola [76]

Answer:

I don't know if this is right or not, but here's what I think.

There are 36 butterflies on each flower.

Step-by-step explanation:

<u>Question:</u>

For each 10 flowers, there are <u>36 butterflies resting on the flower</u> with the same number on each flower. How many butterflies are on one flower?

3 0

3 years ago

The number of events is 29, the number of trials is 298, the claimed population proportion is 0.10, and the significance leve

Nina [5.8K]

Answer:

$z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155$

$p_v =2*P(Z$

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .

Step-by-step explanation:

1) Data given and notation

n=298 represent the random sample taken

X=29 represent the events claimed

$\hat p=\frac{29}{298}=0.0973$ estimated proportion

$p_o=0.1$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is 0.1 or no.:

Null hypothesis: $p=0.1$

Alternative hypothesis: $p \neq 0.1$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .

We can do the test also in R with the following code:

> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)

7 0

3 years ago