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2 years ago

Wich of the following equations would NOT contain the point (4,12)

Mathematics

1 answer:

nlexa [21]2 years ago

8 0

Given:

The given point is (4,12).

To find:

The equation that would NOT contain the point (4,12).

Solution:

We need to check each equation for the point (4,12).

In option A, the given equation is:

$y=-2x+20$

Putting $x=4$ , we get

$y=-2(4)+20$

$y=-8+20$

$y=12$

This equation contains the point (4,12).

In option B, the given equation is:

$y=\dfrac{1}{2}x+8$

Putting $x=4$ , we get

$y=\dfrac{1}{2}(4)+8$

$y=2+8$

$y=10$

This equation does not contain the point (4,12).

In option C, the given equation is:

$y=-\dfrac{1}{2}x+14$

Putting $x=4$ , we get

$y=-\dfrac{1}{2}(4)+14$

$y=-2+14$

$y=12$

This equation contains the point (4,12).

In option D, the given equation is:

$y=\dfrac{3}{4}x+9$

Putting $x=4$ , we get

$y=\dfrac{3}{4}(4)+9$

$y=3+9$

$y=12$

This equation contains the point (4,12).

Only the equation in option B does NOT contain the point (4,12). Therefore, the correct option is B.

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3 years ago

Read 2 more answers

In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

Data given and notation

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

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 $p_o$ .

Part a: Test the hypothesis

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

Calculate the statistic

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

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

Statistical decision 

P value method or p value approach . "This method consists on 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 significance level provided is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

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2 years ago

Which of the following could be the equation of the graph shown below?

Mrac [35]

Answer:

According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.

Step-by-step explanation:

To evaluate such, a comprehension of linear Cartesian data is required:

Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.

Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.

X-intercept: The peculiar point in which the linear data observed intersects the x-axis.

Since this is a negative linear, all negative slopes apply.

The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.

A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.

B. Contains a negative slope, thus is disclosed as a correct answer.

C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

2x + y = 4

Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.

D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:

X - y = 9

-y = -x + 9

Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).

Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.

*I hope this helps.

8 0

2 years ago

What is the step by step to solved a divide decimal 1.52 divide by 1.9

lora16 [44]

ANSWER

0.8

EXPLANATION

We want to simplify

$1.52 \div 1.9$