Which algebraic expression is equivalent to the one below

Given the equation -2x + 8y = 24, determine the x- and y-intercepts. PLZ HELP???

attashe74 [19]

Answer:

$x=(-12,0)$

$y=(0,3)$

Step-by-step explanation:

x-intercept

$-2(x-4y)=24$

$x-4y=-\frac{24}{2}$

$x-4y=-12$

$x=4y-12$

$x=4(0)-12$

$x=-12$

y-intercept

$-2(x-4y)=24$

$x-4y=-\frac{24}{2}$

$x-4y=-12$

$-4y=-12-x$

$y=-\frac{-12-x}{4}$

$y=-\frac{-12-(0)}{4}$

$y=\frac{12}{4}$

$y=3$

5 0

3 years ago

An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and

Maslowich

Answer:

Null hypothesis: $\mu_{Visa}=\mu_{Mastercard}$

Alternative hypothesis: $\mu_{Visa} \neq \mu_{Mastercard}$

$t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108$

$p_v =2*P(t_{26}>2.108)=0.0448$

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

Step-by-step explanation:

Data given and notation

$\bar X_{Visa}=66970$ represent the mean for Visa

$\bar X_{Mastercard}=59060$ represent the mean for the sample Mastercard

$s_{Visa}=9500$ represent the population standard deviation for Visa

$s_{Mastercard}=10000$ represent the population standard deviation for Mastercard

$n_{Visa}=11$ sample size for the group Visa

$n_{Mastercard}=17$ sample size for the group Mastercard

t would represent the statistic (variable of interest)

$\alpha=0.1$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{Visa}=\mu_{Mastercard}$

Alternative hypothesis: $\mu_{Visa} \neq \mu_{Mastercard}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$z=\frac{\bar X_{Visa}-\bar X_{Masterdcard}}{\sqrt{\frac{s^2_{Visa}}{n_{Visa}}+\frac{s^2_{Mastercard}}{n_{Mastercard}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

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

$t=\frac{66970-59060}{\sqrt{\frac{9500^2}{11}+\frac{10000^2}{17}}}}=2.108$

What is the p-value for this hypothesis test?

First we need to calculate the degrees of freedom given by:

$df= n_{Visa}+n_{Mastercard}-2 = 11+17-2= 26$

Since is a bilateral test the p value would be:

$p_v =2*P(t_{26}>2.108)=0.0448$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and a would be a significant difference between the in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold at 10% of significance .

4 0

3 years ago

How to estimate the quotient of 57.8÷81

monitta

Round 57.8 to 60 and round 81 to 80.

60/80 or, if you simplify it, 3/4

And it is common knowledge that 3/4 = .75

So the quotient of 57.8/81 is ~.75

3 0

3 years ago

Read 2 more answers

What is the simplified form of the following expression?

ziro4ka [17]

For this case we must simplify the following expression: $7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})$