Simplify the fraction 4t ^ 2 - 16 ÷8 ÷ t

kipiarov [429]

Well, it would end up to 3x=14 which is x=4.33

6 0

3 years ago

Not Answered Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal f

ehidna [41]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688$

$p_v =2*P(Z>2.688)= 0.0072$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair in 2012

$X_{2}=315$ represent the number of people indicating that their financial security was more than fair in 2010

$n_{1}=1000$ sample 1 selected

$n_{2}=900$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of people indicating that their financial security was more than fair in 2012

$p_{2}=\frac{315}{900}=0.350$ represent the proportion estimated of people indicating that their financial security was more than fair in 2010

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Part a: Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

Hypothesis testing

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+315}{1000+900}=0.382$

z-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 statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>2.688)= 0.0072$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

3 0

4 years ago

The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock

FinnZ [79.3K]

Answer:

$855,000
Dividend per share of common stock = $1.06

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = $\frac{2,645,000}{2,500,000}$

= $1.06

7 0

4 years ago

A car travels 322 miles on 11.5 gallons of gas. What is the cars miles per gallon

kolbaska11 [484]

28 miles per gallon. To find miles per gallon you do miles divided by gallons which in this case is 322/11.5=28.

If you need any more help feel free to message me.

6 0

3 years ago

For #8 and #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.

garik1379 [7]

Applying the equation for the area of the trapezoid, it is found that the height is of 10 cm.

The <em>area of a trapezoid</em> is <u>half the multiplication of the sum of the bases and the height</u>, that is:

$A = \frac{h}{2}(b_1 + b_2)$