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3 years ago

I’m confused on this one

Mathematics

1 answer:

Mashutka [201]3 years ago

5 0

Greetings!

The formula for the area of any triangle is as followed:

$A_{triangle}=\frac{bh}{2}$

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<u>Let Statements:</u>

Let the variable...

→ $b$ represent the length of the base of the triangle

→ $h$ represent the length of the height of the triangle

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Using the information provided from the question, we can substitute its values in place of the variables and solve for the last remaining variable:

$10=\frac{(4)(x+3)}{2}$

Distribute the parenthesis<em> (The Distributive Property) </em>:

$10=\frac{((4)(x)+(4)(3))}{2}$

$10=\frac{4x+12}{2}$

Reduce the fraction to lowest terms:

$10=2x+6$

Add -6 to both sides of the equation:

$(10)+(-6)=(2x+6)+(-6)$

$4=2x$

Divide both sides of the equation by 2:

$\frac{4}{2}=\frac{2x}{2}$

$2=x$

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The Answer to this Problem is:

$\boxed{x=2}$

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I hope this helped!

-Benjamin

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Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sa

xxMikexx [17]

Answer:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

Since the p values is higher than a significance level for example $\alpha=0.05$ , we can reject the null hypothesis at 5% of significance, and we can conclude that the two variables are dependent at 5% of significance.

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Solution to the problem

Assume the following dataset:

Size Company/ Heal. Ins. Yes No Total

Small 32 18 50

Medium 68 7 75

Large 89 11 100

_____________________________________

Total 189 36 225

We need to conduct a chi square test in order to check the following hypothesis:

H0: independence between heath insurance coverage and size of the company

H1: NO independence between heath insurance coverage and size of the company

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*189}{225}=42$

$E_{2} =\frac{50*36}{225}=8$

$E_{3} =\frac{75*189}{225}=63$

$E_{4} =\frac{75*36}{225}=12$

$E_{5} =\frac{100*189}{225}=84$

$E_{6} =\frac{100*36}{225}=16$

And the expected values are given by:

Size Company/ Heal. Ins. Yes No Total

Small 42 8 50

Medium 63 12 75

Large 84 16 100

_____________________________________

Total 189 36 225

And now we can calculate the statistic:

$\chi^2 = \frac{(32-42)^2}{42}+\frac{(18-8)^2}{8}+\frac{(68-63)^2}{63}+\frac{(7-12)^2}{12}+\frac{(89-84)^2}{84}+\frac{(11-16)^2}{16}=19.221$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.221)=0.000067$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.221,2,TRUE)"

3 0

3 years ago

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sukhopar [10]

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18.
A. I have attached the graph.
B. A triangle
C. $A= \frac{a*b}{2} = \frac{4*4}{2} = \frac{16}{2} =8 m^{2}$

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Nadusha1986 [10]

<h2>Hello!</h2>

The answer is:

There will be necessary 13 ounces of salad dressing.

Why?

Since we already know that there will be needed 0.56 ounces of salad dressing per cup, and the recipe calls 2.1 cups of lettuce per person, we need to calculate the total ounces of salad dressing per each person, and then, calculate it for 11 persons.

So, calculating we have:

$SaladDressingPerPerson=Cups*SaladDressing=2.1*0.56oz\\\\SaladDressingPerPerson=1.176oz$

Therefore, we know that there will be needed 1.176 ounces of salad dressing per person.

Then, calculating the ounces of dressing for 11 dinner guests, we have:

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Hence, we have that there will be necessary 13 ounces of salad dressing.

Have a nice day!

8 0

3 years ago

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