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DedPeter [7]
3 years ago
11

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.

Mathematics
2 answers:
iogann1982 [59]3 years ago
5 0

the answer is C guys lol

Leno4ka [110]3 years ago
3 0
Really, we don't need to use that much math--we can use logic instead. Since the two congruent sides must be longer than 30in, the total has to be greater than 60in (the longest side plus the congruent sides.) So for our answer, we want the smallest total that is above sixty, which in this case is 72.44in.

Hope I helped, and let me know if you have any questions :) I can explain the real math if you want, it was just unnecessary here.
You might be interested in
A researcher used a sample of n = 60 individuals to determine whether there are any preferences among six brands of pizza. Each
Blizzard [7]

Answer:

1) χ² ≥ 11.07

2) Goodness of fit test, df: χ²_{3}

Independence test, df: χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3) e_{females.} = 80

4) H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

5) χ²_{6}

Step-by-step explanation:

Hello!

1)

The researcher took a sample of n=60 people and made them taste proof samples of six different brands of pizza and choose their favorite brand, their choose was recorded. So the study variable is the following:

X: favorite pizza brand, categorized in brand 1, brand 2, brand 3, brand 4, brand 5 and brand 6.

The Chi-square goodness of fit test is done with the following statistic:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Where k represents the number of categories of the study variable. In this example k= 6.

Remember, the rejection region for the Chi-square tests of "goodnedd of fit", "independence", and "homogeneity" is allways one-tailed to the right. So you will only have one critical value.

χ²_{k-1; 1 - \alpha }

χ²_{6-1; 1 - 0.05 }

χ²_{5; 0.95 } = 11.070

This means thar the rejection region is χ² ≥ 11.07

If the Chi-Square statistic is equal or greather than 11.07, then you reject the null hypothesis.

2)

The statistic for the goodness of fit is:

χ²= ∑\frac{(O_i-E_i)^2}{E_i} ≈χ²_{k-1}

Degrees of freedom: χ²_{k-1}

In the example: k= 4 (the variable has 4 categories)

χ²_{4-1} = χ²_{3}

The statistic for the independence test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

If the information is in a contingency table

r= represents the total of rows

c= represents the total of columns

In the example: c= 2 and r= 2

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(2-1)(2-1)} = χ²_{1}

The goodness of fit test has more degrees of freedom than the independence test.

3)

To calculate the expected frecuencies for the independence test you have to use the following formula.

e_{ij} = n * P_i. * P_.j = n * \frac{o_i.}{n} * \frac{o_.j}{n}

Where o_i. represents the total observations of the i-row, o_.j represents the total of observations of the j-column and n is the sample size.

Now, this is for the expected frequencies in the body of the contingency table, this means the observed and expected frequencies for each crossing of categories is not the same.

On the other hand, you would have the totals of each category and population in the margins of the table (subtotals), this is the same when looking at the observed frequencies and the expected frequencies. Wich means that the expected frequency for the total of a population is the same as the observed frequency of said population. A quick method to check if your calculations of the expected frequencies for one category/population are correct is to add them, if the sum results in the subtotal of that category/population, it means that you have calculated the expected frequencies correctly.

The expected frequency for the total of females is 80

Using the formula:

(If the females are in a row) e_{females.} = 100 * \frac{80}{100} * \frac{0}{100}

e_{females.} = 80

4)

There are two ways of writing down a null hypothesis for the independence test:

Way 1: using colloquial language

H₀: The variables X and Y are independent

Way 2: Symbolically

H₀: P_{ij}= P_{i.} * P_{.j} ∀ i= 1, 2, ..., r and j= 1, 2, ..., c

This type of hypothesis follows from the definition of independent events, where if we have events A and B independent of each other, the probability of A and B is equal to the product of the probability of A and the probability of B, symbolically: P(A∩B) = P(A) * P(B)

5)

In this example, you have an independence test for two variables.

Variable 1, has 3 categories

Variable 2, has 4 categories

To follow the notation, let's say that variable 1 is in the rows and variable 2 is in the columns of the contingency table.

The statistic for this test is:

χ²= ∑∑\frac{(O_ij-E_ij)^2}{E_ij} ≈χ²_{(r-1)(c-1)} ∀ i= 1, 2, ..., r & j= 1, 2, ..., c

In the example: c= 3 and r= 4

Degrees of freedom: χ²_{(r-1)(c-1)}

χ²_{(3-1)(4-1)} = χ²_{6}

I hope you have a SUPER day!

4 0
3 years ago
A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to t
velikii [3]

Answer:

B

Step-by-step explanation:

To answer this, we need to see the to see to the fact that they are both in the same unit before we can take the ratio.

Firstly, we know that 1 foot = 12 inches. 9 feet would this be 9 * 12 = 108 inches.

Now we are told to get the ratio of length of car to length of model.

This means 108:6 = 18:1

5 0
3 years ago
Read 2 more answers
Everythings in the pic!
yanalaym [24]

Answer:

  • D. 32 times; 5/4*40 = 32

Step-by-step explanation:

It is expected the spinner to land on Red 1/5 times.

<u>If the spinner is spun 40 times, then it should land on Red:</u>

  • 1/5*40 = 8 times

<u>And it should not land on red:</u>

  • (1 - 1/5)*40 = 4/5*40 = 32 times

Correct choice is D

3 0
3 years ago
Quotient of 0.72 / 4
sasho [114]

Answer: The answer is 0.18

Step-by-step explanation:

I took the test

5 0
3 years ago
Y = – 3
KonstantinChe [14]

The  best approximation for the solution to this system of equations is (-2.2,-3)

Option C is correct.

Step-by-step explanation:

Solving the system of equations to get the exact value of x:

y = -3\\y = x-0.8

Let

y = -3\,\,eq(1)\\y = x-0.8\,\,eq(2)

Putting value of y from eq(1) into eq(2)

-3=x-0.8

x=-3+0.8

x=-2.2

So, Value of x is -2.2

The  best approximation for the solution to this system of equations is:

x=-2.2 and y = -3

(-2.2,-3)

Option C is correct.

Keywords: System of equations

Learn more about system of equations at:

  • brainly.com/question/9045597
  • brainly.com/question/3739260
  • brainly.com/question/13168205

#learnwithBrainly

6 0
3 years ago
Read 2 more answers
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