If ΔOCD ≅ ΔJAL, then which of the following statements are true? Select True or False for each statement.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questio

hodyreva [135]

Triangles = 180 so you’d use the equation ABC (60) + BAC (50) + ACB (x) = 180
Which equals out to ACB= 79

6 0

2 years ago

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A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

anzhelika [568]

You need to solve for one variable in equation 1 and substitute it in equation 2 to solve.

Equation 1: x+y=24
x= number of 3 pt questions
y= number of 5 pt questions
24= Total number of questions

Equation 2: 3x+5y=100
100= Total point value possible on test
3x= point value of 3 pt questions
5y= point value of 5 pt questions

x+y=24
Subtract y from both sides
x=24-y

Substitute in equation 2:
3x+5y=100
3(24-y) +5y=100
72-3y+5y=100
72+2y=100
Subtract 72 from both sides
2y=28
Divide both sides by 2
y=14

Substitute y=14 back in to solve for x:
3x+5y=100
3x+5(14)=100
3x+70=100
Subtract 70 from both sides
3x=30
Divide both sides by 3
x=10

So there are 10 three point questions
There are 14 five point questions.

Hope this helped! :)

6 0

2 years ago

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Suppose that we want to investigate whether curfews correlate with differences in grades for students in middle school. We selec

Anton [14]

Answer:

Step-by-step explanation:

Hello!

Given the variables

X: Curfew of middle school students (Categorized Yes/No)

Y: Average grade of middle school students. (Categorized: A, B, C, and D)

The objective is to test if there is an association between both variables, you have to conduct a Chi-Square test of independence.

In the null hypothesis, you state that both variables are independent vs. the alternative hypothesis that the variables are dependent.

The hypotheses for this test are:

H₀: Pij= Pi. * P.j i= (1)Yes, (2)No; j= (1)A, (2)B, (3)C, (4)D

H₁: Te variables are not independent.

α: 0.05

$X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~X_{(r-1)*(c-1)}$

Where

Oij is the observed frequency for the i-row and j-column

Eij is the expected frequency for the i-row and j-column

r= number of categories in the rows

c= number of categories in the columns

$X^2_{H_0}= 1.4796703$

p-value: 0.687

The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. So using a 5% significance level, you can conclude that having a curfew and the average grades of middle schoolers are two independent variables.