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Reil [10]
3 years ago
13

NEED HELP I need to fill in the highlighted parts

Mathematics
1 answer:
Gemiola [76]3 years ago
6 0

The statements and reasons why the given statements are true are presented in the following two column proofs;

Question 1

Given: 9·(x + 6) - 41 = 75

Prove \ x = \dfrac{62}{9}

Statement                   {} Reason

S1. 9·(x + 6) - 41 = 75   {}  R1. <u>Given</u>

S2. 9·(x + 6)  =  116        {}R2. <u>Addition property</u>

S3. <u>9·x + 54 = 116 </u>         {}R3. Distributive property

S4. 9·x = 62                   {}R4. <u>Subtraction property</u>

S5. x = \dfrac{62}{9}                     {} R5. <u>Division property of equality</u>

Question 2.

Statement                                     {}        Reason

S1. m∠A + m∠B = m∠D   {}                     R1.  Given

S2. ∠C and ∠D form a Linear Pair   {}   R2. Definition of linear pair

S3. ∠C and ∠D are supplementary   {}R3. <u>Linear pair ∠s are supplementary</u>

S4. <u>∠C + ∠D = 180° </u>  {}                           R4. Definition of supplementary

S5. m∠C + m∠A + m∠B = 180°   {}         R5. <u>Substitution property</u>

Question 3.

Statement                                     {} Reason

S1. ∠BDA ≅ ∠A                             {} R1. Given

S2. ∠BDA ≅ ∠CDE                      {}  R2. <u>Vertical angle theorem</u>

S3. ∠CDE ≅ ∠A                      {}       R3. Transitive property of congruency

S4. m∠CDE = m∠A                    {}   R4. <u>Definition of congruency</u>

S5. <u>(13·x + 20)° = (14·x + 15)°</u>      {}   R5. Substitution Property of Equality

S6. 14·x° = 13·x + 5°                       {}R6. <u>Subtraction property</u>

S7. x = 5                      {}                  R7. Subtraction property

Learn more here:

brainly.com/question/11331230

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In 1998 the average income for middle class families in the US was $37,100 with a population standard deviation of $6362. We wan
sammy [17]

Answer:

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

The best answer would be:

A. Z test

Step-by-step explanation:

Data given and notation  

\bar X=36670 represent the mean average

\sigma=6362 represent the population standard deviation for the sample  

n=1225 sample size  

\mu_o =37100 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal or not to 37100, the system of hypothesis would be:  

Null hypothesis:\mu =37100  

Alternative hypothesis:\mu \neq 37100  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

The best answer would be:

A. Z test

5 0
3 years ago
The area of one of the smaller circles is 8/ in². Find the area of the shaded region.
Ksju [112]

Answer:

Area of shaded region = 16π in² (D)

Step-by-step explanation:

The question is incomplete without the diagram if the circles. Find attached the diagram used in solving the question.

Area of the smaller circle = 8π in²

Area of a circle = πr²

πr² = 8π

r² =8

r = √8 = 2√2

From the diagram, there are two smaller circles in a bigger circle.

The radius of the bigger circle (R) is 2times the radius of the smaller circle (r)

R = 2r

Area of bigger circle = πR²

= π×(2r)² =   π×(2×2√2)²

= π×(4√2)² = π×16×(√2)²

Area of bigger circle = π×16×2

Area of bigger circle = 32π in²

Since there are two smaller circles in a bigger circle

Area of shaded region = Area of bigger circle -2(area of smaller circles)

Area of shaded region = 32π in² - 2(8π in²)

Area of shaded region = 32π in² - 16π in²

Area of shaded region = 16π in²

8 0
3 years ago
Which of the following statements is true of an essay's conclusion?
laiz [17]
The answer is option D.
8 0
3 years ago
A chef uses 2 3 cup of flour for every 1 8 cup of water in a dough recipe. If the chef follows the recipe proportions, which sta
VashaNatasha [74]

Step-by-step explanation:

A chef uses 2/3 cup of flour for every 1/8 cup of water in a dough recipe.

It means,

2/3 cup = 1/8 cup of water

1\ \text{cup}=\dfrac{\dfrac{1}{8}}{\dfrac{2}{3}}\\\\=0.1875

Hence, the constant of proportionality is 0.1875.

5 0
2 years ago
Based on the circle graph how many pounds of milk and eggs does the average American consume each year PLS EXPLAIN FOR BRAINLEST
Gnoma [55]

Answer:

H.  552

Step-by-step explanation:

Circle graph information:

  • Milk and eggs = x%
  • Fruits and vegetables = 38%
  • Cereals = 10%
  • Meat and fish = 10%
  • Sugar = 8%
  • Fats and oils = 4%

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

=\sf \dfrac{30}{100} \times 1840

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

5 0
2 years ago
Read 2 more answers
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