MATHEMATICS COLLEGE

Rewrite the following using the GCF and Distributive properly ?

63 + 27

Answers

Answer 1
Answer: the GCF is 90

Distributive property can be written as
(9)(7) + (9)(3)
or
9(7 + 3)
Answer 2
Answer: 45 is the GCF I’m pretty sure

Related Questions

Solve the equation by completing the square. X^2+10x+24=0
Find the distance between the two points. Round your answer to thenearest tenth.YA(-3,5)(7,1)
S varies inversely as G. If S is 8 when G is 1.5​, find S when G is 3. ​a) Write the variation. ​b) Find S when G is 3.
Renting a car costs $30 per day, or $600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal (after which renting monthly is cheaper)?
Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Nora, an office manager, needs to find a courier to deliver a package. The first courier she isconsidering charges a fee of $14 plus $5 per kilogram. The second charges $15 plus $4 perkilogram. Nora determines that, given her package's weight, the two courier services areequivalent in terms of cost. What is the weight? How much will it cost?

In a study of 788 randomly selected medical malpractice​ lawsuits, it was found that 494 of them were dropped or dismissed. Use a 0.05 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed.Which of the following is the hypothesis test to be conducted?
A.
Upper H 0 : p less than 0.5
Upper H 1 : p equals 0.5
B.
Upper H 0 : p greater than 0.5
Upper H 1 : p equals 0.5
C.
Upper H 0 : p equals 0.5
Upper H 1 : p not equals 0.5
D.
Upper H 0 : p equals 0.5
Upper H 1 : p less than 0.5
E.
Upper H 0 : p not equals 0.5
Upper H 1 : p equals 0.5
F.
Upper H 0 : p equals 0.5
Upper H 1 : p greater than 0.5
What is the test statistic?
Z =
(Round to two decimal places as needed.)
What is the conclusion about the null hypothesis?
A. Reject the null hypothesis because the P-value is greater than the significance level, alpha.
B. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
C. Fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha.
What is the final conclusion?
A.There is sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
B.There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.
C.There is sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.
D.There is not sufficient evidence to warrant rejection of the claim that most medical malpractice lawsuits are dropped or dismissed.

Answers

Answer:

Step-by-step explanation:

A. Upper H 0 : p equals 0.5

Upper H 1 : p not equals 0.5

B. Using the tests promotion formula, we have (p - P) / √P(1-P)

Where p (sample promotion) = 494/788 = 0.6269, P (population proportion) = 0.5,

(0.6269 - 0.5) / (√0.5(1-0.5))

0.1269/ √(0.5 (0.5))

0.1269/ √0.25

0.1269/0.5

Test statistics is equal to 0.2538

C. We will use the p value to determine our result, thus the p value at 0.05 level of significance is 0.79965, thus we fail to reject the null hypothesis because the P-value is greater than the significance level, alpha.

Then we conclude that There is not sufficient evidence to support the claim that most medical malpractice lawsuits are dropped or dismissed.

Write a word problem that could be solved with the equation
0.15x + 200 650

Answers

Answer:

13.3

Step-by-step explanation:

One thousand tonnes (1000 t, one t equals 10 cubed kg) of sand contains about a trillion (10 super 12) grains of sand. How many tonnes of sand are needed to provide 1 mol of grains of sand? (b) Assuming the volume of a grain of sand is 1.0 mm3 and the land area of the continental United States is 3.6 multiplication 10 super six square miles, how deep would the sand pile over the United States be if this area were evenly covered with 1.0 mol of grains of sand?

Answers

Answer with Step-by-step explanation:

Since 1 mole of sand will contain Avagadro's Number of sand particles (by definition of 1 mole)

Thus we have

1 mole of sand = 6.022* 10^(23) sand particles

Thus in number of trillion sand particles we have no of trillion sand particles in 12 mole is

(6.022* 10^(23))/(10^(12))=6.022* 10^(11)

Now since it is given that mass of 1 trillion sand particles is 1000 tonnes Thus the mass of 6.022* 10^(11) trillion sand particles is

Mass=1000* 6.022* 10^(11)=6.022* 10^(14)tonnes

Part 2)

Since it is given that volume of 1 sand particle is 1.0mm^(3) thus the volume of 1 mole of sand is volume of 6.022* 10^(23) sand particles

Thus volume of 1 mole is V=1.00* 10^(-18)km^(3)* 6.022* 10^(23)=6.022* 10^(5)km^(3)

Now since the Area of united states is A=3.6* 10^(6)mile^(2)=5.8* 10^(6)km^(2)

Thus the depth of the sand pile is

Depth=(Volume)/(Area)=(6.022* 10^5)/(5.8* 10^6)=0.10387km=103.8meters

Write a formula that will compute the final grade for the course, using G to represent the final grade, H to represent the homework average, Q to represent the quiz average, P to represent the project grade, T to represent the test average, and F to represent the final exam grade. Note: Keep in mind how you must write the percentages that show the weighting of each category when doing computations!

Answers

Answer:

To calculate final grade we use the formula:

Final grade = H( the weight of h) + Q( the weight of q) + P (the weight of project) +T (the weight of test) + F(the weight of final exams).

This formula help us to calculate the grade we need to get.

Step-by-step explanation:

Solution:

Suppose grade breakdown for certain college course is as follow:

Homework = 15%

Quizzes = 20%

Project = 10%

Test = 40%

Final exam= 15%

Let G represent the final grade

H represents homework average,

Q represents quizzes and P represent project, T represent test average and F represent final exam.

To calculate final grade we use the formula:

Final grade = H( the weight of h) + Q( the weight of q) + P (the weight of project) +T (the weight of test) + F(the weight of final exams).

This formula help us to calculate the grade we need to get.

Final answer:

The final grade, G, can be computed by adding together the weighted values of the homework average, quiz average, project grade, test average, and final exam grade. This can be represented by the formula G = 0.20*H + 0.20*Q + 0.25*P + 0.15*T + 0.20*F.

Explanation:

To compute the final grade for the course, you will need to multiply each category by its weighting percentage, then add the results together. This can be represented as the following formula:

G = 0.20*H + 0.20*Q + 0.25*P + 0.15*T + 0.20*F

In this formula, G is the final grade, H is the homework average, Q is the quiz average, P is the project grade, T is the test average, and F is the final exam grade. The coefficients (0.20, 0.20, 0.25, 0.15, and 0.20) represent the weighting percentages in decimal form for each respective category.

Learn more about final grade calculation here:

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Max has been offered positions by two car companies. The first company pays a salary of $7,500 pluscommission of $1000 for each car sold. The second company pays a salary of $17,500 plus a commission of
$500 per car sold. How many cars would need to be sold to make the total pay the same?

Answers

The number of cars would need to be sold to make the total pay the same is 20.

Given that, the first company pays a salary of $7,500 plus commission of $1000 for each car sold.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of cars be x.

The first company pays = 7500+1000x

The second company pays = 17500+500x

So, 7500+1000x=17500+500x

⇒ 1000x-500x=17500-7500

⇒ 500x=10000

⇒ x=10000/500

⇒ x=20

Therefore, the number of cars would need to be sold to make the total pay the same is 20.

To learn more about an equation visit:

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Answer:

11 for the first company and 2 for the second company

Find the area of the figure to the nearest square unit.

Answers

Answer:

357 mi²

Step-by-step explanation:

The shape is made of a triangle and a half-square

we will calculate the area of each one

  • The half square:

let A1 be the area of the half-circle:

A1= (10²*π)/2 = 50π mi²

  • The rectangle:

Let A2 be the area of the triangle:

A2= 10*20=200 mi²

  • The whole shape:

let At be the total area:

At =A1+A2= 200+50π =357.07≈ 357 mi²
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