Final answer:
Factoring prime numbers is not applicable as they are already in their simplest form. In calculations involving exponents with prime numbers, exponent rules can be used to simplify or alter the expression. Understanding these rules empowers you to verify the results and improve your mental math skills.
Explanation:
Prime numbers are the building blocks of the number system, but interestingly, they cannot be factored further since they have only two distinct divisors: one and themselves. Therefore, the concept of factoring prime numbers doesn't apply because they are already in their simplest form. However, when you work with exponents and prime bases, such as in 24 × 10¹², you can manipulate the expression by using exponent rules to simplify or alter its form.
Exponents represent how many instances a base number is multiplied by itself. For example, 10³ equals 10 × 10 × 10, which is 1,000. Similarly, when you see an operation like (53)4, you can multiply the exponents (3 × 4) to understand this as 512, which is 5 multiplied by itself 12 times.
Mastering these concepts avoids confusion and allows for mathematical operations to be performed more readily in your head. Calculators handle these numbers with ease, but understanding the rules lets you confirm the accuracy of your work and can help in developing a life-long skill.
Jackson has 2,000 baseball cards in his collection. Gabe has 1/10
as many baseball cards in his collection as Jackson. How many baseball cards does Gabe have in his collection?
Answer:
200 cards
Step-by-step explanation:
Given: Jackson has 2,000 baseball cards in his collection. Gabe has [tex]\frac{1}{10}[/tex] as many baseball cards in his collection as Jackson.
To Find: How many baseball cards does Gabe have in his collection.
Solution:
Total number of cards Jackson has in his collection [tex]=2000[/tex]
Let number of cards Gabe has =[tex]\text{x}[/tex]
Now,
Number of cards Gabe has [tex]= \frac{\text{total cards Jackson has}}{10}[/tex]
[tex]\text{x}= \frac{\text{total cards Jackson has}}{10}[/tex]
putting values
[tex]\text{x}= \frac{2000}{10}[/tex]
[tex]\text{x}= 200[/tex]
Hence Gabe has 200 baseball cards in his collection.
There are 200 baseballs in Gabe's collection
Total number of baseball in Jackson's baseball = 2000
Gabe's fraction of Jackson's baseball = 1/10
The Number of baseball in Gabe's collection is :
[tex](2000 \times ( \frac{1}{10} )) = \frac{2000}{10} = 200[/tex]
Therefore, the Number of baseball in Gabe's collection is 200.
Learn more : https://brainly.com/question/18109354
melanie michael has a salaried and exempt job. she earns $825 a week. one week she worked 46 hours. find her gross weekly earnings.
Carey correctly graphs a linear function. The slope of the function is –1. The y-intercept is 3. Which is Carey’s graph?
Answer:
The linear function is [tex]y=-x+3[/tex]. The graph of function is given below.
Step-by-step explanation:
The slope intercept form of a linear function is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
Since the slope is -1 and the y-intercept is 3, therefore the linear function is,
[tex]y=-x+3[/tex]
put y=0, to find x-intercept.
[tex]0=-x+3[/tex]
[tex]x=3[/tex]
Therefore the line intersect the y-axis at y=3, x-intercept is x=3 and the as the value of x increases the value of y decreases.
The graph of the linear function [tex]y=-x+3[/tex] is given below.
The first graph.
It's right on edge
If Ryan pays his car insurance for the year in full, he will get a credit if $28. If he chooses to pay a monthly premium, he will pay a $10 late fee for any month the payment is late
A.which of these values could be represented with a negative number?explain.
Answer:
The value that represented with a negative number is the $10 fee that Ryan pay as a late fee.
Step-by-step explanation:
Consider the provided information.
Ryan pays his car insurance for the year in full, he will get a credit of $28.
Here credit represented with a positive number because $28 added to his account.
If he chooses to pay a monthly premium, he will pay a $10 late fee for any month the payment is late.
Here late fee represented by a negative number because if he will miss his monthly payment then $10 will be subtracted from his account.
Thus, we can say that the value that represented with a negative number is the $10 fee that Ryan pay as a late fee.
Which is a measure of the efficiency of an investment?
Answer:
ROI
Step-by-step explanation:
To measure the efficiency of the an investment, we use a term called "ROI"
That is return on investment. which is calculated by the formula
(return earned/ capital invested)*100.
Lets assume that you invested $10000 in any bank or business venture, and you earned a profit or return of $2000. So your percentage of return is (2000/10000)*100 = 20%
What 2 facts can you double to find 8x4? Explain.
Yoko is buying a car from a local car dealership. She wants to get the lowest interest rate possible. Which will most likely help her get the lowest interest rate?
A)asking nicely
B)making sure she has a positive credit history
C)explaining that she has many outstanding loans
D)showing her driver’s license
Answer:
B)making sure she has a positive credit history
Step-by-step explanation:
Yoko is buying a car from a local car dealership. She wants to get the lowest interest rate possible.
B) making sure she has a positive credit history - will most likely help her get the lowest interest rate.
Getting low interest rates does not depend on the way you talk or if you have a driver licence.
It depends on your previous credit history and credit scores. When you have good scores, this means you have always paid your debts on time and this makes sure that you will do the same in future.
So, you get low interest rates based on good credit history.
To get the lowest interest rate she should make sure that she has a positive credit history. Option (B) is correct.
Further Explanation:
Given:
The options are as follows,
(A). Asking nicely
(B). Making sure she has a positive credit history
(C). Explaining that she has many outstanding loans
(D). Showing her driver’s license
Explanation:
Yoko is buying a car from a local car dealership. She wants to get the lowest interest rate possible.
To get the lowest interest rate she should make sure that she has a positive credit history. Option (B) is correct.
Option (A) is not correct.
Option (B) is correct.
Option (C) is not correct.
Option (D) is not correct.
Learn more:
If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard https://brainly.com/question/2479097. Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? https://brainly.com/question/1446243.Answer details:
Grade: High School
Subject: Mathematics
Chapter: Loan schedule
Keywords: Yoko, buying, car, local car, dealership, lowest interest rate, possible, asking nicely, credit history, positive credit history, loan, license, outstanding.
The quotient of the opposite of 30 and 6 plus the opposite of 8
What is the value of the expression? (−3)3+6^3/12 Enter your answer in the box.
(6^3/12 is a fraction) and (6^3 means 6*6*6)
PLEASE HELP AND ANSWER BOTH QUESTIONS
Adonica made snacks for her friends by putting equal amounts of trail mix into small bags. If she started with 3 4/5 cups of trail mix and put 3/4 cup into each bag, how many complete bags did she make?
Answer:
5 bags
Step-by-step explanation:
Given,
The total number of cups in trial mix = [tex]3\frac{4}{5}[/tex],
The number of cups in each bag = [tex]\frac{3}{4}[/tex]
So, the number of bags,
[tex]=\frac{\text{Total cups}}{\text{Cups in each }}[/tex]
[tex]=\frac{3\frac{4}{5}}{\frac{3}{4}}[/tex]
[tex]=\frac{\frac{19}{5}}{\frac{3}{4}}[/tex]
[tex]=\frac{76}{15}[/tex]
[tex]=5\frac{1}{15}[/tex]
Hence, 5 complete bags would made.
Trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden as and divides the rest equally into 10 flower pots. What fractionof a package of seeds is planted in each flowerpot?
We are required to find the fraction of a package of seeds is planted in each flowerpot.
The fraction of a package of seeds planted in each flowerpot is 7/120
Given:
Total package of seed = 3/4
Quantity of seeds planted in his garden = 1/6
Quantity of seed remaining = Total package of seed - Quantity of seeds planted in his garden
= 3/4 - 1/6
= (18 - 4) /24
= 14 / 24
Quantity of seed remaining = 7 / 12
Number of flowerpots = 10fractionof a package of seeds is planted in each flowerpot = Quantity of seed remaining ÷ Number of flowerpots
= 7/12 ÷ 10/1
= 7/12 × 1/10
= (7 × 1) / (12 × 10)
= 7/120
Therefore, the fraction of a package of seeds planted in each flowerpot is 7/120
Read more:
https://brainly.com/question/2261275
What is 0.9 1/ 10th of
In the diagram, AB:BC is 3:4 and AC:42 Find BC
the square of m minus the cube of n is sixteen
If b = 9 cm, c = 7 cm, and m∠A = 66°, what is the approximate area of ABC?
A) 28.78 cm2
B) 12.81 cm2
C) 14.62 cm2
D) 57.55 cm2
Thank you!
Which is the simplified form of (2ab/a^-5 b^2)^-3?
Answer:
A on e2020/edge
Step-by-step explanation:
Brad has $1.65. He spends 75 cents to buy a card. How much change does he get back ?
Final answer:
After purchasing a card for 75 cents, Brad receives 90 cents back in change from his initial $1.65.
Explanation:
The student's question is about calculating change returned after a purchase, which is a basic arithmetic problem. Brad starts with $1.65 and spends 75 cents on a card. To find out how much change Brad gets back, we subtract the cost of the card from the amount Brad started with.
$1.65 - $0.75 = $0.90
Therefore, Brad gets 90 cents back in change after buying the card.
A drawing with the scale of 3 cm for each meter shows where Adam wants to plant flowers. If the actual distance of the flower planting is 25 m long, how long is the scale distance on the drawing?
A plane flies over city A and reaches city B, 115 miles away, in 15 minutes. Find the speed of the plane in miles per hour assuming the plane flew at a constant speed.
A. 300 mph
B. 460 mph
C. 600 mph
D. 680 mph
Answer:
B
460
Step-by-step explanation:
I am a mutiple of 60. I am between 400 and 600 . I am 40 away from a multiple of 100. who am i
Imagine you are drawing a comic strip showing how to solve the problem 72 divided into 4 to new 4th graders. Create a script to explain how you can keep dividing after getting a remainder of 3 tens in the first step
1.6 x 10^8)(5.8 x 10^6)
---------------------------
(4 x 10^6)
Expreesed in Scientific Notataion
A marathon is 131 over 5 miles long. If for people divide up the distance equally, how many miles does each person need to run?
Answer:
6.55 miles to run
Step-by-step explanation:
A distance of marathon is = [tex]\frac{131}{5}[/tex] miles long.
or [tex]26\frac{1}{5}[/tex] miles
If four people divide up the distance equally.
To calculate the distance each person need to run we will divide [tex]\frac{131}{5}[/tex] by 4
= [tex]\frac{\frac{131}{5} }{4}[/tex]
= [tex]\frac{131}{5}[/tex] × [tex]\frac{1}{4}[/tex]
= [tex]\frac{131}{20}[/tex]
= [tex]6\frac{11}{20}[/tex]
= 6.55 miles
each 4 person need 6.55 miles to run.
in the figure below line DE is parallel to line FG and transversal AG
Answer: The answer is 147° and 33°.
Step-by-step explanation: We are given a figure in which the line DE is parallel to the line FG and AG is a tranversal. We are to find the value of 'x' and 'y' from the figure.
Also, given that
∠ABE = (5y - 18)°.
We can see from the figure that ∠DBG and ∠ABE are vertically opposite angles, so they must be equal.
That is,
[tex]\angle DBG=\angle ABE\\\\\Rightarrow x=5y-18\\\\\Rightarrow 5y-x=18.~~~~~~~~~~~~~~~(i)[/tex]
Also, since ∠DBG and ∠FGB are interior angles on the same side of the transversal, so their sum is 180°.
That is
[tex]\angle DBG+\angle FGB=180^\circ\\\\\Rightarrow x+y=180.~~~~~~~~~~~~~~~~~(ii)[/tex]
Adding equations (i) and (ii), we get
[tex]y+5y=18+180\\\\\Rightarrow 6y=198\\\\\Rightarrow y=33,[/tex]
and from equation (ii), we get
[tex]x=180-33=147.[/tex]
Thus, x° = 147° and y° = 33°.
What is the y-intercept of the function f(x) = –x + ?
State the value of m and the value of b!
A. F(x):m= , b=
B. G(x): m= , b =
C. H(x): m = , b=
Write he ratio that compares $7 1/2 dollars to 3/4 pound of coffee dollars to pounds of coffee=
The ratio that compares $7 1/2 dollars to 3/4 pound of coffee dollars to pounds of coffee is 10.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
$7 1/2 = $(7 + 1/2) = $15/2
$30/4 → $3/4 × 10
3/4 pounds
Ratio = 10
Hence "The ratio that compares $7 1/2 dollars to 3/4 pound of coffee dollars to pounds of coffee is 10".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ2
Cookies are on sale! Today each cookie costs $0.75 less than the normal price. Right now if you buy 7 of them it will only cost you $2.80! Write an equation to determine the normal price of each cookie. Find the normal price of each cookie.
Answer:
The price of each cookie is $ 1.15.
Step-by-step explanation:
Let x be the normal price of each cookie,
Since, each cookie costs $0.75 less than the normal price,
Thus, the new price of each cookie = ( x - 0.75 ) dollars,
So, the price of 7 cookies = 7( x-0.75 ) dollars
According to the question,
The price of 7 cookies = $ 2.80
⇒ 7( x-0.75 ) = 2.80
Which is the required equation to determine the normal price of each cookies,
For solving the above equation,
Divides both sides by 7,
x - 0.75 = 0.4
Adding 0.75 on both sides,
x = 1.15
Hence, the price of each cookie is $ 1.15.
help me please below........