Answer:
The required absolute equation is: |x-430|=20
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Step-by-step explanation:
Consider the provided information.
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
Let x is the actual weight of the soccer ball.
The difference of actual weight and recommended weight can vary by 20 grams.
Thus, the required absolute equation is:
|x-430|=20
x-430=20 or x-430=-20
x=450 or x=410
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Add 1/7+7/10 as a fraction in simplest form
First, we need to find the least common denominator in order to add these fractions together. The lowest common denominator is 70.
[tex]\frac{10}{70}[/tex] + [tex]\frac{49}{70}[/tex] = [tex]\frac{59}{70}[/tex]
The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second. What are the numbers
Jimmy’s new cell phone cost him $49.99 when he signed a 2 year plan, which was 75% off the original place. What was the original price?
In your own words explain how to round 9660 to the nearest thousand
What is the area of a square deck, if one side is 10 feet long?
Answer:100 square feet
Step-by-step explanation: since we know that a square has all equal sides, and we know one length of one side is 10, we know all sides are ten then. We then multiply 10 x 10 which will equal, 100
Frederick is working on a number puzzle and discovers that the product of the two base numbers is exactly twice as large as the sum of those same base numbers.
Help on this, please?
To solve this problem, we are going to use trial and error.
If the 2 numbers are 3 and 4 then 3 and 4 is 12 and 3 + 4 = 7
which cannot be divided equally, so this is not the answer.
3 and 5 = 15 but this is not divisible by 2.
6 and 3 = 18 and 6 + 3 = 9 which is 1/2 of 18
therefore, one set is 6 and 3.
please help with below question
find the smallest possible constant C such that x,y,z are all integers
2x+y=C
3y+z=C
x-4z=C
Find the value of $ 15,000 at the end of one year if it is invested in an account that has an interest rate of 4.95 % and is compounded in accordance with the rules below. a. compounded monthly b. compounded daily (assuming a 365-day year) c. compounded quarterly
A) compounded monthly; A = $15,759.579
B) compounded quarterly; A = $15,756.396
What is Compound interest?Compound interest, also known as interest on principle and interest, is the practise of adding interest to the principal amount of a loan or deposit.
We have,
P = $15,000
R= 4.95%
a) Using A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /12[tex])^{12[/tex]
A= 15,000 x 1.0506386172
A = $15,759.579
b) Again, A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /365[tex])^{365[/tex]
c) Again, A = P(1+ r/n[tex])^{nt[/tex]
A = 15,000 (1 + 0.0495 /4.1[tex])^{4.1[/tex]
A = 15, 000 x 1.05042644766
A = $15,756.396
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If (x)=x/2-2 and g(x)=2x2+x-3, find (f+g)(x)
If two circles have the same circumference what do you know about their area
What number is greater 87 or 13.688?
The difference between 29 and a number
Which graph represents the function f(x)=8 1/3x
Answer:
The correct option is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=8^{\frac{1}{3}x}[/tex]
At x=0,
[tex]f(0)=8^{\frac{1}{3}(0)}=8^0=1[/tex]
At x=1,
[tex]f(1)=8^{\frac{1}{3}(1)}=8^{\frac{1}{3}}=2[/tex]
At x=2,
[tex]f(2)=8^{\frac{1}{3}(2)}=8^{\frac{2}{3}}=4[/tex]
At x=3,
[tex]f(3)=8^{\frac{1}{3}(3)}=8^{1}=8[/tex]
The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).
According to these coordinates we can say that the graph of f(x) is represented by option 2.
Therefore correct option is 2.
How many pair of socks a person has to take out from the drawer to be sure to have at least 4 pairs of blue socks?
If R is the midpoint of QS, QR= 8x-51 and RS=3x-6, find QS.
Answer: The required length of QS is 42 units.
Step-by-step explanation: Given that R is the midpoint of QS, where
[tex]QS=8x-51,~~RS=3x-6.[/tex]
We are to find the length of QS.
Since R is the midpoint of the segment QS, so we must have
[tex]QR=RS\\\\\Rightarrow 8x-51=3x-6\\\\\Rightarrow 8x-3x=51-6\\\\\Rightarrow 5x=45\\\\\Rightarrow x=\dfrac{45}{5}\\\\\Rightarrow x=9.[/tex]
Therefore, the length of QS is given by
[tex]QS\\\\=QR+RS\\\\=8x-51+3x-6\\\\=11x-57\\\\=11\times9-57\\\\=99-57\\\\=42.[/tex]
Thus, the required length of QS is 42 units.
In 448,244, how is the relationship between the first pair of 4's the same as the relationship between the second pair of 4's?
The similar relationship between the two pairs of '4's in the number 448,244 is based on their order of magnitude or place value each pair differing by one order of magnitude.
Explanation:In the number 448,244, the relationship between the first pair of 4's is the same as the relationship between the second pair of 4's in terms of their place value or order of magnitude.
The first '4' is in the hundred thousands place and the second '4' is in the ten thousands place, a difference of one order of magnitude (105 vs 104). Similarly, the third '4' is in the hundreds place and the second '4' is in the units place, also a difference of one order of magnitude (102 vs 100). So, despite the fact they are located in different parts of the number, the relationship between each pair of '4's is consistent based on their order of magnitude.
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A school party visit the gift shop. They all want to buy a badge. Your friend needs to get 37 badges from the stock room. The badges come in packs of 10. How many packs does she need?
Answer:
She will need 4 packs.
Step-by-step explanation:
The badges come in packs of 10 but this person only needs 37 badges.
If she buys two packs, she will get 20 badges.
If she buys three packs, she will get 30 badges.
Is she buys four packs, she will get 40 badges.
She will need four packs so she can have 37 badges and there will be 3 remaining badges.
The population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the population in 50 years? (round your answer to the nearest person.)
Build the fraction to an equivalent fraction with the specified denominator. State the numerator. 5/12 = ?/60
What multiplies to 14 and adds to -15?
Problem Page Round 84,548 to the nearest thousand.
The ratio of a number and 6 written as an algebraic expression is
The required algebraic expression is x / 6.
Given that,
In the question, was asked to determine the ratio of the number 6 in the form of algebraic expression.
The algebraic expression consists of constant and variable. eg x, y, z, etc.
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Let the number be x,
The ratio of numbers x and 6,
= x / 6
Here above expression is an algebraic expression, because the x is a variable in the equation.
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3. You are looking into two long distance telephone plans offered by GT&T. The “One Rate 5 cents” plan has a monthly fee of $7.95 and all calls are 5 cents per minute. The “One Rate 7 cents” plan has a monthly fee of $4.95 and all calls are 7 cents per minute. Under what circumstances is one plan less expensive than the other?
a. The "One Rate 5 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 1.5 minutes.
b. The "One Rate 7 cents" plan is less expensive for calls lasting less than 1.5 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 1.5 minutes.
c. The "One Rate 5 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 7 cents" plan is less expensive for calls lasting more than 150 minutes.
d. The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.
Answer:
D.The "One Rate 7 cents" plan is less expensive for calls lasting less than 150 minutes. The "One Rate 5 cents" plan is less expensive for calls lasting more than 150 minutes.
Step-by-step explanation:
let the total number of minutes of calls be x minutes.
Now let us find the total cost incurred in both plan for x mins.
Plan 5 cent : 7.95+0.05x
Plan 7 cent : 4.95+0.07x
Let us find the time at which both the plans will give you same Bill.
Hence
7.95+0.05x=4.95+0.07x
7.95-4.95=0.07x-0.05x
3=0.02x
x=150
Hence at 150th min, both the plan will charge you same cost. Hence the plan giving you less Bill for 100 mins will give you high Bill in 200 mins. Let us calculate the bill incurred by both plan at 100th min.
Plan 5 cent : 7.95+0.05×100=12.95
Plan 7 cent: 4.95+0.07×100=11.95
Hence plan 7 cent is lesser than 5 cent for calls more than 150 mins
Let find which plan cost you cheaper
Item 10 A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.
Charissa is eating out with friends, and it is her turn to pay the gratuity. The bill for the food is $26.50. If she plans to tip at 20%, what should she pay if she doesn’t want to leave pennies on the table?
Whats 12 divided by 3 1/2
3 1/2 = 7/2
12 / 7/2 = 12*2 =24/7 = 3 3/7
q(a+y)=67y+93 help me answer this
how to solve -x+4=-2x-6
-x+4 = -2x-6
add 6 to each side:
-x+10 = -2x
add 1x to each side
10 = -x
divide each side by -1
x = -10
Alisa says it is easier to compare the numbers in Set A (45,760 and 1,025,680) than the numbers in Set B (492,111 and 409,867). What is one way you could construct an argument justifying whether Alisa's conjecture is true?
Jackson has 50 megabytes (MB) of space left on his smartphone. He can download songs that each use 3.5 MB or videos that each use 7 MB. He wants to download at least 10 new media files. Which pair of inequalities specifies the number of song files, x, and the number of video files, y, that Jackson can download
Answer:
[tex]3.5x+7y\leq 50[/tex]
[tex]x+y\geq 10[/tex]
Step-by-step explanation:
Given : Jackson has 50 megabytes (MB) of space left on his smartphone. He can download songs that each use 3.5 MB or videos that each use 7 MB. He wants to download at least 10 new media files.
To find : The pair of inequalities specifies the number of song files, x, and the number of video files, y, that Jackson can download.
Solution :
The number of song files Jackson can download is x
The number of video files Jackson can download is y
→ x song files occupy a space of 3.5 MB per file,
So, number of space occupy by songs files = 3.5x MB
→ y media files occupy a space of 7 MB per file,
So, number of space occupy by video files = 7y MB
→ The total amount of MB used is [tex]3.5x+7y[/tex]
Jackson has 50 megabytes (MB) of space left on his smartphone.
The total amount must be less than or equal to 50 MB,
which can be represented as [tex]3.5x+7y\leq 50[/tex]
Jackson wants to download at least 10 media files,
which means [tex]x+y\geq 10[/tex]
Therefore, The two inequality form is
[tex]3.5x+7y\leq 50[/tex]
[tex]x+y\geq 10[/tex]