Answer:
5/8
Step-by-step explanation:
62.5% = 62.5/100
=0.625
=0.625/1 x 1000/1000
=625/1000
=5/8
Which is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
What is an Expression ?Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.
The given expression is 3(7/5x+4)-2(3/2-5/4x)
[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]
(21/5)x +12 - 3 + (5/2)x
((42+25)/10)x + 9
(67x + 90)/10
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
To know more about Expression
https://brainly.com/question/14083225
#SPJ2
You can buy 5 pounds of grapes for $9.95 .what is a proportion that gives the cost c if you buy 4 pounds of grapes
9.95 / 5 = 1.99
4 x 1.99 = 7.96
$7.96
What is the value of (-14⁰)-2
a -1/196
b 1/196
c 0
d 1
The value of (-14°)-2 is the reciprocal of 196 since the negative exponent indicates that we should take the reciprocal of the base raised to the positive exponent. The correct answer is 1/196.
The question asks for the value of (-14°)-2, which represents a mathematical expression that requires simplification using exponent rules. The notation a-n means that you should take the reciprocal of an, which in this case is the reciprocal of (-14°) squared. When squaring a negative degree value, the square of a negative number is positive, so (-14°)2 = 196°. Therefore, taking the reciprocal of 196° gives us 1/196.
The value of (-14°)-2 is 1/196.
The cost of a candy bar in a vending machine is $0.95. The cost of a bottle of water in the same machine is $1.25. Jamie has $25.00 to spend on candy bars and bottles of water for her friends. She must buy nine candy bars. If b represents the number of bottles of water, which inequality represents all the possible values of b?
Final answer:
The inequality representing all possible values of b, the number of bottles of water Jamie can buy, is b ≤ 13, as Jamie has $16.45 left to spend after buying nine candy bars and each bottle costs $1.25.
Explanation:
The student must buy nine candy bars, which cost $0.95 each. The total cost for the candy bars is 9 * $0.95 = $8.55. Jamie has $25.00 to spend, so after buying the candy bars, she will have $25.00 - $8.55 = $16.45 left for bottles of water. Each bottle of water costs $1.25, so the number of bottles she can buy is represented by the inequality $1.25b ≤ $16.45, where b is the number of bottles of water Jamie can purchase.
Now, let's solve this inequality for b. Dividing both sides of the inequality by $1.25 gives us b ≤ 13.16. Since Jamie can't buy a fraction of a bottle, she must buy at most 13 bottles of water.
Therefore, the inequality representing all possible values of b (i.e., the number of bottles of water Jamie can buy) is b ≤ 13.
A proportional relationship between the number of pounds of carrots (x) and the price in dollars (y) is graphed, and the ordered pair (8, 6) is on the graphed line. Part A: What is the price of 1 pound of carrots? Show your work. (8 points)
Answer:
$0.75
Step-by-step explanation:
We have been given that a proportional relationship between the number of pounds of carrots (x) and the price in dollars (y).
We can represent this information as: [tex]y=kx[/tex].
We are also told that the ordered pair (8, 6) is on the graphed line. Let us substitute x= 8 and y= 6 in our proportional equation to find the constant of proportionality.
[tex]6=k*8[/tex]
[tex]k=\frac{6}{8}[/tex]
[tex]k=\frac{3}{4}[/tex]
Now let us substitute k=3/4 and x=1 in our proportionality equation.
[tex]y=\frac{3}{4}*1[/tex]
[tex]y=\frac{3}{4}[/tex]
[tex]y=0.75[/tex]
Therefore, the price of 1 pound of carrots will be $0.75.
Can someone please help
Answer:
3 Bookmarks
Step-by-step explanation:
1) Find the remaining money which is 0.96
2)Divide 0.96 evenly into 3 people, you should get O.32
3) If each bookmark costs 0.10, and each person gets 0,32 the greatest number of bookmarks they can get is 3.
which of the following is equal to the fraction below (5/9)^8
Answer:
the answer is D because both are to the power of 8
Step-by-step explanation:
Answer:
Option D is correct
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Step-by-step explanation:
[tex]\text{Given the fraction }(\frac{5}{9})^8[/tex]
we have to choose the correct option which is equivalent to above.
As we know
[tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]
Put a=5, b=9, x=8
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Therefore, option D is correct
How many 1/2’a are in 7
Answer:
There are 14 halves in seven.
Step-by-step explanation:
7(1/2)=14
7(2)=14
OR, you could just count by halves until you reach 7, but that takes a while. (;
Mr. Mateo ordered several copies of a book that weighs 3/5 of a pound each along with some other school supplies for his classroom. If the total weight of the box that contains the supplies was 10 pounds, what is the maximum number of copies of the bookthat Mr. Mateo could have ordered
Answer:
It's 16 I just did the same question on a quiz
If the total weight of the box that contains the supplies was 10 pound.
The maximum number of copies of the book that Mr. Mateo could have ordered is 16.
Given:
The number of copies of a book = [tex]\frac{3}{5}[/tex] pound
The total weight of the box = 10 pounds
According to question,
[tex]\frac{3}{5} x<10\\3x<50\\x<\frac{50}{3}\\x<16.66[/tex]
let: x = 16
Therefore, the maximum number of copies of the book that Mr. Mateo could have ordered is 16.
For more information:
https://brainly.com/question/1933420
How do you graph square roots
Answer: Simplify the number in the square root.
Step-by-step explanation: For example, √25 can be simplified to 5 because half of 25 is 5. If x=5, graph this on the x-axis or horizontal line on the graph. Another example, √2 can be simplified to approximately 1.414. To graph this, you can use a graphing tool for accurate representation, or create a graph and place a dot right before 1.5 (in between 1 and 2).
HELP RIGHT AWAY PLEASE!!!!
The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 0 and the ordered pair 0, 4. Another straight line labeled B joins the ordered pair 0, 1 and the ordered pair 5, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(1, 2) is the solution to line A but not to line B.
(1, 2) is the solution to both lines A and B.
(0, 1) is the solution to both lines A and B.
(0, 1) is the solution to line A but not to line B.
Answer:
(1,2) is the solution to both lines a and b
Step-by-step explanation:
You find the slope using 2 point and do y2-y1/x2-x1 . To create the equations for the two lines you do y=mx+b where m=slope and b=y-intercept.
A jar contains 133 pennies. A bigger jar contains 1 2/7 times as many pennies. What is 5he value of the pennies in the bigger jar
Answer:
The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value
Step-by-step explanation:
Is 42 and 105 relatively
prime
Answer:
No.
Step-by-step explanation:
42 has the following prime factors: 2, 3, 7
105 has prime factors: 3, 5, 7
Both prime factors 3 and 7 divide 42 and 105. If 42 and 105 were relatively prime (co-prime), the set of prime factors that divide both would be empty.
Need help please help me
y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.
Select any two x values and calculate y values:
[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=0\to(0,\ 2)\\\\for\ x=-4\to y=\dfrac{1}{2}(-4)=-2+2=0\to(-4,\ 0)[/tex]
[tex]y=x+5\\\\for\ x=0\to y=0+5=5\to(0,\ 5)\\\\for\ x=-5\to y=-5+5=0\to(-5,\ 0)[/tex]
Look at the picture.
The solution of the system of equations is the intersection point of the line.
Answer: (-6, -1) → x = -6 and y = -1what is the ratio of triangles to circle 3 trangle 2 circle
Answer:
3:2
Step-by-step explanation:
Triangle:circle
3 triangle:2 circle
combine like terms to simplify the expression. 2x+4y-7x+10y+8
Answer:
-5x + 14y + 8
Step-by-step explanation:
2x + 4y - 7x + 10y + 8
Combine 2x and -7x because they are both being multiplied by x.
-5x + 4y + 10y + 8
Combine 4y and 10y because they are both being multiplied by y.
-5x + 14y + 8
sarahs volleyball team won 12 games of their first 18 games. if the continue to win at this rate, how many games will they lose if they play 36 games
Answer:
They lost 12 games.
Step-by-step explanation:
Set up a proportion.
12/18 = x/36
36 x 12 = 432
432/18 = 24
Because 18 represents how many games they won, the 24 also represents how many games they won. Therefore, you must subtract to find the amount of times that they lost.
36 - 24 = 12
Answer:
they lost 12 games
Step-by-step explanation:
they lost 12 games
Find the missing lengths of the sides
Answer: A
Step-by-step explanation: sin45(9 radical 2)
What algebraic expression is 5+3(2x-7)=5+6x-21
Analyze the reflectional symmetry of the regular polygons. The square has -fold reflectional symmetry. The regular octagon has -fold reflectional symmetry.
Answer:
The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.
Step-by-step explanation:
For a square,
There are two lines of symmetry along two diagonals and
two lines of symmetry along midpoints of two pairs of opposite sides.
Therefore, there are 4 lines of reflectional symmetry in total.
For a regular octagon,
There are four lines of symmetry along four diagonals and
four lines of symmetry along midpoints of four pairs of opposite sides.
Therefore, there are 8 lines of reflectional symmetry in total.
Final answer:
A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.
Explanation:
Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.
For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.
On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.
Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.
recall that the slope, namely the average unit rate of change, is rise/run.
so, what's the slope for the function in the table? well, we can simply pick any two points and get it, or just use the first point rise of 8 and a run of 7, gives us a slope of 8/7 or 1⅐.
now, let's take a peek at the lines, they all have a "rise" of 6, notice they're all lying on the y = 6 line horizontally.
1)
rise = 6, run = 2, slope 6/2 = 3.
well, 3 is more than 2, so no that one.
2)
rise = 6, run = 3, slope = 6/3 = 2.
well 2 = 2, so no that one either.
3)
rise = 6, run = 4, slope 6/4 = 3/2.
3/2 is actually larger than 8/7 and less than 2, you can check. so ✔
4)
rise = 6, run = 5, slope = 6/5.
6/5 or 1⅕ is more than 8/7, and is clearly less than 2, so ✔
5)
rise = 6, run = 6, slope = 6/6 = 1.
well, needless to say 1 is less than 2 but is less than 8/7, recall 8/7 is actually 1⅐.
Answer:
View the picture for your answer!
Have a wonderful day:))
Betty can drive her car 400 miles at a steady speed using 20 gallons of gasoline. at this rate how many gallons of gas will she use to travel 1600 miles
Answer:
80 gal
Step-by-step explanation:
20 gal takes her 400 mi
Vol. of gas = 1600 ×20/400
Vol. of gas = 1600 ×1/20
Vol. of gas = 80 gal
Betty will use 80 gal of gas.
47 POINTS!
PLEASE HELP! (SHOW YOUR WORK)
Answer:
2. No it is not direction variation
3. This is direct variation with the constant being 2
Step-by-step explanation:
The equation for direct variation is y=kx
2. 8y = 3x+1
Divide each side by 8
8y/8 = 3x/8 + 1/8
y = 3/8 x + 1/8
We are adding 1/8 to each time so it is not direct variation
3. 12y = 24x
Divide each side by 12
12y/12 = 24x/12
y = 2x
This matches y= kx, where k=2
This is direct variation with the constant being 2
What is the total surface area
We have two right triangles and three different rectangles.
The formula of an area of a right triangle:
[tex]A_T=\dfrac{1}{2}l_1l_2[/tex]
l₁, l₂ - legs
We have l₁ = 20cm and l₂ = 21cm. Substitute:
[tex]A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2[/tex]
The formula of an area of a rectangle:
[tex]A_R=lw[/tex]
l - length
w - width
We have:
rectangle #1: l = 22cm, w = 29cm
[tex]A_{R1}=(22)(29)=638\ cm^2[/tex]
rectangle #2: l = 22cm, w = 21cm
[tex]A_{R2}=(22)(21)=462\ cm^2[/tex]
rectangle #3: l = 22cm, w = 20cm
[tex]A_{R3}=(22)(20)=440\ cm^2[/tex]
The total Surface Area of the triangular prism:
[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2[/tex]
please help!! Which shape is a continuous line of equal distance from its center?
Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much
Step-by-step explanation:
Travis is sewing a pillow for his Home Arts class. The pillow will be made from 2 identical rectangles. Each rectangle is 1 1/2 feet wide and 1 3/4 feet long. How many square feet of material is used in the sewing of the pillow?
A.2 3/8 sq. feet
B.2 5/8 sq. feet
C.5 1/4 sq. feet
D.6 1/2 sp. feet
Answer:
The answer is A.
Step-by-step explanation:
If the Greatest Common Factor of L and M is 6, write the expression for the Least Common Multiple of these numbers.
Answer:
[tex]\frac{(L x M)}{6}[/tex]
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.
The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.
We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.
As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.
We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.
[tex]\frac{(L x M)}{6}[/tex]
1. find the difference 7 1/4 - 3 1/2 =
a. 3 3/4
b. 4 3/4
c. 3 1/2
d. 4 1/2
2. find the product and write it in simplest form 3/8 x 2/3
a. 9/16
b. 6/24
c. 2/8
d. 1/4
3. find the product and write it in simplest form 2 3/8 x 1 2/3
a. 2 6/24
b. 3 23/24
c. 3 3/4
d. 95/8
4. perform the division and write it in simplest form 7/10 ÷ 3/5
a. 35/30
b. 6/7
c. 21/60
d. 1 1/6
Answer:
1. a
2. d
3. b
4. it would be 7/6 NOT 6/7
Step-by-step explanation:
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 ft/s against the walkway and 5 ft divided by s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Answer: The traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
Step-by-step explanation:
Given: A traveler is walking on a moving walkway in an airport.
Let 't' be the traveler's speed off the walkway and 'w' be the speed of walkway.
Then the traveler's ground speed against the walkway (t-w)= 1 ft/s
And the traveler's ground speed with the walkway (t+w)= 5 ft/s
thus we get the following equations [tex]t-w=1..........(1)\\t+w=5.............(2)[/tex]
Adding (1) and (2), we get
[tex]2t=6\\\Rightarrow\ t=3[/tex]
Subtract (2) from (1), we get
[tex]2w=4\\\Rightarrow\ w=2[/tex]
Therefore, the traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
The Carson’s are on a road trip they paid $62.70 for 16 1/2 gallons of gasoline
Part 1-Find the price of gasoline per gallon show your work
Part 2-Give an example of a cost and amount that would make the gasoline have a rate of $3.49 per gallon
Answer:
$3.92 per gallon
10 gallons of gas at $3.49 a gallon will cost $34.90
Step-by-step explanation:
To find the price per gallon, we take the total cost, and divide by the number of gallons. I will change 16 1/2 to a decimal for ease of math calculations.
16 1/2 = 16.5
cost/gallons
$62.70/16.5
3.91875
Since we are working with money, we round to the nearest cent
$3.92 per gallon
To find the total cost, we multiply the cost per gallon times the number of gallons. We have a cost per gallon of $3.49. If we multiply by 10 gallons
cost = $3.49 * 10
$34.90
10 gallons of gas at $3.49 a gallon will cost $34.90