The unit rate is 2 pounds per gallon.
Henry's likely error could have been that he multiplied fractions instead of dividing.
Given the rate 1/3 / 1/6 pound per gallon, this can be written in the unit rate by dividing 1/3 by 1/6 pound per gallon.
So, 1/3 divided by 1/6 can be written as [tex]\frac{1/3}{1/6}[/tex]
which further can be simplified as [tex]\frac{1}{3}[/tex] × [tex]\frac{6}{1}[/tex]
and the answer comes out to be 2
Hence, the unit rate is 2 pounds per gallon.
Henry's likely error could have been that he multiplied instead of dividing. That is, he multiplied 1/3 by 1/6, Such that he gets
Hence, the 1/27 pound per gallon he got.
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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons.While being inflated, 1/20 of the red balloons, 1/12 of the green balloons, and 1/36 of the yellow balloons popped. The remaining balloons were used as party decorations. What part of all the balloons Marsha purchased to decorate the party?
Hello,
Do these look correct?
3. Given: f(x) = [(3)^-x ] – 2. Find f(-2).
[3^-(-2)] - 2 = 9 - 2 = 7
f (-2) = 7
4. Given h(x) = 4 * 5^(x - 2) – 3. Find h(4).
4 *5^(4-2) - 3 = 4*5^2 - 3 = 4*25 -3 = 97
h(4) = 97
Thank you so much
Answer:
Yes they do :)
(o´▽`o)ﾉ x
(5x-17)+(3x-11)=180 degrees
Step-by-step explanation:
5x+3x-17°-11°=180°
8x-28°=180°
8x=180°-28°
8x=152°
[tex] \frac{8x}{8} = \frac{152}{8} \\ x = 19[/tex]
Answer:
x=26
Step-by-step explanation:
since we are adding, you start by combining like terms. x's with x's and #'s with #'s. that leaves you with 8x-28=180. Your next step is to get x all by itself so you move the -28 to the other side by adding 28 to both parts. that leaves you with 8x=208. now you still have to get x by itself and right now its being multiplied with the 8 so to get rid of it you divide by 8 on both sides and that leaves you with x=26.
Complete the inequality below to describe the
domain of the graph shown.
Domain:
DONE
Complete the inequality below to describe the
range of the graph shown.
Range:
≤y <5
DONE
Intro
-5
5
y
5
X
Answer:
[tex]Domain: \;\boxed{-4 } < x \le 4\\\\Ramge: \boxed{-2} \le y < 5[/tex]
Step-by-step explanation:
Domain
Domain is the set of all valid x values for the function
Looking at the graph we see that the function x values go from x- 4 to x = +4.
Note the unfilled circle at x = -4, y = 5. This means that this point is not included in any set of values that we intend tp find. It will represent a < or > inequality.
A filled circle means that value is included
So the domain of the function is -4 < x ≤ 4 (note that -4 is not included in the domain
Range
The range is the set of all y values for the entire domain. Basically it is defined using the min and max values that y can take
The minimum y value occurs at x = 4 and y is -2 (this is included because of the filled circle)
The max value occurs at x = -4 and the value of y here is 5 (5 is not included)
Therefore the range is -2 ≤ y < 5
A truck's position relative to a Carr's position is 60 feet. The car and the truck move in the same direction, but the car moves 5 feet per second faster for 8 seconds. What operation could be used to find the truck's relative position after 8 seconds?
In linear equation ,The truck's relative position with respect to the car is 100 feet
What is linear equation ?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.If the truck is moving at a seed "V" then its position after 8 seconds is going to be:
XT = V* t = V * 8 = 8 V
The car, which is initially 60 feet ahead of the truck and starts moving at 5 m/s faster than the truck, would have a speed given by: V + 5
And its position (relative to the truck's) would be:
XC = 60 + (V + 5) * t = 60 + (V + 5) * 8 = 60 + 40 + 8 V = 100ft + 8 V
then the position of the truck relative to that of the car would be given by the difference:
XT - XC = 8 V - (100 +8 V) = 8 V - 8 V - 100ft = -100 feet
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let's consider an economy in which firms spend $125 on machinery used in production and home buying totals $200. in addition, people buy $20 in stocks and bonds and businesses add $70 to their inventories.
given this information, calculate economic investment.
The economic investment will be $415.
How to calculate the investment?It should be noted that an investment is simply used to generate further wealth.
Therefore, the investment will be the addition of the values given. This will be:
= $125 + $200 + $20 + $70
= $415
Therefore, the economic investment will be $415.
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Geometry homework… the questions after the photo are “9. Find the value of angle RIG” and “10. Find the value of angle ZIM” If you can seriously help me it would mean a lot. Thanks
Applying the vertical angles theorem, we have:
x = 29
z = 13
How to Apply the Vertical Angles Theorem?Based on the vertical angles theorem, the vertical angles AIZ and GIM are congruent to each other.
Therefore:
7. m<AIZ = m<GIM
Substitute
3x - 56 = x + 2
3x - x = 56 + 2
2x = 58
x = 29
8. 4z + 7 + x + 2 = 90 (complementary angles)
Plug in the value of x
4z + 7 + 29 + 2 = 90
4z + 38 = 90
4z = 90 - 38
4z = 52
z = 52/4
z = 13
Therefore, applying the vertical angles theorem, we have:
x = 29
z = 13
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Solve for x
please i really need this i will give brainly
Answer:
x = 19
Step-by-step explanation:
The two angles shown here are congruent, so we will set them equal to each other. We will solve for x in the equation:
4x + 18 = 6x - 20
Subtract 4x from both sides:
18 = 2x - 20
Add 20 to both sides:
38 = 2x
Divide by 2 on both sides:
19 = x
So, the answer is “x = 19”
Hope this helps you!
The slope of line a is 7. The slope of line b is −1/7 .
Which statement is true?
Options:
The lines are neither perpendicular nor parallel
The lines are perpendicular.
The lines are parallel.
Answer:
Step-by-step explanation:
We know that, If two line are perpendicular to each other wit slopes [tex]m_{1}[/tex] and [tex]m_{2}[/tex] them [tex]m_{1} *m_{2}=-1[/tex]
Hence,
[tex]7*(-1/7)=-1[/tex]
This shows that these two line are perpendicular to each other.
5. Write an equation with:
No solution:
Infinite solutions:
6. Bobby is going bowling. It costs $7.00 per game plus a one time fee of $10 for the
shoe rental. How many games can he play if he only has $59 dollars.
Define Variable___
Equation___
Solution___
Answer:
привет как вы это t6767
Step-by-step explanation:
Assignment Instructions
Martin Berk began an accounting firm called Berk’s Accounting on May 1 of the current year. Record the following May transactions by making the appropriate entries in the general journal. Next, prepare a trial balance as of May 31.
Part A
Martin invested $20,000 cash and a computer valued at $2,000.
Part B
Purchased $6,000 of office furniture from a supplier on credit.
Part C
Completed accounting work for a client and received $2,000 cash in full payment.
Part D
Paid the supplier of the office furniture 50% of the balance owing.
Part E
Completed $3,000 of accounting work for a client on credit.
Part F
Martin withdrew $3,500 cash from the business for personal use.
Part G
Received $2,000 cash as partial payment for the accounting work completed for the client in E.
Part H
Paid $1,200 cash for the secretary’s salary.
Answer:A and C
Step-by-step explanation::
The trial Balance as of May 31 is given in the table.
What is a trial balance?The trial balance shows the total debits and credits for each account and ensures that they balance.
We have,
Part A:
Cash 20,000
Computer 2,000
Martin, Capital 22,000
Part B:
Office Furniture 6,000
Accounts Payable 6,000
Part C:
Cash 2,000
Accounts Receivable 2,000
Part D:
Accounts Payable 3,000
Cash 1,500
Notes Payable 1,500
Part E:
Accounts Receivable 3,000
Accounting Revenue 3,000
Part F:
Martin, Withdrawals 3,500
Cash 3,500
Part G:
Cash 2,000
Accounts Receivable 2,000
Part H:
Salary Expense 1,200
Cash 1,200
Thus,
The trial Balance as of May 31 can be made as given in the table added.
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What is the answer to 8.118 divided by 0.615
Answer:
13.2
Hope this helps :)
Step-by-step explanation:
8.118 ÷ 0.615 = 13.2
You can also solve it by using long division.
Check:
13.2 × 0.615 = 8.118 ✓
-5x-4=7(-7-7x)-x what would be the solution for x? and what steps would I use to solve it
the answer to x=45/45, x=1 We employ the factorization method in this.
What is the method of factorization?Factorization, also known as factoring, is the mathematical process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc. You will mostly learn this idea in your lower secondary classes from grades 6 to 8.
based on the provided statement
How would I approach solving it?
-5x-4=7(-7-7x)-x
-5x-4=-49-49x-x
49-4=-49x-x+5x
45=45x
so x=45/45
x =1
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Find f(- 3), f(0) and f(3) for the following function.
f(x) = 3x
f(- 3) = ?
For f(x)= 3x required values of the function are f(-3)=-9, f(0)=0, f(3)=9
What is the value of a function?
A function gives exactly one output to each input . f(2) means that we should find the value of our function when x equals 2. f(x) is the value of the function
Given function is f(x)= 3x
Then f(-3) = 3(-3) =-9
f(0) = 3(0) =0
f(3) = 3(3) =9
Therefore, values of the function at x = -3,0,3 are -9,0,9 respectively
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Write a slope-intercept equation for a line that passes through (-2,1) and (2,-7).
Answer:
y = -2x -3
Step-by-step explanation:
slope intercept form: y=mx+b
find slope or m:
m= y2-y1 / x2-x1
after plugging in values.. u get..
m= -2
further plug in one point in the slope intercept form.
you get ...
b= -3
Final plug into equation:
y = -2x -3
Find the coordinates of A if M(6, -1) is the
midpoint of AB, and B has the coordinates
(8, -7)
The coordinates of A are (4,5).
Given, the mid-point of AB is M = (6 , ₋1) and
the coordinates of B is (8 , ₋7)
we know that midpoint formula is:
(x₁ ₊ x₂/2 , y₁ ₊ y₂/2) = M(x , y)
let the points be:
A (x, y) = (x₁ , y₁)
B (8 , ₋7) = (x₂ , y₂)
mid point M = (6 , ₋1)
(x₁ ₊ x₂/2 , y₁ ₊ y₂/2) = M(x , y)
substitute the above values in the formula:
(x ₊ 8/2 , y ₊ (₋7)/2) = (6 , ₋1)
x ₊ 8/2 = 6 and y ₋ 7/2 = ₋1
x ₊ 8 = 12 and y ₋ 7 = ₋2
x = 12 ₋ 8 and y= ₋2 ₊ 7
x = 4 and y = 5
hence we get the coordinates of A as (4 , 5).
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D. Highway I-10 is having an extension added
on. It will then be 3,000 miles long. How long
is the extension?
I-10 2,460
The extension of the distance applied on the road is 540 miles.
According to the statement
We have to find that the length of the extension.
So, For this purpose, we know that the
The distance of an object can be defined as the complete path travelled.
From the given information:
Highway I-10 is having an extension added on. It will then be 3,000 miles long. How long is the extension? I-10 2,460
Then
From the given information,
Length of road after extension is = 3,000 miles
Length of road before extension is = 2,460 miles
Then
extension applied on the road = Length of road after extension - Length of road before extension
extension applied on the road = 3000 - 2460
extension applied on the road = 540.
So, The extension of the distance applied on the road is 540 miles.
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HELP ME OUT PLEASE!!!!!!
Answer:
I think its -6
Step-by-step explanation:
Hope it helps! =D
I really need to get this done. I'll mark brainliest.
A)Draw the image of under the dilation with scale factor 3 and the origin as the center of dilation. Label the image . Make sure to include the coordinates of A’, B’, and C’.
B)Draw the image of under the dilation with scale factor and the origin as the center of dilation. Label the image . Make sure to include the coordinates of D’, E’, and F’.
The image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.
Using dilation rules, the dilated triangle is given at the end of the answer. The coordinates of the vertices are as follows:
A'(-6,6), B'(-3,0), C'(3,6).
The rule of the dilation is to dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x,y) -> (ax, ay).
The coordinates of the vertices of ABC are given as follows:
A(-2,2), B(-1,0), C(1,2).
After a dilation with a scale factor of 3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-6,6), B'(-3,0), C'(3,6).
These coordinates are derived multiplying the coordinates of A, B and C by 3.
The image of the triangle is given at the graph at the end of the answer.
Hence, for the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.
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If m∠FDE = (3x−15)° m∠FDE = 3x-15° and m∠FDB = (5x+59)°, find the value of x such that ∠FDE and ∠FDB are supplementary.
The value of x is x = 18.25
How to determine the value of x?The angles are given as
m∠FDE = 3x-15° and m∠FDB = (5x+59)°
The angles are supplementary angles
FDE + FDB = 180
This gives
3x - 15 + 5x + 59 = 180
Evaluate the like terms
8x = 146
Divide by 8
x = 18.25
Hence, the value of x is x = 18.25
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Determine the ammount of fence needed to enclose a rectangular garden with length 19 feet and width 13 feet
Answer: 64 feet of fence
Step-by-step explanation:
To find the amount of fence needed, calculate the perimeter of the garden
P=perimeter of rectangle. l=length. w=width
P=2l+2w
P=2(19)+2(13)
P=38+26
P=64 feet
Dot arranges flowers into vases of roses and daisies. If there are 100 roses and 60 daises. what is the greatest number number of flowers in each group?
Taking into account the greatest common divisor, the greatest number of flowers in each group is 20.
Greatest common divisorThe greatest common divisor is the largest number that exactly divides two or more numbers at the same time.
To calculate the greatest common multiple, follow these steps:
Decompose each number into prime factors (numbers that are only divisible by themselves or by the number 1).Next, the factors common to the numbers are chosen.Next, in each of the commons, the factor with the smallest exponent is chosen.Finally, the chosen factors are multiplied.In summary, the common factors (those that are repeated) are multiplied with their smallest exponent.
Greatest number of flowers in each groupIn this case, there are 100 roses and 60 daises. To calculate the greatest number of flowers in each group, you have to calculate greatest common divisor.
Decomposing each number into prime factors:
100= 2×2×5×5= 2²×5²60= 2×2×3×5= 2²×3×5The greatest common divisor between 60 and 100 is calculated as 2²×5, which results 20.
This means that the greatest number of flowers in each group is 20.
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Please help with this assignment
The equation that can be used to determine the cost of one drink is 2x = 6.09
The sum of the prices for the movie tickets, refreshments, and voucher represents the total sum that Stephen and Paul will be required to pay.
Therefore,
The total amount paid is equal to the cost of two tickets + cost of the two drinks - coupon
So,
( 11 × 2 ) + ( x × 2 ) - 5 = 29.18
22 + 2x - 5 = 29.18
Subtracting 22 from each side of the equation.
22 + 2x - 5 - 22 = 29.18 - $22
2x - 5 = 7.18
Adding 5 on each side of the equation.
2x - 5 + 5 = 7.18 + 5
2x = 12.18
Now, divide each side of the equation by 2.
x = 6.09
Hence, the cost of one drink is $6.09
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The circle below, centred at O, has a radius of 12 cm.
BC = 7 cm.
Work out the length x to 1 d.p.
Fully justify your answer.
Answer:
i am not sure about my answer
The set of all real numbers x that satisfies -3
[-3, 14)
Please select the best answer from the choices provided
true
flase
The set of all real numbers x that satisfies [-3, 14) are :
-3,-2.5, -1.4, -2,-1,0,1, 1.7, 2,π,.....13.
What is Rational number ?
In mathematics, a rational number is any number that can be written as a fraction, in which the numerator (the top number) and the denominator (the bottom number) are both integers, and in which the numerator is not equal to zero. In other words which can be written in p/q form.
Due to the fact that the rational numbers as well as the irrational numbers can be added together, we can derive real numbers. This means that all real numbers are not rational numbers, since they contain irrational numbers as well.
The given set of real number is [-3 , 14) which implies that -3 is included and 14 is excluded in the given set of numbers and it is find the values of x that satisfy the set [-3 , 14) that is :
x includes all the values which can be represented in p/q form for example :
-3,-2.5, -1.4, -2,-1,0,1, 1.7, 2,π,.....13
which includes negative both rational number, whole numbner, integers, natural numbers.
Therefore, The set of all real numbers x that satisfies [-3, 14) are :
-3,-2.5, -1.4, -2,-1,0,1, 1.7, 2,π,.....13.
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<(1,000)
5. 1 × 1 + 9 × (1) + 8 ×(₁0) + 1 ×
Answer:
3
Step-by-step explanation:
Syop doing homework and gdt a life
in a classroom there are 56 boys and 72 girls, find the ratio of girls to the total number of students.
Answer: [tex]\frac{9}{16}[/tex]
Step-by-step explanation:
We need to find the ratio of girls to the total number of students. That means our ratio is going to be 72 (the number of girls) over 56+72 (boys + girls, the total number of students).
When you add 56+72, you'll get 128 in the denominator. Continuing to simplify the fraction, you'll end up with:
[tex]\frac{72}{128}[/tex] = [tex]\frac{9}{16}[/tex]
Depending on what format your teacher wants, this can be written as [tex]\frac{9}{16}[/tex] or 9:16.
Round to the nearest tenth of a percent ________% of 8 gross is 0.04 gross.
Select one:
A. 50.0
B. 0.5
C. 200.0
D. 5.0
Answer:
B. 0.5
Step-by-step explanation:
0.04 ÷ 8 = 4/800
4/800 = 1/200 = 0.5
Eduardo, Martin, & Becky each saved $150 from
their summer jobs. They have decided to donate
a portion of their savings to a charity. Eduardo
donated 2/7 of his savings, Martin gave 2/9, &
Becky donated 2/5. To the nearest penny, how
much should the charity expect?
A. $33.33
B. $42.86
C. $60.00
D. $136.19
E. $180.00
Step-by-step explanation:
much should the charity expect?
A. $33.33
B. $42.86
C. $60.00
D. $136.19
E.
The charity expects a donation of D. 136.19 dollars from Eduardo, Becky, and Martin.
What is a fraction?Fractions describe how many parts of something is there to the total part.
To obtain how much each individual donated we have to multiply the fraction of donation to the amount of money they saved and take the sum.
Eduardo donated 2/7 of his savings which is (2/7)×150 dollars.
= 42.85 dollars.
Martin donated 2/9 of his savings which is (2/9)×150 dollars.
= 33.33 dollars.
Becky donated 2/5 of his savings which is (2/5)×150 dollars.
= 60 dollars.
∴ The total money they donated is ( 42.85 + 33.33 + 60 ) dollars.
= 136.18 dollars.
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Dave Bowers collects U.S. gold coins. He has a collection of 43 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $640. how many of each denomination does he have?
Answer:
There are 22 $10 coins and 21 $20 coins.
Step-by-step explanation:
Let x = the number of $10 coins
Let y = the number of $20 coins
You have two unknows so you need two equations.
x + y = 43
10x + 20y = 640.
Rewrite the first equation solving for x
x + y = 43
x = 43 - y Substitute 43 - y in for x in the second equation.
10x + 20 y = 640
10(43 - y) + 20y = 640
430 - 10y + 20y = 640 Subtract 430 from both sides of the equation
-10y + 20y = 210 Combine the y's
10y = 210 Divide both sides by 10
y = 21 This is the number of $20 coins.
Substitute 21 in for y in either of the original equations to solve for x
x + 21 = 43 Subtract 21 from both sides
x = 22 This is the number of $10 coin.
Check:
Substitute in 21 for y and 22 for x
x + y = 43
21 + 22 = 43
43 = 43 checks
10x + 20y = 640
10(22) + 20(21) = 640
220 + 420 = 640
640 = 640 Checks
