Answer:
(a) 65 gallons per minute
(b) 280 gallons
(c) 8080 gallons
(d) 150 minutes.
Step-by-step explanation:
Water is filled up by pumps into a tank at a constant rate.
The volume of water in the tank V, in gallons, is given by the equation
V(t) = 65t + 280 ......... (1), where t is the time, in minutes.
(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)
(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)
(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)
(d) The tank has a capacity of 10000 gallons of water.
So, if the tank starts to overflow after t minutes, then
10000 = 65t + 280
⇒ 65t = 9720
⇒ t = 149.53 minutes ≈ 150 minutes (Answer)
Final answer:
The rate at which water is being pumped into the tank is 65 gallons per minute, the tank initially had 280 gallons of water, after two hours the volume will be 8,080 gallons, and the pumps will turn off after approximately 150 minutes when the volume reaches 10,000 gallons.
Explanation:
The water tank problem can be analyzed step by step based on the given linear equation v(t) = 65t + 280, which describes the volume V of water in gallons as a function of time t in minutes.
(a) Rate of Water Being Pumped
The coefficient of t in the equation represents the rate at which water is being pumped into the tank. Therefore, the water is being pumped at a constant rate of 65 gallons per minute.
(b) Initial Volume of Water
The constant term in the equation, 280, represents the volume of water that was in the tank when the pumps were turned on. This means the tank initially had 280 gallons of water.
(c) Volume After Two Hours
To convert two hours to minutes, we multiply by 60 minutes per hour, giving us 120 minutes. Plugging this value into the equation gives us v(120) = 65(120) + 280 = 7,800 + 280 = 8,080 gallons. So, after two hours, the volume of water in the tank would be 8,080 gallons.
(d) Time to Reach 10,000 Gallons
To find the time when the volume reaches 10,000 gallons, we set the equation equal to 10,000 and solve for t: 10,000 = 65t + 280. Subtracting 280 from both sides gives us 9,720 = 65t, and dividing both sides by 65 gives us t ≈ 149.54 minutes. To the nearest minute, the pumps will turn off after approximately 150 minutes.
Select all statements that are true about the linear equation.
y= 1/3x + 2
The graph of the equation is a single point representing one solution to the equation.
The point (9,5) is on the graph of the equation.
The graph of the equation is the set of all points that are solutions to the equation.
The point (-3,-1) is on the graph of the equation.
Answer:
The point (9,5) is on the graph of the equation
The graph of the equation is the set of all points that are solutions to the equation
Step-by-step explanation:
we have the linear equation
[tex]y=\frac{1}{3}x+2[/tex]
This is the equation of the line in point slope form
where
the slope is [tex]m=\frac{1}{3}[/tex]
the y-intercept is [tex]b=2[/tex]
Remember that
If a ordered pair is on the graph of the linear equation, then the ordered pair must satisfy the linear equation
The graph of the equation is the set of all points that are solutions to the equation
Verify each statement
case 1) The graph of the equation is a single point representing one solution to the equation
The statement is false
Because the graph of the equation is the set of all points that are solutions to the equation
case 2) The point (9,5) is on the graph of the equation
The statement is true
Because
For x=9, y=5
substitute the value of x and the value of y in the linear equation
[tex]5=\frac{1}{3}(9)+2[/tex]
[tex]5=3+2[/tex]
[tex]5=5[/tex] ----> is true
so
the ordered pair satisfy the linear equation
therefore
The point is on the graph of the equation
case 3) The graph of the equation is the set of all points that are solutions to the equation
The statement is true
case 4) The point (-3,-1) is on the graph of the equation
The statement is false
Because
For x=-3, y=-1
substitute the value of x and the value of y in the linear equation
[tex]-1=\frac{1}{3}(-3)+2[/tex]
[tex]-1=-1+2[/tex]
[tex]-1=1[/tex] ----> is not true
so
the ordered pair not satisfy the linear equation
therefore
The point is not on the graph of the equation
Solve the equation using the zero-product property.
(x - 3)(5x - 6) = 0
Answer:
x = 3 or x = 6/5
Step-by-step explanation:
The zero product property (or rule) tells you the product will only be zero if one (or more) of the factors is zero. Here, that means the solutions are values of x such that ...
x -3 = 0 ⇒ x = 3
5x -6 = 0 ⇒ x = 6/5
A box of laundry detergent contains 35 cups. It takes 1 1/4 cups per load of laundry.
Part A. Write an equation to represent how many loads x you can wash with one box.
Part B. How many loads can you wash with one box.?
Part C. How many loads can you wash with 3 boxes.?
Answer:
I don't know nan molla
Step-by-step explanation:
For example, Kino had a good opportunity to barely have a better life and he could have done anything to save his family but instead of doing that he refused to take the 1500 pesos.
Which of the following best defines 2 to the power of 2 over 3 ? (1 point) Cube root of 4 Square root of 4 Cube root of 2 Square root of 2
Answer:
C) [tex]\sqrt[3]{2}[/tex]
It is C because [tex]\sqrt[3]{2}=1.2599[/tex] which is the closest to [tex]1\frac{1}{3}[/tex]. Because [tex]\frac{2^{2} }{3}=1\frac{1}{3}[/tex].
Answer:
C) Cube root of 2
Step-by-step explanation:
Could someone help me with this?
Answer:
1. 18.74%
2. 33.34%
3. 45.5%
4. 20%
5. 33.11%
6. 16.38%
Step-by-step explanation:
1. For Shoes, the actual price is $79.99 and the selling price is $65.00.
The discount is [tex]\frac{79.99 - 65}{79.99} \times 100 = 18.74[/tex]%.
2. For 12 pack og golf balls, the actual price is $29.99 and the selling price is $19.99.
The discount is [tex]\frac{29.99 - 19.99}{29.99} \times 100 = 33.34[/tex]%.
3. For Exercise bike, the actual price is $1099 and the selling price is $599.
The discount is [tex]\frac{1099 - 599}{1099} \times 100 = 45.5[/tex]%.
4. For Basketball, the actual price is $49.99 and the selling price is $39.99.
The discount is [tex]\frac{49.99 - 39.99}{49.99} \times 100 = 20[/tex]%.
5. For Sports socks, the actual price is $14.95 and the selling price is $10.00.
The discount is [tex]\frac{14.95 - 10}{14.95} \times 100 = 33.11[/tex]%.
6. For Hockey sticks, the actual price is $299 and the selling price is $250.
The discount is [tex]\frac{299 - 250}{299} \times 100 = 16.38[/tex]%.
What are the factors of the polynomial: x^3+5x^2-17x-21
Answer: (x-3)(x+1)(x+7)
Step-by-step explanation:
Answer:D on edge :) (x+7)(x-3)(x+1)
Step-by-step explanation:did the test
suppose x varies directly with x if y=16 and x=-8what is the value of x when y=-14
The value of x when y = -14 is 7
Step-by-step explanation:
Direct variation is a relationship between two variables that can
be expressed by an equation in which one variable is equal to a
constant times the other
If y varies directly with x, then
y ∝ xy = k x, is the equation of variation where k is the constant of variation∵ y varies directly with x
∴ y ∝ x
∴ y = k x
To find k substitute x and y by their initial values
∵ y = 16 and x = -8
- Substitute y by 16 and x by -8 in the equation above
∴ 16 = k(-8)
- Divide both sides by -8
∴ -2 = k
∴ The value of k is -2
- Substitute the value of k in the equation above
∴ y = -2 x ⇒ equation of variation
∵ y = -14
- To find x substitute y by -14 in the equation of variation
∵ -14 = -2 x
- Divide both sides by -2
∴ 7 = x
∴ The value of x is 7
The value of x when y = -14 is 7
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Which point could be removed in order to make the relation a function?
{(0, 2), (3, 8), (-4,-2), (3, 6), (-1, 8), (8, 3)}
O (8,3)
O (3,6)
0 (-1,8)
0(-4,-2)
Answer:
(3,6)
Step-by-step explanation:
the x input cannot repeat in order for it to be a function
what are the vertices of triangle ABC, A(-2, 1), B(-3, -7) and C(4, -1) after translating ysing the rule (x, y)á(x+2,y-3).
The coordinates of triangle ABC after translation according to given rule are:
A'(0,-2), B'(-1,-10) and C'(6,-4)
Step-by-step explanation:
Given vertices are:
A(-2, 1), B(-3, -7) and C(4, -1)
The translation rule is: (x,y) => (x+2, y-3)
In order to translate the vertices, 2 will be added to x-coordinate and 3 will be subtracted from y-coordinate
So,
A(-2, 1) => A' (-2+2, 1-3) => A'(0,-2)
B(-3,-7) = > B'(-3+2, -7-3) => B'(-1, -10)
C(4,-1) => C'(4+2, -1-3) => C' (6, -4)
Hence
The coordinates of triangle ABC after translation according to given rule are:
A'(0,-2), B'(-1,-10) and C'(6,-4)
Keywords: Triangle, Translation
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Anna is a teacher at an elementary school. She purchased 73 tickets to take the first-grade children and some parents on a field trip to the zoo. She purchased
children's tickets for $9 each and adult tickets for $15 each. She spent a total of $771. How many of each ticket did she buy?
Adults
Children
Total
She bought 54 child tickets and 19 adult tickets.
Step-by-step explanation:
No. of tickets purchased = 73
Cost of tickets = $771
Cost of one child ticket = $9
Cost of one adult ticket = $15
Let,
Child ticket = x
Adult ticket = y
According to given statement;
x+y=73 Eqn 1
9x+15y=771 Eqn 2
Multiplying Eqn 1 by 9;
[tex]9(x+y=73)\\9x+9y=657\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 3 from Eqn 2;
[tex](9x+15y)-(9x+9y)=771-657\\9x+15y-9x-9y=114\\6y=114\\[/tex]
Dividing both sides by 6;
[tex]\frac{6y}{6}=\frac{114}{6}\\y=19[/tex]
Putting y=19 in Eqn 1
[tex]x+19=73\\x=73-19\\x=54\\[/tex]
She bought 54 child tickets and 19 adult tickets.
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Final answer:
Anna bought 54 children's tickets at $9 each and 19 adult tickets at $15 each to spend a total of $771 for a field trip to the zoo.
Explanation:
The question is asking us to solve a system of linear equations to find out how many children's and adult's tickets were purchased for a zoo field trip. The total cost of the tickets was $771, with children's tickets costing $9 each and adult's tickets costing $15 each. Anna purchased a total of 73 tickets.
Let's define two variables, C for the number of children's tickets, and A for the number of adult tickets. We have two equations based on the information given:
9C + 15A = 771 (Total cost equation)
C + A = 73 (Total number of tickets equation)
To solve this system, we can use substitution or elimination. Here's how you might solve it using substitution:
From the second equation, we express one variable in terms of the other: A = 73 - C.
Substitute A in the first equation: 9C + 15(73 - C) = 771.
Simplify and solve for C: 9C + 1095 - 15C = 771, which simplifies to -6C = -324, so C = 54.
Use the value of C to find A: A = 73 - 54, so A = 19.
Anna bought 54 children's tickets and 19 adult tickets.
m2 + 8m +7
m² + 5m + 6
m2 + 10m +9
m2 – 6m +8
m2 - 8m + 12
m2 + 11m + 24
How do I factor each trinomial ??
Answer:
m² + 8m + 7 = (m + 1) (m + 7)
m² – 6m + 8 = (m – 2) (m – 4)
Step-by-step explanation:
If a trinomial ax² + bx + c is "factorable", you can use the AC method.
1. Multiply a and c.
2. Find factors of ac that add up to b.
3. Divide the factors by a and reduce.
4. The numerators are the constants, the denominators are the coefficients.
For example:
m² + 8m + 7
a = 1, b = 8, c = 7
1. ac = 1×7 = 7
2. Factors of 7 that add up to 8 are 1 and 7.
3. Divide by 1: 1/1 and 7/1
4. The factors are (m + 1) and (m + 7).
Therefore, m² + 8m + 7 = (m + 1) (m + 7).
Let's try one with a negative coefficient:
m² – 6m + 8
a = 1, b = -6, c = 8
1. ac = 1×8 = 8
2. Factors of 8 that add up to -6 are -2 and -4.
3. Divide by 1: -2/1 and -4/1
4. The factors are (m – 2) and (m – 4)
Therefore, m² – 6m + 8 = (m – 2) (m – 4).
You can check your answers by distributing.
A sheriff patrols several neighborhoods in her patrol car it requires 3/15 of an hour to patrol an entire neighborhood how many neighborhoods can the sheriff patrol in 5/8 of an hour
Answer:
Neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.
Step-by-step explanation:
The Time taken to patrol an entire neighborhood = 3/ 15 hour
Total amount of time, the Sheriff has to do patrolling = 5/ 8 of an hour.
Now, let us assume the total neighborhoods paroled in the given time = m
So, [tex]\textrm{ Number of neighborhoods patrolled} = \frac{\textrm{Total available time}}{\textrm{Time used in 1 paroling 1 neighborhood}}[/tex]
[tex]m = \frac{\frac{5}{8} }{\frac{3}{15} } = {\frac{5}{8} \times {\frac{15}{3} =3.125[/tex]
or, the number of neighborhoods covered = 3.125
Hence, neighborhoods that sheriff patrol in 5/8 of an hour is 3.125.
To find out how many neighborhoods the sheriff can patrol in 5/8 of an hour, divide 5/8 by 3/15, which simplifies to 1/5. The calculation gives us 3.125, meaning the sheriff can complete 3 full neighborhood patrols.
Explanation:The question involves determining how many neighborhoods a sheriff can patrol in 5/8 of an hour if it takes 3/15 of an hour to patrol one neighborhood. To solve this, we divide the total time available by the time it takes to patrol one neighborhood.
First, simplify the fraction that represents the time to patrol one neighborhood, which is 3/15. This reduces to 1/5 when divided by 3.Next, divide the total time available, 5/8 of an hour, by the time per neighborhood, 1/5 of an hour. This is equivalent to multiplying 5/8 by the reciprocal of 1/5, which is 5.The calculation is: (5/8) * (5/1) = 25/8 = 3.125.Thus, the sheriff can patrol 3 full neighborhoods in 5/8 of an hour, with some additional time remaining that is not enough to complete a fourth patrol.
Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?
what is the answer and would it be positive or negative?
Michael is left with $181 and it is positive.
Step-by-step explanation:
Balance in Michael's account = $550
Per month withdrawal = $30.75
One year = 12 months
Total amount of withdrawal = Per month withdrawal * months
Total amount of withdrawal =[tex]30.75*12[/tex]
Total amount of withdrawal=[tex]\$369[/tex]
Net change = Balance in account - Amount of withdrawal
[tex]Net\ change= 550-369\\Net\ change=\$181[/tex]
Michael is left with $181 and it is positive.
Keywords: multiplication, subtraction
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The net change in Michael's account balance following the withdrawals is $181.
none of the option.
To find the net change in Michael's account balance following the withdrawals, we need to calculate the total amount withdrawn over one year and then subtract it from the initial balance.
Amount withdrawn per month: $30.75
Number of months: 12 (one year)
Total amount withdrawn over one year: [tex]\(30.75 \times 12 = $369\)[/tex]
Now, to find the net change in Michael's account balance, we subtract the total amount withdrawn from the initial balance:
Initial balance: $550
Total amount withdrawn: $369
Net change = Initial balance - Total amount withdrawn
Net change = $550 - $369
Net change = $181
The net change in Michael's account balance following the withdrawals is $181.
complete question given below:
Michael had $550 in his savings account. He took out $30.75 every month for one year. What is the net change in Michael’s account balance following these withdrawals?
A.-$519.25
B.-$369
C.$369
D.$519.25
solve the system using elimination 3x+2y=17 and 2x+5y=26
Answer:
3x + 2y = 17
2x + 5 y = 26
Step-by-step explanation:
3x + 2y = 17 }
2x + 5 y = 26}
x - 3y = - 9
x = -9 + 3y
=> 2 (-9+3y)+5y=26
-18+6y+5y=26
-18+11y=26
11y=26+18
11y=44
y= 4
3x + 8=17
3x = 17 - 8
3x = 9
x = 9 : 3
x = 3
Final answer:
By using the elimination method to solve the system of equations, we found that the solution is x = 3 and y = 4 after eliminating y, solving for x, and then substituting x back into one of the original equations to solve for y.
Explanation:
Elimination Method: Solving the System of Equations
To solve the system of equations using the elimination method, we will manipulate the equations to eliminate one variable and solve for the other. The two equations given are:
3x + 2y = 17
2x + 5y = 26
We want to eliminate one of the variables. To do this we find a common multiple for the coefficients of either x or y and then subtract or add the equations. Let's eliminate y by multiplying the first equation by 5 and the second equation by 2, which will give us equations with the same coefficient for y but opposite signs:
5(3x + 2y) = 5(17)
2(2x + 5y) = 2(26)
Now, our two new equations are:
15x + 10y = 85
4x + 10y = 52
Subtract the second new equation from the first:
(15x + 10y) - (4x + 10y) = 85 - 52
11x = 33
Solving for x:
x = 33 / 11
x = 3
Now that we have the value for x, substitute it back into one of the original equations to find y. Let's use the first original equation:
3(3) + 2y = 17
9 + 2y = 17
2y = 17 - 9
2y = 8
y = 8 / 2
y = 4
The solution to the system of equations is x = 3, y = 4.
Simon Wu's deposit includes two checks: $123.45 and $432.90; cash: 3 one-dollar bills, 9 five-dollar bills, 5
ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. Find the total deposit.
The total deposit made by Simon Wu is $634.22 which includes the amount from two checks, various dollar bills and coins.
Explanation:Let's break down Simon Wu's total deposit into components and add them up. First, we have two checks: one for $123.45 and another for $432.90. Then, we have cash which can be further broken down into: 3 one-dollar bills, 9 five-dollar bills, 5 ten-dollar bills, 15 quarters, 10 dimes, 18 nickels, and 32 pennies. You need to add all these amounts together to find the total deposit.
Here is a step-by-step calculation:
Checks: $123.45 + $432.90 = $556.35Dollar bills: 3*1 + 9*5 + 5*10 = $74Coins: 15*0.25 (quarters) + 10*0.1 (dimes) + 18*0.05 (nickels) + 32*0.01 (pennies) = $3.87Final step is to add the value of the checks, the value of the dollar bills and the value of the coins together:
$556.35 + $74 + $3.87 = $634.22
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A hospital has a large tank with a dimension shown. The tank does not have a cover. What is the surface area of the fish tank.
Answer:
Surface area of the fish tank [tex]332\ square\ feet[/tex]
Step-by-step explanation:
We have to find the surface area of the hospital tank.
As mentioned it does not have a cover.
The tank is in cuboid shape as it has different length [tex](l)[/tex],width [tex](w)[/tex] and height [tex](h)[/tex].
Surface area of a cuboid [tex]=2(lw+wh+hl)[/tex]
But here we have to subtract the surface area of the cover,that is [tex](lw)[/tex].
So the equation for the surface area of the cuboid can be re-framed as [tex]2(wh+hl)+(lw)[/tex]
Plugging the values of [tex]h=8\ ft[/tex] and [tex]l=12\ ft[/tex] and [tex]w=5\ ft[/tex]
Now
Surface area of the tank:
[tex]2(wh+hl)+(lw)[/tex]
[tex]2(5\times 8+8\times 12)+(12\times 5)[/tex]
[tex]2(40+96)+(60)[/tex]
[tex]2(136)+60[/tex]
[tex](272+60)=332\ ft^{2}[/tex]
So the surface area of the fish tank in the hospital is [tex]332\ ( ft)^{2}[/tex]
What is the equation of the line that is parallel to y=6x−1 and passes through the point (−3,4)?
The equation will be in slope-intercept form.
Answer:
y=6x+22
Step-by-step explanation:
we know that the slope of a parrallel line is the same as the other line. so that gives us y=6x +b. to find b, x needs to equal 0, so to do that we must add 3 to x. we also need to add 3×6 to the y value of 4 to find the y intercept. therefore, the y intercept is 22
The slope of the given line is 6. The line parallel to this passing through the point (-3,4) would also have a slope of 6. Solving for y-intercept, we get the equation of the line as y = 6x + 22.
Explanation:To find the equation of a line that is parallel to the given line and passes through a particular point, we need to use the fact that parallel lines have the same slope.
Given the equation y=6x-1, we can observe that the slope of this line is 6. As such, the line parallel to this one will also have a slope of 6.
Given the point (-3,4), the equation of the line parallel to the given line and passing through the indicated point in the form y=mx+c, where m is the slope and c is the y-intercept, can be found by substituting the x and y values from the point and the known slope m=6 into the equation to solve for c.
4 = 6*(-3) + c.
After solving, c = 22.
Therefore, our desired equation of the line is y = 6x + 22.
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I NEED HELP PLEASE. LOOK AT PICTURE
Answer:
Part 1) [tex]\frac{a^4}{4b^2}[/tex]
Part 2) [tex]-\frac{v^9}{w^6}[/tex]
Step-by-step explanation:
we know that
When divide exponents (or powers) with the same base, subtract the exponents
Part 1) we have
[tex]\frac{3a^{2}b^{-4}}{12a^{-2}b^{-2}}=(\frac{3}{12})(a^{2+2})(b^{-4+2} )=\frac{1}{4}a^{4}b^{-2}=\frac{a^4}{4b^2}[/tex]
Part 2) we have
[tex]\frac{v^3w^{-3}}{-v^{-6} w^3} =-v^{3+6}w^{-3-3}=-v^9w^{-6}=-\frac{v^9}{w^6}[/tex]
The distance it takes stop a car varies directly at the square of the sure of the car. If it takes 112 feet for a car traveling at 40mph to stop, what distance is required for a speed of 59 mph?
The distance required for a speed 59 mph is 243.67 feet
Step-by-step explanation:
The direct variation is a relation ship between two quantities, the
ratio between them is constant
If y varies directly with x, then y = k xx is the constant of variationTo find k substitute y and x by their initial values∵ The distance it takes stop a car varies directly at the square
of the speed of the car
∴ d = k v², where d is the distance in feet and v is the speed in mph
∵ it takes 112 feet for a car traveling at 40 mph to stop
∴ d = 112 feet , v = 40 mph ⇒ initial values
- Substitute these values in the rule above to find k
∵ 112 = k (40)²
∴ 112 = 1600 k
- Divide both sides by 1600
∴ k = 0.07
∴ d = 0.07 v² ⇒ equation of variation
∵ The speed v = 59 mph
- To find the distance required for this speed substitute v in
the equation of variation by 59
∵ d = 0.07 (59)²
∴ d = 243.67 feet
The distance required for a speed 59 mph is 243.67 feet
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Applying the direct variation formula between the speed and stopping distance of a car, we deduce that a car traveling at 59mph would require approximately 245 feet to stop.
Explanation:In this problem, we use the relation that the distance it takes to stop a car varies directly with the square of the speed- this is an example of a direct variation. Given the initial condition we can establish an equation to relate the speed and the stopping distance: D = kV² where D represents the stopping distance, V is the speed, and k is a constant of variation.
First, we utilize the given information (D=112 feet and V=40 mph) to determine the constant k: 112 = k(40²), yielding k = 112/(40²) = 0.07. This factor remains constant for the car irrespective of its speed.
With the constant k determined, we then substitute V=59 and the constant k into our original equation to calculate the distance required to stop at this speed: D = 0.07*(59²), resulting in D approximately equal to 245 feet. Therefore, a car traveling at 59 mph would require approximately 245 feet to stop.
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a hockey season ticket holder pays $99.26 for her tickets plus $4.50 for a program each game. A second person pays $18.68 for a ticket to evey game, but doesn't buy programs. In how many games will they have paid the same amount
Answer:
7 games
Step-by-step explanation:
First Person:
Fixed Cost of 99.26
Variable Cost of 4.50 per game (program cost)
Second Person:
No Fixed Cost
Variable cost of 18.68 per game (ticket cost)
Now, we let the number of games be "x", so we can write 2 equations for each person. Then we equate and find at what number of games, the amount paid by both person would be same. Shown below:
First Person Equation:
99.26 + 4.50x
Second Person Equation:
18.68x
Now, equate and solve for x:
99.26 + 4.50x = 18.68x
99.26 = 18.68x - 4.50x
99.26 = 14.18x
x = 99.26/14.18
x = 7
So, the answer is 7 games
If 27 cards are in the whole set, how many are in 3/9 of the set
Answer: 9 cards
Step-by-step explanation:
x=27
3/9x = 1/3x = 27/3 = 9
At the movie theater, childs admission is $6.10. Adult admission is $9.40. On Tuesday four times as many adult tickets as child tickets were sold. For a total of $1179.90. How many child tickets were sold that day?
Answer:
The number of children's tickets sold was 27
Step-by-step explanation:
Let
x ----> the number of children's tickets sold
y ----> the number of adult's tickets sold
we know that
[tex]6.10x+9.40y=1,179.90[/tex] ----> equation A
[tex]y=4x[/tex] ----> equation B
Solve the system by substitution
Substitute equation B in equation A
[tex]6.10x+9.40(4x)=1,179.90[/tex]
solve for x
[tex]6.10x+37.6x=1,179.90[/tex]
[tex]43.7x=1,179.90[/tex]
[tex]x=27[/tex]
therefore
The number of children's tickets sold was 27
James paid $37.50 for 5 movie tickets.
What is the unit rate representing the cost of 1 movie ticket?
Answer: $7.50 per ticket
Step-by-step explanation: To solve this problem, we can rewrite the given statement using fractions.
All my work will be attached in the image provided.
to find out what will go in the blank, notice that we have a 1 in the denominator of our second fraction so we want to find a fraction that is equivalent to 37.50/5 that has a 1 in the denominator.
If we divide the numerator and the denominator of 37.50/5 by 5, we get the equivalent fraction 7.50/1 or $7.50 for 1 movie ticket.
This means that the unit rate for $37.50 for 5 movie tickets is $7.50 per ticket.
Answer:187.50 cents
Step-by-step explanation:37.50*5=187.5 so it would be 187.50 cents
Kamille is attending a community college to obtain a two-year degree. the annual cost of tuition is $3,750. Kamille has obtained an annual scholarship of $1,250 and anual grants in the amount of $835. the remainder of kamille’s tuition and fees will be paid be paid for using student loans. At the end of the two-year degree, what will kamille’s student loan balance be ?
The balance of student loan will be $3330 at the end of two year degree.
Step-by-step explanation:
Annual cost of tuition = $3750
As it is two year degree, therefore, total cost of tuition;
Total cost of tuition = 3750*2 = $7500
Annual scholarship = $1250
Annual grant = $835
Total = 1250 + 835 = $2085
As this is one year amount, she will get same the next year.
Total amount received in 2 years = 2085*2 = $4170
Balance in student loans = Total cost of tuition - Total amount received as grant and scholarship
Balance in student loan = [tex]7500-4170 =\$3330[/tex]
The balance of student loan will be $3330 at the end of two year degree.
Keywords: multiplication, subtraction
Learn more about multiplication at:
brainly.com/question/2654504brainly.com/question/2657284#LearnwithBrainly
Answer:
The balance of student loan will be $3330 at the end of two year degree.
Step-by-step explanation:
given that the area of the smaller square is 10cm2 .find the area of the larger square.
The calculated area of the bigger square is 22.5 square cm
How to determie the area of the larger square
From the question, we have the following parameters that can be used in our computation:
The square
Where, we have
Area of smaller square = 10 cm²
Using the above as a guide, we have the following:
Area of bigger square = Area of smaller square * Scale factor²
In this case, we have
Scale factor = 1.5
Substitute the known values into the equation
Area of bigger square = 10 * 1.5²
Evaluate
Area of bigger square = 22.5
Hence, the area of the bigger square is 22.5 square cm
Somebody please help me with this
Answer:
see the explanation
Step-by-step explanation:
Part 1) Record the coordinates of the given triangle
Looking at the graph
Let
A(-4,2)
B(-2,5)
C(3,2)
Part 2) Translate the given triangle down 2 units and right 5 units. Graph the translation
we know that
A translation of 5 units at right means (x+5)
A translation of 2 units down means (y-2)
so
The rule of the translation is equal to
(x,y) -----> (x+5,y-2)
Apply the rule of the translation at each vertices
A(-4,2) ----->A'(-4+5,2-2)
A(-4,2) ----->A'(1,0)
B(-2,5) -----> B'(-2+5,5-2)
B(-2,5) -----> B'(3,3)
C(3,2) -----> C'(3+5,2-2)
C(3,2) -----> C'(8,0)
using a graphing tool
The graph in the attached figure
use slope to determine whether the points A(3,5) B(-2,6) and C(-5,7) are on the same line
Answer:
The points are not on the same lineStep-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the given points:
for A(3, 5) and B(-2, 6):
[tex]m_{AB}=\dfrac{6-5}{-2-3}=\dfrac{1}{-5}=-\dfrac{1}{5}[/tex]
for B(-2, 6) and C(-5, 7):
[tex]m_{BC}=\dfrac{7-6}{-5-(-2)}=\dfrac{1}{-5+2}=\dfrac{1}{-3}=-\dfrac{1}{3}[/tex]
[tex]\large\boxed{m_{AB}\neq m_{BC}}[/tex]
find the area of the shaded region
Answer:
21 centimeters is the answer
Select the graph of the solution. Click until the correct graph appears. |x| = 2
Graph of |x| = 2 is two vertical lines symmetric about the y-axis, intersecting x-axis at (2, 0) and (-2, 0).
The equation |x| = 2 represents two parallel vertical lines symmetrically positioned about the y-axis. These lines intersect the x-axis at points (2, 0) and (-2, 0), indicating the absolute value of x being equal to 2. The graph exhibits symmetry with respect to the y-axis, forming a V-shape.
It conveys that any value of x, whether positive or negative, yielding an absolute value of 2 satisfies the equation. The graph emphasizes the notion that the distance of x from the origin is fixed at 2 units, illustrating a clear geometric representation of the absolute value function.
Please help with 11c!?
Answer:
"To the nearest year, it would be about 9 years"
Step-by-step explanation:
11c)
This is compound growth problem. It goes by the formula:
[tex]F=P(1+r)^t[/tex]
Where
F is the future amount
P is the present (initial) amount
r is the rate of growth, in decimal
t is the time in years
Given,
P = 20,000
r = 8% = 8/100 = 0.08
F = double of initial amount = 2 * 20,000 = 40,000
We need to find t:
[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]
To solve exponentials, we can take Natural Log (Ln) of both sides:
[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]
Using the rule shown below we can simplify and solve:
[tex]Ln(a^b)=bLn(a)[/tex]
We can write:
[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]
To the nearest year, that would be about 9 years