The constant of proportionality on this case is 3.2
What is constant of proportionality?
The ratio between any two given values that establishes what is referred to as a proportional relationship is the constant of proportionality.
Main body:
Total amount spent by Mom = $ 72
total gallon bought = 22.5
So constant of proportionality can be found by finding value of 1 gallon of gasoline, which can be found by dividing as follows,
Price of 1 gallon = total spent/ total gasoline bought
= 72/22.5
= 3.2
Hence constant of proportionality is 3.2.
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please help me I will give you brainiest, please
x + 9 = 13
3x = 12
x + 5 − 9 = 0
2x + 5 = 17
5x − 3 = 17
x − 3 = 1
7x = 35
[tex]\frac{4x}{4} =4[/tex]
3( x + 4) = 15
8 + x − 5 = 7
The values of the variables x in the equations are;
x = 4x = 4x = 4x = 6x = 4x = 4x = 5x = 4x = 1What is an equation?An equation is a mathematical statement that connects two mathematical expression with an equals sign.
x + 9 = 13
Subtracting 9 from both sides of the equation, we get;
x = 13 - 9 = 4
x = 43•x = 12
Dividing both sides of the equation by 3, we get;
x = 12 ÷ 3
x = 4x + 5 - 9 = 0
Subtracting (5 - 9) from both sides of the equation, we get;
x = 9 - 5 = 4
x = 42•x + 5 = 17
Subtracting 5 from both sides of the equation, we get;
2•x = 17 - 5 = 12
2•x = 12
Dividing both sides of the equation by 2, we get;
x = 12 ÷ 2 = 6
x = 65•x - 3 = 17
Adding 3 to both sides of the equation, we get;
5•x = 17 + 3 = 20
5•x = 20
Dividing both sides of the equation by 5, we get;
x = 20 ÷ 5 = 4
x = 4x - 3 = 1
Adding 3 to both sides of the equation, we get;
x = 1 + 3
x = 47•x = 35
Dividing both sides of the equation by 7, we get;
x = 35 ÷ 7 = 5
x = 5[tex]\frac{4\cdot x}{4} = 4 [/tex]
Multiplying both sides of the equation by 4 and dividing the result by 4, we get;
x = 4 × 4 ÷ 4 = 4
x = 43•(x + 4) = 15
Dividing both sides of the equation by 3, we get;
x + 4 = 15 ÷ 3 = 5
x + 4 = 5
Subtracting 4 from both sides of the equation, we get;
x = 5 - 4 = 1
x = 18 + x - 5 = 7
Adding 5 and subtracting 8 from both sides of the equation, we get;
x = 7 + 5 - 8 = 4
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
Answer:
Option 3 ) 18x - 9 = 72
Step-by-step explanation:
Algebraic equations:
[tex]\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\[/tex]
Multiply each term of (30x - 15) by 3/5,
[tex]\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72[/tex]
The given equation is same as 18x - 9 = 72
Evaluate 5 (2)² – 6.
5(2)² - 6 =
Answer:
14
Step-by-step explanation:
Check the file
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5(2)^2 - 6}[/tex]
[tex]\mathsf{= 5(2 \times 2) - 6}[/tex]
[tex]\mathsf{= 5(4) - 6}[/tex]
[tex]\mathsf{= 20 - 6}[/tex]
[tex]\mathsf{= 14}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Select all the expressions that are equivalent to 8^3/2^3
Mary spent a total of $355.58 for a party. She spent $200.93 on food, plus an additional $30.93 for each hour of the party. How long was the party? A. 5 hours B. 7 hours C. 4 hours D. 6 hours
Answer:
Option A
Step-by-step explanation:
We are here given that Mary spent a total of $ 355.58 for a party , $200.93 on food , and an additional charge of $30.93 for each hour of party .
So the total money spent for staying at party , will be ;
[tex]\longrightarrow \$ 355.58 - \$200.93 [/tex]
[tex]\\\longrightarrow \$ 154.65 [/tex]
We can calculate the no. of hours spent at the party by dividing this amount by the rate of staying per hour at party as ;
[tex]\\\longrightarrow \dfrac{ \$ 154.65}{\$ 30.93 / hr } [/tex]
[tex]\\\longrightarrow 5 \ hrs . [/tex]
Hence she spent 5hrs at the party .
An open-top box is to be constructed from a sheet of tin that measures 32 inches by 18 inches by cutting out squares from each corner as shown and then folding up the sides. Let V(x) denote the volume of the resulting box.
The answer of resulting box volume = 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
What are example and volume?
The volume of an object serves as a gauge for its capacity. For instance, if the brim of a cup can hold 100 ml of water, that cup is said to have a 100 ml capacity.. Another way to quantify volume is how much room a three-dimensional object occupies.
Volume = length x breath x height
length = 32-2[tex]x[/tex]
Breath = 18-2[tex]x[/tex]
Height = [tex]x[/tex]
Volume = (32-2[tex]x[/tex]) x (18-2[tex]x[/tex]) x ([tex]x[/tex])
= 576 - 64[tex]x[/tex] - 36[tex]x[/tex] - 4[tex]x^{2}[/tex] x ([tex]x[/tex])
= 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
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Can slmeone please explain this and give me the answer ill be very grateful.
Answer:
D
Step-by-step explanation:
Since Δ QTS is isosceles then the base angles are congruent , that is
∠ TQS = ∠ QST = y
∠ QST and ∠ RST are a linear pair and sum to 180° , that is
∠ QST + ∠ RST = 180
y + ∠ RST = 180 ( subtract y from both sides )
∠ RST = 180 - y
the sum of the 3 angles in Δ TRS = 180° , that is
∠ RTS + ∠ TRS + ∠ RST = 180
∠ RTS + x + 180 - y = 180 ( subtract 180 from both sides )
∠ RTS + x - y = 0 ( subtract x - y from both sides )
∠ RTS = y - x
the student council sold $661$ t-shirts, some at $\$10$ and some at $\$12$. when recording the number of t-shirts they had sold at each of the two prices, they reversed the amounts. they thought they made $\$378$ more than they really did. how many t-shirts actually were sold at $\$10$ per shirt?
The student council sold $273$ t-shirts were sold at $\$10$ per shirt.
Let $x$ be the number of shirts sold at $\$10$
Let $y$ be the number of shirts sold at $\$12$
$x+y=661$
$10x+12y=3780$
$x=y+101$
$10y+12y=3780$
$22y=3780$
$y=172$
$x=172+101$
$x=273$
Hence $273$ t-shirts were sold at $\$10$ per shirt.
If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.
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Please help!!
5x -10y = 10
x + 2y = -18
(Enter the solution like this: ( , ) )
The value to the system of equations is (-10, -4)
How to determine the solution to the system of equations?In this case, the system of equations is given as
5x -10y = 10
x + 2y = -18
Make x the subject in the second equation
So, we have the following representation
x = -2y - 18
Substitute x = -2y - 18 in the equation 5x -10y = 10
So, we have
5(-2y - 18) -10y = 10
Open the brackets
This gives
-10y - 90 - 10y = 10
Evaluate the like terms
-20y = 80
Divide by -20
y = -4
Recall that x = -2y - 18
So, we have
x = -2 * -4 - 18
Evaluate
x = -10
Hence, the solution is (x, y) = (-10, -4)
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Tell which ordered pair is a solution of the inequality y < x + 12.
(−4, 12)
(−7, 9)
(−5, 8)
(−3, 5)
Answer:
(-3,5)
Step-by-step explanation:
we just plug the solutions in the equation to see if it’s true
y<x+12
12<-4+12
12<8
Not true 12 is not less than 8
9<-7+12
9<5
not true 5 is not greater than 9
8<-5+12
8<7
Not true 8 is not less than 7
5<-3+12
5<9
true 5 is less than 9
Hopes this helps please mark brainliest
What is -5/2 times -41
The solution of the mathematical statement is 102.5
How to evaluate the expression?From the question, we have the following mathematical statement that can be used in our computation:
"What is -5/2 times -41"
This means that
-5/2 times -41
Express as numbers
So, we have
-5/2 * -41
Divide 5 by 2
So, we have
-2.5 * -41
Evaluate the product
102.5
Hence, the result is 102.5
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What is the value of a?
Enter your answer in the box.
a
25
20
Answer:
the side a is equal to 15.
Step-by-step explanation:
I entered it into my calculator.
Enter your answer and show all the steps that you use to solve this problem.
What is the vertex form of the equation?
y=-z²+12z-4
The vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.
What is a parabola?A parabola's vertex is the location where the curve turns steepest. If a parabolic function has the shape of a 'U', it has a minimum value; otherwise, it has a maximum value. The parabola's axis of symmetry intersects with the parabola at its vertex.
For any parabola Ax² + Bx + C, the x-coordinate of the vertex is given by -B/(2A).
So, according to our question
A = -1
B = 12
C = -4
So, z = - 12/2(-1)
z = - 12/- 2
z = 6
Plug the value in the equation
y = - (6)² + 12(6) -4
y = -36 +72 -4
y = 32
So, the vertex of the parabola will be at (6, 32) and the vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.
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For f(x) = −7x − 13, find f(x) when x = −1.
Answer:
-6
Step-by-step explanation:
-7 x -1 = 7
7 - 13 = -6
look at the table. is the relationship between x and y a proportional relationship?
yes or no
Answer:
Yes, the relation is proportional
Step-by-step explanation:
For a proportional relation, the ratio of X/Y (and thus Y/X) should be constant. You can verify, for examply dividing each Y by the corresponding X:
9 / -3 = -3
6 / -2 = -3
-3 / 1 = -3
-6 / 2 = -3
-9 / 3 = -3
As you can see, the ratio is the same, so the relation is proportional.
What is the product?
(-2x -9y^2) (-4x - 3)
A.-8^2 -6x -36xy^2 -27y^2
B.-14x^2 -36xy^2 +27y^2
C.8x^2+6x36xy^2 +27y^2
D.14x^2 + 36xy^2 + 27y^2
Answer:
C
Step-by-step explanation:
(-2x -9y^2) (-4x - 3)
= 8x^2+6x + 36y^2x+27y^2
[tex]12=\frac{c-6}{2}[/tex]
Answer: c = 30
Step-by-step explanation:
[tex]12=\frac{c-6}{2}\\ \\12(2)=c-6\\\\24=c-6\\\\c=24+6=30[/tex]
If f(x)=2x^3-6x^2-16x-20f(x)=2x *3 −6x *2−16x−20 and f(5)=0, then find all of the zeros of f(x)f(x) algebraically.
The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:
x = 5, x = -1 + i, x = -1 - i.
How to obtain the solutions to the equation?The equation is defined by the rule presented as follows:
f(x) = 2x³ - 6x² - 16x - 20.
One solution for the equation is given as follows:
x = 5.
Because f(5) = 0.
Then (x - 5) is a linear factor of the function f(x), which can be written as follows:
2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).
This is because the product of a linear function and a quadratic function results in a cubic function.
Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:
2x³ - 6x² - 16x - 20 = = ax³ + (b - 5a)x² + (c - 5b)x - 5c.
Then these coefficients are obtained comparing the left and the right side of the equality as follows:
a = 2.-5c = -20 -> c = 4.b = -6 + 5a = 4.Hence the equation is:
2x² + 4x + 4.
Using a quadratic equation calculator, the remaining zeros are given as follows:
x = -1 + i.x = -1 - i.More can be learned about the solutions of an equation at brainly.com/question/25896797
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Two sides of a parallelogram are 38 feet and 88 feet. The measure of the angle
between these sides is 132º. Find the area of the parallelogram to the nearest square
foot.
Answer:
Area under the curve f (x) = 38 on interval [88, 132]: 38 132 -3344 (Decimal: 1672)
Step-by-step explanation:
help! what does this mean?
n/16 lies between 4/16 and 8/16
So, n can be 5,6,7
Answer:
5, 6 , 7
Step-by-step explanation:
Change 1/4 and 1/2 to the values they would be if their denominator was 16
1/4 will become 4/16
1/2 will become 8/16
the values between these are 5/16, 6/16, 7/16
n can be 5, 6 or 7
The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. When m=8kg and d=5meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.
Answer:
Step-by-step explanation:
EQUATION: F = km / d²100 = k(8) / (5)²100 = k 8 / 25100 ÷ 8 / 25 = k 8 / 25 ÷ 8 / 25625 / 2 = kF = (625 / 2)(2) / (15)²F = 625 / 225F = 25 / 9
Find the circumference and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, If
necessary
Erin solved 3 word problems in 10 minutes.
If she were to solve the remaining 8 word problems at the same rate, how long would it take to the nearest minute?
During hibernation, a bear's heart rate decreases to 62% of its usual rate. Alex says that means if a bear's heart rate during hibernation is 19 beats per minute, its usual heart rate is 31 beats per minute. Is Alex correct? Explain your reasoning.
Answer:
Yes, he is correct
Step-by-step explanation:
100% : x
62% : 19
Cross multiply
19*100% = 62%x
19 = 0.62x
19/0.62 = x
x = 30.645
Rounds up to 31
make r the subject of formula in V= pie h square(r-h/3)
When r is made the subject of the formula we have; V + πh^3/3πh^2
What is the subject of a formula?The term subject of a formula has to do with the variable that we are trying to obtain in the equation. Hence the subject of the formula must be written on the left hand side of the mathematical equation.
We have;
V = πh^2(r - h/3)
We open the bracket;
V = πrh^2 - πh^3/3
Adding πh^3/3 to both sides, we have;
V + πh^3/3 = πrh^2
Then we divide both sides by πh^2
r = V + πh^3/3/πh^2
r = V + πh^3/3πh^2
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At a carnival you win a prize if you get a heads, you must first choose a coin. There is a fair and a biased coin, while choosing each coin is equally likely, the biased coin has a 78% of landing tails. What is the probability of choosing the biased coin if you won a prize.
Probability of choosing the biased coin if you won a prize is 0.30
Let "B" be the event of selecting biased coin and "H" be the event of getting head.
P(B) = 0.5
P(getting head when coin was biased) = 100% - 78%
= 22% = 0.22
Using conditional Probability that biased coin was selected given that you have won the prize that is getting head
we have to calculate ,
P(B | H ) = P(B∩H)/P(H)
here , P(B∩H) = P(biased coin selected and getting head) = 0.5 × 0.22
and P(H) = P(getting head)
P(getting head when coin was biased) + P(getting head when coin was unbiased) = 0.5 × 0.22 + 0.5 × 0.5
putting all together ,
P(B | H ) = P(B∩H)/P(H) = 0.5 × 0.22 / 0.5 × 0.22 + 0.5 × 0.5
cancelling 0.5 from numerator and denominator
= 0.22 / 0.5+ 0.22
= 0.22 / 0.72 = 22/72
=0.30
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Aidan buys used bicycles, fixes them up, and sells them. His average cost to buy and fix each bicycle is $47. He also incurred a one-time cost of
$840 to purchase tools and a small shed to use as his workshop. He sells bikes for $75 each. Use this information for the exercises.
WRITE Write revenue and cost functions R(x) and C(x) for Aidan's situation, where x is the number of bicycles. How do you include the one-time
cost in C(x)?
WRITE Write a profit function P(x) such that P(x) = R(x)-C(x). In words, what does P(x) represent?
PERSEVERE List key features for the profit function P(x). Then use the key features to sketch a graph, on a separate sheet of paper, that shows
the profit P(x) as a function of x bicycles.
ANALYZE Which key feature of the graph represents Aidan's break-even point (profit = 0)? Explain how to use your graph to find the most
accurate value for this feature.
Answer:
P(x) = $31x - $840
Step-by-step explanation:
Let x be the number of bicycles. The total cost for purchasing and repairing the bikes is $47x, plus a one-time purchase of $840 for a workshop and tools. Total cost, C is therefore:
C(x) = $47x + $840
We learn Aidan sells the bikes for $75 each. Total revenue, R, is:
R(x) = $75x
Profit, P, would be the difference of revenue, R, and costs, C:
P(x) = R(x) - C(x) or $75x -($47x + $840)
P(x) = $75x -$47x - $840
P(x) = $31x - $840
P(x) represents the total profit for x bicycles.
See the attached graph. Note the key features of the graph are the breakeven (27 bikes) and the initial investment (-$840). We can find the breakeven point by looking for the value of x when the profits are $0. A more accurate determination can be found by solving the equation we developed for the case in which P(x) = $0:
P(x) = $31x - $840
0 = $31x - $840 for P(x) = 0 (breakeven)
$31x = $840
x = 27.1 units. We need to round to 27 units since 0.1 of a bicycle makes no sense in this context.
g\one cannot tell whether a data set is close to symmetric or not by looking at a histogram. true false
False, one can tell if a data set is close to symmetric or not by watching a histogram.
The histogram exhibit a symmetrical distribution of given data. The data is symmetrical if we are able to draw a vertical line at some point in the histogram such that its shape on both sides of the left and the right of the vertical line exactly reflected images to each other. The mean, the median, and the mode are can be taken as examples to prove the symmetricity using histogram for these data.
In an altogether symmetrical distribution, the mean and the median are alike. Such as the mode has one mode (unimodal), and the mode is the alike as the mean and median.
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Construct rectangle ABCD in which b) BC = 5.4 cm and BCA = 45°
Step-by-step explanation:
Please refer to photo for drawing
if the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 4 defective parts from a sample of 100? (assume that the process follows a binomial distribution.)
There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.
Probability of a machine producing a defective part is 0.05,
p = 0.05
q = 1 - p = 1 - 0.05 = 0.95
n = 100
P(x) = ⁿCₓ pˣqⁿ⁻ˣ
x = 4
P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶
P(4) = 0.215569
= 0.2156
0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.
The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.
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