The amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy. You spent $16.56 to fill up your car with gasoline. If you bought 6 gallons of gasoline, what is the constant of variation
Let "m" represent the money required.
Let "n" represent the number of gallons filled.
Since it is given to us that the amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy, therefore, this can be written mathematically as:
[tex] m\propto n [/tex]
We know that when we remove the "varies to" sign we have to replace it with the equal to sign and the constant of variation, which we will represent by the letter "k".
Therefore the above expression will become:
[tex] m=k\times n [/tex]
Now, it is given that m=$16.56 and n=6 gallons
Therefore, [tex] 16.56=k\times 6 [/tex]
Dividing both sides by 16.56 we get:
[tex] \therefore k=\frac{16.56}{6}=2.76 [/tex]
Thus, k=2.76 $/gallon is the value of the constant of variation.
What is the volume of the composite figure ?
A bakery supplier receives an order for 2 tons of flour from a bakery chain. The flour is shipped in crates. Each crate holds eight 10-pound bags of flour. How many crates does the supplier need to ship to fulfill the order?
NEED HELP ASAPPP
Figure TUVW is transformed to T’U’V’W’, as shown:
Which of the following sequences of transformations is used to obtain figure T’U’V’W’ from TUVW?
Reflection about the y-axis followed by a translation left by 2 units
Reflection about the x-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
The correct answer is Reflection across the y-axis and then Translation 2 units to the left. In a translation, the sign on the x of every point is changed. The reflected image is too far to the left to be just a reflection or even a rotation. That is why I said it was translated 2 units
Step-by-step explanation:
The velocity of an airplane heading east is 400 knots with a wind velocity of 50 knots blowing toward the northeast. Calculate the resultant speed and direction of the plane. Round to the nearest tenth.
the ratio of the areas of two similar polygons is 81:64. If the perimeter of the first polygon is 32 cm, what is the perimeter of the second polygon? Round to the nearest tenth
In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :
Ratio of area =[tex] a^{2} :b^{2} [/tex]
Given ratio of area =81:64
Or 81:64=[tex] a^{2} :b^{2} [/tex]
Taking root of both sides
9:8=a:b
The ratio of perimeter of any two similar polygon is equal to the ratio of sides.
Ratio of perimeter = a:b
Perimeter of first polygon is 32 cm.
Let the perimeter of second polygon be x.
32:x=a:b
Or, 32:x=9:8
[tex] \frac{32}{x} =\frac{9}{8}
[/tex]
Cross multiplying
9x= (32)(8)
9x=256
Dividing both sides by 9
x=28.4.
The perimeter of second polygon is 28.4cm.
Last week, you finished Level 2 of a video game in 32 minutes. Today, you finished Level 2 in 28 minutes. What is your percent of change?
The first step to solve this problem is to compute how much change in minutes were you able to have today compared to the last week.
32 minutes – 28 minutes = 4 minutes faster than last week
To compute the percent of change you have to divide the change in minutes to the duration in minutes for the last week:
4 minutes / 32 minutes = 0.125 or 12.5% faster than last week
Can anyone solve this?
if the temperature at 9:00 pm was 12 degrees farenheit,and after 6 hours the temperature dropped to 6 degrees Fahrenheit below 0,what was the rate of change in temperature per hour?
PLEASE HELP
If a student is chosen at random find the probability the student is male given that its a senior. Round to the nearest while percent.
The probability that a randomly selected senior student is male is 40%.
Given Data:
We have a two-way table representing the number of students by gender and grade level.
The relevant information is that there are 2 male seniors.
Event Definitions:
Let’s define the following events:
A: Student is male.
B: Student is a senior.
Conditional Probability:
We want to find the probability that a student is male given that they are a senior: (P(\text{Male}|\text{Senior})).
We can use the formula for conditional probability: [tex][P(\text{Male}|\text{Senior}) = \frac{P(\text{Male and Senior})}[/tex][tex]{P(\text{Senior})}][/tex]
Calculations:
From the table, we know:
Number of male seniors (A and B): 2
Total number of seniors (B): 5
Therefore: [[tex]P(\text{Male}|\text{Senior}) = \frac{2}{5} = 0.4][/tex]
Rounded Answer:
Rounding to the nearest whole percent:
([tex]0.4 \times[/tex]100% = 40%)
Summary: The probability that a randomly selected senior student is male is 40%.
What is the simplified version of (1/3) (9x - 9)
How do I solve 20% out of 75
The original price of an item is $130. The item is on a discount of 1/5 off the original price. You then pay a sales tax of 10%. What is the amount you paid for the item?
what is the slope of the line (2,-2) and (9,3)
Determine o X do triângulo na questão b
For your party you purchased balloons for $.79 each. You spent a total of $11.85. About how many balloons were purchased?
Let us suppose the number of balloons purchased is x in number.
It is given balloons are purchased for $.79 each
Cost of x balloons = .79x.
Total amount spent on purchasing balloons = $11.85
Cost of x balloons = Total cost of balloons.
.79x=11.85
With x .79 is multiplied .Opposite of multiplication is division.
We perform the opposite operation both sides
Dividing both sides by .79
x=11.85÷.79
x=15
Total number of balloons purchased is 15.
Radius is 8 what is the area of the circle then ?
Please help asap
The table below shows which sports events have sold out and which have not.
Given the function f(x) = 2x-5/3, which of the below expression is correct?
F^-1(x) = 5-2x/3
F^-1(x) = 3x-5/2
F^-1(x) = 3x+5/2
F^-1(x) = -2x - 5/3
I think you’re subtracting 5. So now it’s f^-1(x)= 3x+5/2. Not too sure but hope this may help. So, C.
? - 12 = -6
What is the missing number?
A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid. If the height is 6 cm, the volume of the pyramid is cm3.
Answer:
128
Step-by-step explanation:
Just did the test ;)
find the slope of a line that is parallel to the line -0.75 x minus y equal 3 the slope of a parallel line is
Write 6 percent as a decimal
Please could someone help with this one . Thanks I will brainlist
What do you draw to show that 50,000 pennies is equivalent to 100 five dollar bills?
triangle LMN is similar to triangle XYZ with altitudes KL and WX. Find KL
The side length (KL) of the triangle ΔLMN will be 7. Then the correct option is B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔLMN is similar to triangle ΔXYZ with altitudes KL and WX.
The ratio of the corresponding sides will remain constant. Then the equation is given as,
KL / XW = LN / XZ
KL / 3 = 28 / 12
KL = (28 x 3) / 12
KL = 84 / 12
KL = 7
The side length (KL) of the triangle ΔLMN will be 7. Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
How do you get the value of x
HELP WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!
Give me 5 fun facts about Octogons!
is a simplified version of 5(x+8)-10x =60
What is the value of x?
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