Answer:
4 gallons of gasoline the car has left after it has traveled 330 miles.
Step-by-step explanation:
We are given with the following data of Distance Traveled and Gas Left in Tank below;
Distance Traveled (in miles) Amount of Gas Left in Tank (in gallons)
0 15
90 12
180 9
270 6
330 ?
As we can see from the table that for every 90 miles of distance traveled, there has been a reduction of 3 gallons of gas which is left in the tank, i.e;
From 90 to 180 - Gas reduced from 12 to 9
This means that in 1 gallon of gas, the distance traveled is = [tex]\frac{90}{3}[/tex] = 30 miles
So, from distance 270 to 300, the amount of Gas Left in Tank = 6 - 1 = 5 gallons
From distance 300 to 330 miles, the amount of Gas Left in Tank = 5 - 1 = 4 gallons
Hence, 4 gallons of gasoline is left after the car has traveled 330 miles.
The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.
Answer:
The Elegant Home Architects charges are less than Rock the House Digital Designs charges for hours worked more than 2.
If the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then Rock the House Digital Designs will be a better option .
Step-by-step explanation:
Let ℎ represent the number of hours for which the Johnson family hires the design firm.
Suppose the Johnson family hires the design firm for ten hours so h= 10
Then the charges by the Rock the House Digital Designs will be
$ 500 + 50(10)= $ 500+ $500= $1000
And the charges for the services by Elegant Home Architects will be
$75.00(10) = $ 750
Therefore the Elegant Home Architects charges are less than Rock the House Digital Designs charges.
But if the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then Rock the House Digital Designs will be a better option .
Rock the House Digital Designs
For 2 hours
$ 500 + 50(2)= $300
For 1 Hour
$500 + 50 (1)= $ 550
Elegant Home Architects
For 2 hours
$75.00(2) = $ 300
For 1 Hour
$75.00(1) = $ 75
Why isn’t the maximum ACT score (36) at the 100th percentile?
Answer and Explanations
ACT score percentile help colleges compare students with one another, rather than just looking at everyone’s score. The score range is between 1 and 36, the highest score that one can receive on the ACT is 36. Moreover, 36 is the perfect score.
The maximum ACT score (36) is that in 2018, only 3,741 students (out of millions of test-takers) scored a perfect 36 on the ACT. The 99th percentile of test-takers includes those who earn 35 or 34 on the ACT. We can miss up to five questions on the ACT and still earn a 36. That is a reason why the maximum ACT score is 36 at the 100th percentile.
The ACT score report will provide more information about test-taking experience in the form of sub score. The higher the score, you will get into the colleges of your choice.
The maximum ACT score is not at the 100th percentile. because the student cannot score more than himself as well as others whom scored the same.
Although your question lacks some data a general answer have been provided above
For the maximum score ( 36) to be at the 100th percentile the individual who scores the maximum ACT score, must have scored higher than others and also him/herself in the data set.
Even if a student scores the highest score (36) it does not mean they have scored higher than others who had the same score ( 36 ) with them or him/her self.
Hence we can conclude that the maximum ACT score ( 36 ) cannot be at the 100th percentile because the student cannot score more than himself as well as others whom scored the same.
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Which relationship is always true for the angles r, x, y, and z of triangle ABC? A triangle is shown with a leg extending past the top vertex. The vertices are labeled ABC. Angle y is located inside the triangle at vertex B. Angle z is located inside the triangle at vertex C. Angle x is located outside the triangle between beside vertex A and the extended leg. Angle r is located inside the triangle at vertex A. x + z = y 180 degrees − x = r x + y + z = 180 degrees x + y + z = 90 degrees
Answer:
y+z=x
Step-by-step explanation:
we know that
The Exterior Angle Property of a Triangle states that the measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles
In this problem
Angle y and angle z are interior angles of triangle ABC and angle x is a exterior angle of triangle ABC
therefore
Applying the Exterior Angle Property of a Triangle
y+z=x
Hope This Helps!
Answer: (180 degrees − x = r)
Step-by-step explanation:
I took the test
Joshua rolls two dice to form a two-digit
integer. If the number on the first die rep-
resents the tens digit and the number on the
second die represents the units digit, what
is the probability that the integer formed is
divisible by 8?
*Does anyone know which “category” or topic this question would fall under? Like what would I search to find more questions similar to this?
Answer:
fits under statistics category (also probability or math :\)
Write the slope-intercept form of the equation of the line through the given points.
Answer:
12) [tex] y = -x - 5 [/tex]
Step-by-step explanation:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
12) (0, -5), (-1, -4)
[tex] y - (-5) = \dfrac{-4 - (-5)}{-1 - 0}(x - 0) [/tex]
[tex] y + 5 = \dfrac{-4 + 5}{-1}(x) [/tex]
[tex] y + 5 = \dfrac{1}{-1}(x) [/tex]
[tex] y = -x - 5 [/tex]
Answer:
work is pictured and shown
If the size of the matrix B is 4 × 5, the size of the matrix D is 4 × 2 and the order of the matrix E is 5 × 4, then the order of the matrix D^T × (BE) is:
Answer:
The order of the matrix D^T × (BE) is 2 × 4
Step-by-step explanation:
In the multiplication of matrix, the number of columns in the first matrix must be equal to the number of rows of the second matrix. The resulting matrix from the product will have the same number of rows as the first matrix and the same number of column as the second matrix. For example, given Matrix A of order (m × n) and Matrix Z of order ( n × k), the product of the two matrices will give a matrix ( say Y) of order (m × k).
AZ = Y
(m x n)(n x k) = (m x k)
Now, From the question,
The order of Matrix B is 4 × 5,
the order of the matrix D is 4 × 2
and the order of the matrix E is 5 × 4.
To determine the order of the matrix D^T × (BE)
First, will find the order of (BE)
Order of BE = (4 × 5) (5 × 4)
Order of BE = (4 × 4)
Hence, the order of matrix (BE) is 4 × 4.
Now, we will determine the order of matrix D^T
D^T means the transpose of matrix D.
The transpose of a matrix is defined as a new matrix whose rows are the columns of the original matrix and the columns of the new matrix are the rows of the original matrix. This means given Matrix A of order (m × n), the transpose of Matrix A (A^T) will have an order of (n × m).
The order of the matrix D is 4 × 2
Hence, the order of the transpose of matrix D (D^T) will be 2 × 4
Now, the order of the matrix D^T × (BE) will be
Order of the matrix D^T × (BE) = (2 × 4) × (4 × 4)
Order of the matrix D^T × (BE) = 2 × 4
Hence, the order of the matrix D^T × (BE) is 2 × 4.
An empty can weighs 30 grams. The weight of the same can filled with liquid is 47.3 grams. Which equation could be used to find w, the weight of the liquid?
Answer:
w = y - x is the equation to find w
Where,
w = Weight of the liquid
x = Weight of the empty can
y = Weight of the can with liquid
Step-by-step explanation:
Let
Weight of the empty can = x
Weight of the liquid = w
Weight of the can with liquid = x + w = y
x= 30 grams
w = ?
y= 47.3 grams
y = x + w
w = y - x
= 47.3 - 30
= 17.3
w= 17.3 grams
Therefore, the weight of the liquid is 17 .3 grams
Mr. DeLuca had $568.34 in a bank account. How much money did he have left in his bank account after he used his debit card two times, each time for $27.50?
Answer:
$513.34
Step-by-step explanation:
Mr. DeLuca used his debit card twice, each time for $27.50. This is a total of $55 spent.
$27.50 × 2 = $55
You now have to subtract the money spent from his bank balance.
$568.34 - $55 = $513.34
$513.34 was left in his bank account.
what is the minimum amount of colors to be used to shade 4 different regions?
The four color theorem-No more than 4 colors are required to color the regions map
What is 124.62 rounded to the nearest whole number? Please ASAP!
124.62 rounded to the nearest one is 125.
Rounding 124.62 to the nearest one is equivalent to finding the integer multiple of one nearest to 124.62.
What is the nearest number?" Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. "
124 ≤ 124.62 ≤ 125
The distance from to 124.62 to 124 is = 124.62 - 124 = 0.62
The distance from to 124.62 to 125 is = 125 - 124.62 = 0.38
So, the rounded to the nearest whole number is 125.
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don't get any of this
Answer:
the value of the printer is going down over the years because it is getting older. all you need to do for this is label the x and y axis with the nbers on the graph and then fill it in
has ur teacher gone over how to fill in graphs yet?
Represent "The product of 5 and a number z" mathematically.
Answer:
5z
Step-by-step explanation:
Answer:
5z
Step-by-step explanation:
'The product of 5 and a number' would be 5 * n.
Since the number in the question would be 'z', we will write it as '5 * z'.
However, the most ideal way to write this is '5z'. So, "The product of 5 and a number z" would be '5z'.
Hope this helps.
Given this inequality. please solve for v. If you can explain your steps.
Answer:
v > -1
Step-by-step explanation:
v satisfies both these inequalities:
(*) -17 + 4v < 10v - 11
(**) 10v - 11 < 11v + 6
(*) <=> -17 + 11 < 10v - 4v
<=> -6 < 6v or 6v > -6
<=> v > -1
(**) <=> -11 - 6 < 11v - 10v
<=> -17 < v or v > -17
Combine (*) and (**)
--> Solution for this inequality is v > -1
b) James went to Black Rock coffee shop and ordered
2 coffees and 5 bagels for which he paid $24. The next
morning he returned to buy 3 coffees and 4 bagels for
$22. Based on this information, determine how much
each item costs.
Answer:
Coffees cost $2 each and bagels cost $4 each
Step-by-step explanation:
Let
Coffee=c
Bagels= b
2 coffees and 5 bagels for which he paid $24
2c + 5b= 24 (1)
he returned to buy 3 coffees and 4 bagels for
$22
3c + 4b = 22 (2)
2c + 5b= 24 (1)
3c + 4b = 22 (2)
Multiply (1) by 3 and (2) by 2
6c + 15b = 72 (3)
6c + 8b = 44 (4)
Subtract (4) from (3)
15b - 8b = 72 - 44
7b = 28
Divide both sides by 7
b= 28 / 7
= 4
b= $4
Substitute b=4 into (1)
2c + 5b= 24
2c + 5(4) = 24
2c + 20 = 24
2c = 24 - 20
2c = 4
Divide both sides by 2
c= 4 / 2
c= $2
Therefore,
Coffees cost $2 each and bagels cost $4 each
Lucy wants to be exempt from her semester exam. In order for that to happen, she has to average an 85 over 3 test grades. Her first 2 test grades were 81 and 86. What does Lucy need to make on her third test in order to have an exact average of 85 and be exempt from her exam?
Answer:
Grades to be scored in 3rd exam = 88
Step-by-step explanation:
Given that average of 3 numbers is 85.
First two numbers are 81 and 86.
To find:
3rd number so that average is 85
Solution:
Let the third number = [tex]x[/tex]
Formula for average is:
[tex]Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}[/tex]
Here, sum of numbers = [tex]81+86+x =167+x[/tex]
Total count of numbers = 3
[tex]85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}[/tex]
Grades to be scored in 3rd exam = 88
Simplest form 9/10-4/10 ?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
9 - 4 = 5
[tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
4/10 = 2/5
9/10 - 2/5
LCD = 10
make the denominators the same as the LCD
9/10- 2x2 / 5x2
9/10 - 4/10
join the denominators
9-4/ 10
5/10 = simplify
=
1/2
Simplify by combining like terms. Type the terms in alphabetical order. -5y+9x+9y+5x=
================================================
Explanation:
x is a variable or placeholder for a number. Think of it like a box.
1x = 1 box
2x = 2 boxes
and so on
9x = 9 boxes
5x = 5 boxes
9x+5x = 9 boxes + 5 boxes = 14 boxes = 14x
So that's one way to see how 9x+5x = 14x.
Or you could add the coefficients 9 and 5 to get 9+5 = 14. Then tack an x onto everything.
----------
The y terms are handled in a similar fashion.
-5y + 9y = 4y
which is the same as
9y - 5y = 4y
You could think of it like this
(9 yaks) - (5 yaks) = 4 yaks
So we started with 9 yaks and took away 5 of them to be left with 4 yaks.
----------
After getting the results 14x and 4y. We would then have the final answer 14x+4y
The x and y terms cannot be combined since they are not like terms. So we leave that expression as is.
16.When writing a repeating decimal as a fraction, does the number of repeating
digits you use matter? Explain.
Answer:
Yes. It needs to be clear that it is on going. So as long as it is evident that it repeats, you're good.
Step-by-step explanation:
A 0.40 kg bird is flying at a constant speed of 8.0 m/s. What is the bird's kinetic energy?
Answer:
The correct answer is 12.8 J.
Step-by-step explanation:
To solve this problem, we must remember how to calculate the kinetic energy of an object.
The kinetic energy is represented by the formula K = 1/2 * m * v^2, where m represents the mass of the object and v represents the speed or velocity of the object. If we plug in the given values into the formula, we get:
K = 1/2 * m * v^2
K = (1/2) * (0.40) * (8.0)^2
Our first step is to square the velocity. After doing this step, we get the following:
K = (1/2) * (0.40) * (64)
Finally, we can perform the multiplication, to get:
K = 12.8
The unit for kinetic energy is joules, so the correct answer is 12.8 J.
Hope this helps!
Kinetic energy is the energy due to motion of an object
The kinetic energy of the bird is 12.5 joules
Reason:
The known parameter are;
The mass of the bird, m = 0.50 kg
The speed of the bird, v = 8.0 m/s
Required:
To find the kinetic energy of the bird
Solution:
[tex]Kinetic \ energy = \dfrac{1}{2} \cdot m \cdot v^2[/tex]
Therefore;
[tex]The \ kinetic \ energy \ of \ the \ bird = \dfrac{1}{2} \times 0.40 \ kg \times (8.0 \ m/s)^2 = 12.8 \ J[/tex]
The kinetic energy of the bird is 12.8 J
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If x is to 9 as 8 is to 12, then x is equal to _____
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
This is basically just a ratio in disguise. Ratios can be represented as fractions, and we can write these ratios to be equal to each other.
[tex]\frac{x}{9} = \frac{8}{12}[/tex]
We can solve for x using the cross products property:
[tex]9\cdot8=72\\\\72\div12=6[/tex]
Hope this helped!
Answer:
x=6
Step-by-step explanation:
We can write ratios to solve
x 8
----- = -----------
9 12
Using cross products
12x = 8*9
12x = 72
Divide by 12
x = 72/12
x =6
brainlist if CORRECT
If [x] + x + y =10 AND \y] + x - y =12 then find the value of x + y
Answer:
hope it helps
Step-by-step explanation:
2x+y=10
x-2y=12
2x+y=10
2x-4y=24
y=-14/5
2x=10+14/5
2x=64/5
x=32/5
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/x-1
f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)
To confirm that f(x) and g(x) are inverses.
f(g(x)) = x
g(f(x)) = x
f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)
f(g(x)) = (-15x² -15x)/(-15x² - 15)
f(g(x)) = -15x/-15
f(g(x)) = x
g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)
g(f(x)) = (-15x² - 105x)/(-15x²- 105)
g(f(x)) = -105x/-105
g(f(x)) = x
f(x) and g(x) are inverses.
A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it punctures the bike’s tire. After the bike has moved forward another 56π inches, how high above the ground is the screw? Round to the nearest tenth of an inch. 4 inches 8 inches 12 inches 16 inches
Answer:
The correct option is;
16 inches
Step-by-step explanation:
The parameters of the motion given are;
The diameter, D of the bicycle = 16 inches;
The distance the bike moves (forward) after the screw punctures the tire = 56·π inches
We note that the circumference of the bicycle = π·D = π × 16 = 16·π inches
Therefore;
56·π inches/(16·π inches) = 3.5
Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.
The height, h of the screw in the final half turn is given by the relation;
h = A×cos(Bx - C) + D
A = Amplitude of the motion = Diameter/2 = 16/2 = 8
P = The period of the motion 2·π/B
B·x = The angle described by the motion = Half of one revolution = π = 180°
C = Phase shift = π
D = The midline = Diameter/2 = 8 inches
Therefore;
h = 8×cos(π - π) + 8 = 16 inches
After the bike moves forward another 56·π inches the height of the screw = 16 inches.
Answer:
16 inches
Step-by-step explanation:
just took the assignment
Consider the expression below.
(a + 4)(a + 9)
For (x + 4)(x + 9) to equal 0. either (x + 4) or (x + 9) must equal
The values of x that would result in the given expression being equal to o, in order from least to greatest, are
and
Answer:
x = - 9, x = - 4
Step-by-step explanation:
Set (x +)(x + 9) equal to zero, that is
(x + 4)(x + 9) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 9 = 0 ⇒ x = - 9
Thus
x = - 9, x = - 4
M is between points c and q. Cm =22 and cq =39. What is mq
Answer: mq = 17
Step-by-step explanation:
If cm is 22 and cq which is the whole distance, then subtract the distance of cm which is 22 from the distance of cq which is 39.
39 - 22 = 17
If DE= 4x–1, EF= 9, and DF= 9x–22 , find the value of x
Answer:
The correct answer is x = 6.
Step-by-step explanation:
To solve this problem, we first must recognize that DE + EF = DF.
From this information, we can set up the following equation when we substitute in the given values:
DE + EF = DF
(4x-1) + 9 = 9x - 22
Our first step is going to be to combine like terms on the left side of the equation. This is modeled below:
4x - 1 + 9 = 9x - 22
4x + 8 = 9x - 22
Then, we should subtract 4x from both sides of the equation.
8 = 5x - 22
Now, we can add 22 to both sides of the equation.
30 = 5x
Finally, we can divide both sides by 5.
x = 6
Therefore, the correct answer is x = 6.
Hope this helps!
3x + 5 + 5x – 2
Combine the like terms
- 5 – 8p = – 3p
What is the correct solution?
Answer:
p = -1
Step-by-step explanation:
Step 1: Write out equation
-5 - 8p = -3p
Step 2: Add 8p to both sides
-5 = 5p
Step 3: Divide both sides by 5
-1 = p
Step 4: Rewrite
p = -1
Answer:
P=-1
Step-by-step explanation:
-5-8p=-3p
+8p +8p
------------------
-5=5p then divide both sides by 5
P=-1
what is
[tex] \frac{2}{3}and \frac{5}{6} [/tex]
as a decimal?
The ratio of girls to the total number of students in class is 4 to 7. How many students are girls if class has 21 students in all?
Answer:
12
Step-by-step explanation:
There would be 12 girl students in a class of 21 students.
What is proportion?"A proportion is a mathematical statement where two or more ratios are equivalent."
We have been given that, the ratio of girls to the total number of students in class is 4:7
We need to find the number of girl students if the class has 21 students in all.
Let 'n' represents the number of girl students.
⇒ [tex]\frac{4}{7} = \frac{n}{21}[/tex]
⇒ [tex]4\times 21 = n\times 7[/tex] ......................(cross product)
⇒ [tex]84 = n\times 7[/tex]
⇒ [tex]n=\frac{84}{7}[/tex] ......................(Divide each side by 7)
⇒ [tex]n=12[/tex]
Hence, there would be 12 girls if class has 21 students in all.
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