Answer:
a. 8 gallons
b. (11-0.75t) gallons
Step-by-step explanation:
a. Here in this question, we are told that the total amount of fuel in the fuel tank is 11 gallons and the car consumes 0.75 gallon per hour. We are interested in knowing the amount of fuel left in the tank after driving for four hours.
We proceed as follows;
Since 0.75 gallon is consumed in an hour, the amount of fuel consumed in 4 hours would be the amount consumed in an hour * 4 hours
Mathematically, that would be 0.75 * 4 = 3 gallon
Now, the amount of fuel left is simply the difference between the initial amount of fuel in the tank minus the amount of fuel present after 4 hours.
That would be; 11 - 3 = 8 gallons
b. Like above, we want to know the amount of fuel left after t hours.
Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 * t = 0.75t
Now, the amount of fuel that would be left in the tank would be the difference between what we had initially and what was used up.
Mathematically, that would be 11- 0.75t
How many three-letter permutations
can you make using the letters in
BEACH?
Can someone please help me?
Answer:
60
Step-by-step explanation:
nPr=n!/(n-r)!
5!/(5-3)!
(5*4*3*2*1)/(2*1)
120/2
60
Answer:
60
Step-by-step explanation:
A permutation is a rearrangement of its elements in any sequence or linear order.
We are asked to rearrange the word BEACH into three letter permutations.
We find that each letter represents the first letter 5 x 3 = 15
Then distributes 5 places, so that 15 x 5 = 60
Which graph represents a function?
Answer:
The first Answer:
Step-by-step explanation:
The x-values are not the same on one line:
Image
The line connecting isn't perfect but see what I mean?
A farm has a square fenced-in area with side length x where the farm gives children pony rides. Adjacent to one entire side of the square area, there is a roped-off rectangular area where the children line up. This rectangle is 4 yards wide and x yards long.
1.The total area of the square and rectangular areas together is 2,700 square yards. Write an equation that represents this situation.
2. Use your equation from part a to find the dimensions of the roped-off rectangular area.
please help so i can pass my class!!
Answer:
1) x²+4x=2700
2) 50x50
Step-by-step explanation:
Pony area = x²
line-up area=4x
x²+4x=2700
x²+4x-2700=0
(x-50)(x+54)
So x= 50 or -54. Since it can’t be a negative number, it must be 50.
CHECK:
Square = 50x50 = 2500
Line up area = 50x4 = 200
2500+200=2700 YES
Could you help with maths please? All shown on the picture :)
Answer:
4 is tenths (a) and 5 is hundredths (b)
Step-by-step explanation:
Now, 0.45
0 indicates the ones place (it comes before the decimal)
0.45 can also be written as:
0.4+0.05
= 4/10+5/100
what can we conclude from this?
we can say that 4 is in the tenths whilst 5 is in the hundredths.
therefore, a is 4 and b is 5.
Hope this helps you! :)
SOMEONE HELP ME!!!! I WILL GIVE BRAINLIEST!!!
Answer:
B
Step-by-step explanation:
well if we draw the graph we have the following image, and the only one that applies is
B
because 4>3
Estimate the solution to the system of equations.
Hey there! I'm happy to help!
Since we are using graphs, we will do not need to algebraically solve this system of equations.
When you graph a system of equations, the solution is always the point at which the two lines intersect.
Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3
Have a wonderful day! :D
help pleasseeeee ! 15 points
the answers are
(-1,-5)
(0,-3)
(4,5)
(9,15)
Answer:
(0,-3)
Step-by-step explanation:
2x-y = 3
x+2y = -6
Multiply the first equation by 2 so we can eliminate y
2(2x-y =3)
4x -2y = 6
Add this to the second equation
4x -2y = 6
x+2y = -6
-----------------
5x +0y = 0
x = 0
Now find t
x+2y = -6
0+2y = -6
2y =-6
Divide by 2
y = -3
Answer:
Step-by-step explanation:
Let's try to eliminate y.
First we multiply the first equation by 2,
4x - 2y = 6
x + 2y = -6
Then we add them together
5x = 0
x = 0
Now we plug x into the first equation,
4(0) - 2y = 6
-2y = 6
y= -3
Now we plug x into the second equation,
0 + 2y = -6
2y = -6
y = -3
So our answer is,
(0,-3)
Which equation represents the line that is perpendicular to y=1/4 and passes through (-6,-9)?
Answer:
perpendicular means
m1 = 1/4
m2= -1/(1/4)
= -4 (Perpendicular slope)
(-6,-9) = (x1,y1)
so,
y-y1 = m (x-x1)
y-(-9)= -4 (x-(-6))
y+6 = -4 (x+6)
y+6 = -4x-24
y= -4x-24+6
y= -4x-18
hope it helps ^°^
Answer:
[tex]\displaystyle \boxed{y = -4x - 33}[/tex]
Step-by-step explanation:
[tex]\displaystyle y = \frac{1}{4}x[/tex]**
Now, perpendicular equations have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so [tex]\displaystyle \frac{1}{4}[/tex]becomes −4 and you do the following:
−9 = −4[−6] + b
24
[tex]\displaystyle -33 = b \\ \\ y = -4x - 33[/tex]
I am joyous to assist you at any time.
on a map the distance between rip and Janeiro Brazil and San Jose Costa Rica is 4 inches.the scale on the map shows that 1 inch=200 miles ,or if you write it as a ratio.. how would set up a proportion if you want to figure out how many miles it is form Rio de Janeiro to San jose.?
Answer:
The way a proportion is set is as follows;
[tex]\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}[/tex]
The Distance from Rio de Janeiro and San Jose Costa Rica is then found as 800 miles
Step-by-step explanation:
The dimension of the distance between Rio de Janeiro and San Jose Costa Rica = 4 inches
The map scale = 1 inch to 200 miles
To figure out how many miles it is or the actual distance from Rio de Janeiro and San Jose Costa Rica, we have;
[tex]\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}[/tex]
Therefore, we have;
(4 inches × 200 miles)/(1 inche) = Distance from Rio de Janeiro and San Jose Costa Rica
Which gives;
Distance from Rio de Janeiro and San Jose Costa Rica = 800 miles.
Please answer this question now
Answer:
112°
Step-by-step explanation:
Arc CD is part of arc BCD, which is intercepted by the inscribed angle A.
Based on the inscribed angle theorem on circle, the sum of arc CD and CB is twice the measure of angle A.
That is:
CD + CB = 2(129°)
CD + 146 = 2*129
CD + 146 = 258
Subtract 146 from both sides to find CD
CD + 146 - 146 = 258 - 146
CD = 112°
How to do this question plz answer me step by step plzz plz plz plz plz plz plz plz
Answer:
288.4m
Step-by-step explanation:
This track is split into a rectangle and two semi-circles.
We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].
[tex]2\cdot3.14\cdot30\\188.4[/tex]
However this is half a circle, so:
[tex]188.4\div2=94.2[/tex].
There are two semi-circles.
[tex]94.2\cdot2=188.4[/tex]
Since there are two legs of 50m each, we add 100 to 188.4
[tex]188.4+100=288.4[/tex]m
Hope this helped!
Answer:
Step-by-step explanation:
To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.
For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.
15 * 2π ≈ 94.2477796077
We add that to 100m and get:
194.2477796077
daniel thinks of a number and subtracts 2
from it. He divides 32 by the result. If
his answer is 4, what number does he
think of
Answer:
the number is 126
Step-by-step explanation:
1) multiply each side by 32: (n-2) / 32 = 4
2) subtract 2 from each side: n-2 = 128
3) n = 126
Answer:
130
Step-by-step explanation:
So basically this number, minus 2, divided by 32 is 4, so lets write the unknown number as x.
So, (x-2)/32 = 4.
First multiply both sides by 32 to get rid of the denominator.
(32)(x-2)/32 = 4(32) x-2 = 128
Now the -2 remains to figure out x, so you add 2 to both sides to get rid of the -2.
So, x-2+2 = 128+2, -2 +2 is 0, and 128 +2 is 130, so you have x = 130.
4. The function g is defined by
the value of (60) ?
Answer:
Here for the comments .
Step-by-step explanation:
20liters of mixture contain milk nad water in the ratio 5:3 if 4liters of the mixture are replaced by 4 liters of milk find the new ratio of milk to water
Answer:
the new ratio milk/water is 14:6 or 7:3
Step-by-step explanation:
milk/water=5/3
milk +water=5+3=8
ratio of milk=5/8 and ratio of water=3/8
if 4 liter removed from mixture then: 20=4= 16 liter
the amount of milk in 16 liter=16*5/8=10 liter of milk
the amount of water in 16 liter=16*3/8= 6 liter
add 4 liter of milk to the mixture: 10+4=14 liter of milk and 6 liter of water
the new ratio milk/water is 14:6 or 7:3
PLEASE HELP Give me an example of a negative correlation
Answer:
Step-by-step explanation:
An example of a negative correlation is tv viewing and student test grades.
Another example is the video game playing and test grades
Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
Learn more about the standard deviation visit:
https://brainly.com/question/475676
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Michelle's last electric bill listed a previous reading of 17.934 kWh. This month, the electric meter reading is
18,796 kWh. If the electric company charges $0.09 per kWh, what is the charge for usage?
Answer:
charge = 18796 * 0.09$
=1691.64$
Step-by-step explanation:
Answer:
18796 * 0.09$
=1691.64$
Step-by-step explanation:
Given the following three points, find by hand the quadratic function they represent.
(-1,-8), (0, -1),(1,2)
(1 point)
Of(x) = -51% + 87 - 1
O f(x) = -3.2? + 4.1 - 1
Of(t) = -202 + 5x - 1
Of(1) = -3.1? + 10.1 - 1
Answer:
The correct option is;
f(x) = -2·x² + 5·x - 1
Step-by-step explanation:
Given the points
(-1, -8), (0, -1), (1, 2), we have;
The general quadratic function;
f(x) = a·x² + b·x + c
From the given points, when x = -1, y = -8, which gives
-8 = a·(-1)² + b·(-1) + c = a - b + c
-8 = a - b + c.....................................(1)
When x = 0, y = -1, which gives;
-1 = a·0² + b·0 + c = c
c = -1.....................................................(2)
When x = 1, y = 2, which gives;
2 = a·1² + b·1 + c = a + b + c...............(3)
Adding equation (1) to (3), gives;
-8 + 2 = a - b + c + a + b + c
-6 = 2·a + 2·c
From equation (2), c = -1, therefore;
-6 = 2·a + 2×(-1)
-2·a = 2×(-1)+6 = -2 + 6 = 4
-2·a = 4
a = 4/-2 = -2
a = -2
From equation (1), we have;
-8 = a - b + c = -2 - b - 1 = -3 - b
-8 + 3 = -b
-5 = -b
b = 5
The equation is therefore;
f(x) = -2·x² + 5·x - 1
The correct option is f(x) = -2·x² + 5·x - 1.
what is another expression equivalent to 3(8-2)
Answer:
3(6)
??
Step-by-step explanation:
What is the slope and the y-intercept of the line on the graph below? On a coordinate plane, a line goes through points (0, 1) and (4, 0).
The slope is the change in Y over the change in x:
Slope = (0-1) / 4-0) = -1/4
Slope = -1/4
Y intercept is the Y value when x is equal to 0. In the point (0,1) x is 0 and y is 1, so the y-intercept is 1
I need Helpppp quick!!!!
Answer:
G
Step-by-step explanation:
let his fixed price be x and his hourly fee be y;
270 = 4y + x
420 = 7y + x
x is common in both equations
equate the two;
x = 270-4y and x = 420-7y
270-4y = 420-7y
3y = 150
y = 50
x = 270-4*50
x = 70
Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours. Carey’s Earnings h 0 1 3 a $0 $9.75 ? Which value completes the table to show the amount Carey earns for working 3 hours?
Answer:
$29.25
Step-by-step explanation:
For every 1 hour, Carey earns $9.75. Multiply $9.75 by 3 to find out how much she earns for 3 hours of work.
$9.75 × 3 = $29.25
Carey earns $29.25 for working 3 hours.
Answer:
29.25
Step-by-step explanation:
I got it right on edge!! trust me
B is the midpoint of AC. What is the value of x if AC = 52 and AB = 3x - 4
Answer:
x = 10
Step-by-step explanation:
Since B is the midpoint of AC then AB = BC = 3x - 4 and
AB + BC = AC , thus
3x - 4 + 3x - 4 = 52, that is
6x - 8 = 52 ( add 8 to both sides )
6x = 60 ( divide both sides by 6 )
x = 10
what is -7(w+6)^2+21=0.
-18 = -3x + 6 can anybody help me solve this problem
Answer:
[tex]\huge\boxed{x = 8}[/tex]
Step-by-step explanation:
[tex]\sf -18 = -3x+6\\Subtracting \ 6 \ to \ both \ sides\\-18-6 = -3x\\-24 = -3x\\Dividing \ both \ sides \ by \ -3\\8 = x\\OR\\x = 8[/tex]
Answer:
x = 8
Step-by-step explanation:
Here, -3x = -24
x = 8
hope that helps you
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of minutes and a standard deviation of minutes. Find the probability that a randomly selected athlete uses a stairclimber for (a) less than minutes, (b) between and minutes, and (c) more than minutes. (a) The probability that a randomly selected athlete uses a stairclimber for less than minutes is nothing. (Round to four decimal places as needed.) (b) The probability that a randomly selected athlete uses a stairclimber between and minutes is nothing. (Round to four decimal places as needed.) (c) The probability that a randomly selected athlete uses a stairclimber for more than minutes is nothing.
Answer:
Step-by-step explanation:
Let S be the sample space, n(S) = 60
a) Let A be the event that the selected athlete uses
s less than a minute, n(A) = 59
The probability that a randomly selected athlete uses less a minute, P(A) = n(A)/n(S) = 59/60 = 0.9833
b) 1 - 0.9833 = 0.0167
c) 1 - 1 = 0
Of the 40 specimens of bacteria in a dish, 3 specimens have a certain trait. If 5 specimens are to be selected from the dish at random and without replacement, which of the following represents the probability that only 1 of the 5 specimens selected will have the trait?1) (5/1)/(40/3)
2) (5/1)/(40/5)
3) (40/3)/(40/5)
4) (3/1)(37/4)/(40/3)
5) (3/1)(37/4)/(40/5)
Answer:
[tex]\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]
Step-by-step explanation:
The total number of ways in which 5 specimens can be selected from the dish at random is given as C(40, 5).
Since only one of the five specimens would have the trait, the number of ways of selecting the one specimen out of the 3 specimens with the trait is C(3, 1).
3 specimens have the trait therefore 37 specimens (40 - 3) do not have the trait. The number of ways in which the remaining 4 specimens out of the 5 spemimens that do not have the trait is C(37, 4).
Therefore, the probability that only 1 of the 5 specimens selected will have the trait = [tex]\frac{C(3,1)*C(37,4)}{C(40,5)} =\frac{(^3_1)*(^{37}_4)}{(^{40}_5)}[/tex]
Need help pleases 5 stars
Answer:
The third option is the correct answer
Step-by-step explanation:
I am a 100% sure.
Hope this helps....
Have a nice day!!!!
solve 15x²+8x+1÷ 2x-y
Answer:
\frac{\left(5x+1\right)\left(3x+1\right)}{2x-y}
Step-by-step explanation:
15x^2+8x+1:\quad \left(5x+1\right)\left(3x+1\right)
add on 2x -y as the denominator of the fraction
Solve for w. | – w|≥2 Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form.
Answer:
[tex]-2 \geq w \geq 2[/tex]
Step-by-step explanation:
Given
[tex]|-w| \geq 2[/tex]
Required
Solve for w
[tex]|-w| \geq 2[/tex]
In absolution functions;
[tex]|-w| = |w|[/tex]
So, the given expression can be rewritten as
[tex]|w| \geq 2[/tex]
Removing the absolute sign, will gibe
[tex]w \geq 2[/tex] or [tex]w \leq -2[/tex]
When the second inequality os rewritten, it gives
[tex]w \geq 2[/tex] or [tex]-2 \geq w[/tex]
Reorder both inequalities
[tex]-2 \geq w[/tex] or [tex]w \geq 2[/tex]
Lastly, both inequalities are combined
[tex]-2 \geq w \geq 2[/tex]
