[tex]\frac{1}{2}[/tex] of the water takes [tex]\frac{1}{2}[/tex] of the fuel and empty tank takes [tex]\frac{1}{6}[/tex] of the fuel, the
fraction that would will be spent if there was no leak is [tex]\underline{\dfrac{11}{18}}[/tex] of the fuel
How can the fraction of the fuel spent be found?
The given parameters are;
The volume of oil consumed = [tex]\mathbf{\dfrac{1}{2}}[/tex] of the fuel tank
Volume consumed if the water tank was empty = [tex]\dfrac{1}{6}[/tex] of the fuel tank
Let w represent the weight of the water that fills the tank.
Therefore;
[tex]The \ average \ weight \ carried \ by \ oil = \dfrac{w + \dfrac{w}{2} }{2} = \mathbf{\dfrac{3 \cdot w}{4}}[/tex]
The amount of fuel consumed by the water that leaked = [tex]\dfrac{1}{2} - \dfrac{1}{6} = \dfrac{1}{3}[/tex]
Let x represent the amount of oil used to carry only the water if there
was no leak, therefore;
[tex]\mathbf{\dfrac{\frac{3 \cdot w}{4} }{w} }= \dfrac{\frac{1}{3} }{x}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot w}{4} \times x}} = \dfrac{1}{3} \times w }[/tex]
[tex]x = \dfrac{4}{3 \times 3} = \dfrac{4}{9}[/tex]
The total amount of fuel that will be consumed without leakage is
therefore;
[tex]Total \ amount \ of \ fuel = \dfrac{4}{9} + \dfrac{1}{6} = \mathbf{ \dfrac{11}{18}}[/tex]
The amount of oil consumed if there was no leakage is therefore;
[tex]\underline{\dfrac{11}{18} \ of \ the \ fuel \ tank}[/tex]Learn more about averages here;
https://brainly.com/question/24398353
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
No option is correct.
Step-by-step explanation:
See attached image (without the student).
You pay $900 rent per month your first year. Each year after your rent increases by
10%. After 10 years living in the apartment, what is the total amount of rent you will
have paid?
Answer:
$1,800
Step-by-step explanation:
($900)(0.1)(10) = $900
$900 + $900 = $1,800
write an equivalent expression for (x+y)(x-y)
Step-by-step explanation:
(x+y)(x-y)
=> [tex] {x}^{2} - {y}^{2} [/tex]
Nichole is out shopping and finds a $51.00 bike that was
marked down by 92%.
How much was the item originally?
it was originally "x" or that is 100%. We also know that she found it for 51 bucks, and that those 51 bucks are 100% - 92% = 8% of the original price, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 51&8 \end{array}\implies \cfrac{x}{51}=\cfrac{100}{8}\implies \cfrac{x}{51}=\cfrac{25}{2} \\\\\\ 2x=1275\implies x=\cfrac{1275}{2}\implies x=637.5[/tex]
What is an equation of the line that passes through the point (-4, 5) and is perpendicular to the line 4x + y = 7?
Answer:
x -4y = -24
Step-by-step explanation:
Given the equation of a line in standard form, you can write the equation of the perpendicular line by swapping the coefficients and negating one of them. The constant needs to be adjusted to make the equation true at the point you want the line to pass through.
4x +y = 7 . . . . given line
x -4y = constant . . . . equation with coefficients swapped, one negated
x -4y = (-4) -4(5) = -24 . . . . equation with appropriate constant
An equation for the desired line is ...
x -4y = -24
__
Additional comment
The standard form equation has a positive leading coefficient, so the choice of which coefficient to negate will take that into account.
The slope of the standard form line ...
ax +by = c
is m = -a/b.
The slope of the perpendicular line is the opposite reciprocal of this:
m' = -1/m = b/a
You can see that this swaps the coefficients and negates one of them.
Which statement describes the graph of X = 4?
A) It is paralel to the x-axis.
B) It has a slope of 4.
C) It is parallel to the y-axis.
D) It passes through the point (0,4).
Answer:
the answer is D
Step-by-step explanation:
Because the point of x=4 is passed through the point (0,4).
Find the lengths of AC. Round your answer to the nearest whole number. C a 22.69 B 13 cm A
The triangle ABC is a right triangle
The length of AC is 12.00 cm
How to determine the length of ACFrom the figure, we have the following parameters:
Length AB = 13 cm
Angle A = 22.6 degrees
Represent the length AC with b.
So, we have the following cosine ratio
[tex]\cos(A) = \frac{b}{AB}[/tex]
Substitute known values
[tex]\cos(22.6) = \frac{b}{13}[/tex]
Make b the subject
[tex]b = 13 * \cos(22.6)[/tex]
Evaluate the product
[tex]b = 12.00[/tex]
Hence, the length of AC is 12.00 cm
Read more about right triangles at:
https://brainly.com/question/16249977
Susan did a puzzle in 5 minutes and 55 seconds. Jamal did the same puzzle in 11 minutes and 42 seconds. Susan says, ‘I did the puzzle in less than half the time Jamal did the puzzle. Is Susan right?
Answer:
No, Susan is not right.
Step-by-step explanation:
Susan's time = 5:55
Jamal's time = 11:42
Half of Jamals time = 5:51
5:55<5:51
Susan is not right
Solve for x. Round to the nearest tenth, if necessary.
х
F
F
3.5
1167
E
Check the picture below.
Make sure your calculator is in Degree mode.
What is the anwser I need to get this done!!
Answer:
1. none of these
2. vertical angles
Step-by-step explanation:
itz cuz im that bi/tch
What is true about sides opposite congruent
angles within a triangle?
Answer:
The converse of the base angles theorem is always true. The base angles theorem states that if two sides of a triangle are congruent the angles opposite them are also congruent. The converse of this statement is that if two angles in a triangle are congruent, then the sides opposite them will also be congruent
Step-by-step explanation:
Cos s=-2/5 and sin t=4/5, s and t are in quadrant 4 find cos(s+t) and cos(s-t)
With Cos s=-2/5 and sin t=4/5, s and t are in quadrant 4, cos(s+t) and cos(s-t) is mathematically given as
cos(s+t)= 0.493
cos(s-t)= 0.97321
What are the values of cos(s+t) and cos(s-t)?Question Parameter(s):
Cos s=-2/5 and sin t=4/5, s and t are in quadrant 4
Generally, the equation for the s and t as functions of the 4 qudrants is mathematically given as
cos(s+t) = cos(s)*cos(t) - sin(s)*sin(t)
Therefore
cos(s+t)= -4/5 * [tex](-\sqrt{21}[/tex]/5) - (-3/5)*(-2/5)
cos(s+t)= 4*[tex]\sqrt{21}/[/tex]25 - 6/25
cos(s+t)= 0.493
In conclusion,
cos(s-t) = cos(s)*cos(t) + sin(s)*sin(t)
cos(s-t)= -4/5 * (-[tex]\sqrt{21}/[/tex]5) + (-3/5)*(-2/5)
cos(s-t)= 4[tex]*\sqrt{21}[/tex]/25 + 6/25
cos(s-t)= 0.97321
Read more about Lenght
https://brainly.com/question/8552546
Area of a triangle 11.7 m
11.7 m
19.2 m
12.3 m 2
Answer:
Step-by-step explanation:
Unit of area is m^2, so last choice
(GIVING BRAINLIST)
The tables in the pottery class sit 8 students each. If there are 35 students in the class, how many tables are needed?
Group of answer choices
5
4
280
4.375
Answer:
The answer for this oblique question is 4.375
Step-by-step explanation:
for 35 ÷ 8 = 4.375
Answer:
35/8=4.375
5 tables needed
Step-by-step explanation:
35/8=4.375
you have to round cuz there can't be 0.375% of a student
and there can't be 0.375 of a table...so it's 5 tables
Please help me, the question is in the screenshot. GIVING 50 POINTS!! and brainliest<3
Solution:
Note that:
Volume of spherical asteroid = 4πr³/3Finding the volume:
Volume of spherical asteroid = V = 4πr³/3=> V = 4 x π x (8.5 x 10²)³/3=> V = 4 x π x (8.5 x 10²)(8.5 x 10²)(8.5 x 10²)/3=> V = 4 x 3.14 x 8.5 x 10² x 8.5 x 10² x 8.5 x 10²/3=> V = 7713.41 x 10⁶/3=> V ≈ 2571.14 x 10⁶Converting into scientific notation:
=> V ≈ 2571.14 x 10⁶=> V ≈ 2.57114 x 10⁹ ≈ 2.57 x 10⁹ (Option A)television has a normal price of 675
in a sale, the price is reduced by 32%
work out the price of the television in the sale
Answer:
$459
Step-by-step explanation:
Given the following question:
32% of 675
To find the answer to this question we need to use the formula to calculate 32% of 675. Then we subtract that answer from our original price which will then give us our answer.
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{32\times 675}{100}[/tex]
[tex]32\times675=21600[/tex]
[tex]21600\div100=216[/tex]
[tex]=216[/tex]
Subtract from the original price:
[tex]675[/tex]
[tex]675-216=459[/tex]
[tex]=459[/tex]
The television after a 32% discount will cost "$459."
Hope this helps.
The radius, R , of a sphere is 3.2 m. Calculate the sphere's volume, V . Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answer:
=137.2m^3
Step-by-step explanation:
Formula:
V=4/3πr^3
=4/3*3.14*3.2^3
=4/3*3.14*32.768
V=137.188693333m^3
V Rounded=137.2m^3
Can someone help me
Answer:
Q1/6.5
Q2/ 12.5
.....
.....
.....
......
......
.....
.
.....
.
Step-by-step explanation:
per minute means ÷ mins (on the denominator)
There are 8 red marbles and 9 blue marbles in a bag. What is the ratio of blue marbles to red marbles?
Answer:
8:9
Step-by-step explanation:
when it comes to ratios and it asks you what the ratio is and theirs no division, adding, multiplication, subtraction, or anything like then you just take the first number and the second number then put this : between the two numbers and that's it
Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat. suppose Bobbys cat and dog were 6 miles apart after 30 min. Write an equation to describe this situation
The equation to describe this situation is that Bobby's cat and dog were 6 miles apart after 30 minutes is 0.5x = 6
Bobby's cat's speedSince Bobby's cat runs at x mph, its speed is x mph.
Bobby's dog's speedAlso, Bobby's dog runs twice as fast as his cat. So, his dog's speed is v = 2x.
TimeSince they both move a distance in t = 30 min = 30 min × 1 h/60 min = 0.5 h.
Bobby's cat's distanceBobby' cat's distance in 30 mins is d = x × 0.5 h
= 0.5x miles
Bobby's dog's distanceAlso, Bobby's dog covers a distance in 30 min, D = v × 0.5 h
= 2x × 0.5 h
= x miles
The required equationSince Bobbys cat and dog were 6 miles apart after 30 min, we have that
D - d = 6
x - 0.5x = 6
0.5x = 6
So, the equation to describe this situation that Bobby's cat and dog were 6 miles apart after 30 minutes is 0.5x = 6
Learn more about linear equations here:
https://brainly.com/question/15602982
Answer:
1.5x=6
Step-by-step explanation:
after 30 min they will be 1.5x miles apart from each other, so you know that they traveled 6 miles, 1.5x=6 :)
Rsm sucks :(
polynomials worksheet
Answer:
yes what the person above said.
Step-by-step explanation:
g(×)=(3×+12)/4
Find g^-1(×)
g^-1(6)
Answer:
fog)(x)=f(g(x))=2(3x+2)−1=6x+4−1=6x+3=3(2x+1)
f
(
x
)
=
3
−
2
x
,
g
(
x
)
=
3
x
2
+
2
Set up the composite result function.
g
(
f
(
x
)
)
Evaluate
g
(
f
(
x
)
)
by substituting in the value of
f
into
g
.
g
(
3
−
2
x
)
=
3
(
3
−
2
x
)
2
+
2
no one will probably answer but just Incase.. please help me with this
Answer:
50
Step-by-step explanation:
10 (x - y)
Substitute the given values for x and y.
10 (8 - 3)
= 10 (5)
= 10 x 5
= 50
hope this helps!! p.s. i really need brainliest :)
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
c = 18, ∡ A = 45
Answer:
ok 1920
Step-by-step explanation:
Homework Section 9.. On a photograph of a triangular piece of land, the lengths of the three sides are 6 cm, 8 cm, and 9 cm, respectively The shortest side of the actual piece of land is 180 m long Find the lengths of the other two sides
Answer:
Step-by-step explanation:
180m = 180 * 100 = 18000 cm
Scale factor = 6 : 18000
= 1 : 3000
Length of other two sides:
8*3000 = 24000 cm = 240 m
9 * 3000 = 27000 cm = 270 m
How would you describe the amount of money earned over six weekends?
decreasing
can't be determined
staying the same
increasing
Answer:
Cant
Step-by-step explanation:
Cole rides his bike to the ball field starting from home. This describes his trip:
A. Rides toward the field
B. Stops to wait for a friend
C. Continues to ride toward the field
Drag one segment to each box to show the shape of the graph of Cole's distance from home for each interval of time. PLS HELP I GIVE 25 points
Answer:
i think it is a because that the answer
Find angle C, can someone help me with this please?
Answer:
m∠C = 98°
Step 1: Derive an Equation
To solve this problem, we will use what is called the Exterior Angle Theorem. This states that in a triangle, the measure of an exterior angle is equal to the sum of the measures of its 2 corresponding remote interior angles.
Exterior angle - an angle formed by the extension of 1 side of the triangleRemote interior angles - the 2 angles that don't share a vertex with the exterior angleIn this case, the exterior angle is ∠T (the obtuse one) and the remote interior angles are ∠C and ∠Y. Therefore, m∠T = m∠C + m∠Y.
Substituting the given measures into the equation, we get:
[tex]3x+2+x=130[/tex]
Step 2: Solve the Equation
[tex]3x+2+x=130[/tex]
[tex]4x+2=130[/tex] (Combine like terms)
[tex]4x=128[/tex] (Subtract 2 from both sides to isolate [tex]x[/tex])
[tex]x=32[/tex] (Divide both sides by 4 to get rid of [tex]x[/tex]'s coefficient)
Step 3: Answer the Question
We now know what [tex]x[/tex] is. Therefore, m∠C = [tex]3*32+2=\bf 98 \textdegree[/tex].
To learn more about the Exterior Angle Theorem, check out the following questions:
https://brainly.com/question/17147409https://brainly.com/question/6330929Simplify (8^2/3)^4.
I have to type this to post it
Answer:
256
Step-by-step explanation:
(a^n)^m = a^nm
=(8^⅔)⁴ =8^⅔×⁴
=2³×⅔×⁴ (8 = 2³)
=2^8 =256
Please mark my answer the brainliestAnswer:
Step-by-step explanation:
8 = 2*2*2 = 2³
[tex]\left[8^\left(\dfrac{2}{3}\right) \right]^{{4}}=\left[2^{3}^\left(\dfrac{2}{3}\right) \right]^{{4}}\\\\\\=2^{3*\dfrac{2}{3}*4}\\\\\\=2^{2*4}\\\\\\=2^{8}[/tex]
GIVING BRAINLIEST!!!!
Answer:
Zack is correct with the -4.5
Step-by-step explanation:
When multiplying by .5 just cut the number in half so 4.6 becomes 2.3 and since the .5 was negative the 2.3 becomes a negative so -2.3 -2.2=-4.5
Hope this helped.
A brainliest is always appreciated.