Answer:
a : b : c = 12 : 10 : 15
Step-by-step explanation:
Given that: b = [tex]\frac{2}{5}[/tex] of c
i.e b = [tex]\frac{2c}{5}[/tex] ............... 1
2c = 5b
So that;
c = [tex]\frac{5b}{2}[/tex] .................... 2
Also,
4a = 3c
a = [tex]\frac{3c}{4}[/tex] ................ 3
⇒ a = [tex]\frac{3}{4}[/tex] × ([tex]\frac{5b}{2}[/tex])
a = [tex]\frac{15b}{8}[/tex] ................. 4
15b = 8a
b = [tex]\frac{8a}{15}[/tex] ................. 5
Comparing the derived equations:
From equations 2 and 3,
a:c = [tex]\frac{15b}{8}[/tex]: [tex]\frac{5b}{2}[/tex] = 4:5
From equations 1 and 2,
b:c = [tex]\frac{2c}{5}[/tex] : [tex]\frac{5b}{2}[/tex] = 2:3
But a common value of b = 15, gives;
a : c = 12 : 15 and b : c = 10 : 15
Thus, a : b : c = 12 : 10 : 15
The ratio a:b:c in its simplest form is 15:8:20
Ratios and ProportionsGiven the following parameters
b = 2/5 c4a = 3ca = 3/4cTo get the ratio of a:b:c, we will substitute the value of a and b into the ratio to have:
a:b:c = 3/4c : 2/5c :c
Multiply through by 20 to have:
a:b:c = 3/4c * 20 : 2/5c * 20: 20c
a:b:c = 15c:8c:20c
a:b:c = 15:8:20
Hence the ratio a:b:c in its simplest form is 15:8:20
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Tom wants to have $50,000 saved sometime in the future. How much must he deposit every month into an account that pays 1.45% interest, compounded monthly to reach the goal in 5 years?
Answer:
$ 809.78
Step-by-step explanation:
Given that
F = future value = $50,000
Interest rate = r = 1.45% = 0.0145
Number of period per year = 12months
Time expressed in years = 5years
The present value of a periodic deposit
P =( F ×r/n)/{ (1+r/n)^nt} -1
Substituting the values into the above formula
P = (50000× 0.0145/12)/(1+0.0145/12)^12×5}-1
= 50000×0.001208/(1+0.0012)^60}-1
= 60.4/1.0012)^60}-1
60.416/1.074608-1
60.4/0.07460
= $ 809.779
His monthly deposit will be $ 809.78
Solve.
a + 1 = Vb + 1 for b.
Answer:
b = a² + 2a
Step-by-step explanation:
a + 1 = √(b + 1)
(a + 1)² = b + 1 (Square both sides)
a² + 2a + 1 = b + 1 (Expand left side)
a² + 2a = b (Subtract 1)
9) A grandmother is nine times older than her grandson. If she is also 56 years older than
him, what is the age of her grandson after 6 years?
a) 7 years
b) 9 years
c) 11 years
d) 13 years
Answer= 13 years
Solution,
Let the age of grandmother be y
Let the age of grandson be X
according to question,
9x=y ( equation I)
X+56=y( equation ii)
Substituting,
9x=x+56
or,9x-x=56
or,8x=56
or,X=56/8
X=7
Again,
Age of grandson after 6 years
=7 years+6 years
=13 years
Hope it helps
Good luck on your assignment
The age of her grandson after 6 years is 13 years.
What is the algebraic equation?A mathematical statement in which two expressions are set equal to each other is known as an algebraic equation. A variable, coefficients, and constants are commonly included in an algebraic equation.
How to solve this problem?Let the age of the grandmother be x and the age of her grandson be y.
Since the grandmother is 9 times older than her grandson, we can write
x = 9y ...(1)
Since the grandmother is 56 years older than her grandson, we can also write
x = y + 56 ...(2)
We have to solve these two algebraic equations.
Equating the L.H.S. of (1) and (2),
9y = y + 56
i.e. 9y - y = 56
i.e. 8y = 56
i.e. y = 56/8 = 7
So, now the age of her grandson is 7 years.
Therefore the age of her grandson after 6 years is 6+7= 13 years.
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PLEASE HELP. Will give brainliest to whomever answers first.
Answer:
2π/3 I believe !
Step-by-step explanation:
Which expressions are equivalent to RootIndex 3 StartRoot 128 EndRoot Superscript x? Select three correct answers.
128 Superscript StartFraction x Over 3 EndFraction
128 Superscript StartFraction 3 Over x EndFraction
(4RootIndex 3 StartRoot 1 EndRoot)x
(4 (2 Superscript one-third Baseline) ) Superscript x
(2)x
Answer:
(A)[tex]128^{x/3}[/tex]
(D)[tex](4(2^{1/3}))^x[/tex]
Step-by-step explanation:
We want to determine which of the expression is equivalent to:
[tex]\sqrt[3]{128}^ x[/tex]
By the law of indices:
[tex]\sqrt[3]{128}=128^{1/3}\\$Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}[/tex]
Similarly:
[tex]\sqrt[3]{128}^ x \\=\sqrt[3]{64*2}^ x\\=(4\sqrt[3]{2})^ x\\=(4(2^{1/3}))^x[/tex]
The expressions that are equivalent to (∛128)ˣ are; (128)^(x/3) and (4(2^(1/3))ˣ
How to use law of indices?We want to find the expression that is equivalent to (∛128)ˣ
From law of indices, we have that;
(∛128)ˣ = [(128)^(1/3)]ˣ
This can be further expressed as;
(128)^(x/3)
Similarly, we have the simplified expression at;
[(128)^(1/3)]ˣ = (64 * 2)^(x/3)
⇒ (4³ * 2)^(x/3)
⇒ (4(2^(1/3))ˣ
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The weight of a honeybee is 1.2\cdot10^{-1}\text{ g}1.2⋅10 −1 g1, point, 2, dot, 10, start superscript, minus, 1, end superscript, start text, space, g, end text. The weight of the pollen collected by the bee on one trip is 6.0 \cdot 10^{-2} \text{ g}6.0⋅10 −2 g6, point, 0, dot, 10, start superscript, minus, 2, end superscript, start text, space, g, end text.
Answer:1.8*10^-1
Step-by-step explanation:
Answer: 1.8 x 10^−1
Step-by-step explanation:
4x + 3y - 8z
-5x + 7y + 10Z
(+) - 4x – 3y - 8z
Answer:
and 4x-5x-4x+3y+7y-3y-8z+10z-8z
-5x+7y-6z :this is the answer
I don’t understand, what’s the answer and why?
You can rent time on computers at the local copy center for a $9 setup charge and an additional $150 for every 5 minutes. How much time can be rented for $26?
Select the correct choice below and fill in the answer box to complete your choice
A. The independent variable is time (t) in minutes, and the dependent vanable is rental cost (), in dollars. The linear function that models this situation is
(Simplify your answer. Do not include the $ symbol in your answer)
B. The independent variable is rental cost (t), in dollars, and the dependent variable is time (t), in minutes. The linear function that models this situation ist
(Simplify your answer. Do not include the 5 symbol in your answer.)
minutes can be rented for $26
(Round to the nearest minute as needed)
A linear model
reasonable for this situation
Answer:
(A) The independent variable is time (t) in minutes, and the dependent variable is rental cost (), in dollars. The linear function that models this situation is
R(t) = 30t +8
The time that can be rented for $26 = 1min
Step-by-step explanation:
Based on the information given:
Setup charge on Rent at local copy center = $9
an additional $150 for every 5 minutes. To determine the time that can be rented for $26, let's find the relationship between the rental cost and the time.
For every 5min = $150
For 1 min = $150/5
For t min = 150t/5
Where t = number of minutes of rental time
Rental cost = set up charge + additional cost
Let Rental cost = R(t)
R(t) = 9 + 150t/5
Writing it in form of a linear equation: y = mx + c
R(t) = 150t/5 +9
R(t) = (150/5) ×t + 9
R(t) = 30t + 9
The independent variable is time (t) in minutes, and the dependent variable is rental cost (), in dollars. The linear function that models this situation is
R(t) = 30t + 9
The time that can be rented for $26:
Rental cost = $26
R(t) = 30t +9
26 = 30t +9
26-9 = 30t
17 = 30t
t = 17/30 = 0.57
t is approximately = 1min (nearest minute)
The time that can be rented for $26 = 1min
PLEASE HELP WILL MARK BRAINLIEST
Find the area of the right triangle.
Answer:
Step-by-step explanation:
This right triangle is on a grid.
The area is the height * base/2
The base is on a line segment parallel to the x axis which is 6 squares.
The height is on a line segment parallel to the y axis which is 2 squares
The area is the height * base /2
Area = 6 * 2 /2 = 12/2 = 6 square units.
(3 1/4 + 2 5/6) + 1 3/4
19/6
Step-by-step explanation:
3/4 + 5/3 +3/4
3/4 + 3/4 = 3/2
3/2 + 5/3 =19/6 or 3.16....
compared to jenny, sally is 5/6 as tall and may is 4/5 as tall. How many time taller is sally than may
Answer:
25/24
Step-by-step explanation:
Let
Sally=S
May=M
Sally is 5/6 as tall
S = 5/6
May is 4/5 as tall
M = 4/5
S/M = 5/6/4/5
=5/6×5/4
=25/24
I will mark you brainliest!!! Select the answer that includes the correct explanation.
Answer:
Linear. The choice A is correct.
Step-by-step explanation:
In an election of housing society,there are 30 voters.Each of them gives the vote.Three persons X,Y and Z are standing for post secretary.If Mr.X got 2/5 of the total votes and Me.Z got 1/4 of the total votes then how much did Mr.Y get?
Answer:
Mr Y got 10 votes
Step-by-step explanation:
The election of the housing society has 30 voters. Each of them gives the vote. The three person vying for the post of secretary are X, Y and Z.
Le us calculate the votes of each contestant
Mr X
He got 2/5 of the total votes
number of votes = 2/5 × 30
number of votes = 60/5
number of votes = 12
Mr Z
He got 1/4 of the total votes
number of votes = 1/4 × 30
number of votes = 30/4
number of votes = 1/4 × 30
number of votes = 7.5 ≈ 8 votes
Mr Y
The remaining votes will be 30 - 12 - 8 = 10 votes
Therefore,
Mr Y got 10 votes
A biologist uses a box-shaped fish trap that measures 1/4meter by 2/3meter by 3/5meter. What is the volume of the trap in the cubic meters.
To find the volume of a box-shaped fish trap, we have to multiply the three dimensions of it:
(1/4 m)* (2/3 m)* (3/5 m)
= (1*2*3)/ (4*3*5) m^(3)
= 6/ 60 m^(3)
= 1/10 m^(3)
= 0.1 m^(3)
The volume of the box-shaped fish trap is 0.1 m^(3).
Hope this is helpful~
Please help me with my question!!!
Answer: They can make 18 ornaments
Step-by-step explanation:
you make 4 and 1/2 into the common denominator of 4. So then you get 4 and 2/4 you multiply 4 by 4 to get 16 and then add it to the 2/4 to get 18/4 each takes 1/4 so you have 18(1/4)
HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. Obtuse
Step-by-step explanation:
Supplementary Angles: either of two angles whose sum is 180°
Adjacent: have a common side, a common vertex, and don't overlap
A standard six-sided die is rolled three times. Use multiplication to determine the probability that a one or two appears on the second roll, and an odd number appears on the third roll
Answer:
1/6
Step-by-step explanation:
Since we don't care what appears on the first roll
P( outcome) = 1
Second roll
P(1 or 2) = number of 1 or 2 / total number of outcomes
=2/6 = 1/2
Third roll
odd numbers 1,3,5
P( odd number)= number of odd numbers/ total
=3/6 =1/2
P( outcome, 1or 2, odd) = P( outcome) *P(1 or 2) *P( odd number)
= 1* 1/3 * 1/2
= 1/6
Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters. In parallelogram PQSR, what is PQ
Answer:
9 cm
Step-by-step explanation:
Since PQ and RS are opposite each other, then in a parallelogram, the lengths will be congruent.
Therefore 2x+5=4x+1
2x=4
x=2
If you plug x=2 into the the original equation, you get 9 cm.
The measure of PQ is 9 centimeters.
Important information:
In parallelogram [tex]PQSR, PQ=(2x+5),RS=(4x+1)[/tex]Parallelogram:The oppositie sides of a parallelogram are equal.
[tex]PQ=RS[/tex]
[tex]2x+5=4x+1[/tex]
[tex]5-1=4x-2x[/tex]
[tex]4=2x[/tex]
Divide both sides by 2.
[tex]2=x[/tex]
Now, find the measure of PQ.
[tex]PQ=2x+5[/tex]
[tex]PQ=2(2)+5[/tex]
[tex]PQ=4+5[/tex]
[tex]PQ=9[/tex]
Therefore, the measure of PQ is 9 centimeters.
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How many solutions exist for the system of equations 3x+y=18 3x+y=16
Answer:
no solutions
Step-by-step explanation:
Subtract the two equations
3x+y=18
-(3x+y=16)
--------------------
0 + 0 = -2
0 does not equal negative 2
This is never true so there are no solutions
Answer:
The number of solutions is 0.
Step-by-step explanation:
The x and y terms are equal. The constants are different. The lines are parallel. No solution.
84 is 12%of what number
please hurry!!!!!!
Answer: 700
84 is 12% of What Number:
12% of 700 is 84
100% of 700 is 700, therefore 12 percent of 700 equals 84.
To check this, 12% of 700 IS 84 (Check on Calculator)
Hope this helps!!
Solve for x. -7x= -8x+7
Answer:
x = 7
Step-by-step explanation:
-7x= -8x+7
Add 8x to each side
-7x+8x= -8x+8x+7
x = 7
Answer:
The value of [tex]x[/tex]:
[tex]x = 7[/tex]
Step-by-step explanation:
Solve for [tex]x[/tex]:
[tex]-7x = -8 x + 7[/tex]
Add both sides by [tex]8x[/tex]:
[tex]-7x + 8x = -8x + 8x + 7[/tex]
[tex]x = 7[/tex]
So, the final answer is [tex]x = 7[/tex] .
Seventy of Myra’s classmates are traveling by bus to a football game in another town. They hired 2 buses, but there were only 64 seats. The remaining 6 students had to travel in a separate van.
The equation 2b + 6 = 70 represents the given scenario. What does b represent?
Answer:
32
Step-by-step explanation:
2b+6=70
-6=70-6=64
[tex]\frac{2b}{2}[/tex]=64÷ 2
b=32
beaten it's a visable line beween the equal line
Expand and simplify . 4a(2+3b)-5b(4a-10). PLEASE HELP. BEST ANSWER RECEIVES A BRIANLIEST
Answer:
12a+62b
Step-by-step explanation:
4a(2+3b)-5b(4a-10)
opening brackets
=8a+12b-20a+50b
=8a-20a+12b+50b
=-12a+62b
Please help someone help me! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
The diameter of a circle is 222 units. What is the radius of the circle?
Answer:
111 units
Step-by-step explanation:
the diameter is double the radius so divide 222 by 2 to get 111 units.
What is the measure of c?
1489
42°
С
90°
422
489
O 42°
O 48°
O 90°
0 180°
Please help me with this question
BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!!
Answer:
C. x²+12x+36
Step-by-step explanation:
Since a square's area is figures out with [tex]length^{2}[/tex] and since the length is x+6, then we get:
(x+6)²=
(x+6)(x+6)=
Use FOIL method.
First: x²
Outer: 36
Inner: 6x
Last: 6x
x²+36+6x+6x=
x²+12x+36
The answer that fits is C. x²+12x+36.
Answer:
C. x²+12x+36
hope this helped
Find the y-intercept of the following equation. Simplify your answer.
y = 7x + 3
y-intercept =
Answer:
y-intercept is 3
Step-by-step explanation:
This equation is a linear equation [tex]y=mx+b[/tex].
m is the slope.
b is the y-intercept.
[tex]y=mx+b[/tex] is the same as [tex]y=7x+3[/tex]
7 would be the slope.
3 would be the y-intercept.
Factorise polynomials 15^2p-7p
Answer:
p ( 15p - 7)
Step-by-step explanation:
15 p^2 - 7p
The only common term is p so factor out p
p ( 15p - 7)
____________________________
15p^2-7p
take the common,
Ans: p(15p-7)
hope it helps
Good luck on your assignment
__________________________
