Answer: 31 : 9
Step-by-step explanation:
Assume the following:
Alice's amount = P
Bob's amount = Q
Amount received = n
If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.
P + n = 4(Q - n)
P + n = 4Q - 4n
P = 4Q - 4n - n
P = 4Q - 5n - - - - (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob
P - n = 3(Q + n)
P - n = 3Q + 3n
P = 3Q + 3n + n
P = 3Q + 4n - - - - - - (2)
Equating both equations - (1) and (2)
4Q - 5n = 3Q + 4n
4Q - 3Q = 4n + 5n
Q = 9n
Express P in terms of n, use either equation (1) or (2)
From equation 2:
P = 3Q + 4n
Substituting Q = 9n
P = 3(9n) + 4n
P = 27n + 4n
P = 31n
Alice's amount = P, Bob's = Q
Ratio = P:Q
31 : 9
Answer:
31:9
Step-by-step explanation:
Let $A$ and $B$ be the amount of money Alice and Bob have, respectively, at the beginning. We know that
\begin{align*}
A + n &= 4(B - n),\\
A - n &= 3(B + n).
\end{align*}
Simplifying, we have
\begin{align*}
A + 5n &= 4B, \\
A &= 3B + 4n.
\end{align*}Subtracting the first equation from the second gives $5n = B - 4n$, so $B = 9n$. Substituting this into the first equation gives $A + n = 4(9n - n)$, from which we get $A = 31n$.
Therefore, the desired ratio is $\frac{A}{B} = \frac{31n}{9n} = \boxed{\dfrac{31}{9}}$.
Which of the following is the equation of a line that passes through the point
(3.2) and is parallel to the yaxis?
Answer:
y=2 is the correct ans.
here, tge equn of st line passing through the point (3,2) and is also parallel to y axis.
we have, equn of st line parallel to y xaus is y= b
so , the equn of st line passing through the point (3,2) is y= 2 (where 2 is likely to b).
The police department uses a formula to determine the speed at which a car was going when the driver applied the breaks, by measuring the distance of the skid marks.The equation d=0.03r^2+r models the distance, d, in feet, r miles per hour (r is the speed of the car) Factor the equation. d=?
Answer:
0.03 feet
Step-by-step explanation:
d = 0.03r² + r
When d = 0: 0.03r² + r = 0
r(0.03r + 1) = 0
∴ r = 0
When r = 0: d = 0.03 feet
Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?
hello,
the first term is 250 so this is the initial invested amount
[tex](1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}[/tex]
is to compute 8% annual interest compounded monthly (there are 12 months in a year)
and then multiply by 4 means that it is computed for 4 years so
finally the answer is
$250 is invested at 8% annual interest compounded monthly for 4 years
hope this helps
WILL GIVE BRAINLEIST!!!
Answer:
40
Step-by-step explanation:
Once you plot the data, the middle values will be 39 and 41. To calculate the median, you add them up and divide by two, which will result in 40!
Median is the middle value.
Write the numbers out from smallest to largest:
35, 38, 38, 39, 39, 41, 42, 43, 43, 44
There are 10 total numbers, find the middle two:
39 and 41
Add them Together and divide by 2:
39 + 41 = 80
80/2 = 40
Median = 40
y=(x+9)÷(x-3)
Find the value of y when x=5
solution,
X=5
[tex]y = \frac{x + 9}{x - 3} \\ = \frac{5 + 9}{5 - 3} \\ = \frac{14}{2} \\ = 7[/tex]
hope this helps...
Good luck on your assignment..
Answer:
When x=5
Y=(5+9)÷(5-3)
= 14 ÷2
= 7
If you are given the graph of h(x) = log6x, how could you graph M(x) = log6(x+3)?
Answer:
Translate 3 units to the left
Step-by-step explanation:
Please answer this question fast in two minutes
Answer:
132 degree
Step-by-step explanation: angle kjh is 132 degree and since lk is a straight line it is 180 degree. angle kjh is 132 degree so, angle LJM is 132 degree. This is because adjacent angles are equal as you can see, Angle LJM is adjacent to Angle KJH.
How is it that it is (-11/4,-1/2) ?
Answer:
Choice 3
Step-by-step explanation:
A(-5,-1) and B(4, 1)
Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2
Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:
-5 + 9/4= (-20+9)/4= -11/4-1 +2/4= (-4+2)/4= -2/4= -1/2So P= (-11/4, -1/2) and choice 3
What is the range? Explain
Answer:
Range = [5, ∞)
Step-by-step explanation:
The initial number of snakes is 5 and it is increasing at a high rate so the maximum number is infinite. The population is increasing exponentially according to the equation P = 5(2)^t where t = the number of years.
what is the volume of the cylinder below?
Answer:
A
Step-by-step explanation:
vol of a cylinder = pie* r^2×h
r= 5
h= 9
......vol= 9×5^2 pie= 225pie units ^3
find a18 of the arithmetic sequence 2, -5, -12, -19
Answer:
The 18th term of the sequence is -117.
Step-by-step explanation:
The given sequence is 2,-5,-12,-19
From this AP,
First term, a = 2
Common difference, d = -5-2 = -7
It is required to find the 18th term of the sequence. The nth term of an AP is given by :
[tex]a_n=a+(n-a)d\\\\a_{18}=a+17d\\\\a_{18}=2+17\times (-7)\\\\a_{18}=-117[/tex]
So, the 18th term of the sequence is -117.
The play director spent 190190190190 hours preparing for a play. That time included attending 35353535 rehearsals that took varying amounts of time and spending 933493 \dfrac{3}{4}934393, start fraction, 3, divided by, 4, end fraction hours on other responsibilities related to the play. What question does the equation 35x+9334=19035x+93\dfrac{3}{4}=19035x+9343=19035, x, plus, 93, start fraction, 3, divided by, 4, end fraction, equals, 190 help answer?
Answer:
The equation above represents the total time the play director spent preparing for a play.
Step-by-step explanation:
The time spent by the play director for preparing for a play is, 190 hours.
Of these 190 hours, the director spent varying amounts of time attending 35 rehearsals for the play.
Let the varying amounts of time be denoted by, x.
The director also spent 3/4th of an hour, i.e. 45 minutes, on other responsibilities related to the play.
The equation provided is:
[tex]35x+\frac{3}{4}=190[/tex]
The equation above represents the total time the play director spent preparing for a play.
Which equation represents a graph with a vertex at (-1,6)?
Answer:
B. [tex]y = 3x^2 -6x -3[/tex]
Step-by-step explanation:
Well, we can use the following formula to find the x coordianate of the vertex -b / 2a.
So let’s start with a)
-6 / 6
-1
A. is wrong because its vertex starts with -1.
b)
6 / 6
1
now that we have our x coordinate we can plug it into the equation to get our y.
3 - 6 - 3
So the y coordinate is -6.
Hence, the answer choice B. [tex]y = 3x^2 -6x -3[/tex]
look at the image below.
A 7-column table with 2 rows. Column 1 is labeled Sample with entries catfish, all fish. Column 2 is labeled 1 with entries 3, 20. Column 3 is labeled 2 with entries 5, 20. Column 4 is labeled 3 with entries 7, 20. Column 5 is labeled 4 with entries 5, 20. Column 6 is labeled 5 with entries 6, 20. Column 7 is labeled 6 with entries 8, 20. The mean number of catfish in all 6 samples is approximately 5.7. If 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population? StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 5.7 over 20 EndFraction = StartFraction 200 over x EndFraction StartFraction 34 over 20 EndFraction = StartFraction x over 200 EndFraction StartFraction 8 over 20 EndFraction = StartFraction 20 over x EndFraction
Answer: The correct option is 5.7/20 = x/200
Step-by-step explanation: Please refer to the diagram attached for more details.
From the 7-column by 2-row table drawn, you can determine that the mean number of catfish as given in the question is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (3 + 5 + 7 + 5 + 6 + 8)/6
Mean = 34/6
Mean = 5.6667
Mean ≈ 5.7
Also the mean number of all fish is derived as follows;
Mean = Summation of observed data / Number of observations
Mean = (20 + 20 + 20 + 20 + 20 + 20)/6
Mean = 120/6
Mean = 20
Using relative frequency, we can confidently predict the number of catfish population in the pond. This simply means, if the mean number of catfish is 5.7 and the mean number of all fish is 20, then the relative frequency would be 5.7 over 20 of the total fish population.
Hence, if there is a total of 200 fish in the pond then to predict the proportion which would be catfish can be expressed as follows;
StartFraction 5.7 over 20 EndFraction = StartFraction x over 200 EndFraction.
OR better expressed as;
5.7/20 = x/200
Answer:
5.7/20 = x/200
Step-by-step explanation:
In a group of 45 students, 5 study both Art and Biology. 8 study Biology but not Art. 9 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Data provided in the question
There is a total group of 45 students
Art + biology = 5
8 study biology but not Art
Neither subject studied = 9
Based on the above information, the probability of student that studies
art and biology is
Since there is a group of 45 students out of which 5 study both art and biology
So, the ratio is
4: 5
Now divide both sides by 5
So, now the ratio is
9:1
Therefore it means the probability is [tex]\frac{1}{9}[/tex]
Find the volume of the cylinder express your answers in terms of pi
Answer:
704 pi in ^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = pi ( 8)^2 * 11
V = pi (704)
V = 704 pi in ^3
Answer:
[tex]704 \: \pi \: {inches}^{3} [/tex]Step-by-step explanation:
Solution,
Radius(R)= 8 in.
Height (h)= 11 in.
Volume of cylinder=?
Now,
Volume of cylinder:
[tex]\pi {r}^{2} h[/tex]
[tex]\pi \: {(8)}^{2} \times 11 [/tex]
[tex]\pi \times 64 \times 11[/tex]
[tex]704\pi \: {inches}^{3} [/tex]
Hope this helps...
Good luck on your assignment..
Through any 2 points there is exaclty_____line.
Answer:
One
Step-by-step explanation:
Through any 2 points, there is exactly one line.
Answer:
ONE
Step-by-step explanation:
Through any 2 points there is exaclty ONE line.
Complete the equation of the line through (-8,8)(−8,8)left parenthesis, minus, 8, comma, 8, right parenthesis and (1,-10)(1,−10)left parenthesis, 1, comma, minus, 10, right parenthesis.
Answer:
[tex]y = -2x - 8\\OR\\2x+y+8=0[/tex]
Step-by-step explanation:
Given that there are 2 points
[tex]A(-8,8)[/tex] and
[tex]B(1,-10)[/tex]
So, the coordinates are:
[tex]x_2 = 1\\x_1 = -8\\y_2 = -10\\y_1 = 8[/tex]
Equation of a line is given as:
[tex]y =mx+c[/tex]
where 'm' is the slope of the line, formula for 'm' is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x,y)[/tex] are the points that satisfy the equation of the line.
[tex]c[/tex] is the [tex]y -[/tex] intercept.
Calculating the value of m using the given coordinates:
[tex]m=\dfrac{-10-8}{1-(-8)}\\\Rightarrow m=\dfrac{-18}{9} = -2[/tex]
So, the equation of line becomes:
[tex]y =-2x+c[/tex]
Now, putting the coordinates of point [tex]A(-8,8)[/tex]
[tex]8 =-2\times (-8)+c\\\Rightarrow 8 = 16+c\\\Rightarrow c = -8[/tex]
Please refer to the graph of given equation of line.
The equation of line is:
[tex]y =-2x+-8\\OR\\2x+y+8=0[/tex]
Triangle ABC is rotated 45° about point X, resulting in triangle EFD. Triangle A B C is rotated 45 degrees about point X to form triangle E F D. The lengths of sides A C and D E are congruent, the lengths of sides A B and E F are congruent, and the lengths of sides D F and C B are congruent. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB? 3.3 cm 3.6 cm 4.2 cm 4.5 cm
Answer:
CB = 3.6 cm
Step-by-step explanation:
Here, triangle ABC is rotated about point X which results in triangle EFD. Since triangle ABC is rotated it retains its shape and dimensions. This means that triangle ABC is parallel to triangle EFD ie, ABC≈EFD, also both dimensions will be congruent.
Thus
AB = EF
BC = FD
AC = ED
CB = DF
BA = FE
CA = DE
Since length of side DF = length of side CB, and DF = 3.6 cm. Therefore, CB = DF = 3.6 cm
Length of CB = 3.6 cm
Answer: B it's B
Step-by-step explanation: I got it right
I need help please help
Answer:
21u-16v+18w
Step-by-step explanation:
(7u-4v+4w) 14u-12v+14w
21u-16v+18w
Answer:
= 21u−16v+18w
Step-by-step explanation:
Let's simplify step-by-step.
7u−4v+4w−2(−7u+6v−7w)
Distribute:
=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)
=7u+−4v+4w+14u+−12v+14w
Combine Like Terms:
=7u+−4v+4w+14u+−12v+14w
=(7u+14u)+(−4v+−12v)+(4w+14w)
=21u+−16v+18w
Answer:
=21u−16v+18w
Solve I=PRT for P if I=312.50, r=25%, and T=0.25
Answer: I = $ 19.53
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 25%/100 = 0.25 per year,
then, solving our equation
I = 312.5 × 0.25 × 0.25 = 19.53125
I = $ 19.53
The simple interest accumulated
on a principal of $ 312.50
at a rate of 25% per year
for 0.25 years is $ 19.53.
Answer:
P = 5000
You need to multiply r and T together, then divide 312.50 by that.
write the monomial in standard form. name it's coefficient and identify its degree.
2/3m^2 n *4.5n^3
Answer:
[tex]Standard\ Form = {3n^2} m^{-2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]
Required
Write in Standard Form
To start with; the two monomials have to be multiplied together;
[tex]\frac{2}{3m^2n} * 4.5n^3[/tex]
[tex]Standard\ Form = \frac{2 * 4.5n^3}{3m^2n}[/tex]
Split the numerator and the denominator
[tex]Standard\ Form = \frac{2 * 4.5 * n^3}{3 * m^2 * n}[/tex]
Multiply Like terms
[tex]Standard\ Form = \frac{9 * n^3}{3 * m^2 * n}[/tex]
Divide 9 by 3 to give 3
[tex]Standard\ Form = \frac{3 * n^3}{m^2 * n}[/tex]
Divide n³ by n to n²
[tex]Standard\ Form = \frac{3 * n^2}{m^2 }[/tex]
Split fraction
[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex]
From laws of indices;
[tex]\frac{1}{a^n} = a^{-n}[/tex]
[tex]Standard\ Form = {3 * n^2} * \frac{1}{m^2 }[/tex] becomes
[tex]Standard\ Form = {3 * n^2} * m^{-2}[/tex]
Multiply all together
[tex]Standard\ Form = {3n^2} m^{-2}[/tex]
Which statement is true about the equations –3x + 4y = 12 and 1/4x-1/3y=1
Answer: No solution
Step-by-step explanation:
This system of equation has no solution because...
-3x+4y=12
1/4x-1/3y=1
[tex]-3x+4y-4y=12-4y[/tex]
[tex]-3x=12-4y[/tex]
[tex]\frac{-3x}{-3}=\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]\frac{12}{-3}-\frac{4y}{-3}[/tex]
[tex]x=-\frac{12-4y}{3}[/tex]
substitute
[tex]\frac{1}{4}\left(-\frac{12-4y}{3}\right)-\frac{1}{3}y=1[/tex]
[tex]-1=1[/tex]
-1=1 is false so therefore this system has no solution
A machine in a shoe factory produces shoelaces. The number of shoelaces it produces is proportional to the time. It car
produce twelve shoelaces in three minutes. Write an equation to represent this proportional relationship. In your
answer, make sure to define the variables you used.
Answer:
s = 4t
Step-by-step explanation:
Let number of shoelace produced be S and time taken to produce then be T
If the number of shoelaces it produces is proportional to the time, this can be expressed using a direct relationship as:
S∝T
S = kT where
k is the proportionality constant
If 12 laces of shoes can be produced in 3 minutes, then S = 12 and T = 3
The relationship above on substitution becomes
12 = 3k
k = 12/3
k = 4
If the proportionality constant is 4, then the equation representing the relationship will be:
s = 4t
please mark me brainliest!
Answer: y = 4x (y = shoelaces & x = minutes)
Step-by-step explanation: We know that 12 shoelaces are produced in 3 minutes and that the ratio of shoelaces produced to minutes spent is proportional. We can figure out, therefore, that if you multiply the number of minutes by 4, you will get the number of shoelaces. As an equation, this would be y = 4x (y = shoelaces & x = minutes).
I do not understand this/ help me answer these
Answer:
-6b -6c3w -122x -246 + 3r8y - 16xStep-by-step explanation:
Avery wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3.2% and the other bank is offering a rate of 3% compounded annually. If Avery decides to deposit $7,000 for 5 years, which bank would be the better deal? 1. a simple interest rate of 3.2% 2. a compound interest rate of 3%
Answer: a simple interest rate of 3.2% will be the better deal.
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r/n) nt
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Nominal Interest Rate (decimal form, 3/100= 0.03)
n= number of compounding periods in each year (1)
Replacing with the values given
A = 7000 (1+0.03/1)^(1x5)
A = 7000( 1.03)^5 = $8,114.92
For simple interest:
I = p x r x t
Where:
I = interest
Replacing with the values given:
I = 7000 x (3.2/100) x 5 = $1,120
Adding the principal amount: 7000+1120 = $8,120
Since 8,120 (simple) >8,114.92(compound)
a simple interest rate of 3.2% will be the better deal.
Which expression is equivalent to.......
See pictures
Answer:
[tex] \sqrt{ {2}^{5} } [/tex]
Step-by-step explanation:
[tex]\huge \bigg( {2}^{ \frac{1}{2} }. {2}^{ \frac{3}{4}} \bigg)^{2} \\ \\ \huge = {2}^{ \frac{1}{2} \times 2 }. {2}^{ \frac{3}{4} \times 2} \\ \\ \huge = 2 \times {2}^{ \frac{3}{2} } \\ \\ \huge = {2}^{ \frac{3}{2} + 1 } \\ \\ \huge = {2}^{ \frac{3 + 2}{2} } \\ \\ \huge = {2}^{ \frac{5}{2} } \\ \\ \huge = \sqrt{ {2}^{5} } [/tex]
Mrs. Brown has 11 more boys than girls in her class and has a total of 28 students. Which of the following systems of equations could be used to solve this problem?
Answer:
g=number of girls in the class b=number of boy in the class
g+b=28
g=11+b
Find the missing side length
Which of the following can be represented by the inequality below? 69h + 126 > 540 A. Yvonne is driving more than 540 miles on a trip. She has already driven 126 miles and drives 69 miles each hour. B. Yvonne is driving less than 540 miles on a trip. She has already driven 126 miles and drives 69 miles each hour. C. Yvonne is driving less than 126 miles on a trip. She has already driven 69 miles and drives 540 miles each hour. D. Yvonne is driving more than 540 miles on a trip. She has already driven 69 miles and drives 126 miles each hour.
Answer:
The answer is A.
Step-by-step explanation:
The inequality states that the amount that Yvonne drives is more than 540 miles. Since h represents the number of hours, we know that 69 probably means the number of miles Yvonne can drive per hour. Finally, 126 shows the amount of miles that Yvonne has already driven.