Answer:
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
Step-by-step explanation:
Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year.
I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.
Step 1
We have to calculate the total interest earn on the initial capital
P = $2,560
R = 7.25% = 0.0725
T = 1
I = $2,560 × 0.0725 × 1
I = $185.60
Let the amount Invested in the account that paid 6% interest = x
Let the amount Invested in the account that paid 8% interest = y
Hence:
$185.60 = x × 6% + y × 8%
$185.60 = 0.06x + 0.08y......Equation 1
$2560 = x + y........ Equation.2
x = $2560 - y
$185.60 = 0.06x + 0.08y......Equation 1
185.60 = 0.06(2560 - y) + 0.08y
185.60 = 153.6 - 0.06y + 0.08y
185.60 - 153.60 = 0.02y
y = 32/0.02
y = $1600
x = $2560 - y
x = $2560 - $1600
x = $960
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
PLEASE HELP
On graduating from college, you recieve $3,000 in gifts from family and friends. You want to invest it for later use as $15,000 down payment on a house. You have found an opportunity that locks in a 10% annual interest rate. How many years will it take to turn your graduation gifts into a down payment?
Answer:
6,346
Step-by-step explanation:
add add multiply and add
PLEASE HELP!!
Choose yes or No to tell whether the expressions are equivalent.
(4^3)^3 and 4^3 • 4^3
(3^4)^4 and 3^8 • 3^8
6^4 • 3^4 and 18^8
4^3 • 5^3 and 20^ 3
Answer:
no
yes
no
yes
Step-by-step explanation:
Cindy deposited $350 into a savings account. As long as the account balance remains at or above $200, she does not have to pay a service fee for the account. For how long can she withdraw $30 a month without having to pay service fees? A) 5 months B) 6 months C) 7 months D) 8 months E) 9 months
Answer:
5 months
Step-by-step explanation:
Cindy deposited $350 into a savings account
The acct balance remains above $200
We are required to find the number of months that it will take to $30 a month
Let y represent the number of months
y × 30 < 350-200
30y < 150
Divide both sides by the coefficient of y which is 30
30y/30 < 150/30
y < 5
Hence the number of months required is 5 months
Simplify the algebraic expression 5x+3+7x+4
Answer:
12x +7
Step-by-step explanation:
First determine what numbers are coefficients. Because 3 and 4 don't have a variable in them, we know they are coefficients. You can then add them together to get 7. After that, we see that 5x and 7x both share the variable x. Because they share the same variable you can add them together to get 12x. Because 12x and 7 don't have the same variable you cannot add them together. This means that 12x + 7 is your final answer.
Complete the recursive formula of the arithmetic sequence –3,-1,1,3,....
Answer:
b(1)=-3
b(n)=b(n−1)+2
Step-by-step explanation:
Given the sequence −3,−1,1,3,...
We can infer that the first number of the sequence is -3, and the difference is +2
b(1)=first number of the sequence
b(n)=b(n−1) diffrence
If we fill this in, we get:
b(1)=-3
b(n)=b(n−1)+2
The cost of parking a car in an hourly lot can be represented by the following equation y = 3x + 2 What does the 3 tell you about the cost of parking?
A) The hourly rate is $3
B) You can only park for 3 hours
C) There is a $3 fee to park
D) it costs 5 dollars to park all day
Answer:
A
Step-by-step explanation:
The three represents the amount it costs for each hour parked, and is continuous, which is a rate.
How is quadrilateral ABCD related to quadrilateral A'B'C'D' shown below?
Answer:
i think its a
Step-by-step explanation:
Which of these equations represents a line that has an undefined slope and is
perpendicular to the line represented by y = 5?
A x = 5
B y = 0
C y = −5
D No such line exists.
Step-by-step explanation:
D. no such line exits
you have to know the gradient of the line given and there is no gradient given
HELP PLEASE PLEASEEEEEEE
Answer:
about 1854.55 miles (rounded to the hundredth)
Step-by-step explanation:
1.
[tex] \frac{44}{100} = \frac{816}{x} [/tex]
The first fraction represent the percentage of the distance.
The second one represent the number of 816 miles out of x
2. 100 × 816 = 44 × x
3. You'll get 81,600 = 44x
4. and then you divided both side by 44 to solve for x
If Courtney paid a total of $27.93 to download songs, which includes $2.06 for tax, how many songs did she download at a cost of $1.99 per song?
Answer:
13 songs.
Step-by-step explanation:
$27.93 - $2.06 = $25.87 in order to get the price of the songs before the tax.
Since each song cost $1.99, $25.87 divided by $1.99 is equal to 13
Answer:
13 songs
Step-by-step explanation:
The total cost of the songs is $27.93, including the tax. The tax cost should be removed from the total cost to find how many songs Courtney downloaded because she didn't pay $2.06 for the songs.
[tex]27.93 - 2.06 = 25.87[/tex]
The cost of all the songs is $25.87. Each one costs $1.99 so, to find how many songs she bought, the cost of each song should be divided from the total cost.
[tex]25.87 \div 1.99 = 13[/tex]
Mt. Young bought some hamburgers for his cookout. The price was $32,17, but, le found that hamburger parties were on special for $22.692. What was hubs DOcent Bio
A $3.20
B. 29.68%
OC45%
D. $87.25
Which point on the coordinate plane is closest to ______ ?
Answer:
its point D hope this helps :)
Box of 36 rubber bands he used 1/4 of the rubber bands in the box how many rubber bands did use
Pleas help
Answer:
9 rubberbands
Step-by-step explanation:
If it helps. Think of 1/4 as dividing by 4 and then multiplying by 1.
36/4 = 9 x 1 = 9.
please help :(( (will mark brainliest!!!!)
Answer:
(-8,0) (0,-4) (4,-6)
Step-by-step explanation:
A plane takes off and climbs steadily for 15 minutes until it
reaches 30,000 feet. It travels at that altitude for 2 hours until
it begins to descend to land, which it takes 15 minutes at a
constant rate.
Step-by-step explanation:
Mark each mark by 15 mins add an extra tick at the time section
the corner before the first 15 min mark make a tilted line to 15 mins and 30,000 feet draw a straight line till 2 hours and 15 mins draw titled down to 2 hours and 30 mins
Hay dos números naturales consecutivos y la suma del cuadrado de esos números es 221¿cuáles serán esos números?
Una caja contiene 448 mascarillas, las cuales se deben acomodar en 3 cajas más pequeñas. En la primera se deben poner ; 1/8, del total, en la segunda 3/8 y en la tercera 4/8 ¿Cuántas mascarillas van en cada caja y cuántas quedan en la caja original?
Step-by-step explanation:
Si una caja contiene 448 cajas y debe acomodarse en tres cajas más pequeñas, si la primera contiene 1/8 del total, entonces el número de cajas en la primera será:
[tex]= \frac{1}{8}\times 448\\ = \frac{448}{8}\\ = \frac{8\times56}{8}\\ = 56[/tex]
Por lo tanto, la primera caja contiene 56 cajas más pequeñas.
Si el segundo contiene 3/8 del total, entonces el número de casillas en el segundo será:
[tex]= \frac{3}{8}\times 448\\ = \frac{3\times448}{8}\\ = \frac{8\times 3 \times 56}{8}\\ = 3 \times56\\= 168[/tex]
Por lo tanto, la segunda caja contiene 168 cajas más pequeñas.
Si el tercero contiene 4/8 del total, entonces el número de casillas en el tercero será:
[tex]= \frac{4}{8}\times 448\\ = \frac{1}{2} \times 448\\ = 224[/tex]
Por lo tanto, la tercera caja contiene 224 cajas más pequeñas.
La cantidad que quede en la casilla original se expresará como
= 448- (56 + 168 + 224)
= 448-448
= 0
Por lo tanto, no quedó ninguno en la caja original.
What is the slope of the given lines ?
Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, - 8) and (x₂, y₂ ) = (7, 8) ← 2 points on the green line
m = [tex]\frac{8+8}{7+5}[/tex] = [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex]
Repeat with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (3, - 2) ← 2 points on the blue line
m = [tex]\frac{-2+6}{3-0}[/tex] = [tex]\frac{4}{3}[/tex]
Since the slopes of both lines are equal, then the lines are parallel
Quinn has a large family. She has 4 cousins who live in Texas, 3 cousins who live in Nebraska, and 9 cousins who live in Michigan...
What is the ratio of Quinn's cousins who live in Texas to her cousins who live in Michigan?
Answer:
c)4:9
Step-by-step explanation:
what's 4 divided by 5 as a fraction
Answer:
four fifths because if you divided 4 by 5 is 0.8 and that equals four fifths
The amount Troy charges to mow a lawn is proportional to the time it takes him to mow the lawn. Troy charges $30 to mow a lawn that took him 1.5 hours to mow.
Which equation models the amount in dollars, d, Troy charges when it takes him h hours to mow a lawn?
A) d = 20h
B) h = 20d
C) d = 45h
D) h = 45d
First, let's find the amount of money Troy charges per hour.
$30 / 1.5hrs = $20 / hr
d = $20h
A is the correct answer choice.
Write an equation for the line that passes through (2,5) and (6,7)
Answer:
[tex]y=\frac{1}{2}x+4[/tex]
Step-by-step explanation:
Find the slope of the line first using the slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the two given points into this formula.
[tex]\frac{7-5}{6-2} =\frac{2}{4} =\frac{1}{2}[/tex]Now that you have a slope and a point that the line passes through, you can use the point-slope formula to find the equation of the line.
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Substitute m = 1/2 for the slope and one of the points; I'm going to use (2, 5).
[tex]y-(5)=\frac{1}{2} (x-(2))[/tex]Simplify the equation so it's easier to read.
[tex]y-5=\frac{1}{2} (x-2)[/tex]Distribute 1/2 inside the parentheses.
[tex]y-5=\frac{1}{2}x-1[/tex]Add 5 both sides of the equation.
[tex]y=\frac{1}{2}x+4[/tex]Answer:
The slope is the change in y over the change in x.
(7-5) / (6-2) = 2 / 4 = 1 / 2
In y = mx + b, we know y, m, and x. Now solve for b:
Let's use the point (2, 5).
5 = (1/2)(2) + b
5= 1 + b
b = 4
Now put it together:
y = (1/2)x + 4
Step-by-step explanation:
Cape Corp. Will pay a dividend of $4.40 next year. The company has stated that it will maintain a constant growth rate of 5 percent a year forever. a. If you want a return of 17 percent, how much will you pay for the stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.G., 32.16.) b. If you want a return of 10 percent, how much will you pay for the stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.G., 32.16.)
Answer:
Step-by-step explanation:
a. If you want a return of 17 percent, how much will you pay for the stock?
The price of the stock can be calculated as:
= dividend next year/(required return - growth rate)
= 4.4/(17% - 5%)
= 4.4/12%
= 4.4/0.12
= 36.67
b. If you want a return of 10 percent, how much will you pay for the stock?
At 10%
= 4.4/(10% - 5%)
= 4.4/5%
= 4.4/0.05
= 88
If y varies directly as x, and y = -85 when x = 5, what is the value of y when x = 19
Answer:
-323
Step-by-step explanation:
y varies x
make k the unknown
y=kx
-85= 5k
:• k = -17
when x= 19
we can say...
y= -17(19)
y = -323 ✓
If you roll two six-faced dice together, you will get 36 possible outcomes. 4 pts 1. List all possible outcomes of the experiment. 2 pts 2. What is the probability of getting a sum of 11 in these outcomes? 2 pts 3. What is the probability of getting a sum less than or equal to 4? 2 pts 4. What is the probability of getting a sum of 13 or more?
Given:
Two dice are rolled together.
Total number of possible outcomes.
To find:
The list of total possible outcomes.
The probability of getting a sum of 11 in these outcomes.
The probability of getting a sum less than or equal to 4.
The probability of getting a sum of 13 or more.
Solution:
If two dice are rolled together, then the total number of possible outcomes is 36 and list of total possible outcomes is
S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Sum of 11 in these outcomes = {(5,6),(6,5),(6,6)} = 3
The probability of getting a sum of 11 in these outcomes is
[tex]P(\text{sum=11})=\dfrac{3}{36}[/tex]
[tex]P(\text{sum=11})=\dfrac{1}{12}[/tex]
Therefore, the probability of getting a sum of 11 in these outcomes is [tex]\dfrac{1}{12}[/tex].
Sum less than or equal to 4 = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)} = 6
The probability of getting a sum less than or equal to 4 is
[tex]P({sum\leq 4})=\dfrac{6}{36}[/tex]
[tex]P({sum\leq 4})=\dfrac{1}{6}[/tex]
Therefore, the probability of getting a sum less than or equal to 4 is [tex]\dfrac{1}{6}[/tex].
Sum of 13 or more = empty set because maximum sum is 12.
The probability of getting a sum of 13 or more is
[tex]P(sum\geq 13)=\dfrac{0}{36}[/tex]
[tex]P({sum\geq 13})=0[/tex]
Therefore, the probability of getting a sum of 13 or more is 0.
*30 POINTS!*
Determine if each equation represents the graph below. Choose ALL correct equations. You will select more than one answer.
The options are:
1. y= 2x-1
2. x-2y =2
3. y= 1/2x - 1
4. y+3 = 1/2 (x+4)
5. y-2= 1/2 (x-2)
Answer:
2, 3 and 4 represent the graph in the pic
Step-by-step explanation:
When you look at the graph, you can immediately tell the gradient and the y-intercept. The gradient is 1/2 and the y-intercept is -1
Hence the graph in the picture follows the formula: y = 1/2x - 1
When you expand/rearrange the options (1-5) into the slope form you would be able to see which of these options matches with the formula of the line.
1. y= 2x-1: Isn't the same as the equation of the line in the pic
2. Rearrange:
-2y = -x + 2 (divide both sides by 2)
y = x/2 - 1 (x/2 = 1/2x, its the same thing)
3. y= 1/2x - 1 (this is the formula of the line)
4. Expand right-hand-side:
y + 3 = 1/2x + 2 (rearrange)
y = 1/2x - 1 (this is the formula of the line)
5. Expand right-hand-side
y - 2 = 1/2x - 1 (rearrange)
y = 1/2x + 1 (is not the formula of the equation)
Answer:
The officeStep-by-step explanation:
“Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.” – Michael G. Scott
write an expression that is equivalent to 25x^2 -20x + 4
If angle P measures 60 degrees, what is the measure of angle C?
A)120
B)30
C)60
Answer:
Answer is 120
Step-by-step explanation:
3 Comcast charges $50 per month for basic cable and $5.00 for each premium movie channel. Xfinity charges $41 per month for the same cable package and $6.50 for each premium movie channel. B. Write an inequality to represent how many movie channels a customer needs to purchase from Xfinity Cable to pay at least as much as a Comcast subscriber.
Answer:
18Step-by-step explanation:
let us model the cost
let the cost be y and the number of movie channel be x
for 3 comcast
y=50+5x-----1
and for Xfinity
y=41+6.5x-------2
to solve for the number of movie channel so that the two (3 comcast and Xfinity) will pay the same, we need to equate 1 and 2
50+5x=41+6.5x
50-41=6.5x-5x
9=0.5x
x=9/0.5
x=18
Please help! Geometry.