Solution :
Given :
Principal amount deposited, P = $ 6000
Rate of interest, r = 5%
Number of years, t = 4 years
When the deposited amount is compounded semiannually, i.e. n = 2
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{2}\right)^{2 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.025)^8$[/tex]
= 6000 x 1.2184
= 7310.4
Therefore, after 4 years there will be $ 7310.4 in the amount when compounded semi annually.
When the deposited amount is compounded quarterly, i.e. n = 4
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{4}\right)^{4 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.0125)^{16}$[/tex]
= 6000 x 1.219889
= 7319.334
Therefore, after 4 years there will be $ 7319.334 in the amount when compounded quarterly.
When the deposited amount is compounded monthly, i.e. n = 12
Therefore,
Future value,
[tex]$FV = P\left( 1 +\frac{r}{n}\right)^{nt}$[/tex]
[tex]$FV = 6000\left( 1 +\frac{0.05}{12}\right)^{12 \times 4}$[/tex]
[tex]$FV = 6000 \times (1.0041667)^{48}$[/tex]
= 6000 x 1.22089
= 7325.34
Therefore, after 4 years there will be $ 7325.34 in the amount when compounded monthly.
How many solutions does the system have?
2x+3y=−6
3x−4y=−12
9514 1404 393
Answer:
1 solution
Step-by-step explanation:
The ratios of x- and y-coefficients are different, so the lines have different slopes. Lines with different slopes intersect at exactly one point. That point is the solution to the system of equations.
There is exactly one solution.
PLEASE ANSWER FAST I NEED HELPPP
Plsss help ty I’ll mark u
Answer:
7/4 meter
Step-by-step explanation:
their all in fractions of 8 so let reduce
Corn - 8 goes into 19 twice with the remander of 3 --> 2 and 3/8
Pepper 5/8 cause that cant be reduced any lower
Squash - 7/8 cant be reduced any more
Now its asking to subtract the tallest plant from the smallest to see the diffrence
The tallest plant is Corn and the shortest is Pepper
19/8 - 5/8 = 14/8
reduce 7/4
Answer:
It is 14/5 meters taller.
Step-by-step explanation:
[tex]\frac{19}{8}[/tex] - [tex]\frac{5}{8}[/tex] = [tex]\frac{14}{8}[/tex]
Give me 2 exponents that equal to 8 :)
Simplify this equation:
-4(c+2d)-2(3c-4d)
Answer:
-10c
Step-by-step explanation:
-4(c+2d)-2(3c-4d) = (-4c-8d) + (-6c+8d)
Multiply (-4) to both terms in the first bracket and multiply (-2) to both terms in the second bracket.
(-4c-8d) + (-6c+8d) = -4c-8d-6c+8d
Evaluate like terms.
-4c-8d-6c+8d = -10c
The partial factorization of x2 – 3x – 10 is modeled with algebra tiles. An algebra tile configuration. 1 tile is in the Factor 1 spot: and is labeled + x. 6 tiles are in the Factor 2 spot: 1 is labeled + x and 5 are labeled negative. 18 tiles are in the Product spot: 1 is labeled + x squared, 2 are labeled + x, the 5 tiles below + x squared are labeled negative x, and the 10 tiles below the + x tiles are labeled negative. Which unit tiles are needed to complete the factorization?
Answer:
2 positive unit tiles is needed
Step-by-step explanation:
Given the expression x^2 – 3x – 10, the partial factorization is as shown;
x^2 – 3x – 10
= x^2 +2x – 5x – 10
= x(x+2)-5(x+2)
= (x-5)(x+2)
Note that negative values are represented as tiles labelled below (negative tiles) while positive values are tiles labelled above (positive tiles)
From the second line we can see that first term 1 is labeled + x squared, second is labelled +2x (two positive tiles above), then the 5 tiles below + x squared are labeled negative x, and the 10 tiles below the + x tiles are labeled negative.
Hence base on the partial factorization and the underlined statement, we can see that 2 positive unit tiles is needed to complete the factorization
Answer:
B i think
Step-by-step explanation:
6th grade math:) please help..
Answer:
Okay the ratio of starfish to fish is 3:6 or 3/6 but simplified it is 1/2
The starfish ratio to 16 fish would be 8 or 16:8
and if there was one less starfish in the line the ratio would be 2:6 or 2/6 but simplified would be 1/3
Step-by-step explanation:
Okay to solve the first question we see that there are 6 fish and 3 starfish, when put into a ratio it is 3:6 (the reason the number of starfish is first in the ratio is because it is starfish to fish hence starfish goes first ). If you are wanting the ratio to be in fraction form you are going to put 3/6 and since 3 goes into 3 once and 6 twice so the fraction is 1/2
3:6 = 3/6 = 1/2
Since the ratio from starfish to fish is 1/2 of that number you are going to divide 16 by 1/2 or more like multiply:
16/ 1/2 = 16/1 * 1/2 = 16/2 = 8
I hope this helps you!!!
When the ratio of starfish is short of one then the ratio would be 2: 6 or in fraction form 2/6 but simplified is 1/3.
2:6 = 2/6 = 1/3
Greg invested $11,000 in two accounts.
• The first account pays 5% interest per year.
• The second account pays 8% interest per year.
Greg earned a total of $752.50 in interest at the end of the first year.
How much did Greg invest in the 5% account?
A) 6750
B) 3415
C) 5500
D) $4250
Answer:
D; $4,250
Step-by-step explanation:
Here, we want to know the amount that was invested in the 5% account
We proceed as follows;
Let the amount invested in the 5% interest account be $a and the amount invested in the 8% interest account be $b
We have it that the total investment amount is $11,000
Mathematically, since total is 11,000; we can add a and b to give this
a + b = 11,000 •••••••••(i)
Now, let us work with the interests
Interest earned will be;
Percentage of interest * Amount invested
For the 5% interest account, the interest earned will be;
5/100 * a = 5a/100 = 0.05a
For the 8% interest account , the interest earned will be;
8/100 * b = 0.08b
By adding the interests on both account, we can get the total amount of interest earned
We can have this as;
0.05a + 0.08b = 752.50 •••••(ii)
From equation i above;
b = 11,000 - a
Substitute this into ii
0.05a + 0.08(11,000-a) = 752.5
0.05a+ 880 - 0.08a = 752.5
0.08a-0.05a = 880-752.5
0.03a = 127.5
a = 127.5/0.03
a = $4,250
Can anybody answer these 2 please hurry
Answer:
the first one is b= 52
the second one is b= 63
6th grade math i mark as brainliest
Answer:
9. 30/6
10. 7.6 and u
Step-by-step explanation:
Solve and describe the graph of the inequality: j + 16 ≥ -21
Answer:
j ≥ -37
Step-by-step explanation:
j + 16 ≥ -21
move constant to the right hand side and change its sign
j ≥ -21 - 16
calculate the difference (subtract)
j ≥ -37
The graph would be a closed circle on -37 with an arrow pointing to the right.
To solve and describe the graph.
What is inequality?A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions. The quality of being unequal or uneven.
Given that:
The inequality is
j + 16 ≥ -21
Move constant to the right hand side and change its sign
j ≥ -21 - 16
calculate the difference (subtract) the constant term
j ≥ -37
So, the graph would be a closed circle on -37 with an arrow pointing to the right.
Learn more about inequality here:
https://brainly.com/question/19846294
#SPJ5
The Micro Devices Company earned 3,632,859,678 dollars this year. 2,459,632,852 dollars were earned last year. Which is the best estimate of how many more dollars were earned this year than last year?
Answer:
$1,173,226,826
Step-by-step explanation:
The estimate of the increase in dollars earnings is the difference between this year's earnings and last year's earnings. In other words, the increase in earnings is the excess of current year's earnings over last year's earnings as computed below:
increase in earnings=this year's earnings-last year's earnings
this year's earnings=$3,632,859,678
last year's earnings=$2,459,632,852
increase in earnings=$3,632,859,678-$2,459,632,852
increase in earnings=$ 1,173,226,826
$2,300 invested at 7.5% for 10 years. In simple interest
Answer:
here's the answers............
Margo can purchase tile at a store for $0.69 per tile and rent a tile saw for $36. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?
Answer:
30 tiles need to buy for same cost in both store.Step-by-step explanation:
Let x be the number of tiles to buy for same cost in both store.
18+0.69 · n = 1.29 · n,
1.29n -0.69n =18 or
0.6n =18
n =18/0.6=30
Therefore, 30 tiles need to buy for same cost in both store.[Ans]
Answer:
I think you need to cross multiply
Plz help. Will give brainliest
Answer:
17.1
Step-by-step explanation:
Answer 17. 1
Step-by-step explanation:
is -4x-8=4x+8 one solution no solution or many solutions
Answer:
One solution.
Step-by-step explanation:
This question has different coefficients so it has one solution.
PLEASE PLEASE PLEASE HELP ME!!!!!!
Answer:
C
Step-by-step explanation:
The solution to a system of equations given graphically are at the points of intersection of the 2 graphs.
The graphs intersect at (- 2, - 4 ) and (4, 8 )
Thus the solutions to the system are (- 2, - 4) and (4, 8 )
I’ll mark brainlist whoever gives the right answer!
Answer:
y=-2/3x+2/3 i think... :)
Step-by-step explanation:
y=mx+b
-4=-2/3(-7)+b
-4=14/3+b
b=2/3
y=-2/3x+2/3
CAN SOMEONE HELP ME WITH THIS IXL ITS P.7 EIGHTH GRADE!!!!
Which expression is equal to
-18b^-4
Answer:
[tex] - \frac{18}{ {b}^{4} } [/tex]
Step-by-step explanation:
[tex] - 18b {}^{ - 4} [/tex]
express b^-4 with a positive exponent using:
[tex]a {}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
[tex] - 18 \frac{1}{ {b}^{4} } [/tex]
[tex] - \frac{18}{ {b}^{4} } [/tex]
What is the solution to the following system of equations?
2x + y = 0
x + 2y = 3
Group of answer choices
(0, 0)
(-1, 2)
(2, -4)
(-5, 4)
can someone help me understand this
Answer:
The answer for the question is E.
The baseball team has a double-header on Saturday. The probability that they will win both games is 42%. The probability that they will win the first game is 60%, What is the probability that the team will win the second game given that they have already won the first game?
The probability that the team will win the second game given that they have already won the first game is 7/10
Event win in the 1st game is represented with A
Event win in the 2nd game is represented with B
In the question
i. The probability that they will win both games is P(AnB) = 42%
ii. The probability that they will win the first game is P(A) = 60%
The probability that the team will win the second game given that they have already won the first game is:
P(B/A) = P(BnA) / P(A)
P(B/A) = P(AnB) / P(A)
From the question
P(B/A) = 42% / 60%
P(B/A) = 0.42 / 0.60
P(B/A) = 7/10
In conclusion: The probability that the team will win the second game given that they have already won the first game is 7/10
See related question here https://brainly.com/question/23423241
PLZ HELP ANSWER ONLY LAST QUESTION PLEASE!
pls help i need to get a good grade on this final so I can get my pc Best awnser gets brainliest
Answer:
d
Step-by-step explanation:
hope this helps
A chef uses 1/2 cup of cheese for a small pizza. There are 6 grams of fat in 1/4 cup of cheese.
Drag one expression next to each question. The correct expression for each row is a way to answer that question.
Drag one expression next to each question. The correct expression for each row is a way to answer that question. PLZZ help!!
Answer:
The correct options are;
1) How many grams of fat are in 1/2 cup of cheese = [tex]6 \div\dfrac{1}{4} \cdot \dfrac{1}{2}[/tex]
2) How many cups of cheese will the chef need to make 13 small pizzas = [tex]\dfrac{1}{2} \cdot 13[/tex]
3) How many small pizzas could the chef make if he has 3/4 cup of cheese is given as follows;
[tex]\dfrac{3}{4} \div \dfrac{1}{2}[/tex]
Step-by-step explanation:
1) How many grams of fat are in 1/2 cup of cheese
The number of grams of fat per 1/4 cup of cheese = 6 grams
Therefore;
The number of grams of fat per kilogram of cheese = 6/(1/4)
The number of grams of fat per 1/2 kilogram of cheese = 6/(1/4) × 1/2, which can be written as follows;
[tex]6 \div\dfrac{1}{4} \cdot \dfrac{1}{2}[/tex]
2) How many cups of cheese will the chef need to make 13 small pizzas
The number of cups of cheese per small pizza = 1/2 cup of cheese
Therefore, the number of cups of cheese in 1 small pizza = 1/2 × 13, which can be written as follows;
[tex]\dfrac{1}{2} \cdot 13[/tex]
3) How many small pizzas could the chef make if he has 3/4 cup of cheese is given as follows;
Given that 1/2 cup of cheese can make one small pizza
(1/2)/(1/2) = 1 cup of cheese can make 1/(1/2) small pizza
3/4 cup of cheese can make 3/4 × 1/(1/2) = (3/4)/(1/2) small pizza, which can be written as follows;
[tex]\dfrac{3}{4} \div \dfrac{1}{2}[/tex]
Jordan is running a race that is 13 miles long. From his training, he knows that it takes him 72 minutes for every 12 miles he runs and he runs each mile in the same amount of time.
How long will it take for Jordan to run the 13th mile in the race (assuming he runs at the same speed as the first 12 miles)?
Answer:
78 minutes
Step-by-step explanation:
72/12=6
6*13=78
A building is 50 feet tall and casts a 25 foot shadow. If Mark is 6 feet tall, how long would
his shadow be?
Answer:
Mark's shadow would be 3 feet.
Step-by-step explanation:
If a building is 50 feet tall and casts a 25 foot shadow, then the shadow of an object is 1/2 the length of the actual object.
This can be supported by the division problem:
50 ÷ 2 = 25
If Mark is 6 feet tall, then we need to divide 6 by 2 in order to find the length of the shadow.
6 ÷ 2 = 3
Therefore, Mark's shadow would be 3 feet.
Hope this helps! :D
pls help this is due today!!! if correct I'll make Brainliest!!!!
1= 1/8
2= 4/8
3= 2/8
Step-by-step explanation:
A city has 5 new houses for every 9 old houses. If there are 35 new houses in the city, how many old houses are there?
A.
61
B.
65
C.
63
D.
68
Answer:
C.) 63
Step-by-step explanation:
You know what you insisted on me answering, so I'll answer here.
35 ÷ 5 = 7
7 x 9 = 63
35/5 = 7
7 * 9 = 63
Therefore, there are 63 (C) old houses in the city.