The principal amount is 85227.27 and the interest is 64772.73.
Solution:
Given:
Amount (A)= 150000
Number of years (n)= 8
Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]
To find: The principal (P)
We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]
This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]
The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]
On equating (1) and (2) we get,
[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]
On substituting the values we get,
[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]
On solving we get,
[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]
On grouping the like terms together we get,
[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]
[tex]\bold{\Rightarrow 150000=1.76P}[/tex]
[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]
[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]
If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]
A coffee shop served hot and cold coffee to a total of 340 people. 45% of the people chose cold coffee.
How many people chose hot coffee?
Answer:
187 people
Step-by-step explanation:
340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.
Answer:
187 people
Step-by-step explanation:
340 people multiplied by 0.45 or 45% is 153. Subtract 153 from 340 and you get 187 people.
Determine whether the random variable described is discrete or continuous.
The height of a randomly chosen basketball player.
The height of a randomly chosen basketball player is a continuous random variable since height is measured and can take on an infinite range of values.
The random variable described, the height of a randomly chosen basketball player, is a continuous random variable. This is because height can take an infinite number of possible values within a range and is measured rather than counted. Unlike discrete random variables, which have countable values such as the number of heads in a coin toss, continuous random variables like height are measured and can include values such as 6'1" or 6'1.5". The values are on a continuous scale, and therefore the probability distribution of a continuous random variable is concerned with the probability of the variable falling within a certain range, rather than taking specific countable values.
Your neighbor has decided to enlarge his garden. The garden is rectangular with width 6 feet and length 15 feet. The new garden will be similar to the original one, but will have a length of 35 feet. Find the perimeter of the original garden and the enlarged garden.
The perimeter of original garden is 42 feet
The perimeter of enlarged garden is 82 feet
Solution:
The perimeter of rectangle is given as:
Perimeter = 2(length + width)
Original Garden:Given that,
The garden is rectangular with width 6 feet and length 15 feet
Length = 15 feet
Width = 6 feet
Therefore, perimeter is given as:
Perimeter = 2(15 + 6)
Perimeter = 2(21)
Perimeter = 42
Thus perimeter of original garden is 42 feet
Enlarged Garden:The new garden will be similar to the original one, but will have a length of 35 feet.
Length = 35 feet
Width = 6 feet
Therefore, perimeter is given as:
Perimeter = 2(35 + 6)
Perimeter = 2(41) = 82
Thus perimeter of enlarged garden is 82 feet
Helppppppp let’s get to 100!!!!
Answer: 3
Step-by-step explanation:
10 had sprinkles and 2 did not which mean there are 12.
So would it be 3 that not have a sprinkles?
I think so.
f(x)=−x+2, find f(-5)f(−5).
To calculate f(-5) for the function f(x)=-x+2, we substitute -5 in place of x, which gives us f(-5) = 7.
Explanation:To find the value of f(-5) for the function f(x)=−x+2, we simply substitute x with -5:
f(-5) = −(-5) + 2
Now, we perform the operations:
f(-5) = 5 + 2
f(-5) = 7
Therefore, the answer is 7.
the average number 1 0 1 5 6 3 4
Answer: 2
Step-by-step explanation: Edge 2023
Final answer:
To find the average number from a list of numbers, add up all the numbers and then divide the sum by the total number of numbers.
Explanation:
The question asks for the average number from a given list of numbers. To find the average, you add up all the numbers in the list and then divide the sum by the total number of numbers in the list.
In this case, the average of the numbers 1, 0, 1, 5, 6, 3, and 4 can be found by adding those numbers together (1 + 0 + 1 + 5 + 6 + 3 + 4) and then dividing the sum by 7 (the total number of numbers in the list). So, the average is 4.
WILL MAKE BRAINLEST!! Which equation best represents the line??
A. Y=1/3X-1
B. Y=3X-1
C. Y= -X+ 1/3
D. Y= 3X+1
Answer:
B is the answer. ........
Answer:
B
Step-by-step explanation:
it intercepts the y line at -1 and the rise over run is 3
Katy bought a candy bar and shared it with her two sisters. She gave her youngest sister 1/4 of the candy bar. Her older sister received 1/3 of the candy bar. How much of the candy bar did Katy keep?
Answer:
Step-by-step explanation:
Since the candy bar is just one
Giving 1/4 of it to her younger sister make her left with 3/4 of the candy bar i.e 1 - 1/4 = 3/4
Then giving 1/3 of the left over to her elder sister it becomes 3/4 * 1/3 =1/4
Then the remaining candy bar will be 3/4 - 1/4 = 1/2
Then she will be left with 1/2 i.e half of the candy bar.
Please help ASAP will give BRAINLIEST ANSWER!!!!!!!
Answer:A $35 decrease followed by a $25 increase is less than the original.
A 50% decrease then 33.333% increase is the same.
A 30% increase then 15% decrease is more.
A 50% decrease then 100% increase is the same.
A 70% increase then 50%decrease is less.
Step-by-step explanation:
Ryan’s heart beats 9 times per 10 seconds while Ryan is resting. About how many times would Ryan’s heat beat during 3 minutes of rest.
Find the circumcenter of the triangle ABC.
A( - 4,3), B(5,7), C(-4,7).
Answer:
Circumcenter O (0.5 , 5)
Step-by-step explanation:
Circumcenter O (x , y)
OA = OB = OC
OA² = (x + 4)² + (y - 3)²
OB² = (x - 5)² + (y - 7)²
OC² = ( x + 4)² + (y - 7)²
OA² = OC² : (x + 4)² + (y - 3)² = ( x + 4)² + (y - 7)²
(y - 3)² = (y - 7)² y² - 6y + 9 = y² -14y + 49
8y = 40
y = 5
OB² = OC² : (x - 5)² + (y - 7)² = ( x + 4)² + (y - 7)²
x² - 10x + 25 = x² + 8x + 16
18x = 9
x = 0.5
Circumcenter O (0.5 , 5)
In order to find the height of a cliff, you stand at the bottom of the cliff, walk 60 feet
from the base, and place a mirror on the ground. Then you face the cliff and step back
5 feet so that can see the top of the cliff in the mirror. Assuming your eyes are 6 feet
above the ground, explain how to use this information to find the height of the cliff.
(The angles marked congruent are congruent because of the nature of the reflection of
light in a mirror.)
Q5ft
60 ft
K
Mirror
Answer: 72 ft
Step-by-step explanation:
We can solve this problem using geometry, if we draw two righ triangles (figure attached):
-One formed by you, assuming you are 6 ft tall, and the ground
-The other formed by the height of the cliff, the bottom of the cliff and the ground.
Both triangles are congruent, having the mirror as a common vertex, hence we can use the following relation to find :
[tex]\frac{6 ft}{y}=\frac{5 ft}{60 ft}[/tex]
Isolating :
[tex]y=\frac{(60 ft)(6 ft)}{5 ft}=72 ft[/tex] This is the height of the cliff
The calculated height of the cliff is 72 feet.
To determine the height of the cliff, we use a mirror and the property of the reflection of light. Here are the steps to solve the problem:
Place the mirror 60 feet from the base of the cliff and stand back 5 feet from the mirror.Since your eyes are 6 feet above the ground, the light reflecting from the mirror at the point where you see the top of the cliff will create similar triangles based on the reflection.The triangles formed involve your height of 6 feet over the 5 feet back from the mirror and the unknown height of the cliff over the 60 feet from the mirror.Set up the proportion from the similar triangles:height of cliff / 60 feet = 6 feet / 5 feet.
5. Solve for the height of the cliff:
height of cliff = (6 feet / 5 feet) * 60 feet = 72 feet.
Thus, the height of the cliff is 72 feet.
I NEED HELP ASAP!!!!
What is the change in temperature from 15 degrees to -9 degrees? -6, 6, -24, 25
Answer:
24 degrees
Step-by-step explanation:
The distance from 15 degrees to 0 degrees is 15, and the distance from 0 degrees to -9 degrees is 9, so then the total distance from 15 degrees to -9 degrees is (15+9 degrees) which adds up to be 24 degrees
Trevin puts 8 gallons of gas in his car and pays $22, ate this rate what is the cost for 9 gallon of gas
Answer:
$24.75
Step-by-step explanation:
Find the unit rate for 1 gallon, to dothis divide $22 by the 8 gallons of gas. 22/8 is $2.75. now that we know the unit rate, multiply it by 9 for our answer. 2.75*9=24.75,the cost for 9 gallons.
Trevin puts 8 gallons of gas in his car and pays $22. The cost of 9 gallons of gas at this rate is $24.75
Word problems in mathematics involve a careful understanding of the question. It is usually written or expressed in one or more sentences and it requires pupils to apply their arithmetic skills to a real-life issue.
From the information given:
Trevin put 8 gallons of gas in his car and pays $22 for iti.e
8 gallons = $22We are to determine the rate he will pay for 9 gallons. i.e.
9 gallons = xFrom the above two expressions, by cross multiplying, we have:
[tex]\mathbf{x = \dfrac{9 \ gallons \times \$22 }{8 \ gallons}}[/tex]
x = $24.75
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Colin invests £3500 into his bank account.
He receives 5% per year compound interest.
How much will Colin have after 6 years?
Give your answer to the nearest penny where appropriate.
Answer: 4,690.33
Step-by-step explanation:
The formula for calculating amount is given by :
A = P [tex](1+r)^{n}[/tex]
Where :
A = amount = ?
P = Principal = 3500
r = rate = 0.05
n = number of years = 6
substituting the given values into the formula , we have
A = 3500[tex](1+0.05)^{6}[/tex]
A = 3500 [tex](1.05)^{6}[/tex]
A = 3500 (1.340095640625)
A = 4690.3347421875
A = 4,690.33
Final answer:
To calculate Colin's investment with compound interest after 6 years, we use the formula for compound interest and determine that he will have £4690.33 to the nearest penny.
Explanation:
To calculate how much Colin will have after 6 years with compound interest, we use the formula for compound interest:
A = P(1 + r/n)nt
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In Colin's case, we have:
P = £3500
r = 5% or 0.05
n is not mentioned, so we assume it is compounded once per year, thus n = 1
t = 6 years
Plugging these values into the formula:
A = £3500(1 + 0.05/1)1×6 = £3500(1 + 0.05)6
A = £3500 × (1.05)6 = £3500 × 1.340095
A = £4690.3325
To the nearest penny, Colin will have
£4690.33 after 6 years.
The difference between the solutions of the equation 5x2−x−k=0 is 1.8. Find the solutions.
The solutions are - 0.8 and 1
Step-by-step explanation:
In the quadratic equation ax² + bx + c = 0
The sum of the two solutions of the equation is [tex]\frac{-b}{a}[/tex] The product of the two solutions is [tex]\frac{c}{a}[/tex]Assume that the solutions of the equations are m and n
∵ 5x² - x - k = 0
- By comparing it by the form above
∴ a = 5, b = -1 , c = -k
- Use the rule of the sum of the two solutions above
∵ The sum of the two solutions = [tex]\frac{-b}{a}[/tex]
∴ The sum of the two solutions = [tex]\frac{-(-1)}{5}=0.2[/tex]
∵ The two solutions are m and n
∴ m + n = 0.2 ⇒ (1)
∵ The difference of the two solutions is 1.8
∴ m - n = 1.8 ⇒ (2)
Now we have a system of equations to solve
Add Equations (1) and (2) to eliminate n
∴ 2m = 2
- Divide both sides by 2
∴ m = 1
- Substitute the value of m in equation (1) to find n
∴ 1 + n = 0.2
- Subtract 1 from both sides
∴ n = -0.8
The solutions are - 0.8 and 1
If you want to find the value of k
∵ The product of the solutions is [tex]\frac{c}{a}[/tex]
∴ The product of the solutions = [tex]\frac{-k}{5}[/tex]
∵ m × n = 1 × (-0.8) = - 0.8
- Equate [tex]\frac{-k}{5}[/tex] by - 0.8
∴ [tex]\frac{-k}{5}=-0.8[/tex]
- Multiply both sides by -5
∴ k = 4
∴ The equation is 5x² - x - 4 = 0
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Answer:
x = 1; x = -0.8
Step-by-step explanation:
Here is a simpler approach if needed for future students:
5x^2-x-k = 0,
System of Equations: x1 - x2 = 1.8 & x1 + x2 = 1/5 = 0.2 (if x1 and x2 are roots)
Now let's add the two:
x1 - x2 = 1.8
+ x1 + x2 = 0.2
----------------------
2x1 = 2,
x1 = 2/2 = 1
- x2 = 1.8 - 1 = 0.8 => x2 = -0.8
What is a real world situation for the problem 42.48 Divided by 25
Answer:
At the donut shop, Karley and 24 of her co-workers have split the tip jar. There is $42.48 in the tip jar. How much money does each worker get from the jar?
2. Tickets to a play cost $8 each. Write an
expression that gives the ticket cost in dollars
for a group of g girls and b boys.
Expression that gives the ticket cost in dollars for a group of g girls and b boys is (8g + 8b) dollars
Solution:
Given that tickets to play cost $ 8 each
To find: Expression that gives the ticket cost in dollars for a group of g girls and b boys
From given,
cost of 1 ticket = $ 8
Number of girls = g
Number of boys = b
Thus the expression can be framed for total cost as:
Total cost = (number of girls + number of boys)(cost of 1 ticket)
[tex]Total\ Cost = (g + b) \times 8\\\\Total\ Cost = 8g + 8b[/tex]
Thus the expression that gives total cost is (8g + 8b) dollars
a dragonfly can beat its wings 30 times per second. write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times that dragonfly beats its wings
-3х + 40 = 10
I don’t know how to solve
Answer:
Step-by-step explanation:
Darcy’s house is 6 times as far from school as her friend’s house. If her friend’s house is 3/4 mile from school, how many miles from school is Darcy’s house?
How Do You Write The Expression For Triple 9 Then Multiply 8
Alexis and 3 friends are at the mall.each person buys a pretzel for 4$, sauce for $1, and a drink for $2. write and expression for the total and find the total cost.
Answer:
(4+1+2)3= 21
Step-by-step explanation:
you add the cost of snacks then multiply by 3 because there are 3 people to get total cost.
4+1+2=7 7*3=21Answer:
4+4+4+1+1+1+2+2+2=25
when x-y=3 work out the value of 2x-2y
Answer:
6
Step-by-step explanation:
Given
2x - 2y ← factor out 2 from each term
= 2(x - y) ← substitute x - y = 3 into the expression
= 2(3)
= 6
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
x - y = 3
2x - 2y
The value of 2x - 2y is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x - y = 3 _____(1)
The value of 2x-2y.
= 2x - 2y
Taking 2 as common.
= 2 (x - y)
From (1) we get,
= 2 x 3
= 6
Thus,
The value of 2x - 2y is 6.
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What is gcf of 24, 60, and 36
Answer:
12
Step-by-step explanation:
What is the expression for triple 9 then multiply 8
Answer:
3R
Step-by-step explanation:
Simplify: (5x^6y^-4)^3(2x^8y^3)
Answer:
250x^26/y^9
Step-by-step explanation:
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Shawn got a haircut at the barber shop. It cost $11, and he left a $3 tip.
What percent tip did he leave the barber?
Answer: He left a 27.27272727% tip
1. if x and y are both even whole numbers. what is a possible solution for x + y?
a. 5
b. 9
c. 4.6
d. 8
2. assume n and m are both even whole numbers and m > n. what is a possible solution for m - n?
a. 16
b. 1/2
c. 0
d. -2
1. The possible solution for x + y is 8 ⇒ d
2. The possible solution for m - n is 16 ⇒ a
Step-by-step explanation:
Lets explain some notes about the even numbers
Their sum is evenTheir difference is evenTheir product is even1.
∵ x and y are both even whole numbers
∴ Their sum is even whole number
∵ 5 and 9 are odd numbers ⇒ impossible
∵ 4.6 is not a whole number ⇒ impossible
∵ 8 is an even whole number ⇒ possible
∴ x + y could be 8
The possible solution for x + y is 8
2.
∵ n and m are both even whole numbers
∵ m > n
∴ m - n must be positive even whole number
∵ 1/2 is not a whole number ⇒ impossible
∵ 0 is not a positive number ⇒ impossible
(zero is not positive nor negative)
∵ -2 is not a positive number ⇒ impossible
∵ 16 is a positive even whole number ⇒ possible
∴ m - n could be 16
The possible solution for m - n is 16
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