Answer:
To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal or investment amount
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the investment is held
Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:
r/12 = 0.034/12 = 0.002833
Now we can plug in the values into the formula:
A = P(1 + 0.002833)^(12*14)
A = P(1.002833)^(168)
We know that A = $1,450 and we want to find P (the initial principal or investment amount).
So we can rearrange the equation to find P:
P = A/(1.002833)^(168)
Solving for P, we get:
P ≈ $973.99
So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.
Step-by-step explanation:
The total age of Sana, Rabia and Saleem is 47 years. What was the total of their ages three years ago?
Answer:
38
Step-by-step explanation:
I'll say that Sana's age is A, Rabia's age is B, and Saleem's age is C.
A + B + C = 47
Three years ago, everyone was three years younger, so we can write the expression as:
(A-3) + (B-3) + (C-3) = x
x is the total age three years ago.
The above equation is the same thing as:
A + B + C - 9 = x
Since we know that A + B + C is 47, we use that number instead.
47 - 9 = x
38 = x
So three years ago, their total age was 38 years old.
John goes for a jog every third day and every Saturday he goes to the gym. If he goes to the gym and also runs today, how long will it take before there is another day on which he does both?
It will take 21 days before there is another day on which he does both.
What is lowest common multiple (LCM) ?The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.
Given,
John goes for a jog every third day and every Saturday he goes to the gym.
That means he goes to the gym on every seventh day, and goes for a jog every third day.
Therefore, he goes for both on the days which are LCM of 3 and 7.
But, LCM of 3 and 7 is 21.
Hence, he goes for both in every 21 days.
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A side of a regular polygon is 10cm. If each interior angle is 156. Calculate its perimeter.
Answer:
150 cm
Step-by-step explanation:
The total of exterior angles is 360°. We can use this fact to find the number of sides. The perimeter is the total length of all of the congruent sides.
Exterior anglesThe measure of an exterior angle of the regular polygon is the supplement of the adjacent interior angle:
exterior angle = 180° -156° = 24°
The total of n of these angles is 360°, so n is ...
24°×n = 360°
n = 360°/24° = 15
The polygon has 15 exterior angles, hence 15 sides
PerimeterThe perimeter is the total length of the 15 congruent sides:
P = 15×(10 cm) = 150 cm
The perimeter of the regular polygon is 150 cm.
On Friday a local hamburger shop sold a combined total of 460 hamburgers and cheeseburgers The number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold Friday
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:
x + y = 460 (1)
Also:
y = 3x (2)
From both equations:
x = 115, y = 345
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
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A car’s purchase for $27,000 after each year the resale value decreases by 35% what will the resale be after four years
The resale value of the car after four years is $4820
How to determine the resale value?The given parameters are:
initial value, a = $27,000
Rate, r = 35%
The value of the car each year is represented as:
Value = a *(1 - r)^t
So, we have:
Value = 27000 *(1 - 35%)^t
After four years, we have:
Value = 27000 *(1 - 35%)^4
Evaluate
Value = 4820
Hence, the resale value of the car after four years is $4820
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What is the equation of the line that is perpendicular to the line defined by the equation 2x = 4y – 8 and goes through the point (1, 2)?
The equation of the perpendicular line is y = -2x + 4
How to determine the line equation?The line equation is given as:
2x = 4y - 8
Make y the subject
4y = 2x +8
Divide by 4
y = 0.5x + 2
The slope of the above equation is
m = 0.5
The slopes of perpendicular lines are opposite reciprocals.
This means that, the slope of the perpendicular line is:
n = -1/m
This gives
n = -1/0.5
n = -2
The equation is then calculated as:
y = n(x - x1) + y1
This gives
y = -2(x - 1) + 2
Expand
y = -2x + 2 + 2
Evaluate
y = -2x + 4
Hence, the equation of the perpendicular line is y = -2x + 4
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Consider the following functions. f=[(-1,1),(1,-2),(3,-4) and g=[(5,0),(-3,4),(1,1),(-4,1)} Find (f-g)(1) =
The difference between the functions give:
(f - g)(1) = f(1) - g(1) = -3
How to find the difference between the functions?
For two functions f(x) and g(x), the difference is defined as:
(f - g)(x) = f(x) - g(x).
Then:
(f - g)(1) = f(1) - g(1)
By looking at the given tables, we know that:
f(1) = -2
g(1) = 1
Replacing that we get:
(f - g)(1) = f(1) - g(1) = -2 - 1 = -3
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Find DE
3x - 28
3x - 30
D
G
E
F
33
Answer:
11 units
Step-by-step explanation:
We first need to solve for x
3x -28 +3x -30 + x = 33 Combine the x's
7x - 28 -30 = 33 Combine -28 and -30
7x - 58 = 33 Add 58 to both sides
7x = 91 Divide both sides by 7
x = 13 Now plug 13 into the expression for DE
3x - 28
3(13) - 28
39 -28
11
A man ordered 4 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.41 per box, and felt-tip pens cost $3.44. If the man's order of pens totaled $63.24, how many boxes of each type of pen did he buy?
How many boxes of felt-tip pens did he buy?
Answer:
3
Step-by-step explanation:
Let x = # of boxes of felt-tip pens.
(x)(3.44)+(4x)(4.41) = 63.24
21.08x = 63.24
x = 3
Because x = 3, the man bought 3 boxes of felt-tip pens and 12 boxes of ballpoint pens.
3 On Saturday Keisha ran 35
she ran 41 kilometers. How much farther did she run on
Saturday than on Sunday?
By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.
How to Subtract Decimals?When subtracting decimals, the number value is taken into consideration.
Distance ran by Keisha on Saturday = 3.218 kilometers.
Distance ran by Keisha on Sunday = 2.41 kilometers.
Subtract both decimals to determine how much farther she run on Saturday than on Sunday.
3.218 - 2.14 = 1.078 kilometers.
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15) Allie Young has to get a new car because someone hit and destroyed her old one. She feels she can afford to
pay $90 each month, and the best loan terms she has found offer her an 8.33 percent interest rate on a 4-year
loan. What is the maximum value of the car Allie should be looking for? Give answer to nearest hundred dollars.
a.) $3900
b.) $3800
c.) $3600
d.) $3700
Answer:I beleive the answer is c-3600
Step-by-step explanation:
90$ a month for 48 months=4320
Plus the interest rate of 8.33 so 4320x0.833=3598.56
Then you have to round up from 3598.56 to the nearest 100 dollars, so it would be 3600.
One yellow daisy and two pink carnations tied with ribbon will be used for corsages at a Mother's Day banquet. Each corsage takes 6 inches of ribbon. The daises are $0.85 each, the carnations are $0.50 each, and the ribbon is $0.24 per foot. There will be 24 corsages. What is the total cost?
Answer:
$47.28
Step-by-step explanation:
The total cost is found by adding the costs of the components.
Component costThere is one daisy, at $0.85 each.
There are to carnations at $0.50 each, for a total of 2×$0.50 = $1.00.
The is 6 inches of ribbon. That amount is 1/2 foot, so its cost is ...
(1/2 ft)×$0.24/ft) = $0.12.
Total costThe total cost of the components of one corsage is ...
daisy cost + carnation cost + ribbon cost = $0.85 +1.00 +0.12 = $1.97
There are 24 corsages, so their total cost will be 24 times this amount, or ...
24 × $1.97 = $47.28
The total cost of the 24 corsages is $47.28. All the costs of the components required for making a corsage are added to get the total cost of the corsage.
How to calculate the total cost?Total cost is the sum of all the individual component costs.Consider a and b are the two components with a cost K of each. Then the total cost = aK + bKCalculation:It is given that,
The components and their costs:
The cost of each daise = $0.85
The cost of each carnation = $0.50
The cost of the ribbon per foot = $0.24 (1 foot = 12 inches)
The components for making one single corsage:
One yellow daisy + two pink carnations + 6 inches of ribbon = 1 corsage
Then, calculating the price for one single corsage,
1 × $0.85 + 2 × $0.50 + (1/2) × $0.24 = cost of 1 corsage
⇒ $0.85 + $1 + $0.12
⇒ $1.97
For 24 corsages, the total cost = 24 × $1.97 = $47.28
Therefore, the total cost of the 24 corsages is $47.28.
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express using positive exponent
[tex] {3c}^{ - 2} [/tex]
Answer: [tex]\frac{3}{c^2}[/tex]
Step-by-step explanation:
This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].
A dairy needs 336 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 336 gallons?
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
How to work with percentages?Let x = number of gallons of 3% milk
Thus;
336 - x = number of gallons of 7% milk
Therefore;
0.03x + 0.07(336 - x) = 0.06(336)
0.03x + 23.52 - 0.07x = 20.16
-0.04x = -3.36
x = 84 gallons
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
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WILL GIVE BRAINLIEST
1. Write an expression for each of the following:
a. the sum of 6 and z
b. the difference between 20 and x
c. 8 less than the quotient of x divided by 6
d. x increased by 5 divided by 4
The expressions for each of the given statements are
a. 6 + z
b. 20 - x
c. x/6 - 8
d. x + 5/4
Writing an expressionFrom the question, we are to write an expression for each of the given statement
a. the sum of 6 and z
That is,
6 + z
b. the difference between 20 and x
That is,
20 - x
c. 8 less than the quotient of x divided by 6
That is,
x/6 - 8
d. x increased by 5 divided by 4
That is,
x + 5/4
Hence, the expressions for each of the given statements are
a. 6 + z
b. 20 - x
c. x/6 - 8
d. x + 5/4
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Find the sum of the series: 4+8+12+........to 20 term. In (n
Answer:
16
Step-by-step explanation:
4 , 8 , 12 , 16 , 20 , ....................... ans goes on
A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn? Please show me how you figured this out.
A. 6 2/5
B. 9 3/5
C. 2 1/4
D. 5 1/2
If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.
How many hours will it take to mow the lawn?Let's say that each person works at a rate R.
8 people can mow the lawn in 6 hours, then we can write:
(8*R)*6 hours = 1 lawn.
Solving for R:
R = (1/48 lawns per hour).
If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:
(5*R)*T = 1 lawn.
Replacing the value of R:
(5/48 lawns per hour)*T = 1 lawn.
Then we have:
T = (48/5) hours.
We can rewrite that as:
T = (45/5 + 3/5) hours
T = 9 + 3/5 hours.
Then we conclude that the correct option is B.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The solution of the inequalities is (0.375, 4.25)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x + 12
2x + y ≤ 5
Next, we plot the inequalities on a graph (see attachment)
From the graph, both inequalities intersect at
(x, y) = (0.375, 4.25)
This represents the solution of the inequalities
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f(x)=- x ^ 2 - 1,x ne5\\ -3,x=5 lim x -> 5 f(x) = lim x -> 5 f(x) Find if
Answer:
the answer to the question is 1
Answer:
-26 Is the correct answer
Step-by-step explanation:
evaluate f(x)=4|x|+3 for x=-5
Sometimes, terminology such as "the odds are 1 in 10" of an event is used. This is interpreted to mean "the probability of the event is 1/10" or "the odds in favor of the event are 1 to 9"
The odds that a member of a certain country's Senate (selected randomly) has a law degree is 1 in 1.4. What is the probability that a member of the Senate (selected randomly) has a law degree?
The probability is
Answer:
71.4% ( i think)
Step-by-step explanation:
If we translate 1 in 1.4 using what is described, it turns into (1/1.4)
Putting this into a calculator, we get 0.714286. Translated into a percent, that becomes 71.4286%
The probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.
When the odds are given as "1 in 1.4," it means that there is 1 chance of success (having a law degree) for every 1.4 chances of failure (not having a law degree).
To find the probability that a member of the Senate (selected randomly) has a law degree, you can use the formula:
Probability = 1 / (1 + Odds)
In this case, the odds are 1 in 1.4, so the probability is:
Probability = 1 / (1 + 1.4) ≈ 1 / 2.4 ≈ 0.4167
So, the probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.
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Y=x2+1 ordered pairs
The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
How to determine the ordered pairs?The function is given as:
y = x^2 + 1
the ordered pairs are the x and y values of the function
So, we stet x = 0, 1, 2, 3 and 4
y = 0^2 + 1 = 1
y = 1^2 + 1 = 2
y = 2^2 + 1 = 5
y = 3^2 + 1 = 10
y = 4^2 + 1 = 17
Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
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Write an equation for this word
sentence: one fifth of a number
equals 16.
Answer: x / 5 = 16
x = 80
Please help me quick
The product of the ages 2 years from today is 924
System of equationLet the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;
xyz = 1716
If the product of their ages last year is 1320, then;
(x-1)(y-1)(z-1) = 1320
Two years ago, the product of their ages will be;
(x-2)(y-2)(z-2) = 1320- (1716-1320)
(x-2)(y-2)(z-2) = 1320-396
(x-2)(y-2)(z-2) =924
Hence the product of the ages 2 years from today is 924
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Let sets A and B be defined as follows.
A is the set of integers greater than -14 and less than -5.
B={h,i,s,x,z}
a) find the cardinalities of A and B
n(A)=
n(B)=
b) select true or false
-12 ∈ A
-21 ∈ A
s ∈ B
m ∉ B
A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.
-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.
Cardinalities of A and B
It is given that,
A = {n : -14 < n < -5, n ∈ Z} ............ (1)
B = {h, i, s, x, z} ......... (2)
Thus, from (1),
A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)
Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,
n(A) = 8
n(B) =5
Reason Behind True or False
As seen from (3), set A contains the element -12. Thus, -12 ∈ A is True.Again from (3), we can see that -12 does not belong to the set A. Thus, -21 ∈ A is FalseFrom (2), s is present in set B. Hence, s ∈ B is TrueSimilarly, m is not present in set B. Therefore, m ∉ B is TrueLearn more about cardinalities here:
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please help me! i’m really confused on this because i keep getting -5 outside the thing
Answer: D.
Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So the answer should look like: 5x³y(-3x⁵-4z+9).
(-11x+3)-2(-11/4x-5/2)= simplify it
Answer:
(+22x^2+16x+11)/(2x)
One angle of a triangle measures twice the smallest angle. The third angle measures five more than twice the smallest angle. Find the measure of the smallest angle.
Answer: The smallest angle is 35°
Step-by-step explanation:
1 angle: 2x
smallest angle: x
third angle: 2x + 5
all angles in a triangle add up to 180 degrees. Therefore,
2x+x+2x+5 = 180
5x+5=180
5x+5(-5)=180(-5)
5x = 175
5x/5 = 175/5
x = 35
The smallest angle is 35°
How do i plot 3 points on a graph when all I am given is "x=4" ? and I need to find "x and y" for 3 points.
Answer:
(4,-1) (4,0) (4,1)
Step-by-step explanation:
If you graph this, it will be a straight vertical line. No matter what y is, x will always be 4.
How do i convert the follwing Powers Of Ten into standard numbers?
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The standard numbers are obtained from the given numbers as follows;
10⁷ → 1000000010⁵ → 10000010⁸ → 10000000010¹² → 100000000000010⁶ → 1000000Which method can be used to express the numbers in standard form?The standard form of numbers is obtained by expressing the number completely and not using powers of 10
The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;
Number → Standard form
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