Therefore $754.94 will be in account after 15 years.
Step-by-step explanation:
Given , Sarah opens a saving account that has a 2.75% annual interest rate , compounded monthly. She deposits $500 into the account.
P = $500, r = 2.75% = 0.0275 , t = 15 years and n= 12
[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]
[tex]=\$500(1+\frac{0.0275}{12})^{(12\times15)}[/tex]
=$754.94
Therefore $754.94 will be in account after 15 years.
After 15 years with a 2.75% annual interest rate, compounded monthly, an initial deposit of $500 in a savings account will grow to approximately $754.94.
Explanation:The student has asked how much money will be in a savings account after 15 years with an initial deposit of $500 if the account has a 2.75% annual interest rate, compounded monthly. To calculate the future value of this account, we can use the compound interest formula:
A = P (1 + r/n)^(nt)
Where:
Here, P is $500, r is 0.0275 (2.75% expressed as a decimal), n is 12 (since the interest is compounded monthly), and t is 15 years.
So, the calculation is:
A = $500 * (1 + 0.0275/12)^(12*15)
By computing this, we can determine the future value of the savings account after 15 years:
A ≈ $500 * (1 + 0.00229167)^(180)
A ≈ $500 * (1.00229167)^180
A ≈ $500 * 1.510383954
A ≈ $754.94
Therefore, the amount in the savings account after 15 years will be approximately $754.94.
Are these equations infinite solution, no solution, or one solution?
1: -14-8x=-2(-3x+7)
2: 3+5x=5(x+2)-7
3: 36-7x=-7(x-5)
Answer:
1) one solution
2) Infinitely many solution
3) no solution
Step-by-step explanation:
The first equation is -14-8x=-2(-3x+7)
Let us expand the right hand side to get:
-14-8x=-2*-3x+-2*7
We multiply -14-8x=6x-14
We group similar terms to get:
-8x-6x=-14+14
Combine similar terms to get:
-14x=0
Divide through by -14 to get:
x=0
2) The second equation is 3+5x=5(x+2)-7
We expand to obtain:
3+5x=5x+5*2-7
Multiply to get:
3+5x=5x+10-7
This gives us
3+5x=5x+3
5x=5x
1=1
There is infinitely many solutions
3) The third equation is: 36-7x=-7(x-5)
We expand to get:
36-7x=-7x+35
Group similar terms;
-7x+7x=35-36
0=-1
This statement is not true so there is no solution.
Complete the function table using the function rule f(x)=5x and answer the following questions
Ronnie charged his customers a flat fee of $25 to fix computers computers.Then he charge $30 for each hour that he spent fixing the computer. If Ronnie made $175 off of his first customer how many hours did he spend working.
Answer:$200
Step-by-step explanation:
Answer:
7.5 Step-by-step explanation: Ronnie charges $25 plus $20 per hour. This means that he made the following depending on how many hours he spent on it: Hours Dollars 0 25 = 25 + 0(20)=25 1 25+20 = 25 + 1(20)=45 2 25+20+20 = 25 +2 (20)=65 3 25+20+20+20 = 25 +3 (20)=85 4 25+20+20+20+20 = 25 +4 (20)=105 5 25+20+20+20+20+20 = 25 +5 (20)=125 n 25+n(20)=175 To find how many hours he worked for $175 we solve the equation using inverse operations: 25+n(20)=175 25-25+n(20)=175-25 n(20)=150 n= 7.5 hoursWhich of the following models can be used to find the product of (2x + 1)(x + 6)?
A
2x(x + 6) – 6(x + 1)
B
2x(x – 6) + 1(x – 6)
C
x(x – 6) + 2x(x – 6)
D
x(2x + 1) + 6(2x + 1)
Answer: No, it D
Step-by-step explanation: i choose c but it was wrong, it d
Math, ,,,,,,,,,,,,,,,,,,,,
Answer:
the Answer here is A
Step-by-step explanation:
Simplify:
{[(16 ÷ 4) × (2 × 6)] ÷ 6} + 4 =
Answer:
12
Step-by-step explanation:
divided 16 by 4 which is 4. then multiply 2 by 6, which is 12. then multiply 4 by 12. Remember to always do ( ) first. 4 by 12 is 48. Then do 48 divided by 6 which is 8. then add 8+4 which is 12.
Chicken costs $3.20 per pound, and beef costs $4.59 per pound. How much more does 3 pounds of beef cost than 3 pound of chicken?
To find the difference, first calculate how much 3 pounds of each meat costs.
$3.20 × 3 = $9.60 for 3 pounds of chicken
$4.59 × 3 = $13.77 for 3 pounds of beef
Now, take the difference.
$13.77 - $9.60 = $4.17
Answer:3 pounds of beef costs $4.17 more than 3 pounds of chicken.
Answer:
3 pounds of beef costs $4.17 more than 3 pounds of chicken
Step-by-step explanation:
Which statements about the factors of the terms in the expression 12x+18xy-24y are true. Select three options
A:the factors common to 12x and 18xy are 1,2,3,6,x,y
B:the factors common to 12x and 18xy are 1,2,3,6,x
C:the factors common to 12x and 24y are 1,2,3,4,6,12
D:the GCF of the expression is 6xy
E: the GCF of the expression is 6
The factors common to 12x and 18xy are 1, 2, 3, 6, and x.
The factors common to 12x and 24y are 1, 2, 3, 4, 6, and 12.
The GCF of the expression is 6.
Answer: Options B, C and E.
Explanation:
Factors are numbers we can increase together to get another number. At the point when we discover the components of at least two numbers, and afterward discover a few variables are the equivalent ("normal"), at that point they are the "basic elements".
These are the factors which are common in the whole expression or are common in any two equations at the time of comparison. The common factor which is the biggest is known as the greatest common factor.
Answer:
B,C,E
Step-by-step explanation:
A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 12 years ?
Answer:
503,049
Step-by-step explanation:
250,000 × 1.06^12 is the formula.
You take the percentage which is 6% and you add 1 to it.
So, you get 1.06
Then you take the 1.06 and raise it to the number of years which is 12.
1.06^12
Then you multiply that number to the base number which is 250,000 and get 503,049.
Hope this helps!
Final answer:
To find the population after 12 years given a 6% annual growth, we apply the exponential growth formula. With an initial population of 250,000, the formula gives approximately 503,054 as the population after 12 years.
Explanation:
To calculate the population of a city after 12 years when it grows by an annual rate of 6%, we utilize the formula for exponential growth, P(t) = P0 * [tex](1 + r)^t[/tex], where P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the number of years.
Given:
Initial population P0 = 250,000Growth rate r = 6% or 0.06Time t = 12 yearsThe population after 12 years can be calculated as follows:
P(12) = 250,000 * [tex](1 + 0.06)^{12}[/tex]
P(12) = 250,000 * [tex](1.06)^{12}[/tex]
P(12) ≈ 250,000 * 2.0122
P(12) ≈ 503,054
Therefore, the estimated population after 12 years is approximately 503,054.
Valentine's day cards cost 3/4 of dollars Emily has $20 she has to buy 20 cards for her class how much money will she be left with
Answer:
$5
Step-by-step explanation:
3/4 is the same as .75;
.75•20=15
20-15=5
Fifty people were surveyed about their favorite flavor of frozen yogurt. The results of the survey are displayed in the circle graph. How many people prefer banana?
Answer:
2
Step-by-step explanation:
4 divided by 2 equals 2
Answer:
3
Step-by-step explanation:
Which of the following represents the sum of the series? 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26
Answer:
the awnser is A I just got it right
Graph -5x-4=10 help me
This is the graph:
-5x=14
x=-2.8
If there are 6 hours in a school day, 5 school days in a week, 4 school weeks in a
month and 9 months in a school year, how many hours are there in a school
years
Answer:
1080hrs
Step-by-step explanation:
[tex] \frac{6hr}{1day} \times5 \frac{days}{week} [/tex]
days cancel, redefine week as =5days
[tex] \frac{30hr}{1week} \times 4 \frac{weeks}{month} [/tex]
weeks cancel redefine 4 weeks = 1 month
[tex] \frac{120hr}{1month} \times 9 \frac{month}{1year} [/tex]
months cancel, redefine 9months= 1years
[tex] \frac{120 \times 9}{1year} [/tex]
1080hrs per year (if I mathed 120x9 correctly that is, I didn't use a calculator so please double check that 120x9=1080)
Answer: 1080 hours
Step-by-step explanation:
Jake paid 13.50$ for admission to the country fair and bought 9 tickets to play games. If he spent a total of $36, what is the cost,c, of one ticket?
Terry Wade's variable costs for his car
totaled $1,876.88 last year and his fixed
costs totaled $1,685. If he drove 10,846
miles last year, what was his cost per
mile? Round to the nearest cent.
A $0.45
B $0.33
C $0.64
D $0.35
To find Terry Wade's cost per mile, his variable and fixed costs are summed and then divided by the total miles driven, yielding a cost per mile of approximately $0.33.
Explanation:To calculate Terry Wade's cost per mile for using his car, we first need to add together his variable and fixed costs, and then divide this total by the number of miles he drove last year.
This gives us the cost per mile.
Step 1: Add variable and fixed costs.
Variable costs = $1,876.88
Fixed costs = $1,685
Total costs = Variable costs + Fixed costs = $1,876.88 + $1,685 = $3,561.88
Step 2: Divide the total costs by the number of miles driven.
Number of miles driven = 10,846 miles
Cost per mile = Total costs ÷ Number of miles driven = $3,561.88 ÷ 10,846 miles
Cost per mile ≈ $0.328 or rounded to the nearest cent, $0.33.
Therefore, the cost per mile for Terry Wade last year was $0.33, making the correct answer B $0.33.
Write an expression that is equivalent to the following expression by factoring out the GCF 16y+18m
Answer:
2(8y+9m)
Step-by-step explanation:
for an unknown polynomial function p(x),p(2)+4=4, which binomial is a factor of p(x)?
Answer:i think it is 0
Step-by-step explanation:
You can use the fact that if (x-root) is a factor of a single variable polynomial function p(x) = 0
A binomial factor of p(x) is (x-2)
How to get factor of a single variable polynomial function if we know its one of the roots?Let its root be x = k
Then we have one of the factor of polynomial as (x-k)
What is a root of a single variable polynomial function p(x) ?Root of a polynomial function p(x) is a value of x such that putting that value in place of x makes the output 0.
Thus, if x = k is a root of the polynomial p(x), then
p(k) = 0
How to get a factor of the considered polynomial function?Since it is given that
p(2) + 4=4
thus,
p(2) = 4-4 = 0
Thus, x = 2 is a root of the polynomial function, and thus, using the aforesaid conclusions, we have (x-2) as one of the factors of the considered polynomial function.
Thus,
A binomial factor of p(x) is (x-2)
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Find the Center and the radius of the circle
x2 + y2 - 6x + 8y- 7 = 0.
Final answer:
The center of the circle is (3, -4) and the radius is approximately 5.66 units.
Explanation:
To find the center and radius of the given circle, we need to rewrite the equation in the standard form of the equation of a circle. The standard form is: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
So, let's complete the square for both x and y terms in the given equation:
(x^2 - 6x) + (y^2 + 8y) = 7
(x^2 - 6x + 9) + (y^2 + 8y + 16) = 7 + 9 + 16
(x - 3)^2 + (y + 4)^2 = 32
Now we can see that the center of the circle is (3, -4) and the radius is √32 or approximately 5.66 units.
13,500 deposit earning 3.3% compound monthly after 1 year
Answer:
$13,952.30
Step-by-step explanation:
refer to attached graphic
the formula for compound interest is given as
A = P [ 1 + (r/n) ] ^ (nt)
where
A = final amount (we are asked to find)
P = principal amount = $13,500
r = rate = 3.3% = 0.033
n = 12 (compounded monthly)
t = 1 year
substituting these values into the equation
A = 13500 [ 1 + (0.033/12) ] ^ [(12)(1)]
A = 13500 [ 1 + 0.00275 ] ^ 12
A = 13500 [1.00275 ] ^ 12
A = 13500 (1.0335)
A = $13,952.30
The balance on a $13,500 deposit earning 3.3% and compound monthly after 1 year is equal to $13,952.30.
How to determine the future value after 1 year?In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where:
A represents the future value.n represents the number of times compounded.P represents the principal.r represents the interest rate.t represents the time measured in years.By substituting the given parameters into the formula for compound interest, we have the following;
[tex]A(1) = 13500(1 + \frac{0.033}{12})^{12 \times 1}\\\\A(1) = 13500(1.00275)^{12}[/tex]
Future value, A(1) = $13,952.30.
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Complete Question;
Find the balance in each account after the given period. $13,500 deposit earning 3.3% compound monthly after 1 year.
PLEASE HELP (answer only if you know it) step by step pleaseeeeeeeeeeeeee
Step-by-step explanation:
Given the coordinate of C is (-3,1) and D is (5,6)
The length of a line segment [tex]\bar {AB}[/tex]with endpoint A at [tex](x_1,y_1)[/tex] and endpoint B at [tex](x_2,y_2)[/tex] is = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here [tex]x_1=-3 ,y_1=1[/tex] and [tex]x_2=5,y_2=6[/tex]
Therefore the length of a line segment [tex]\bar {CD}[/tex] is [tex]\sqrt{(5+3)^2+(6-1)^2}[/tex]
=[tex]\sqrt{89}[/tex] units
=9.43 units
A __________ guarantees that there is one and only one output for every input.
Answer: y intercept
Step-by-step explanation:
90 km is 8% of what distance
YOU WON'T ANSWER THIS!!!!
Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?
explain answer step by step
Answer:
7.5
Step-by-step explanation:
The given exponential function is
[tex]f(x) = {2}^{x} + 3[/tex]
The average rate of change over a≤x≤b is given by;
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
This implies that the average rate of change between the values 1 ≤ x ≤ 5 is
[tex] \frac{f(5) - f(1)}{5 - 1} [/tex]
We evaluate to get:
[tex]\frac{ {2}^{5} + 3 - {2}^{1} - 3}{4} = \frac{30}{4} = \frac{15}{2} = 7.5[/tex]
Given f(x)=3x+3, solve for x when f (x) = 6.
Answer:
x=1
Step-by-step explanation:
hello :
3x+3 =6
means : 3x+3-6 =6-6
3x -3 =0
add 3 : 3x = 3 divid by 3 : x=3/3=1
The required simplified value of the x for which the function gives f(x) = 6 is given as x = 1.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given function,
f(x)=3x+3,
Since we have given f(x) = 6, we have to determine the value of x for which the function gives 6,
Now,
f(x)=3x+3
Substitute f(x) = 6
6 =3x + 3
3x = 6 - 3
3x = 3
x = 1
Thus, the required simplified value of the x for which the function gives f(x) = 6 is given as x = 1.
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When the expression 3(n + 7) is evaluated for a given value of n, the result is 33. What is
the value of n?
Answer:4
Step-by-step explanation:What +7=11 bause the () make a multiplication and 11x3=33
Answer:
n=4
Step-by-step explanation:
3(n+7)=33
Lets mulitply..
3n+21=33
Then we need 3n alone...
To do this subract 21 from 33 and you get 12.
3n=12
Divide 3n by 3 and 12 by 3.
n=4
The sum of two numbers is 76 and their difference is 54. Find each of the numbers.
Answer:
The numbers are 11 and 65
Step-by-step explanation:
11 + 65 = 76
65 - 11 = 54
What are the values of m∠ABC, m∠CBF, m∠ABD and m∠DBE in the given figure? Explain or show your work.
The given figure is missing so I attached it below
m∠ A B C = 72°
m∠ F B C = 108°
m∠ A B D = 90°
m∠ D B E = 18°
Step-by-step explanation:
Vertical opposite angles formed from intersecting of two lines in a point, they are equal in measuresA pair of linear angles formed from intersecting a ray and a line in a point, the sum of their measures is 180°∵ Lines A F and C E are intersected at point B
∴ ∠ A B C and ∠ F B E are vertical opposite angles
- That mean they are equal in measures
∴ m∠ A B C = m∠ F B E
∵ m∠ F B E = 72°
∴ m∠ A B C = 72°
∵ Ray F B and line E C are intersected at B
∴ ∠ C B F and ∠ F B E formed a pair of linear angles
- Their measures is 180°
∴ m∠ C B F + m∠ F B E = 180°
∵ m∠ F B E = 72°
∴ m∠ C B F + 72 = 180
- Subtract 72 from both sides
∴ m∠ C B F = 108°
∵ Ray B D ⊥ to line A F
- That mean ∠ A B D and ∠ F B D are formed a pair of linear
angles equal in measures, then their measures is 180 ÷ 2 = 90
∴ m∠ A B D = m∠ F B D = 90°
∴ m∠ A B D = 90°
∵ Ray B E divides ∠ D B F into two angles D B E and F B E
∵ m∠ F B D = 90°
∴ m∠ D B E + m∠ F B E = 90°
∵ m∠ F B E = 72°
∴ m∠ D B E + 72 = 90°
- Subtract 72 from both sides
∴ m∠ D B E = 18°
Learn more:
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3 brothers have 58 years in total. How old is the youngest brother if 3/4 of his age equals to 2/3 of middle brother's age and 3/4 of youngest brother's age equals to half of oldest brother's age?
Step-by-step explanation:
Let O represents older brother
M represents middle brother
& Y represents younger brother.
Therefore, according to the given condition:
[tex] \frac{3}{4} y = \frac{2}{3} m = \frac{1}{2} o \\ \\ \therefore \: \frac{3}{4} y = \frac{2}{3} m \\ \implies \: m = \frac{3}{2} \times \frac{3}{4} y = \frac{9}{8} y \\ \\ next \: \: \frac{3}{4} y = \frac{1}{2} o \\ \implies \: o = \frac{2}{1} \times \frac{3}{4} y = \frac{3}{2} y \\ \\ \because \: o + m + y = 58 \\ \\ \therefore \: \frac{3}{2} y + \frac{9}{8} y + y = 58 \\ \\ \therefore \: \frac{12}{8} y + \frac{9}{8} y + \frac{8}{8} y = 58 \\ \\ \therefore \: \frac{29}{8} y = 58 \\ \\ \therefore \: y = 58 \times \frac{8}{29} \\ \\ \therefore \: y = 2 \times 8 \\ \\ \therefore \: y = 16 \: years[/tex]
Thus youngest brother is 16 years old.
two fifths of twenty
Answer:
8
Step-by-step explanation:
2/5*20= 8
You can use the attachment above ^^
Answer: It would Be 8
Step-by-step explanation:
You would just multiplie
2/5 x 20
So 2x20/5= 40/5
Then simplify to 8