Answer:
Monthly deposit, P = $776.41
Step-by-step explanation:
Interest rate per annum = 5.5%
number of years = 25
Since she pays monthly, number of payments per annum = 12
Interest rate per period, r = (Interest rate per annum)/(number of payments per annum)
r = 5.5%/12 = 0.46%
Number of periods, n = number of years * number of payments per annum
n = 25 * 12 = 300
Future value of annuity, FVA = $500,000
Monthly deposit will be:
[tex]P = \frac{(FVA) * r}{(1+r)^{n} -1} \\P = \frac{(500000) * 0.46/100}{(1+0.46/100)^{300}-1 }[/tex]
P = $776.41
Answer:
MP = $778.77
she should put $778.77 into the account each month
Step-by-step explanation:
This problem can be solved using the compound interest formula;
FV = MP{[(1+r/n)^(nt) - 1]/(r/n)} .......1
Where;
FV = Future value
MP = monthly contribution
r = yearly rate
n = number of times interest is compounded per year.
t = number of years
Given
FV = $500,000
t = 25 years
r = 5.5% = 0.055
n = 12 months/year
From equation 1, making MP the subject of formula;
MP = FV/{[(1+r/n)^(nt) - 1]/(r/n)}
Substituting the given values we have;
MP = 500,000/(((1+0.055/12)^(12×25) -1)/(0.055/12))
MP = $778.77
she should put $778.77 into the account each month
Which pair shows equivalent expressions?
2 (two-fifths x + 2) = 2 and two-fifths x + 1
2 (two-fifths x + 2) = four-fifths x + 4
2 (two-fifths x + 4) = Four-fifths x + 2
2 (two-fifths x + 4) = 2 and two-fifths x + 8
Answer:c
Step-by-step explanation:
I think
The daily high temperatures in Philadelphia for the first 15 days in February is normally distributed with a standard deviation of 2.5°. If it was 37° on Valentine's Day with a z-score of 2.4, the mean temperature is _________°.Immersive Reader
Answer:
The mean temperature is 31.
Step-by-step explanation:
The formula for the z-sore is
x - mean
z = ----------------------
(std dev)
In this case let's multiply both sides by (std dev), obtaining:
x - mean = z*(std dev).
Solving for (mean), we get
mean = x - z*(std dev)
Substituing 37 for x, 2.4 for z and 2.5 for (std dev), we get:
mean = 37 - (2.4)(2.5) = 31
The mean temperature is 31.
Final answer:
To find the mean temperature with the given z-score and standard deviation, the z-score formula is used. After calculation, the mean temperature in Philadelphia for the first 15 days of February is determined to be 31°.
Explanation:
The question is asking us to find the mean temperature in Philadelphia for the first 15 days in February, given that the daily high temperatures are normally distributed with a standard deviation of 2.5° and that on Valentine's Day (February 14th), the temperature was 37° with a z-score of 2.4. To solve for the mean temperature, we can use the z-score formula:
Z = (X - μ) / σ
Where:
Z is the z-score,
X is the value in the dataset,
μ is the mean, and
σ is the standard deviation.
We know Z = 2.4, X = 37°, and σ = 2.5°. Plugging these values into the z-score formula, we can solve for the mean (μ).
2.4 = (37 - μ) / 2.5
Multiplying both sides by 2.5, we get:
2.4 x 2.5 = 37 - μ
6 = 37 - μ
μ = 37 - 6
μ = 31°
Therefore, the mean temperature in Philadelphia for the first 15 days in February is 31°.
An animal pen is in the shape of a triangle. One of the interior angles of the triangle is 40 degrees. The measure of the other interior angles are in the ratio 3 : 5. What are the measures of the other interior angles?
Final answer:
In a triangle, the sum of all interior angles is always 180 degrees. Given the ratio of the other interior angles, we can find their measures.
Explanation:
In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 40 degrees, let's denote the measures of the other two angles as 3x and 5x. The sum of all three angles is 40 + 3x + 5x = 180. Simplifying this equation, we get 8x + 40 = 180. Subtracting 40 from both sides gives us 8x = 140. Dividing both sides by 8, we find x = 17.5.
Now, we can substitute the value of x back into the expressions for the other two angles. So, the first angle is 3x = 3(17.5) = 52.5 degrees, and the second angle is 5x = 5(17.5) = 87.5 degrees.
The number of laughs (denoted by L) can be defined as a function of the number of jokes (denoted by J), the amount of knowledge about the joke material (denoted by K), and the familiarity with the jokes (denoted by F) using this formula: L=J⋅K2F L, equals, start fraction, J, dot, K, squared, divided by, F, end fraction Select an appropriate measurement unit for number of laughs.
Answer:
(A) [tex](Jokes * Knowledge^2) / Familiarity[/tex]
Step-by-step explanation:
The number of laughs (denoted by L) is a function of
The number of jokes (denoted by J), The amount of knowledge about the joke material (denoted by K).Given [tex]L=\frac{J\cdot K^2}{F}[/tex]
The appropriate measurement unit for number of laughs will be:
[tex](Jokes * Knowledge^2) / Familiarity[/tex]
In this diagram, like segment AD is tangent and line segment AC is secant. If AB = 6 and BC = 18, what is the length of line segment AD?
9514 1404 393
Answer:
12
Step-by-step explanation:
The applicable relationship here is ...
AD² = AB·AC
AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144
AD = 12
What is 7 more than five times the number 9 divided by 15?
Answer:
10
Step-by-step explanation:
As the amount of time on homework increased, their grade in class ____________.
Answer:
Increases
Step by Step Explanation:
More time on your homework means more time to cheat/figure the answer out.
Answer:
Improved
Step-by-step explanation:
The more you study or do homework, the more you learn, and the better your grade
What is the value of x in the equation 8 + 4 = 2 (x minus 1)?
A.5
B.StartFraction 11 Over 2 EndFraction
C.StartFraction 13 Over 2 EndFraction
D.7
Answer:
It is actually 7
Step-by-step explanation:
yup :)
Solve the inequality.
8+8(x + 4) >32
The solution is
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x > - 1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
To solve, we must isolate the variable, x
8+8(x + 4) >32
Distribute the 8
8+ 8*x +8*4
8+8x+ 32 >32
Combine like terms
8+32 +8x >32
40 + 8x >32
Subtract 40 from both sides
8x > -8
Divide both sides by 8
x > -1
The results for a survey of 120 students who were selected randomly are as follows 60 students have a cell phone plan with company x. 36 students have a cell phone plan with company y. 24 students do not have a cell phone the total population of students was 380.Based on the data what is the best approximation for the total number of students who have a cell phone plan with company y?
Answer:
114
Step-by-step explanation:
find the solution below
9=8n what does n=
Please help
Solve the equation for all real values of x. 3tan^2x=3tanx
The equation 3tan²x = 3tanx solved for all real values of x is [tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
Solving the equation for all real values of x.
From the question, we have the following parameters that can be used in our computation:
3tan²x = 3tanx
This can be expressed as
3tan²x - 3tanx = 0
Factor out 3tanx
3tanx(tanx - 1) = 0
Expand
3tanx = 0 or tanx - 1 = 0
So, we have
tanx = 0 or tanx = 1
Take the arctan of both sides
x = tan⁻¹(0) or x = tan⁻¹(1)
Evaluate the arctan for all real values of x.
[tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer
The points (2,10) and (minus2,minus10) are plotted on the coordinate plane using the equation yequalsatimesx. How can you use the coordinates to find the value of a? Select the correct answer below, and fill in the answer box to complete your choice. (Type a whole number.) A. The value of a is the number that the y-values are multiplied by to get to the corresponding x-values. So, aequals nothing. B. The value of a is the absolute value of the difference of the y-values. So, aequals nothing. C. The value of a is the number that the x-values are multiplied by to get to the corresponding y-values. So, aequals nothing. D. The value of a is the absolute value of the difference of the x-values. So, aequals nothing.
Answer: The value of a is the number that the x-values are multiplied by to get to the corresponding y-values. So, a equals 5
We have
y=ax
so a is clearly the number we multiply by the x values.
Substituting either points (2,10) and (-2,-10),
10 = a(2)
a = 10/2 = 5
Find the area of the shaded segment. Round your answer to the nearest hundredth.
Answer:
2.57
Step-by-step explanation:
1/4×22/7×3×3=7.07
1/2×9=4.5
7.07-4.5=2.57
PLEASE SOMEONE HELP ME WITH THIS! NO ONE CAN FIGURE IT OUT AND ILL GIVE YOU 60 POINTS PLUS BRAINLIEST IF YOU CAN HELP ME! please do not copy and paste or even comment just for the points, i really need help.
A) Variables:
X = number of weeks she puts money into the account.
Y = total amount in account after x weeks.
B) m would be the amount she puts in per week, b is the starting amount she has in the account
Y = 5x + 40
C) replace x with the x values in the cart and solve for y:
O : y = 40. Coordinates (0,40)
1: Y = 45. (1,45)
2: 50, (2,50)
3: 55, (3,55)
4: 60, (4,60)
D) make the graph using the above points
E) y intercept is when x is 0, which is 40. This was the starting value of how much money was saved.
Answer:
DO you still need help? Considering this was posted a long time ago.
Step-by-step explanation:
Given the following diagram, find the length of CB.
Luisa Díaz drove her vehicle about 7,200 miles last year. Her fixed costs totaled $1,058.40 and her variable costs were $1965.60 how much did it cost per mile
Answer:
$0.42
Step-by-step explanation:
Given:
Luisa Díaz drove her vehicle about 7,200 miles last year.
Total fixed cost = $1,058.40
Total variable cost = $1965.60
Question asked:
How much did it cost per mile ?
Solution:
Total cost of driving 7200 miles = Total fixed cost + Total variable cost
= $1,058.40 + $1965.60
= $3024
By unitary method:
Cost of driving 7200 miles = $3024
Cost of driving 1 mile = $3024 [tex]\div[/tex] 7200
= $0.42
Thus, cost of driving per mile is $0.42
I need help asap i am confused
Answer:
the top one (-40)8 is the correct answer
Emilce pide 5 platos por semana para almorzar en la oficina. El menú ofrece 5 opciones diferentes. De cuantas maneras puede realizar el pedido de la semana si quiere repartir los platos?
Answer:
120 different ways
Step-by-step explanation:
For the first lunch, Emilce has 5 options to choose,
In the second lunch, now she has only 4 options, as one was already chosen.
Then, in the third lunch, she has 3 options.
In the fourth lunch, she has 2 options.
In the last lunch, she has just 1 option.
So, the number of different ways she can order her lunches in the week is:
5 * 4 * 3 * 2 * 1 = 120
She can order in 120 different ways.
Vanessa draws one side of equilateral
△ABC on the coordinate plane at
points A(-2, 1) and B(4,1). What are
the two possible coordinates of vertex
C? Round to the nearest tenth.
Answer:
According to my calculation, the two possible coordinates of vertex C, is [tex](1,\sqrt{27}) and (1,-\sqrt{27})[/tex].
Answer:
According to my calculation, the two possible coordinates of vertex C, is .
Step-by-step explanation:
What type of angles are< 1 and <5?
vertical
supplementary
corresponding
complementary
Answer:
The type of angles of <1 and <5 are corresponding angles
Step-by-step explanation:
Jeremy caught 8 fish in a contest.
The mean weight of the fish was 4.3125 kg.
He forgot to make his own record of the weight of the last fish,
but the first 7 were: 4.3 kg, 5.3 kg, 6.8 kg, 2.6 kg, 3.2 kg, 4.4 kg and 4.8 kg
What was the weight of the last fish?
kg [2]
The weight of the last fish was 3.1 kg. It's found by subtracting the sum of the weights of the first 7 fish from the sum of all weights.
To find the weight of the last fish, we can use the mean weight formula:
[tex]\[\text{Mean weight} = \frac{\text{Sum of all weights}}{\text{Number of fish}}\][/tex]
Given:
- Jeremy caught 8 fish.
- The mean weight of the fish was 4.3125 kg.
- The sum of the weights of the first 7 fish is [tex]\(4.3 + 5.3 + 6.8 + 2.6 + 3.2 + 4.4 + 4.8\).[/tex]
First, let's calculate the sum of the weights of the first 7 fish:
[tex]\[4.3 + 5.3 + 6.8 + 2.6 + 3.2 + 4.4 + 4.8 = 31.4\text{ kg}\][/tex]
Now, let's find the sum of all weights of the 8 fish:
[tex]\[4.3125 \times 8 = 34.5\text{ kg}\][/tex]
To find the weight of the last fish, we subtract the sum of the weights of the first 7 fish from the sum of all weights:
[tex]\[34.5 - 31.4 = 3.1\text{ kg}\][/tex]
So, the weight of the last fish was 3.1 kg.
Brandon works at a nearby electronics store. He makes a commission of 14% on everything he sells. If he sells a camera for $588.00, how much money does Brandon make in commission?
Answer: cc
Step-by-step explanation:
Answer:
670.32
Step-by-step explanation
Average rooms cleaned per maid day is determined by a) number of rooms occupied divided by number of 8-hour maid shifts. b) number of rooms occupied divided by total number of housekeepers. c) number of shifts multiplied by the number of rooms. d) number of housekeepers multiplied by average number of rooms occupied.
Answer:
B
Step-by-step explanation:
Average rooms cleaned per housekeeper day: The average number of rooms cleaned per housekeeper day is performance ratio that gives an idea of how many rooms each housekeeper cleaned.
Average rooms cleaned per housekeeper day = [tex]\frac{ Number of rooms occupied}{Number of full-time housekeepers}[/tex]
Graph f(x) and its inverse, f^-1(x) , in the same coordinate grid.
Answer:
Included in screenshot
whats the area of a circle if the diameter is 24.26 mm
Answer:
approximately 462.24
Step-by-step explanation:
What is the factored form of the polynomial 27x²y - 43xy??
xy(27x – 43y)
x?y?(27 – 43)
3xy(9x – 17y)
3x?y(9 – 14y)
Answer: xy (27x - 43y)
Step-by-step explanation:
plz can any1 help me out on this plz
15 points
Answer:
7/22
Step-by-step explanation:
Drama or Sports:
85 + 200 - 60
225
330 - 225 = 105
Probability: 105/330
7/22
What is the length of a rectangle with width 18 in, and area 135 in 2?
Answer: The length of a rectangle would be 7.5
Step-by-step explanation:
To find the length is [tex]l = \frac{A}{w}[/tex]
-Solve:
[tex]l=\frac{135}{18}[/tex]
-Divide 135 by 18 and you get 7.5
[tex]\frac{135}{18} = 7.5[/tex]
-Result:
[tex]l= 7.5[/tex]
Mary bought 3 cartons of milk for $1.06 each. If she paid for the milk with a five-dollar bill, how much money should she get back
Answer:
shed get $1.82 back
Step-by-step explanation:
Answer:
She would get $1.82 back
Step-by-step explanation:
If she bought 3 cartons costing $1.06 each, you would have to multiply $1.06 by 3
$1.06 x 3 = $3.18
Then if she paid with a five dollar bill you have to subtract $3.18 from 5
5 - 3.18 = 1.82
$1.82 is the answer