Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. he would now like to draw a monthly salary from the account. determine the amount that stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account. a. $69,242.49 b. $69,159.05 c. $333.29 d. $333.71
The annuity of the monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years is $333.71
What is annuity?An annuity is a series of payments made at equal period of time.
future value = annuity x [(1 + i)ⁿ - 1] / i
annuity = $125.30
i = 1.5% / 12 = 0.00125
n = 35 years x 12 months = 420
future value = $125.30 x [(1 + 0.00125)⁴²⁰ - 1] / 0.00125
future value = $69,156.049 ≈ $69,156.05
annuity = [i x (present value)] / [1 - (1 + i)⁻ⁿ]
i = 1.5% / 12 = 0.00125
n = 20 years x 12 months = 240
present value = $69,156.05
annuity = (0.00125 x $69,156.05) / [1 - (1 + 0.00125)⁻²⁴⁰]
annuity = $86.45 / 0.25904
= $333.71
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Simplify Each Radical Expression. Leave in radical form. (Do not use decimals.)
√(7) + √(28) – √(700)
[tex]\sqrt 7 +\sqrt{28} - \sqrt{700}\\\\\\=\sqrt 7 +\sqrt{4 \times 7} - \sqrt{100 \times 7}\\\\\\=\sqrt 7 + 2\sqrt 7 - 10\sqrt 7\\\\\\=-7\sqrt 7[/tex]
If I'm right, none of answer choices are correct. I used substitution and factoring, but couldn't find a solution. I just want anyone's conformation. Thanks!
Answer:
Yes, none of these are correct.
Step-by-step explanation:
We can easily see that none of these are correct just by looking at the second piece of criteria and substituting x and y for their respective numbers.
A cylinder has a base radius of 3 centimeters and a height of 15 centimeters.
What is its volume in cubic centimeters, to the nearest tenths place?
Answer: 424.12
Step-by-step explanation:
A gas station is 9 miles away. How far is the gas station in kilometers? Use the following conversion: 1 mile is 1.6 kilometers.
1 mile = 1.6 kilometers
Multiply total miles by 1.6
9 miles x 1.6 = 14.4 kilometers
Answer: 14.4 kilometers
Answer:
14.4 kilometres
Step-by-step explanation:
Given that,
→ 1 mile = 1.6 kilometres
By using this information 9 miles will be,
→ 9 miles × 1.6 km
→ [ 14.4 km ]
Thus, the gas station is 14.4 km away.
What is the measure of central angle COB?
What is the measure circumscribed angle A>
m<COB
2(30°)60°Our answer is 60°
<A+60=180<A=120°You buy a watch that cost $45.50. The tax on the watch is 7.5%. What is the final cost of the watch? *
Find the volume of the cone shown as a decimal rounded to the nearest tenth. 22m 12m
Answer:
829.4 m³
Step-by-step explanation:
Volume of cone:
diameter = 12 m
r = 12 ÷ 2 = 6 m
h = 22 m
[tex]\sf \boxed{Volume \ of \ cone =\dfrac{1}{3} \pi r^2h}[/tex]
[tex]= \dfrac{1}{3}*\dfrac{22}{7}*6*6*22\\\\=\dfrac{22}{7}*2*6*22\\\\=\dfrac{5808}{7}\\\\= 829.4 \ m^3[/tex]
does the equation 2x+ 3y=-6, 4x+6y=-12 have infinetley many solutions
Answer:
Yes it has infinity of solutions.
Step-by-step explanation:
If you plug in certain numbers it will make the statements true.
Answer:
Infinitely many solutions.
Step-by-step explanation:
Let's solve your system by substitution.
2x+3y=−6;4x+6y=−12
Step: Solve2x+3y=−6for x:
2x+3y=−6
2x+3y+−3y=−6+−3y(Add -3y to both sides)
2x=−3y−6
2x/2 = −3y−6/2
(Divide both sides by 2)
x= −3/2y−3
Step: Substitute −3/2y−3 for x in 4x+6y=−12:
4x+6y=−12 4(−3/2y−3)+6y=−12
−12=−12(Simplify both sides of the equation)
−12+12=−12+12(Add 12 to both sides)
0=0
Answer:
Infinitely many solutions.
what is the measure of OAC
Answer:
27°
Step-by-step explanation:
A tangent meets a radius at 90°Angles in a trainable sum to 180°180 - 90 - 63 = 27°Answer:
∠OAC = 27°
Step-by-step explanation:
The radius of the circle is perpendicular to the tangent line.
Therefore, ∠ACO = 90°
The interior angles of a triangle sum to 180°
⇒ ∠OAC + ∠ACO ∠ COA = 180°
⇒ ∠OAC + 90° + 63° = 180°
⇒ ∠OAC + 153° = 180°
⇒ ∠OAC = 180° - 153°
⇒ ∠OAC = 27°
Find the area of the rhombus shown.
Answer:
I believe the answer is D.96
Step-by-step explanation:
well all rhombuses can be turned into a square or rectangle. and this looks like the sides are really close. just a guess don't get mad if it's wrong
Find the area of the parallelogram please.
Answer: 76.8 mi²
Step-by-step explanation:
The area of a parallelogram can be found be multiplying the base times the height.
A = B * H
A = 9.6 * 8
A = 76.8 mi²
Confused as to why this works? We use the same formula that we do for a rectangle because the "extra triangle" on the left can be moved to fill the empty space on the right. This then gives us a normal rectangle, which allows us to solve for the area
In this question we are provided with the base and height of a parallelogram and we are asked to calculate the area of the parallelogram using the formula.
It is given that the base is 9.6 mi and height is 8 mi.
We know,
[tex] \small\boxed{ \sf {Area_{(parallelogram)} = B × H}}[/tex]
Where,
B stand for BaseH stand for HeightSubstituting the values we get
[tex] \small\sf{ Area_{(parallelogram)} = (9.6 × 8) mi} = 76.8 {mi}^{2} [/tex]
Hence the area of the parallelogram is 76.8 mi².HELP ILL GIVE BRAINLIEST
An equation is shown.
4c + 2c = 4c + 11/2
What value of 2c makes the equation true?
Answer:
[tex]\huge\boxed{\bf\:c = \frac{11}{4}}[/tex]
Step-by-step explanation:
[tex]4c + 2c = 4c + \frac{11}{2}[/tex]
Cancel 4c on both the sides of the equation.
[tex]2c = \frac{11}{2}[/tex]
Bring the 2 in the denominator of 11/2 to the left hand side of the equation.
[tex]2*2c = 11\\4c = 11[/tex]
Bring 4 to the right hand side if the equation.
[tex]\boxed{\bf\:c = \frac{11}{4}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
The two data sets below depict random samples
of the management salaries in two companies.
Based on the salaries below which measure of
center will provide the most accurate estimation
of the salaries for each company?
• Company A:
1.2 million, 242,000, 265,500, 140,000,
281,000, 265,000, 211,000
• Company B:
5 million, 154,000.250,000, 250,000,
200,000, 160,000, 190,000
Answer:
the anwser is company A ( dont know if you need explanation)
Step-by-step explanation:
Could someone help me please. I need it fast
Answer:
10.7 cm
Step-by-step explanation:
V = (4/3)πr³
5128.8467 = (4/3)(3.14)r³
1225.043 = r³
r = 10.7
i need help on part c !!!
The volume of a cone with diameter d (and hence radius d/2) and height h is
[tex]V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h[/tex]
so each scoop holds
[tex]V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3[/tex]
of coffee.
The volume of a cylinder with base diameter d and height h is
[tex]V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h[/tex]
so the coffee can contains
[tex]W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3[/tex]
of coffee.
One full scoop then uses up [tex]\frac VW = \frac1{12,150}[/tex] of the total amount of coffee in the can, so you can make 12,150 cups of coffee.
ratio tables you need 3 sticks of butter for every 24 giant cookies cookie you make
fill out the table
Answer:
Sticks of butter: 2 Number of cookies: 40
Step-by-step explanation:
the ratio begins with 3:24. if you were to divide 3 by 24 it could be 1:8 **2**x 8 =16 so sticks of butter would be 2. 5x8=40.
You are asked to create a 5 LETTER password, how many different passwords can you create if.
a) All letters are capitals and repetition is allowed
b) All letters can be either capitals or lower case, but repetition is
not allowed.
Detailed explanations are most welcome.
We will see that the number of different combinations for each case are:
a) 11,881,376b) 311,875,200How many passwords can we make?
We have 5 selections for each password, we need to find the number of options for each one of these selections.
a) Here we can use only capitals an we can repeat, so for each selection (each letter), we have 26 options.
The total number of combinations will be equal to the product between the numbers of options:
C = 26*26*26*26*26 = 11,881,376
b)Now we can use either capitals or lower case, but we can't repeat. (Here I assume that A is different than a, so we can't use A two times, but we could use A and a).
Then we have 26*2 = 52 options.
For the first letter, we have 52 options.
For the second letter, we have 51 options (because one letter was already used).
For the third letter, we have 50 options, and so on.
The total number of combinations will be:
C = 52*51*50*49*48 = 311,875,200
If you want to learn more about combinations, you can read:
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The radius of a circle is 2 yards. What is the circle's area? r=2 yd Use 3.14 for .
Answer:
12.56
Step-by-step explanation:
pi(r)^2
3.14(2)^2
12.56
f(x) = x². What is g(x)?
A. g(x) = -x² – 3
B. g(x) = -3x²
C. g(x) = x² - 3
D. g(x) = -x²
Answer:
A
Step-by-step explanation:
because g(x) is the opposite of f(x) minus three steps
find the values of a and b such that
x2-4x+9=(x+a)2+b
Answer:
x = [tex]-\frac{1}{2}a-\frac{1}{4}b+\frac{9}{4}[/tex]
Step-by-step explanation:
DP
In a board game, students draw a number, do not replace it, and then draw a
second number. Determine the probability of each event occurring.
The probability of drawing a two and another 2 is 1/72
What is probability?Probability is the likelihood or chance that an event will occur
Since the total number in the board game is 9, hence the probability of drawing a 2 will be 1/9The probability of drawing the second 2 will be 1/8Pr(drawing a 2, then drawing another 2) = 1/9 * 1/8Pr(drawing a 2, then drawing another 2) = 1/72
Hence the probability of drawing a two and another 2 is 1/72
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Which one is it?
Btw this is a Math Question.
Answer:
$1.5
Step-by-step explanation:
9÷6= 1.5
1.5× 1 = 1.5
please help meee :)))))))
Answer:
B, C, D
Step-by-step explanation:
B, C, D
Answer:
A.12
Step-by-step explanation:
x²>100
square root both sides
it becomes x>10
x>10
from the options the only number greater than 10 is 12
Therefore the answer is A. 12
Francie tried to shade all the multiples of 8 on the hundred chart.
1
2 3
4 5
6
7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
What mistake did Francie make?
The multiples of 8 from 1 to 100 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96.
How to calculate the multiples of the number 8?To calculate the multiples of 8 we must multiply 8 by any number and the result will be a multiple of 8.
To identify the multiples of 8 that are between the number 1 and 100, we must multiply the number 8 by the number sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 .
So we will know properly are the multiples of 8 that are between 1 and 100 as shown below:
8 × 1 = 88 × 2 = 168 × 3 = 248 × 4 = 328 × 5 = 408 × 6 = 488 × 7 = 568 × 8 = 648 × 9 = 728 × 10 = 808 × 11 = 888 × 12 = 96Learn more about multiplication in: https://brainly.com/question/23536361
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Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
Answer:
(0, - 3 )
Step-by-step explanation:
the solution to the system is at the point of intersection of the graphs.
the graphs intersect at (0, - 3 )
then solution is (0, - 3 )
Answer:
(0, -3)
Step-by-step explanation:
The solution is where the two lines intersect. The two lines intersect at the point (0, -3).
I hope it helped you!
can anyone help me? no links
Answer:
Step-by-step explanation:
Sum: addition
Difference: subtraction
Product: multiplication
Number Sum Difference Product
1, 4 1 + 4 = 5 4 - 1 = 3 1 * 4 = 4
2, 8 2 + 8 = 10 8 - 2 = 6 2 * 8 = 16
Hope this helps!
3) Mr. Brust is addicted to Red Bull and has decided that he wants to plaster his room at school with Red Bull cans.
He measures a can and finds it is 6.5 inches tall and has a diameter of about 2.5 inches. He decided that he will
just recycle the top and bottom since there is no Red Bull logo on them and just use the sides. How many cans will
Mr. Brust need to cover his wall that is 20 feet long and 9 feet tall?
Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.
What is area of rectangle?Area of rectangle is the product of its sides
i.e., Area of rectangle = length x breadth
What is area of circle?The area of a circle is pi times the radius squared (A = π r²).
What is circumference of circle?The circumference of a circle is defined as the linear distance around it.
( C= 2πr)
The can of red bull is in shape of cylinder.
If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.
Like the given figure given.
The can is 6.5 inches tall and has a diameter of about 2.5 inches.
It shows that the two circle will have the diameter 2.5 inches.
d= 2.5 inch
= 0.208 ft
radius, r= [tex]\frac{d}{2}[/tex]
r= [tex]\frac{0.208}{2}[/tex]
r= 0.104 ft
To get the length of the rectangle , we have to calculate the circumference of the circle.Circumference of the circle be,
= 2πr
= 2 x 3.14 x 0.104
= 0.653 ft
The rectangular sheet will have,
length= 0.653 ft, breadth= 6.5 inches = 0.541 ft
Now, area of rectangular sheet be,= length x breadth
= 0.653 x 0.541
=[tex]0.3532 ft^{2}[/tex]
Area of 2 circle( top and bottom of can) be,= 2 x π[tex]r^{2}[/tex]
= 2 x 3.14 x 0.104 x 0.104
= 6.28 x 0.010816
= 0.0679 [tex]ft^{2}[/tex]
Total area of can be,= Area of rectangular sheet + Area of 2 circle( top and bottom of can)
= 0.3532 + 0.0679
= 0.4211 [tex]ft^{2}[/tex]
Now, we have the wall of dimensions
length= 9 ft, breadth= 20 ft
Area of wall be,= length x breadth
=9 x 20
= 180 [tex]ft^{2}[/tex]
Number of cans required to cover the whole wall be,=[tex]\frac{area \;of\; wall}{area \;of\; can}[/tex]
=[tex]\frac{180}{0.4211}[/tex]
= 427.45 cans
≈ 428 cans
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An ice cream cone has a diameter of 12.8 cm and a slant height of 9 cm. Find the lateral surface area of the cone. Use 3.14 for π. Round your answer to the nearest tenth.
Answer:
about 181 or 180.96
Step-by-step explanation:
π·6.4·6.332+6.42≈180.9555
Kaitlynn needs 3 pounds of fruit for a salad.
She already has 34 pound of apples and 13 pound of grapes.
How many more pounds of fruit does she need to buy?