Mathematics High School

If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately

Answers

Answer 1
The formula is
A=p (1+r/k)^kt
A future value?
P present value 10000
R interest rate 0.0625
K compounded monthly 12
T time 15 years
A=10,000×(1+0.0625÷12)^(12×15)
A=25,473.84
Answer 2
Final answer:

The amount after 15 years is approximately $26,971.67.

Explanation:

To calculate the amount after 15 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of years

In this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:

A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).

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Related Questions

What is the monthly payment for $280000 mortgage with an interest of 6% compounded monthly for 20 years?

Answers

The formula of the present value of an annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 280000
PMT monthly payment?
R interest rate 0.06
K compounded monthly 12
N time 20 years
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=280,000÷((1−(1+0.06÷12)^(
−12×20))÷(0.06÷12))
=2,006.01

Someone please help, I'm stuck!

From the table below, determine whether the data shows an exponential function. Explain why or why not.

x: 3, 1, -1, -3
y: 1, 2, 3, 4

(A) No; the domain values are at regular intervals and the range values have a common sum 1.
(B) No; the domain values are not at regular intervals.
(C) Yes; the domain values are at regular intervals and the range values have a common factor 2.
(D) Yes; the domain values are at regular intervals and the range values have a common sum 1.

Answers

If you plot all the points, you'll see that they lie on the same straight line. Therefore the function is not exponential. 

In terms of the context of your answer choices, the final answer is choice A. The domain values are at regular intervals (in this case 2) while the range values increment by the same value as well (1 in this case).

Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, enter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.

Answers

Check the picture attached.

let m(VTI)= m(ITU)=a   and  let m(VUI)= m(IUT)=b

Then, in triangle TUV:

2a+2b+c=180°

2(a+b)+c=180°

c=180°-2(a+b)


In triangle TUI:

a+b+109°=180°

a+b=180°-109°=71°

substitute in c=180°-2(a+b):

c=180°-2(a+b)=180°-2*71°=180°-142°=38°

Does anyone know how to do this problem? Thanks.

Answers

see picture for answer

Rewrite using standard notation: 2.43 × 104

A: 24,300


B: 2,430


C: 2.43


D: 0.000243

Answers

24300 :)                 that's the answer

Write the event as set of outcomes. We flip three coins and obtain more tails than heads.

Answers

H H H
H H T
H T H
T H H
T T T 1
T T H 2
T H T 3
H T T 4
----------

A country population in 1993 was 94 million. In 1999 it was 99 million. Estimate the population in 2005 using the expoetential growth formula. Round your answer to the nearest million

Answers

First find the rate of growth
The formula is
P=Ae^rt
P 99 million
A 94 million
E constant
R rate of growth?
T time 1,999−1,993=6 years
Solve the formula for r
R=[log (p/A)÷log (e)]÷t
R=(log(99÷93)÷log(e))÷6
R=0.01

the population in 2005
P=Ae^rt
T time 2,005−1,993=12 years
P=93×e^(0.01×12)
P=105 million

The word that best describes two acute angles of a right triangle is:
inductive.
supplementary.
vertical.
complementary.

Answers

Complementary angles equal to 90 degrees. A right triangle is 90 degrees. Two acute angles must equal to 90 degrees in a right triangle. 

So, the angle is the fourth choice, complementary. 

I think is complementary but i'm not sure

10 POINTS AND BRAINLIST ANSWER TO FIRST CORRECT ANSWER

Answers

The correct answer is A
The correct answer is:  [A]:
_________________________________________

the sum of two numbers is 15 one number is twice as large as the second number what are the tw numbers which let statement would you use

Answers

x +2x =15

3x=15

x=15/3

x=5

2x=2*5=10

10+5=15

the two numbers are 5 & 10

A person is standing exactly 36 ft from a telephone pole. There is a 30 degree angle of elevation from the ground to the top of the pole. What is the height of the pole?

Answers

A person stands at point A. BC is a telephone pole.

[tex]tanA = \frac{BC}{AB} \ \ \to \ \\BC = AB * tanA = 36 * \frac{ \sqrt{3} }{3} =12 \sqrt{3} \approx 20.78 \ ft. [/tex]

By using the tangent function in trigonometry, we find that the height of the telephone pole is approximately 20.78 feet. This was calculated using the given angle of elevation and the distance from the pole.

To find the height of the telephone pole, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Given:

Distance from the person to the base of the pole (adjacent side) = 36 ftAngle of elevation from the ground to the top of the pole = 30 degrees

We know that:

tan(30°) = opposite / adjacent

So,

tan(30°) = height / 36 ft

From a trigonometric table or calculator, tan(30°) ≈ 0.5774.

We can set up the equation as:

0.5774 = height / 36 ft

Solving for the height of the pole:

height = 0.5774 * 36 ftheight ≈ 20.78 ft

Therefore, the height of the pole is approximately 20.78 feet.

Which method of reasoning reaches a general conclusion on the basis of a number of observations that form a pattern?

deductive reasoning
inductive reasoning
complementary reasoning
supplementary reasoning

Answers

I would say deductive. It means to deduce a conclusion from the observations, data, evidence, etc ...

Answer:

Deductive reasoning

Step-by-step explanation:

Deductive reasoning can be defined as the process of reasoning based on premises to reach a specific conclusion.

So, in this case, the statement indicate a method of reasoning based on a number of observations that can lead to a conclusion. That's just deductive reasoning, because those number of observations form the system of premises, from which a deductive logic is developed to get to the conclusion.

Therefore, the right answer is the first choicem, deductive reasoning.

What is the sum of the integers between the square root of 12 and 40?

Answers

1.

the closest perfect squares of 12 are 9 and 16, 

that is 9<12<16

so 
[tex] \sqrt{9}\ \textless \ \sqrt{12}\ \textless \ \sqrt{16} [/tex]

[tex]3\ \textless \ \sqrt{12}\ \textless 4[/tex]

this means, [tex]\sqrt{12}[/tex] is  3 point something...


2.

similarly 

36<40<49

so

[tex] \sqrt{36}\ \textless \ \sqrt{40}\ \textless \ \sqrt{49} [/tex]

[tex]6\ \textless \ \sqrt{40}\ \textless \ 7[/tex]

which means [tex] \sqrt{40}[/tex] is 6 point something...

3. 

the sum of the integers between the square root of 12 and 40 is the sum of 4, 5 and 6, since 4 is the smallest integer after root 12, and 6 the greatest integer to before root of 40.


Answer: 15

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

(9x + 7)(4x + 1)(3x + 4) = 0

Answers

The Fundamental Theorem of Algebra states that a polynomial function of degree n, has n roots, Real or Complex.

The polynomial function f(x)=(9x + 7)(4x + 1)(3x + 4) is a third degree polynomial, expressed in factored form.

f has 3 linear (first degree) factors, so 3 roots, which are -7/9, -1/4 and -4/3.

Answer: 3 roots

Answer:

3

Step-by-step explanation:

Tiana takes 3 hours to drive to the coast without stopping. How many minutes will it take her to reach the coast if she stops to ready for 20 minutes

Answers

60 minutes in an hour

3 x 60 = 180 minutes

 180 +20 = 200 minutes total

NEED AN ANSWER ASAP
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
A. (x,y)→(y,−x)
B. (x,y)→(y,x)
C. (x,y)→(−y,x)
D. (x,y)→(−y,−x)

Answers

A. (x,y) - (y,-x) is the rule to rotate the figure 90 degrees clockwise.

Answer:

A. [tex](x,y)\rightarrow (y,-x)[/tex]

Step-by-step explanation:

We have been given that figure ABCD is a rectangle with point A (−2, 5). We are asked to choose the rule that would rotate the figure 90° clockwise.

We know that rule of rotating a figure 90 degrees clockwise is: [tex](x,y)\rightarrow (y,-x)[/tex]

Upon looking at our given choices we can see that option A is the correct choice.

After rotating our given point 90 degree clockwise, the coordinates of point A would be:

[tex](-2,5)\rightarrow (5,--2)=(5,2)[/tex]

The perimeter of a rectangular slab of concrete is 24 meters. If the length of the
rectangular slab is 2 meters longer than its width, what is the width of the slab?
Answers:
A) 5 meters
B) 6 meters
C) 7 meters
D) 8 meters
The answer is 5 meters but i don't know how to get that. HELP

Answers

the perimeter = 2*length + 2*width  = 2L + 2W = 24

also as length = width + 2 we can write the equation L = W+2

now replace the L in the first equation by W+2, we get:-

2(W+2) + 2W = 24

solve for W:-

2W + 4 + 2W = 24
4W = 24-4 = 20

W = 20/4 = 5

width = 5 meters.

The width of the slab is 5 meters which is correct option(A).

What is perimeter of rectangle?

Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.

Let length of slab is L, width is W,

The perimeter of a rectangular slab = 24

2(length) + 2(width)  = 2L + 2W = 24

If the length of the rectangular slab is 2 meters longer than its width

= width + 2

So, the equation L = W+2

Now substitute, L= W+2 in equatioin of perimeter,

2(W+2) + 2W = 24

2W + 4 + 2W = 24

4W = 24-4 = 20

W = 20/4 = 5

W = 5

Hence, the width of the slab is 5 meters.

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The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?

Answers

Final answer:

The value of the test statistic in this scenario is 0.24, calculated using the z-score formula based on the provided sample mean, population mean, standard deviation, and sample size.

Explanation:

The value of the test statistic for a hypothesis testing can be calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / √sample size). In this case, given that the sample mean is 116.2, the population mean is 115, the standard deviation is 25, and the sample size is 25 students, the test statistic can be calculated as follows:

(116.2 - 115) / (25 / √25)

This computation yields a z-score of:

(1.2) / (25 / 5)

(1.2) / 5 = 0.24.

Therefore, the value of the test statistic is 0.24.

Complete the equation of variation where y varies inversely as x and y = 0.125 when x = 8.

Answers

Complete the equation of variation where y varies inversely as x and y = 0.125
when x=8

Choose the correct simplification of (5x3 − 5x − 8) + (2x3 + 4x + 2).

Answers

(5x^3-5x-8)+(2x^3+4x+2)
7x^3-x-6

Answer:

7x^3+x+6

Step-by-step explanation:

Its answer choice A on a test.

please simplify 9/3-2i.

Answers

3-2i is as far as you can simplify
i = sqrt -1

Multiply by 3+2i/3+2i

combine: 9(3+2i)/(3−2i)(3+2i)

foil: 9(3+2i)/3⋅3+3(2i)−2i⋅3−2i(2i)

simplify: 9(3+2i)/9−4i^2
               9(3+2i)/9+4
              9(3+2i)/13
               27+18i/13
Divide each term in the numerator by the denominator.

27/13+18i/13 = answer

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are

Answers

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This is according to the intersection of two tangent theorem. The theorem states that  given a circle, if X is any point within outside the circle and if Y and Z are points such that XY and XZ are tangents to the circle, then XY is equal to XZ.

 

Final answer:

Two tangent segments to a circle that share a common endpoint outside the circle are congruent, meaning they have the same length. This is a fundamental concept in circle geometry, illustrating the unique properties of tangents and their interactions with circles.

Explanation:

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This means the lengths of the two tangent segments from the common external point to their respective points of tangency on the circle are equal. This concept is important in the study of circle geometry, as it helps in understanding relationships between tangents and circles.

A tangent to a circle is a line that touches the circle at exactly one point, ensuring it does not cross the circle at that touchpoint. This property of tangents being congruent when they share an external point is proven using the properties of right triangles and the fact that tangents from a point outside the circle to the circle are perpendicular to the radius at the point of tangency.

An example of this concept in action is if you draw two tangents from a single point outside of the circle to any two points on the circle's boundary, the segments of these tangents from the external point to the points of tangency will have the same length.

What is the solution to this system of linear equations?

x + y = 4

x − y = 6

Answers

This is a simultaneous equation so you have to find the value of x or y. We can do this by adding the 2 equations. This would make 2x, and y + -y = nothing. 4 + 6 = 10. So we have the equation 2x = 10. Divide both sides by 2 and you get the value of x, which is 5. You then plug this into the orignal equation, either one will work. You get a value of -1 for y.
x = 5 when y = -1.

Answer:

x = 5 and y = -1

Step-by-step explanation:

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

To solve for x  and y , we use elimination method

In the given equations, the co efficient of y are same with different coefficient

So we add both equations

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

--------------------------------

[tex]2x=10[/tex]

Divide both sides by 2

x= 5

now we plug in x value in first equation

[tex]5 + y = 4[/tex]

Subtract 5 on both sides

y= -1

Find the area of a regular hexagon with a perimeter of 42 feet. Round to the nearest tenth if necessary. Select one: a. 128.1 units2 b. 256.2 units2 c. 42.7 units2 d. 21.35 units2

Answers

A regular hexagon consists of 6 equilateral triangles
Each triangle has base 42/6 = 7 feet
Height of each triangle  7 * sqrt3/2 = 3.5 sqrt3
Area of 1 triangle  =  3.5^2 sqrt3

area of hexagon = 6 * 3.5^2 sqrt3  =   73.5 sqrt3  or 127.3 sq feet to nearest tenth
I actually got an answer around 127, so it should be A

#27 how do I find x?

Answers

E to F is 6 F to G is x

and overall distance from e to g is 1.6x

 so:

6+x = 1.6x

subtract x from each side

6 = 0.6x

 now divide both sides by .6

x = 6/0.6 = 10

x = 10



A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .

Answers

First let's find the number of the elements in the sample space, that is the total number of codes that can be produced.

The first digit is any of {0, 1, 2...,9}, that is 10 possibilities
the second digit is any of the remaining 9, after having picked one. 
and so on...

so in total there are 10*9*8*7 = 5040 codes.

a. What is the probability that the lock code will begin with 5?

Lets fix the first number as 5. Then there are 9 possibilities for the second digit, 8 for the third on and 7 for the last digit.

Thus, there are 1*9*8*7=504 codes which start with 5.

so 

P(first digit is five)=[tex] \frac{n(first -digit- is- 5)}{n(all-codes)}= \frac{1*9*8*7 }{10*9*8*7 }= \frac{1}{10}=0.1 [/tex]

b. What is the probability that the lock code will not contain the number 0? 

from the set {0, 1, 2...., } we exclude 0, and we are left with {1, 2, ...9}

from which we can form in total 9*8*7*6 codes which do not contain 0.

P(codes without 0)=n(codes without 0)/n(all codes)=(9*8*7*6)/(10*9*8*7)=6/10=0.6

Answer:

0.1 ; 0.6

The probability that the lock code will begin with the number 5 is:

0.1

The probability that the lock code will not contain the number 0 is:

0.6

What is Probability?

This refers to the use of permutations to find the possible occurrence of events.

The total number of elements is 10

Hence, the total codes is 5040.

P(five)= n(first number)/n(all codes)= 1/10= 0.1

Next,

P(codes without zero)= n(codes without zero)/n(all codes)

(9*8*7*6)/(10*9*8*7)=6/10=0.6

=0.6

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I don't know how to do this

Answers

All you do is plug the x coordinate of a pair (the one on the left) in for x in the equation, and plug the y coordinate of the pair (the one on the right) for y and solve! If the answer is the same on both sides, it works for the equation. Hope that helps! Just comment if you don't get it.
Just replace the values of x : 9, -2, -8, 2 in the given equation y = 5x - 3 to obtain the corresponding values of y.
x = 9, y = 5(9) -3 = 42 -> Yes
x = -2, y = 5(-2) - 3 = -13 -> Yes
x = -8, y = 5(-8) - 3 = -43 -> No
x = 2, y = 5(2) - 3 = 7 -> No Hope it helped!

In rectangle JKLM, angle JML is 3x - 15. Find the value of x.

Answers

All angles of a rectangle are right angles.
Right angles measure up to 90 degrees.
JML is also a right angle which means 3x - 15 is equal to 90

3x - 15 = 90
3x = 105
x = 35

$15 represents 20% of the spending money Arie is saving for camp this summer. What is the total amount of money she hopes to take to camp?

Answers

20% of camp spending money = 15

0.20x = 15
x = 15 / 0.20
x = 75 <==

Answer: $75

Step-by-step explanation: i got it right on my quiz

How many different sums can be made with a penny nickel dime quarter?

Answers

1 coin is 4 ways
2 coins is 4*3 ways
3 coins is 4*3*2 ways
4 coins is 4*3*2*1 ways

so total is 4+12+24+24=64 sums
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