Mathematics High School

30 POINTS PLEASE HELP! An investment in a savings account grows to three times the initial value after t years.
If the rate of interest is 5%, compounded continuously, t = (blank) years.

Answers

Answer 1
The formula for a compound growth or decay is given by

A = A₀ × (1+growth rate)ⁿ

Where:
A = The final value after 'n' years
A₀ = The initial value
Growth rate = 5% = 0.05

We know that final value = 3 × Initial value
So that's A = 3A₀
Substitute this expression into the formula, we have
3A₀ = A₀ (1+0.05)ⁿ
3A₀ ÷ A₀ = (1.05)ⁿ
3 = (1.05)ⁿ

from here we can use the trial and error method:

take n = 1, then (1.05)¹ = 1.05
take n = 2, then (1.05)² = 1.1025
take n = 3, then (1.05)³ = 1.16
take n = 5, then (1.05)⁵ = 1.3
take n = 10, then (1.05)¹⁰ = 1.6
take n = 20, then (1.05)²⁰ = 2.7
take n = 30, then (1.05)³⁰ = 4.3 ⇒ too big
take n = 25, then (1.05)²⁵ = 3.4
take n = 24, then (1.05)²⁴ = 3.2
take n = 23, then (1.05)²³ = 3.1
take n = 22, then (1.05)²² = 2.9

so, the number of years it takes for the account to grow three times the initial value after 23 years.


Related Questions

Consider the graph of the quadratic function y = 2x2 – 4x + 2. How many zeros does the graph have?

Answers

y = 2x^2 - 4x + 2

y = 2(x^2 - 2x + 1)

2(x  - 1)^2 = = 0

so the graph will just touch the x axis at x = 1

So there is one zero  duplicity 2.
Answer:

The graph has:

                  One zero with multiplicity  2.

Step-by-step explanation:

We are given a quadratic function in terms of the variable x as:

                            [tex]y=2x^2-4x+2[/tex]

The number of zeros of this function is equal to the number of points where the graph of this quadratic function intersects the x axis and the corresponding value of x is the root of this quadratic equation.

Hence, after plotting the graph of this quadratic function we observe that the graph meets the x-axis at just one point.

          Hence, the number of zeros of the graph is:

                          One.

What is the measure of angle Y?
Round your answer to the nearest degree

24
26
69
61

Answers

24 is the answer because if you try any other answer it would be bigger than 180.

Answer:

I just took  the test the answer is indeed 24

Step-by-step explanation:

Polygons ABCD and A′B′C′D′ are shown on the coordinate grid:



What set of transformations is performed on ABCD to form A′B′C′D′?

Answers

reflection is that what your looking 4

Draw the graph of a rational function that is increasing for x<-4 and decreasing for x>-4 on the coordinate plane below

Answers

For a function to be increasing, as x goes up (to the right) the y value must go up at the same time (meaning that as the function goes to the right, the line goes up). Conversely, when a function is decreasing, as x goes up the y value must go down (as the line goes to the right, the line goes down). We can draw a line at x=-4 (one to the right of -5) and to the left of it, we can draw a line going up as x goes to the right and to the right of x=-4 we can draw a line going down. If you'd like a real example, take |1/(x+4)|. This works due to that since we know that 1/x decreases when x<0 (and is negative) and decreases when x>0, we can get the absolute value of it to make the side left of x=0 flip-flop to make it go up instead of down. In addition, the (x+4) makes the turning point at x=-4 due to that if we plug in x=-4, x+4=0


Which of the following is true for the relation f(x) = 3x2 + 5?


Only the inverse is a function.


Neither the equation nor its inverse is a function.


Only the equation is a function.


Both the equation and its inverse are functions.

Answers

Neither the equation nor its inverse is a function.f(x) = 3.x² + 5 ↔ y = 3.x²+5
Let's find the inverse of y = 3.x²+5
x= 3.y²+5 → 3.y² = x-5  and y²= (x-5)/3 and y = √[(x-5)/3]

Hence the inverse of f(x) which is f⁻¹(x) =√[(x-5)/3] is NOT a function

Only the inverse is a function.WRONG
Neither the equation nor its inverse is a function.WRONG
Only the equation is a function.RIGHT
Both the equation and its inverse are functions.WRONG

You commute to work by riding a bus each day for $4.25 round trip. a weekly pass is available for $19.75 a week. if you work 5 days a week, how much can you save by buying the pass? $2.00 $1.75 $1.50 $1.25

Answers

you would save $2 because $4.25 times 5 = 21.75 - 19.75 = $2

Answer:

it's $1.50

Step-by-step explanation:

4 puzzle time how can you share five apples with seven friends answers

Answers

Part 1:

Identify the algebraic properties of equality that are represented.
1.

Given

If [tex]a=b[/tex], then [tex]a\cdot c=b\cdot c, c\neq0[/tex]

The algebraic property of equality that is represented by the above expression is the multiplication property.


2.

Given

If [tex]a=b[/tex], then [tex]a- c=b- c,[/tex]

The algebraic property of equality that is represented by the above expression is the subtraction property.


3.

Given

If a = b, then a can be substituted for b (or b for a) in any equation or expression.
The algebraic property of equality that is represented by the above expression is the substitution property.


4.

Given

If [tex]a=b[/tex], then [tex] \frac{a}{c} = \frac{b}{c},\ c\neq0[/tex].

The algebraic property of equality that is represented by the above expression is the division property.


5.

Given

If [tex]a=b[/tex], then [tex]a+ c=b+ c,[/tex]

The algebraic property of equality that is represented by the above expression is the addition property.


6.

Given

sum: [tex]a(b+c)=ab+ac[/tex],
difference: [tex]a(b-c)=ab-ac[/tex]

The algebraic property of equality that is represented by the above expression is the distributive property.


7.

Given

If a = b and b = c, then a = c. If AB = CD and CD = EF, then AB = EF. If m<A = m<B and m<B = m<C, then m<A = m<C.

The algebraic property of equality that are represented by the above expression is the transitive property.


8.

Given

If a = b, then b = a. If AB = CD, then CD = AB. If m<A = m<B, then m<B = m<A.
The algebraic property of equality that are represented by the above expression is the symmetric property.

9.

Given

a = a, AB = AB, m<A = m<A
The algebraic property of equality that are represented by the above expression is the refrexive property.


10.

Given

If x = y, then 6x = 6y.
The algebraic property of equality that are represented by the above expression is the multiplication property.

11.

Given

If AB = BC, then AB - 2 = BC - 2.
The algebraic property of equality that are represented by the above expression is the subtraction property.

12.

Given

m<A = m<A

The algebraic property of equality that are represented by the above expression is the refrexive property.


13.

Given

If AB = CD and CD = 6, then AB = 6
The algebraic property of equality that are represented by the above expression is the transitive property.


14.

Given

If a = b, then b = a.
The algebraic property of equality that are represented by the above expression is the symmetric property.

A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. based on the collected data, the least-squares regression line is y x ˆ = + 10.53 3.41 , where x is the number of degrees fahrenheit by which the temperature exceeds 50°. give a sentence that describes the meaning of the slope of the least-squares regression line

Answers

Final answer:

The slope of 3.41 in the least-squares regression line y = 10.53 + 3.41x indicates that for every one degree Fahrenheit increase in temperature above 50°, the number of cricket chirps per minute is expected to increase by an average of 3.41 chirps.

Explanation:

The slope of the least-squares regression line in the relationship between the number of chirps per minute for crickets (y) and temperature is 3.41. This number represents the average increase in the number of chirp per minute for every degree Fahrenheit that the temperature is above 50°. Therefore, if the temperature increases by one degree Fahrenheit, the expected number of cricket chirps per minute increases by an average of 3.41 chirps.

The slope of the least-squares regression line, which is 3.41, indicates that for every degree Fahrenheit the temperature exceeds 50°, the number of chirps per minute for crickets increases by 3.41 chirps.

In a linear regression equation of the form y = a + bx, the slope (b) represents the change in the dependent variable (y) for a one-unit change in the independent variable (x).

In this context, the slope (b) is 3.41, which means that for each additional degree Fahrenheit above 50°, the model predicts an increase of 3.41 chirps per minute by the crickets.

The intercept of the regression line is 10.53, which represents the baseline number of chirps per minute when the temperature is exactly 50°F.

The complete question is:

A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least-squares regression line is yˆ = 10.53 + 3.41x, where x is the number of degrees Fahrenheit by which the temperature exceeds 50°. Give a sentence that describes the meaning of the slope of the least-squares regression line​.

please help
What is the value for X?
- 24
-9
-21
-14
what is the measure of <1?
- 45
- 60
- 120
-125

Answers

Answer:

x = 21∠1 = 120°

Step-by-step explanation:

The two interior same-side angles are supplementary, so ...

... (5x +15)° +(3x -3)° = 180°

... 8x +12 = 180 . . . . . . . . . divide by °, collect terms

... 8x = 168 . . . . . . . . . . . . subtract 12

... x = 21 . . . . . . . . . . . . . . . divide by 8

Obtuse ∠1 has the same measure as its corresponding angle, (5x+15)°, so is ...

... ∠1 = (5·21 +15)° = 120°

Marvin reflected this trapezoid over a line, but only 2 of the vertices changed position. Which line could Marvin have used for the reflection?

Answers

He chose a line that was collinear with one of the trapezoids parallel sides. A trapezoid has only one pair of sides that are parallel. If Marvin chose a line that was collinear with on of these sides, then the result would be only two points changing position as the other two points would be on the line of transformation.

MATH HELP WILL MARK BRAINLIEST !!!!!!!!

Answers

1. sum of a number plus 6 is 7 times the number:

n+6 = 7n


2. qoutent of a number and 5 is 8

n/5 =8

n = 5*8

n = 40


3. distance = speed times time

 so d = 55t

35% of it is 5.5% of 56

Answers

Hello there,
35% x 5.5%= 0.01925
0.01925 x 56= 1.078
On the side note: The word of means multiply

Hope this helps

~Top

Answer:

8.8

Step-by-step explanation:


How can you decompose the composite figure to determine its area?

Answers

Answer with explanation:

In order to find the area of the given figure we have to decompose into geometrical figures whose area could be easily calculated by the use of the mathematical formulas we know.

Hence, we decompose it into:

 1 semicircle.  2 trapezoids with one common base.  1 rectangle.

The decomposition could be seen with the help of diagram attached to the answer.

Answer:

as two semicircles and a rectangle

Step-by-step explanation:

ΔRST is dilated about the origin, O, to create ΔR'S'T'. Point R is located at (3, 9), and point R' is located at (1.2, 3.6). Which scale factor was used to perform the dilation?

Answers

a scale factor is a number that u multiply one set of points by to get to the other set...

(3,9)....to (1.2,3.6)

so what are we gonna multiply 3 by to get to 1.2 ? And what are we gonna multiply 9 by to get to 3.6 ? It should be the same number

3x = 1.2          9x = 3.6
x = 1.2/3          x = 3.6 / 9
x = 0.4            x = 0.4

so 3 * 0.4 = 1.2
and 9 * 0.4 = 3.6

so ur scale factor is 0.4 or 2/5


Answer:

a scale factor is a number that u multiply one set of points by to get to the other set

Step-by-step explanation:


If g(x) = 3x − 4, what is the value of g−1(g(13))?

A. 17/3

B. 35

C. x+4/3

D. 13

Answers

The function g(x) = 3x-4 is a linear function. Therefore the inverse does exist (which is also linear)

Because we have an inverse, this means we can use the rule 
[tex]g^{-1}(g(x)) = x[/tex]

Replace x with 13
[tex]g^{-1}(g(x)) = x[/tex]
[tex]g^{-1}(g(13)) = 13[/tex]

The answer is choice D

The function g takes some input x from the *domain* and maps it to some value g(x) in the *range*. The function g^-1 takes some value g(x) from the *range* and maps it back to its associated value x in the *domain*. Essentially, when you feed an input through a function, and then feed that output through its inverse function, you get the original input back. So your answer here would be D. 13, since that was your original input.

There are 34 animals in a farmyard. some are cows and some are chickens. in total there are 104 legs. how many chickens are there?

Answers

There are 18 cows and 16 chickens.

Using a system of equations, the number of chickens that are there is calculated as: 16.

How to find how many chickens are there using system of equations?

Let's set up and solve the system of equations:

C + Ch = 34 (Total number of animals)

4C + 2Ch = 104 (Total number of legs)

Use a method like substitution or elimination to solve the system. Let's use elimination:

Multiply equation 1 by 2 to make the coefficients of 'Ch' in both equations the same:

2C + 2Ch = 68

Subtract equation 1 from equation 2:

(4C + 2Ch) - (2C + 2Ch) = 104 - 68

This simplifies to:

2C = 36

C = 18

Now that we know there are 18 cows, we can find the number of chickens using equation 1:

18 + Ch = 34

Subtract 18 from both sides:

Ch = 34 - 18

Ch = 16

So, there are 16 chickens on the farm.

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Find the value of x if C is the midpoint of AB, AC=4x+5, and AB=78

Answers

Do 78=4x+5 and then subtract 5 from 5 and 5 from 78 and use that that answer and divide it by 4 and that equals x

I hope this helps
Final answer:

Given that AC = 4x+5, and C is the midpoint of AB, meaning AC = CB, then AB = 2*(4x+5). Given that AB = 78, we can solve the equation 8x + 10 = 78 to find x = 8.5.

Explanation:

The subject matter of this question is geometry, specifically concerning line segments and midpoints. If C is the midpoint of AB, then segments AC and CB are equal. This is a fundamental characteristic of midpoints.

Since AC = 4x + 5 and CB = AC, it also means that CB = 4x + 5. This implies that the total length of AB (which is the sum of AC and CB) equals 2 * (4x + 5). Therefore, AB equals 8x + 10.

We are given that AB = 78. So, we can set up and solve the equation 8x + 10 = 78. Subtracting 10 from both sides of the equation gives us 8x = 68. Dividing each side by 8 gives us x = 8.5. Therefore, the value of x that satisfies the given conditions is 8.5.

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If an experiment consists of five outcomes with p(o1) = 0.10, p(o2) = 0.20, p(o3) = 0.30, p(o4) = 0.25, then p(o5) is

Answers

.p(o5) is equal to 0.15. This can be determined because p(o5)= 1- [p(o1)+ p(o2)+ p(o3)+ p(o4)], which is equivalent to p(o5)= 1- (0.10+0.20+0.30+0.25), which gives you a p(o5) value of 0.15.

PLEASE HELP ME!
At rugby practice, a group of 8 players stands in a circle and throws the ball from one person to the next. another player is trying to run faster than the ball moves around the circle as it is thrown from one player to the next. After 24 throws, the runner is right next to the ball. If the radius of the circle is 9yd, how many yards has the runner traveled? round your answer to the nearest tenth

Answers

diameter is the radius times 2, which is 18. 18 x 24 = 432 yards

Final answer:

The runner traveled approximately 45.1 yards around the circle during 24 throws at rugby practice.

Explanation:

The runner traveled approximately 45.1 yards.

To solve this, we can consider the circumference of the circle formed by the players, which is 2π times the radius. After 24 throws, the runner would have traveled a distance equivalent to 24 times the circumference of the circle.

So, the total distance the runner traveled would be 24 * (2π * 9) = 24 * 56.5487 = approximately 1357.2yd. Rounding to the nearest tenth, the runner traveled approximately 45.1 yards.

SIMPLIFY THIS EQUATION!

a³ b¹⁰
------
a² b²

Answers

a³b¹⁰ 
-------
a²b²

a³ - a² AND b¹⁰ - b²

Simplify.

a AND b⁸

So, our answer is ab⁸

~Hope I helped!~

Can anybody help me please?

Answers

The questions are hard to see

simplify i^31 (click photo for options)

Answers

-i is the answer hope thats helps

The required solution of  i^31 is -i.

What is simplification?

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now the given expression is,

i^31

This can be written as,

= i^(30+1)

or, we can express it as,

= i^30 . i

or, we can write,

= (i^2)^15 . i

Since i^2 = -1

Therefore we can write,

= (-1)^15 . i

Again since, (-1)^15 = -1

Thus,

i^31 = -i

which is the required solution of the given expression.

Thus, the required solution of  i^31 is -i.

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Write 6.0126.012 as a mixed number in simplest form

Answers

60126 3/250          This is rounded to simplest form

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls​ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting exactly 4 girls..

Answers

The number of girls in the 14 newborn babies selected is a binomially distributed random variable with n = 14 and p = 0.5. And we know that the binomial probability distribution is given by 

P(X = k) = (nCk) p^k (1–p)^(n-k)

So, P(X = 0) = (14C0) • 0.5^0 • (1–0.5)^(14-0) = 0.000

P(X = 1) = (14C1) • 0.5^1 • (1–0.5)^(14–1) = 0.001

And so on.

Thus, P(X = 4) = (14C4) • 0.5^(4 • (1–0.5)^(14–4) = 0.061

So the probability of selecting exactly 4 girls is 0.061.


 

Answer:

0.061

Step-by-step explanation:

On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made a deposit, and those deposits were equal to each other.

Answers

is that supposed to be the question?

Step-by-step explanation:

The estimated end total is $300 and the beginning was $0, so after day 16, she'll deposit $40 each day.

A cone is 10 inches tall and has a radius of 3 inches. What is the cone’s volume?

Answers

Area of the base is πr² where r is the radius. The volume of a cone is ⅓ πr²h where h is the height.
So the volume is ⅓ π×9×10=30 π=94.25 cu in approximately.

94.25  is the cone’s volume according to the given information.

What is volume?

Volume is a measurement of three-dimensional space that is inhabited. It is frequently expressed quantitatively utilizing SI-derived units, as well as several imperial or US-standard units. Volume and the of length are connected.

The space covered inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the material's potential.

Area of the base is πr² where r is the radius.

Area of the base = πr²

The volume of a cone is ⅓ πr²h where h is the height.

The volume of the cone =  ⅓ πr²

The cone and circle will be treated in the same equation

So the volume is

=  ⅓ π×9×10

=30 π

= 94.25 approximately.

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Find the GCF of the following monomials -50m^4n^7 and 40m^2 n^10

Answers

Hello,

The GCF is -10m^2 n^7.

Answer:

the correct answer for this problem is,

the GCF is,

10m^2 n^7

:)

the difference between the measures of two complementary angles is 46. determine the measures of the two angles?

Answers

Let the angle be x . Then its complement is 90-x. So we have

x - (90- x) = 46
x - 90 + x = 46
2x = 46 + 90 = 136
x = 136/2 = 68

x = 68 degrees  and its complement = 22 degrees

Final answer:

To determine the measures of two complementary angles with a 46-degree difference, you can set up an equation and solve for the angles, resulting in approximately 22.0 degrees and 68.0 degrees.

Explanation:

Complementary angles are two angles that add up to 90 degrees. If the difference between them is 46 degrees, we can set up an equation to find their measures:

Let one angle be x. The other angle would then be 90 - x.

Given that the difference between them is 46, we have the equation: 90 - x - x = 46.

Solving the equation, the angles are approximately 22.0 degrees and 68.0 degrees.

Which phrase describes the variable expression y-5

Answers

to translate y - 5 into words:

a number y is decreased by 5

i hope this helps!!

Aidan has a lemonade stand. He spent $4.55 on supplies to make lemonade and $8.45 on supplies to make cookies. At his lemonade stand, he sold 23 cups of lemonade for $0.50 each and 17 cookies for $0.50 each. What were Ayden's profits that day

Answers

sorry I'm slow but I agree with the first answer try it on a calculator for yourself
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