Halle deposited $4000 into an account that earns 5% interest each year. the growth of her investment can be expressed by the exponential equation a = 4000(1 + 0.05)t , where a is the amount in the account after t years. in how many years will her account exceed $10,000?

Answers

Answer 1

After 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest, each year.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]

where a is a constant and a>1

We have an exponential equation:

[tex]\rm a = 4000(1+ 0.05)^t[/tex]

Plug a = $10,000

[tex]\rm 10000 = 4000(1+ 0.05)^t[/tex]

After calculating:

[tex]\rm 1.05^t= 2.5[/tex]

t = 18.78 ≈ 18.8 years

Thus, after 18.8 years, Halle account exceed $10,000 if Halle deposited $4000 into an account that earns 5% interest each year.

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Related Questions

Which measurements could create more than one triangle?
A. Angles measuring 85°, 45°, and 60°
B. Angles measuring 95°, 35°, and 50⁰
C. Sides measuring 8 cm and 15 cm and an included angle measuring 60°
D. Sides measuring 5 inches, 7 inches, and 13 inches

Answers

Answer:

Step-by-step explanation:

The sum of angles of a triangle is 180. if you add 85+45+60 you get 190. That is more than 180.

K is an example of.
O an equation
O a formula
O a constant
O a variable

Answers

the answer is (a variable)

Answer:

a variable.

Step-by-step explanation:

I know this because I had a test today that I studied for but I of course failed it…

It was for math.

I saw this in a newspaper – it was a puzzle for adults, fully grown humans, but I think you will find it easy.

All the digits from 1 to 9 are used in this grid, but only once. Can you work out their positions in the grid so that each of the six different sums work?

Two of the numbers have been inserted in order to get you started. Just identify the other seven numbers.

(NOTE: perform operations in the order they appear, e.g., 3+4×5=35 (not 23))
a=
b=
c=
d=
e=
f=

Answers

Answer:

d=9

Step-by-step explanation:

any other idea

helpp plss

What is the height??

Answers

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, we have given

One isosceles triangle that means the given triangle having two sides equal. The dimensions of the triangle are 21cm, 21 cm and 16 cm.

Consider the given triangle as ABC . In ΔABC, AD acts as a median. It means Angle ADB = 90°

Therefore,

By using Pythagoras theorem,

It states that the sum of the squares of base and perpendicular height is equal to the square of the hypotenuse.

That is,

[tex]\bold{ ( Hypotenuse) ^{2} = (Perpendicular) ^{2} + (base) ^{2}}[/tex]

Subsitute the required values

[tex]\sf{ AC^{2} = AB^{2} + BC^{2}}[/tex]

[tex]\sf{ (21)^{2} = (h) ^{2} + (16)^{2}}[/tex]

[tex]\sf{ 441 = (h)^{2} + 256}[/tex]

[tex]\sf{ (h)^{2} = 441 - 256}[/tex]

[tex]\sf{ h^{2} = 185}[/tex]

[tex]\sf{ h = \sqrt{185}}[/tex]

[tex]\bold{ h = 13.6 \: cm}[/tex]

Hence, The required height of the given isosceles triangle is 13.6 cm.

[ Note :- you can also solve this problem by using Heron's Formula but it's too lengthy to solve that's why I have used simple method ]

For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form

Answers

Answer: 3

Step-by-step explanation:

The required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]

For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.

What is a complex number?

The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi

[tex]z = 5\sqrt{3}/4 - 5/4i[/tex]
the polar form complex numbner can be given as
[tex]z = rcos\theta +rsin\theta i[/tex] - - - - - -(1)
where r = [tex]\sqrt{a^2+b^2}[/tex]
and [tex]\theta=tan^-\frac{b}{a}[/tex]

Since a = 5√3/4 and b = -5/4
[tex]r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}[/tex]
r = 10/4
r = 5/2
Now,
[tex]\theta=tan^-\frac{b}{a}[/tex]
[tex]\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30[/tex]

Now the polar form is given by substituting the values of r and [tex]\theta[/tex] in equation 1
Here,
[tex]z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i[/tex]

Thus, the required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]

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four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.

Answers

Let's solve ourselves instead of believing anyone

[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]

a^m+a^n=a^m+n

[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]

[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]

[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]

[tex]\\ \rm\Rrightarrow x^2=1[/tex]

[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]

0 is also a solution

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

[tex](x^2)^?=x^4 \cdot x^8[/tex]

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

First, simplify the equation by applying exponent rules to either side of the equation:

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^{4+8}[/tex]

[tex]\implies x^{2y}=x^{12}[/tex]

Now, apply the exponent rule:

[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]

Therefore,

[tex]x^{2y}=x^{12}\implies 2y=12[/tex]

Finally, solve for y:

[tex]\implies 2y=12[/tex]

[tex]\implies 2y \div 2 = 12 \div 2[/tex]

[tex]\implies y=6[/tex]

Therefore, Joe is correct as the unknown number is 6.

The original price of a hat is $35. The sale price is $19.95. What is the percent of discount?

Answers

Answer:

43%

Step-by-step explanation:

19.95 ÷ 35 = .57 or 57%

100 - 57 = 43

hello people, can anybody solve it

Answers

[tex]\\ \rm\Rrightarrow \left(\dfrac{x^a}{x^{-b}}\right)^{a^2-ab+b^2}\times \left(\dfrac{x^b}{x^{-c}}\right)^{b^2-bc+c^2}\times \left(\dfrac{x^c}{x^{-a}}\right)^{c^2-ca+a^2}=1[/tex]

[tex]\\ \rm\Rrightarrow (x^{a+b})^{a^2-ab+b^2}\times (x^{b+c})^{b^2-bc+c^2}\times (x^{c+a})^{c^2-ac+a^2}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{(a+b)(a^2-ab+b^2)}\times x^{(b+c)(b^2-bc+c^2)}\times x^{(c+a)(c^2-ca+a^2)}=1[/tex]

a³+b³=(a+b)(a²-ab+b²)

[tex]\\ \rm\Rrightarrow x^{a^3+b^3}\times x^{b^3+c^3}\times x^{c^3+a^3}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{a^3+b^3+b^3+c^3+c^3+a^3}=1[/tex]

[tex]\\ \rm\Rrightarrow x^{2a^3+2b^3+2c^3}=x^0[/tex]

[tex]\\ \rm\Rrightarrow 2(a^3+b^3+c^3)=0[/tex]

[tex]\\ \rm\Rrightarrow a^3+b^3+c^3=0[/tex]

Parallel to y=−3/4x, through (4, -1)
Write the slope intercept form of each equation of the line. Use a fraction for slope if needed.

y = ___x + ___

Answers

Answer:

[tex]y=-\frac{3}{4}x+2[/tex]

Step-by-step explanation:

The slope-intercept form is given by y=mx+c, where m is the slope and c is the y-intercept.

Slope of given line= [tex]-\frac{3}{4}[/tex]

Parallel lines have the same slope. Thus, the slope of the line would also be [tex]-\frac{3}{4}[/tex].

[tex]y=-\frac{3}{4}x +c[/tex]

The value of c can be found by substituting a pair of coordinates.

When x= 4, y= -1,

[tex]-1=-\frac{3}{4} (4)+c[/tex]

-1= -3 +c

Add 3 to both sides:

c= -1 +3

c= 2

Thus, the equation of the line is [tex]\bf{y=-\frac{3}{4}x+2[/tex].

Additional:

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What is the solution for x in the equation?
-2x+14+ 10x=34
OA. x = 6
OB. x = 5/2
OC. x = 1/8
OD. x = 2/5

Answers

Answer:

B. x = 5/2

Step-by-step explanation:

-2x+14+ 10x=34

-2x+10x=34-14

8x=20

x=20/8 =5/2

. Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.

Answers

You can’t see the table

What is the difference between the highest and lowest points in a data set?the mean the median the mode the range

Answers

Answer:

Range

Step-by-step explanation:

Range is found by subtracting the highest and lowest point in the dataset

Mode is the number that occurs most frequently in the set

Median is the central number in the dataset when arranged from lowest to highest

Mean is the sum of all the numbers in the dataset divided by how many numbers there are.

For example, take this list of numbers: 10, 10, 20, 40, 70.

The mean (also known as average) is found by: 10 + 10 + 20 + 40 + 70 / 5 = 30.

The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.

Justin did push-ups for the past 555 days.The following data points are the number of push-ups he did each day.
21,24,24,27,29
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
push-ups

Answers

Answer: σ: 2.76

Step-by-step explanation:

Count, N: 5

Sum, Σx: 125

Mean, μ: 25

Variance, σ2: 7.6

Steps

look at attached pic for formula

σ^2 = [tex]\frac{Σ(xi - μ)^{2} }{N}[/tex]

[tex]\frac{(21 - 25)2 + ... + (29 - 25)2}{5}[/tex]

⇒ [tex]\frac{38}{5}[/tex]

⇒ 7.6

σ = [tex]\sqrt{7.6}[/tex]

⇒ 2.756809750418

⇒ or 2.76

6. What is the measure of angle A rounded to two decimal places? 15 A) 25.02° B)27.82° C) 62.18° D)64.98°

Answers

sin A=Perpendicular/ Hypotenuse

sin A = 7/15

A= arcsin(7/15)

= 27,82 degree

Answer is option (B)

Through aregular hexagonal prism whose base edge is 8cm whose height 12 cm ahole in the shape of aright prism with its end being arhombus with diagonals 6cm and 8cm is drilled find total surface area of remaining solid and the volume

Answers

Answer:

96 cm2, 48 cm2

Step-by-step explanation:

Basically you times the first two questions and then the other 2, that leads you with the answer

Nick wants to write a 1,260 page science-fiction novel.
How many pages will Nick need to write each month to finish his novel in 1 year?

Answers

105 pages a month

Divide 1,260 by 12 cuz there’s 12 months in a year and you get 105

1 year = 12 months

Pages to write in 12 months = 1260

Pages to write in 1 month = 1260/12

= 105 pages per month

50% if £80 pls helppp

Answers

Answer:

50%×€80

50/100×80

€40

Step-by-step explanation:

please mark me as brainlest

Answer:

£40

Step-by-step explanation:

▪︎ Method I:

£80 - 100%

£x - 50%

x = (£80 * 50%) / 100% = £40

▪︎ Method II:

50% is one half

Therefore, 50% of £80 is £80 / 2 = £40

The oblique prism below has an isosceles right triangle
base.
x
(x+2)
(x+3)
Mark this and return
53:21
What expression represents the volume of the prism, in
cubic units?
01/2+2²
028+22²
02 +2
O²+37²2²
Save and Exit
Submit
Next

Answers

The volume of the prism, in cubic units is V = 1/2*x³ + x²

The figure and options are in the figure attached

What is an Oblique Prism ?

An oblique prism is a polyhedron figure , with a rectangular base and triangular side faces .

It is given that

The oblique prism below has an isosceles right triangle base.

In the figure attached, the oblique prism is shown.

The volume of the prism is given by

V = b*h

h is the height and b is the Area of the base

It is given that the base is an isosceles right triangle, its area is:

Area of a Triangle = (1/2) base * height

here the base and height is x

b = 1/2*x²

The height of the prism is (x + 2).

Then, the volume is:

V = 1/2*x²*(x + 2)

V = 1/2*x³ + x² cu. units

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Sid has a water dispenser in his refrigerator as shown in the figure.
PLS HELP!

A prism has a length of 4 inches, height of 14 inches, and width of 8 inches.

Sid would like to have three water dispensers in his refrigerator. How much cubic space will all three dispensers take up in Sid’s refrigerator?

448 in.3

896 in.3

1,200 in.3

1,344 in.3

Answers

Answer:

c. I'm sorry if I'm wrong

Step-by-step explanation:

13) Circle O is shown with point A, B, C, and D on Circle O.

If x = 50, what is the value of y and the angle measurement of angle AOB?

y = _____

m
(25) (50) (100) (not enough information)

Answers

The value of y is 50

The angle measurement of angle AOB is 100°

Circle Geometry

From the question, we are to determine the value of y and the measure of angle AOB

From one the circle theorems, we have that

Angles in the same segment are equal

In the given diagram, x° and y° are angles in the same segment

∴ x° = y°

From the given information,

x = 50

∴ y = 50

Hence, the value of y is 50

Also, from another circle theorem,

Angle at the center is twice the angle at the circumference

∴ ∠AOB = 2x° = 2y°

Then,

∠AOB = 2×50°

∠AOB = 100°

Hence, the angle measurement of angle AOB is 100°

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MATH!!! 15 points;))) find the surface area of the composite figure
please answer correctly and check over your work...

Answers

The area of a 2D form is the amount of space within its perimeter. The surface area of the composite figure is 76.8 ft².

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The surface area of the composite figure,

Surface area = 2(3.6×2) + (4×2) + 3(3.6×4) + 2(5.6)

= 14.4 + 8 + 43.2 + 11.2

= 76.8

Hence, the surface area of the composite figure is 76.8 ft².

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The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.

(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.

(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas

Answers

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be

How to calculate the values?

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:

= (1520 - 1232)/1232

= 288/1232

= 0.234

The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:

= (1448 - 1333)/1333

= 115/1333

= 0.086

The regional governing board that should receive the new board member is Salinas.

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what type of function is this?

Answers

Answer:

It's a sech x function

Step-by-step explanation:

Explanation is in attached file

it is a sech x function

This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes. cubes boxes number of cubes 1 n 5 625 8 1,000 what is the unknown value representing the unit rate? 8 125 140 156

Answers

The unknown value representing the unit rate is 125.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes.

Cubes boxes number of cubes

1 5

n 625

8 1,000

If the unit cube box has 5 number of cubes.

then,

n cubes boxes = 625/5

= 125

The unknown value representing the unit rate is 125.

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Answer:

125

Step-by-step explanation:

A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). write the equation of the parabola

Answers

The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)

What is a Parabola ?

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

The equation of the parabola is

(x-2)² = (y+2)

Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)

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HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r

Answers

Celina says true that each of the following expressions is actually a binomial expression.

What is binomial?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a. 5abc - 2a² + 6abc = 11abc - 2a²