The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945

Answers

Answer 1

A = P(1+r)^(t/5) A = 500000(1+0.05)^(15/5) A = 500000(1.05)^(15/5) A = 500000(1.05)^3 A = 500000*1.157625 A = 578812.5 Telling us that the population will be about 578,812 people in the year 2005

Related Questions

Find the area of the quadrilateral in the figure

Answers

answer is option C 19.64 sq units

In the given figure the area of quadrilateral is 19.64 square units.

Option (C) is correct.

What is a triangle?

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180.

In the given figure,

A quadrilateral is shown.

The quadrilateral can be seen as two triangles,

One triangle whose sides are 6, 6 and 5

And second triangle whose sides are 3, 4, and 5.

In first triangle, use Heron's formula to find the area,

The area of triangle = √ S.(S- a).(S -b).(S-c)

The semi perimeter of triangle = 6 + 6 +5 / 2 = 17 / 2 = 8.5

Area = √ 8.5 x (8.5 - 6) x (8.5 - 6) x (8.5 - 5)

= √8.5 x 2.5 x 2.5 x 3.5

= 13.635

The second triangle whose side are 3, 4 and 5, makes a right angle.

The area of second triangle = 1/2 x base x height = 1/2 x 4 x 3 = 6

Total area = 13.635 6 + 6 = 19.635

The required area of quadrilateral is 19.635 square units.

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Factor 5k 2 - 35k 3.

A. 5k2(1 - 7k)

B. 5k3(1 - 7k)

C. 5k(1 - 7k2)

Answers

Answer:

The correct answer is A) 5k^2(1 - 7k)

Step-by-step explanation:

To factor, take out the greatest common multiple. Each term has a factor of 5 that can be taken out as a constant and k^2 as a variable. Take both of these out and divide each term by that expression.

5k^2(1 - 7k)

its A) 5k^2(1 - 7k) :)

if the measure of angle 1 is (3x-4)° and the meadure of angle 2 is (4x+10)° what is the measure of angle 2 in degrees?

Answers

3x-4 + 4x+10 = 90
=>
7x + 6 = 90
=>
7x = 84 => x = 84/7 = 12

<2 = 4x + 10 = 4*12 + 10 = 48 + 10 = 58

The answer is: 58

Answer:

The measure of ∠ 2 in 58° .

Step-by-step explanation:

As given

if the measure of ∠ 1 is (3x-4)° and the measure of ∠ 2 is (4x+10)° .

As shown in the picture given in the question

90° + ∠1 + ∠2 = 180°

(By linear pair property)

Put the value of ∠1 and ∠2 in the above

90° + (3x -4)° + (4x+10)°= 180°

90 + 3x -4 + 4x + 10 = 180

7x + 6 = 180 - 90

7x + 6 = 90

7x = 90 -6

7x = 84

[tex]x = \frac{84}{7}[/tex]

x = 12

Put the value of x in the (4x+10)° .

∠2 = (4 × 12 + 10)°

∠2 = 58°

Therefore the measure of ∠ 2 in 58° .

a rectangle has an area of 12m and a width of 400cm. what is the length?

Answers

the length is 0.03 because of the formula
hope it helped :)

3 meters or 300 cm bc 400 cm is 4 meters and 12/4 is 3 meters or 300 cm

Write equations for the vertical and horizontal lines passing through the point (8, 7).

Answers

Let A(8,7)
that means x = 8 and y = 7.
The vertical line (// to y-axis) passing through A, will have always x = 8,
Then the equation of the vertical line is x = 8

The Horizontal line (// to x-axis) passing through A, will have always y = 7,
Then the equation of the Horizontal line is y = 7

Find the sum of the solutions of this equation 20x^2-39x-80=0

Answers

This is 'nice':

The sum of the solutions is the coefficient with 'x', change it sign and divide by the coefficient of x^2:

sum = 39/40.

Choose one of the factors of x3 + 343

Answers

Hello there!

The factorization for x³ + 343 is (x + 7)(x² - 7x + 49)

I hope that helps!

AB=diameter of the circle O. OC=radius. Arc AXB is an arc of the circle with centre C. Prove areas of the shaded region are =

Answers

1.
Draw a circle with center C And radius CA, as shown in the attached picture.

Let the lengths of radii AO, OB, OC be R. Triangle ABC is inscribed in the circle with center O and one of its sides is a diameter, this means that the angle ACB is a right angle.
|AO|=|OC|=R, by the Pythagorean theorem |AC|=[tex] \sqrt{2}R [/tex].

these are all shown in the picture.

2.

Area of triangle ABC is 1/2 * 2R * R= R^2

3.

Let the area between arc BXA and chord AB be Y. (the yellow region).

and let G be the shaded region between arcs AB and AXB.

G=1/2(Area circle with center O)-Y
=[tex] \frac{1}{2} \pi R^{2}-Y [/tex]

To find Y:

Notice that the area of the sector ACB is 1/4 of the area of circle with center C, since m(ACB) is 1/4 of 360 degrees.

So Area of sector ACB = [tex]\frac{1}{4} \pi (\sqrt{2} R)^{2}=\frac{1}{4} \pi*2 R^{2} =\frac{1}{2} \pi R^{2}[/tex]

Y =area of sector ABC-Area(triangle ABC)=[tex]\frac{1}{2} \pi R^{2}- \frac{1}{2}*2R*R=\frac{1}{2} \pi R^{2}- R^{2} [/tex]

4.

Finally,

[tex]G=\frac{1}{2} \pi R^{2}-Y=\frac{1}{2} \pi R^{2}-(\frac{1}{2} \pi R^{2}- R^{2})=R^{2}[/tex]

This proves that the 2 shaded regions have equal area.

Name all sets of numbers to which each real number belongs

Answers

Real Number
Whole Numbers:0,1,2,3,4,5,6,7,8,9,10,etc.
Counting Numbers:1,2,3,4,5,6,7,8,etc.
Natural Numbers:which is whole or counting numbers depends on the topic
Integers:-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,etc.

Best explained and correct answer gets brainliest.

Answers

value = 45 x (1+0.015)^15

45 x 1.015^15=

45 * 1.25 = 56.26

answer is B $56.26

The sum of a certain number and 3 times the number is 40. what is the number?

Answers

3n + n = 40
4n = 40
n = 40/4
n = 10 <==

The value of x is 10 if the sum of a certain number and 3 times the number is 40 and the equation will be 3x + x = 40.

What is linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The sum of a certain number and 3 times the number is 40

Let the number is x

From the question, we can frame a linear equation in one variable

3x + x = 40

Adding like terms:

4x = 40

Divide by 4 into both sides

x = 40/4

x = 10

Thus, the value of x is 10 if the sum of a certain number and 3 times the number is 40 and the equation will be 3x + x = 40.

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The formula for the volume of a pyramid is V=13BhV=13Bh, where B is the area of the base and h is the height. Rearrange the formula to solve for the height (h).

h=B3Vh=B3V

h=V3Bh=V3B

h=3VBh=3VB

h=3BV

Answers

The volume of a pyramid
[tex]V = \frac{1}{3}Bh \ \ \to \ \ h= \cfrac{V}{ \frac{1}{3}B } = \cfrac{3V}{B} [/tex]

To solve for the height h in the volume formula V = 1/3Bh for a pyramid, the formula needs to be rearranged to h = 3V/B by first multiplying both sides by 3 and then dividing by B.

The formula for the volume of a pyramid is V = 1/3Bh, where B is the area of the base and h is the height. To solve for the height, h, we need to rearrange the formula.

Starting with V = 1/3Bh, we want to isolate h:

Multiply both sides of the equation by 3 to cancel out the fraction: 3V = Bh.

Next, divide both sides by B to solve for h: h = 3V/B.

The correct formula to solve for height is h = 3V/B.

A certain forest covers an area of 3900 km2 . suppose that each year this area decreases by 8% . what will the area be after 10 years? use the calculator provided and round your answer to the nearest square kilometer.

Answers

A = P(1-r)^t

A = 3900(1-0.08)^10

A = 3900(0.92)^10

A = 3900(0.434388454)

A = 1694.11

1694 square km

Take a look at the table of possible outcomes when a pair of fair dice is rolled. What is the probability that the sum of the numbers rolled is either even or a multiple of 5?

Answers

Mark the entries in the table that are even. Those values are: 2, 4, 6, 8, 10, 12
There are 1+3+5+5+3+1 = 18 cases where this happens

Now mark the entries that are 5 or 10. There are multiples of 5. There are 4+3 = 7 cases of either 5 or 10.

If we add up 18 and 7, we get 18+7 = 25. Now subtract out the cases where we get both an even number AND a multiple of 5. So the three tens are counted twice. We go from 25 to 25-3 = 22

Divide this value (22) over the total number of outcomes (6*6 = 36). Doing this gets us
22/36 = 11/18

The answer is choice A

Answer:

He is correct

Step-by-step explanation:

If f(x) = ∣(x2 − 8)∣, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem?

Answers

First let us find the slope of the straight line formed when x1 = 0 to x2 = 2.5.

y = x^2 – 8

y1 = 0^2 – 8 = - 8

y2 = 2.5^2 – 8 = -1.75

The formula for finding the slope is:

m = (y2 – y1) / (x2 – x1)

m = (-1.75- (- 8)) / (2.5 – 0)

m = 2.5

The mean value theorem states that the slope must be 2.5 at least once between x1 = 0 to x2 = 2.5.

Taking the 1st derivative (slope) of the equation:

dy / dx = 2x

Since dy / dx = m = 2.5

2x = 2.5

x = 1.25

Therefore the answer is: One number at x = 1.25

The area of the trapezoid is 40 square units.

What is the height of the trapezoid? __ Units

Answers

The answer is 5. The formula for area of trapezoid is A=a+b/2*h
When you input 40 for A and 6 for a and 10 for b, then you should get 5
hope this helps:))

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

where

b1 and b2 are the parallel bases of the trapezoid

h is the height of the trapezoid

In this problem we have

[tex]b1=6\ units\\b2=10\ units\\A=40\ units^{2}[/tex]

substitute in the formula

[tex]40=\frac{1}{2}(6+10)h[/tex]

Solve for h

[tex]40*2=16h[/tex]

[tex]h=80/16=5\ units[/tex]

therefore

the answer is

The height of the trapezoid is [tex]5\ units[/tex]

A box with a volume of 40 cubic inches holds 10 balls. A box with a volume of 60 cubic inches holds 15 of the same kinds of balls. Assume the relationship is linear. Which equation models the relationship between the volume, x, and the number of balls y ?

A).y=0.25x+10
B).0.25x
C).y=4x
D).y=4x+60

Answers

Pretend these are coordinates that you can use to find the slope of the line.
(10, 40) and (15, 60). Fit these into the slope formula to find the slope of the line you are looking for:
[tex]m= \frac{60-40}{15-10} [/tex] and the slope is 4. Now use one of the points and the slope of 4 to solve for b, the y-intercept:
40 = 4(10) + b so b = 0. The equation of the line then is y = 4x + 0 or just
y = 4x

Which of the following could not be a value of n? side lengths of 9 and 13
a. 7
b.10
c. 13
d. 22

Answers

The correct answer here would be D. And that is because, in a triangle, the sum of 2 of the sides has to be greater than the third side for all sides. If we add 22 and 13 we get 35, and 35 is greater than 9, for sure. But if we add 13 and 9 we get 22 which is not greater than the third side length of 22; it would be collinear with the side length and it has to be greater than the side length.

The diagonals of a parallelogram are 12 meters and 20 meters and intersect at an angle of 60°. find the length of the longer side.

Answers

Final answer:

To find the length of the longer side of the parallelogram, you can use the law of cosines.

Explanation:

To find the length of the longer side of the parallelogram, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle.

In this case, one of the diagonals is 12 meters and the other is 20 meters. The included angle is 60°.

Letting 'a' be the length of the longer side, we can set up the equation:

a^2 = 12^2 + 20^2 - 2(12)(20)cos(60°)= 304

a=17.43

Which of the following are binomials. (more than one answer)
A. x^11
B. 8x
C. x^2+3
D. x^4+x^2+1
E. 5/7y^3+5y^2+y
F. 6x^2+1/2y^2

Answers

C. x^2+3 and D. x^4+x^2+1

its C) x^2+3 and F) 6x^2+1/2y^2 on apex

Abdul put gas in his car. He paid $18.32 for 8 gallons of gas. What is the unit price?

Answers

Unit price is price per gallon.
18.32/8=2.29
Final answer: $2.29 per gallon

$2.29 a gallon

18.32/8 = 2.29, which represents dollars per gallon.

Select the postulate or theorem that you can use to conclude that triangles are similar.

Answers

Answer:

AA similarity postulate.

Step-by-step explanation:

Two triangles which are of same shape are called similar triangles.

In the given triangles two angles are marked 90 degrees and another pair of angles are marked the same that is equal.

In the given figure:

m∠P==m∠L=90°

m∠J=m∠M.

Two angles are equal .

The AA similarity postulate states: if two pairs of corresponding angles are congruent, then the triangles are similar .

Answer :AA similarity postulate.

Answer:

Step-by-step explanation:

What is the surface area of a cone with a diameter of 28 cm. and height 22 cm in terms of Ï.

196Ï cm2
365Ï cm2
561.1Ï cm2
2202.8Ï cm2

Answers

To find the surface area of a cone, use this formula.

pi (r) (r + [square root of h^2 plus r^2] ) substitute

h = height = 22 r = radius = 28/2 = 14 [ ] = sq. root

pi (14) (14 + [ 22^2 + 14^2 ]) solve exponents

pi (14) (14 + [484 + 196]) add

pi (14) (14 + [680]) solve square root

pi (14) (14 + 2[170]) add

pi (14) (40.0768) multiply

pi (561.075) is about 561.1 rounded to nearest tenth

So the answer is C. 561.1pi cm^2

Laura is now trying to come up with a number where three less than 8 times the number is equal to half of 16 times the umber after it was increased by 1

Answers

8n-3=1/2(16n+1)
is the equation i come up with which would have no solutions.

Which equation represents the vertical asymptote of the graph?

Answers

In this question, with the help of the graph we have to find the vertical asymptote .

First let's check out what is vertical asymptote .

Vertical asymptotes are straight lines of the equation , toward which a function f(x) approaches infinitesimally closely, but never reaches the line.

And in the graph, the function approaches to 12 but never touches it .

So the vertical asymptote is x=12 .

The equation which represents the vertical asymptote of the graph given is; x =12.

The Vertical Asymptote of a graph

The vertical asymptote of a graph is simply a vertical line on the x-axis to which the graph of a function approaches but never touches.

By observation, the line x=12 separates the curves and both curves do not touch the line.

Ultimately, the line x=12 is the vertical asymptote of the given graph.

Answers

Let O be the center of the circle.

Reflex angle XOZ = 296°
Obtuse angle XOZ = 360° - 296° = 64°
Triangle XOZ is an isosceles triangle.

∴ Angle OZX = (180° - 64°) / 2 = 58°
(Base angle of an isosceles triangle)

Angle OZW = 90°
(Tangent to circumference of circle)

Angle XZW = 90° + 58° = 148°

Answer is B.

9.1 ÷ 3576 long division

Answers

The answer is 0.002544743....
If you are trying to do 3576/9.1, then the answer is 392.967033
hope this helps:))

Answer: the answer is 0.00254474272

goooood luck

If AB is the midsegment, find the value of x. Show your work.

Answers

Mid segment means half the segment, so: 3x-1=34/2=17, 3x =18, x =6. Hope it helps

3x-1=34/2

=17

3x =18, x =6

Is the number of free dash throw attempts before the first shot is missed number of free-throw attempts before the first shot is missed a discrete random variable, continuous random variable, or not a random variable?

Answers

The number of free dash throw attempts before the first shot is missed number of free-throw attempts before the first shot is missed is an example of a discrete random variable. A discrete random variable has a probability distribution can give any possible value and the probability of that value in any given data presentation such as graph, table or formula. They are called discrete random variables because they show a specific number of finite or countable infinite values after an event has happened. In here, the number of free throw attempts wit or without missing the first shot can be counted thus making it a discrete random variable.

Answer:

Step-by-step explanation:

What is the value of y in the product of powers below?

Answers

You're trying to find the value of y that would result in 8^-2. When you multiply terms with the same base, you can add the exponents. 3+-5=-2 and -2-(-2) equals 0, so therefore y is equal to 0.

when multiplying you add the powers

3 +-5 = -2 so the power for y = 0

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The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005? A. 578,813 B. 587,712 C. 499,354 D. 512,945

Answers

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The population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the approximate population of the town in 2005?
A. 578,813
B. 587,712
C. 499,354
D. 512,945