2. The million-dollar question! Suppose you
want to have $1,500,000 for retirement in
30 years. If you deposit the same amount
each month into an annuity that earns 6%
interest annually (and compounded
monthly),

what is the amount you need to
deposit each month?

Show your work
using the formula.

Answer:6720m^2

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:  C

Step-by-step explanation:

A.  incorrect.  Acute is when all the angles in the triangle are less than 90, not including 90 ex. (35, 65,80)

B.  incorrect.  Obtuse is when you have 1 angle greater than 90, not including 90.  ex( 100,20, 60)

C. correct, Right is when you have have 1, 90 degree angle.  That symbol in the corner of the triangle means the lines are perpendicular, which means it forms  right angle or 90 degree angle

D, incorrect because C is true

The equation that best represents the population of the town, which increases exponentially at the rate of 6% every year, after x years is C. y = 158,260(1.06)ˣ.

Exponential growth refers to a constant percentage or rate of growth per period.

The opposite of exponential growth is exponential decay and refers to the constant rate of decay in value per period.

The town's initial population = 158,260

Growth rate per year = 6%

Let x = the number of years of growth

Let y = the population after x years

y = 158,260(1 + 0.06)^x

Thus, the correct equation representing population growth after x years is Option C.

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The value of the expression x² + 10x, when x = 2 is 24.

In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:

x² + 10x = 2² + 10(2)

Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.

10(2) means 10 multiplied by 2, which is 20.

So we can substitute these values in the expression:

x² + 10x = 2² + 10(2)

= 4 + 20

= 24

Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.

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The complete question:

Evaluate the expression x² + 10x, when x = 2.

The parabola for the expression are given in attachment.

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix

y=2x(x-7)

Let us take few values of x and y and draw the parabola

Similarly we draw the graph for (x+4)(x-4)

Hence, the parabola for the expression are given in attachment.

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Step-by-step explanation:

Upper problem:

The transformation is a translation of 3 units down.

Lower problem:

The transformation is a translation of 2 units left and 5 units down.

Step-by-step explanation:

For a RIGHT triangle   tan Φ = opposite leg / adjacent leg

 for this triangle

         tan 71 = x / 5.7

       5.7 * tan 71 = x    =   16.6  units

Answer:height = 5 inches  and the base = 10 inches.

Step-by-step explanation:

The vertex of the parallelogram is (5, 13)

We know that in a parallelogram the opposite sides are equal

AB=√(-3-4)²+(-6+3)²

=√49+9

=√58 units

BC=√(6-4)²+(2+3)²

=√4+25

=√29 units

AD=√(-3-x)²+(-6-y)²

AD=√58 units

√58 units=√(-3-x)²+(-6-y)²

58 units=(-3-x)²+(-6-y)²

Now CD=√(6-x)²+(2-y)²

29 units=(6-x)²+(2-y)²

x=5 and y=13 satisfies the equation

Hence, the vertex of the parallelogram is (5, 13)

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The  probability that the student does not own a trampoline is given by the relation P ( A' ) = 5/12

Given data ,

Let the probability that the student does not own a trampoline be P ( A ' )

Given that there are 14 students who own a trampoline out of 24 students in total, the probability of owning a trampoline is 14/24. Therefore, the probability of not owning a trampoline is:

1 - 14/24 = 10/24 = 5/12

So, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12

Hence , the probability is 5/12

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Answer:

C. No, it is not possible to determine the order of the rational numbers because we do not know the signs of the rational numbers.

The surface area of the cylinder is calculated as approximately:

8,444.6 mm².

The surface area of a cylinder (SA) = 2πrh + 2πr², where:

r is the radius

h is the height of the cylinder.

Given the following:

Diagonal of cylinder = 40 mm

Height of cylinder (h) = 32 mm

Radius (r) = √(40² - 32²) = 24 mm [based on Pythagorean Theorem]

Plug in the values:

surface area of the cylinder (SA) = (2 * π * 24 * 32) + (2 * π * 24²)

≈ 8,444.6 mm²

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The value of x in the given diagram is 12.

option C.

The value of x in the given diagram is calculated by apply the principle of intersecting chord theorem as shown below;

The intersecting chord theorem states that angle formed at the circumference is twice the angle at the tangent.

the angle at circumference = 360 - (6 + 20x)

tangent angle = 4x + 9

360 - (6 + 20x) = 2 (4x + 9)

360 - 6 - 20x = 8x + 18

-28x = -336

x = 336/28

x = 12

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Answer:

45%

Step-by-step explanation:

Divide $360,000 by $800,000 to find the percentage

360,000/800,000=.45

To conver the decimal to a percentage, move the decimal point two places to the right, so .45 becomes 45%

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

Answer:

Sidama Cofee Football Team, the Ethiopian premier league club in Yiregalem, plays 70 percent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today’s news, they won yesterday. What is the probability the game was played at night?

The expression that can be represented by product (50)*(-5) is 250

Any number that can be expressed as the product of 50 and -5 can be represented using the expression (50)*(-5).

For example, if we multiply 50 and -5, we get -250. Therefore, -250 can be represented using the expression (50)*(-5).

Similarly, if we multiply 50 and -5 by any other number, we can represent the product using the expression (50)*(-5).

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The level of allergic symptoms in both groups cannot be compared to determine if the medication had a significant effect since, one group only received a placebo accurately describes the benefit of comparison in the experiment shown in the design web.  Thus option A is correct.

A scientific experiment inside that carry out a sequence of tasks and closely monitor their results to discover new information. An investigation is a method that used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that hasn't been tried before.

Although one sample only obtained a placebo inside the investigation depicted in the design web, which is difficult to compare the severity of allergic rhinitis in both groups to establish whether the drug had a substantial impact.

Hence, option A is the correct option.

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answer

a. 5,8

explanation

use numbers in each answer choice

+5 * -8 = - 40

+5 -8 = -3

Consider the form [tex]x^2+bx+c[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex]. In this case, whose product is -40 and whose sum is -3.

[tex]\longrightarrow\boxed{\bold{(-8,5)}}[/tex]

Write the factored form using these integers.

[tex](x-8) \ (x+5)[/tex]

Answer:

you got them all right except graph 4 is a function! The trick is to use the vertical line test. Put your pencil vertically on your paper and move it across the graph. If your pencil passes through the same point twice, it's not a function. :)

Step-by-step explanation:

The maximum volume of the cylindrical can such that the sum of its height and its circumference is 45 cm is  337.5 cm³

Let's denote the radius of the cylindrical can as r, and its height as h.

The circumference of the base of the can is 2πr, so the sum of the height and the circumference can be written as:

h + 2πr = 45..(1)

We want to find the maximum volume of the can, which is given by:

V = πr²h..(2)

From (1), h = 45 - 2πr

Substitute h value in equation above

V = πr²(45-2r)

V = 45πr² - 2π²r³

To find the maximum volume, we have to find the differentiation of V

dV/dr = 90πr - 6π²r² = 0

Solving for r, we get:

r = 15/π cm

Now plug in r value in h

V = π(15/π)²(15)

= 337.5 cm³

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_________________________________

________________________________

Answer:

difference = 12.5

Step-by-step explanation:

the median score is the value of the line inside the box.

median in afternoon = 75

median in morning = 87.5

difference = 87.5 - 75 = 12.5

Answer:

x = 27°

Step-by-step explanation:

using the co-function identity

cos x = sin(90 - x) , then

cos63° = sin(90 - 63)° = sin27° with x = 27°

The power of the kettle if it takes 90 seconds to boil given the inverse proportionality is 3 kilowatts.

Let

number of seconds that it takes for a kettle to boil = n

power of the kettle = p

n = 270/p

If n = 90 seconds

n = 270/p

90 = 270/p

90 × p = 270

90p = 270

divide both sides by 90

p = 270/90

p = 3 kilowatts

Ultimately, the power of the kettle is 3 kilowatts.

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It should be noted that to evaluate whether an organized array of numbers serves as a resolution for a combination of equations, one can apply this method.

Write down the arrangement of equations that you wish to evaluate the solution for. For illustration, let us say that we have this system:

2x + 3y = 7

x - y = 2

Inject the data from the orderly list into the equations. For example, if the ordered list is (x=1, y=3), then we have:

2(1) + 3(3) = 7

1 - 3 = -2

Verify whether the outcome of the equations are equivalent to the values in the ordered list. If they are, then the orderly list is a resolution of the arrangement of equations. On the other hand, if not, then it is not a solution.

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There are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

The organization or positioning of a group of items or components in relation to one another is referred to as an arrangement. It can be used in a variety of situations, such as mathematics, art, or event planning, and can relate to the arrangement, positioning, or grouping of things.

The number of different ways you can arrange 7 books in a specific order is given by the permutation formula:

P(7,7) = 7!

where "!" denotes the factorial operation.

Thus, the number of ways you can arrange your 7 favorite books along a small shelf, assuming that the order of the books makes a difference to you, is:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

Therefore, there are 5,040 different ways you can arrange your 7 favorite books on the small shelf.

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The value of the linear sum ∑(i = 1 to 124) (29a_i - 13b_i) is -30.

We have,

Using the linearity of the sum, we have:

∑(i = 1 to 124) (29a_i - 13b_i)

= 29∑(i = 1 to 124)a_i - 13∑(i = 1 to 124)b_i [Distributive property]

= 29(-10) - 13(-20) [Substitute the given sums]

= -290 + 260

= -30

Therefore,

The value of ∑(i = 1 to 124) (29a_i - 13b_i) is -30.

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