Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?

Answer:

x=80

Step-by-step explanation:

x=0.7x+24

We move all terms to the left:

x-(0.7x+24)=0

We get rid of parentheses

x-0.7x-24=0

We add all the numbers together, and all the variables

0.3x-24=0

We move all terms containing x to the left, all other terms to the right

0.3x=24

x=24/0.3

x=80

Answer:

x = 80

Step-by-step explanation:

We are given the following equation.

x = 0.7x + 24

And we want to solve it for x.

For these kinds of equations, the way to solve for x is to isolate x on one side.

Because we have terms with x on both sides of the equation, we need to remove it from one side.

It's a good idea to remove x from the right side, as we also have our numbers on that side. If we move it to the left side, there aren't any numbers there, so we can more easily solve this equation.

Here is our equation again:

x = 0.7x + 24

Subtract 0.7x from both sides.

x = 0.7x + 24

-0.7x -0.7x

______________________

0.3x = 24

Now, we have variables on one side, and numbers on the other, but we aren't done yet.

Remember that we are solving for x, not 0.3x. (When x is written by itself, it is the same as 1x).

So, in order to find the value of 1x, we need to divide both sides by 0.3, as when a number is divided by itself, the value is 1. If there is a variable, the value will be 1*that variable (e.g. 1n, or n)

**Note that we don't divide by 0.3x, as if we did that, the left side would equal just 1, not 1x.

So, let's divide both sides by 0.3.

0.3x = 24

÷0.3   ÷0.3

__________

x = 80

Topic: solving linear equations

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The value of Ry= -x (P) is P' = (4, 6)

The point is given as:

P = (-6, 4)

The transformation Ry= -x (P) means tha:

(x, y) = (y, -x)

So, we have:

P' = (4, 6)

Hence, the value of Ry= -x (P) is P' = (4, 6)

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Answer:

see below

Step-by-step explanation:

what 3 logy z^9 means you need to break it into two pieces, one log y z^9 means to find the exponent of y, and you can think z^9 as a number, and then if we multiple it with 3, which means three logs are summed,(the property of multiplication:3*2 means 2+2+2), thus log + log

has the property that the y is same z^9*z^9*z^9=z^(9+9+9)=z^27

The value of the stock account at the end of each day is  mathematically given as

x=1010$.

Generally, The price of the stock would have climbed by 1000 points, which is equal to 0.1 times 1000, or 10 dollars.

Therefore, the price of the stock would be 1010 dollars plus 10 dollars, which is 1020 dollars.

In conclusion, Cheryl was required to pay a ten dollar administrative fee, and this cost would be deducted from the stock price.

Following this logic, the price of the stock would be

x=1020-10

x=1010$.

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The booth space and the product brochures are less than $3000 hence the equation of inequality will be  B + P ≤ $ 3000.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let the booth space be B and the product brochures be P.

Then the equation of inequality will be  

B + P ≤ $ 3000

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Complete question:

2.5.2 Project: A Trade Show Booth

The Scenario: Your manager has asked you to help plan your company's participation at a local trade show. You have $3000 to spend on the booth space and product brochures. Use what you know about solving inequalities to prepare the inequality that meets the budget.

The confounding variable which is controlled by randomly assigning individuals to treatments is: C. the time of day participants drank the beverages.

A confounding variable is also referred to as a confounder and it can be defined as a type of variable that has the ability to influence both the independent and dependent variables.

Also, a confounding variable is usually not accounted for by the researcher and as such it can cause a spurious association between the independent and dependent variables.

In this context, we can infer and logically deduce that the time of day at which participants drank the beverages is a confounding variable which is controlled by randomly assigning individuals to treatments.

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Answer:

О  x = 10 3/4

[tex]x = 10\frac{3}{4}[/tex]

Step-by-step explanation:

-1/5 ( x + 1 3/4) = -2 1/2

Particularly:

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4

-2 1/2 = -2 - 1/2 = -4/2 - 1/2 = -5/2

Then:

-1/5 (x + 7/4) = -5/2

(x*-1/5 + 7/4*-1/5) = -5/2

(-x/5 + ((7*-1) / (4*5))) = -5/2

-x/5 + (-7/20) = -5/2

-x/5 - 7/20 = -5/2

-4x/20 - 7/20 = -50/20

-4x - 7 = -50

-4x =  -50  + 7

-4x = -43

x = -43/-4

x = 43/4

43/4 = 40/4 + 3/4 = 10 + 3/4 = 10 3/4

Answer:

147

Step-by-step explanation:

start by multiplying 42 and 7=294

now divide that by 1/2 =147

Answer:

extraneous: 2, 5, 7

not: 1, 3, 4, 6, 8

Step-by-step explanation:

ones that have root of an even number and equal a negative are extraneous

Step-by-step explanation:

Let the first number be = x

Let the second number be = 4x -28

Let the third = x-7

x + 4x+ x -28 - 7

6x - 35

6x -35 = 157

6x = 157 +35

6x = 192

x = 32

therefore, x = 32, the second x = 4(32) -28

728 - 28

x = 100

third x = 32 - 7

x = 25.

Answer: A, C, C.

100%

Step-by-step explanation:

The measures that are true for the quilt piece include:

The value of a will be:

= 90° - 30°

= 60°

The perimeter will be:

= 4 × 4

= 16 inches.

The length of the diagonal will be:

= 2 × 3.46

= 6.92 = 7

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The intersection of A and I are {-2, -1, 1}

The sets are given as;

A={−2,−1,0,1,7} I= {−2,−1,1,2,8}

The intersection of A and I are the common elements in both sets

The common elements in both sets -2, -1 and 1

This means that:

A n I = {-2, -1, 1}

Hence, the intersection of A and I are {-2, -1, 1}

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Answer:

DF = 3

Step-by-step explanation:

BC = DF

Which mean D is (0,2) and F is (3,2)

Here, this is clear that y-intercept is 2

DF = D(x) + F(x) = 0 +3 = 3

Answer: constant of proportionality = 0.75

How to find constant of proportionality?

Constant of proportionality is the same as the slope of a straight line.

Slope formula is given by:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here take two points: (0, 0), (4, 3)

[tex]So, \sf \ slope : \dfrac{3-0}{4-0} = \dfrac{3}{4} \quad or \quad 0.75[/tex]

Hence, the constant of proportionality is 0.75

Answer:

Constant of proportionality = 0.75

Step-by-step explanation:

To find the constant of proportionality of a graph that goes through the origin:

• First select a point on the graph whose coordinates you can easily read; in this case such a point is already marked (4, 3).

• Next, simply divide the y-value by the x-value of the coordinates to find the constant of proportionality:

Constant of proportionality = y ÷ x

                                             ⇒ 3 ÷ 4

                                             ⇒ 0.75

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount invested at 13% and y represent the amount invested at 12%, hence:

x +  y = 14246   (1)

Also:

0.13x = 0.12y + 318.23  (2)

Hence:

x = 8111, y = 6135

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

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Answer: 110

Step-by-step explanation:

<ABC = <DEF

180 - <DEF = 180 - 70

<BED = 110

The least to greatest slope, the segments are B, C, and A.

We have given that,

The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.

A graph represents the water level to fill the tank on Y-axis per time on X-axis.

The rate of increase of water level is indicated by the slope of the segment. The slope is the ratio of rise to run, and is related to the angle the segment makes with the +x axis.

Segments that have more rise for the same run have greater slope. Segments that make a larger reference angle with the +x axis have a larger slope.

Here, segment B has the least slope, followed by C, then A, which has the largest slope.

In order, the least to greatest slope, the segments are B, C, and A.

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Answer: bca

Step-by-step explanation:

B C A

Notice that

5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

{2, 6, 18, ...} = {2×3⁰, 2×3, 2×3², ...}

so a reasonable guess for the next number in the sequence might be 2×3³ = 54.

The sequence might be 2×3^3^3 = 54.

We notice that 5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

{2, 6, 18, ...} = {2×3^0, 2×3^1, 2×3^3, ...}

So the next number in the sequence might be 2×3^3 = 54.

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Answer:

Step-by-step explanation:

we can break up the figure into 2 rectangles by extending the 8m side downward until it meets the bottom (see image)

Area of this rectangle = 10 * 2 =20 sq meters

Area of the other rectangle = 8 *2 = 16 sq meters

Total area = 36 sq meters

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

Mass of radioactive isotopes (m (t)), in grams, decay exponentially in time according to the following model:

[tex]m(t) = m_{o}\cdot e^{-t/\tau}[/tex]     (1)

Where:

The time constant can be found in terms of half-life:

τ = t'/㏑ 2

If we know that t' = 24100 yr, t = 1000 yr and m(t) = 5.4 g, then the initial mass of the radioactive isotope is:

τ = 24100 yr/㏑ 2

τ ≈ 34768.95 yr

[tex]5.4 = m_{o}\cdot e^{-1000/24100}[/tex]

[tex]m_{o} = 5.629\,g[/tex]

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

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Answer:

10x² + 8x + 22

Step-by-step explanation:

The perimeter of a rectangle is the measurements of all four side lengths added together

(you can simply multiply both side lengths by 2, because they are the same on both sides--but I'll write them all out for clarity)

side A (top): 5x² + 3x + 7

side B (right): x + 4

side C (bottom): 5x² + 3x + 7

side D (left): x + 4

perimeter = side A + side B + side C + side D

5x² + 3x + 7 + x + 4 + 5x² + 3x + 7 + x + 4

now, as you might have noticed, this is a long equation

so, we must combine like terms:

(this is the problem reordered so like terms are next to each other:)

(5x² + 5x²) + (3x + x + 3x + x) + (7 + 4 + 7 + 4)

10x² + 8x + 22

So, the perimeter of this rectangle is 10x² + 8x + 22

hope this helps! have a lovely day :)

Using the binomial distribution, it is found that there is a 0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are:

n = 10, p = 0.2.

The probability that at least 3 Canadian are on CERB in the sample is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778.

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222[/tex]

0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

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Hello,

What is the explicit formula for this sequence? -7, -3, 1, 5, ... ?

Aₙ₊₁ = Aₙ + 4 and A₀ = -7

⇒ Aₙ = A₀ + nr = -7 + 4n

Answer:

108

Step-by-step explanation:

if the width of the rectangle is 8, and the triangle is on the width of the rectangle, then the base of the rectangle is 8. the height is 7, so we use the formula area = height * base / 2 to find that the area of the triangular portion is 28. then, we find the area of the rectangle by doing 10 * 8(height * width) for a value of 80. the total area of the front of the house is 28 + 80: 108.

Answer:

m = 10/3

(as a decimal: m = 3.333...)

Step-by-step explanation:

5m - 8 = 2m + 2

 5m - 8 = 2m + 2

- 2m       - 2m              (make all "m" on one side to isolate variable)

 3m - 8 = 2    

      + 8 + 8              (get m entirely on 1 side)

3m = 10

÷3      ÷3                         (divide by 3 to get 1m)

m = 10/3

(as a decimal: m = 3.333...)

hope this helps!! have a lovely day :)

Using the arc length formula, the length of the outer curve is approximately 85 feet.

Arc length = ∅/360 × 2πr.

Apply the arc length formula to find the length of the outer curve, given the following:

Plug in the values

Arc length = 70/360 × 2(3.14)(70)

Arc length = 70/360 × 2(3.14)(70) ≈ 85 feet.

The length of the outer curve is approximately 85 feet.

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Here are the solving steps for the problem.

   Given:

[tex]\displaystyle \frac{-6}{4x}=12[/tex]

    [1] Multiply both sides of the equation by 4x:

[tex]\displaystyle 4x(\frac{-6}{4x})=(12)4x[/tex]

-6 = 48x

    [2] Divide both sides of the equation by 48:

[tex]\displaystyle \frac{-6}{48} = \frac{48x}{48}[/tex]

[tex]\displaystyle x=-\frac{1}{8}[/tex]

I am not sure how to solve the equation in one step, so here is it in two steps. My apologies.

Answer:

[tex] - \frac{1}{8} [/tex]

Step-by-step explanation:

The Algebraic Equation -6 divide by 4x = 12 can be stated mathematically as :

[tex] \frac{ - 6}{4x} = 12 \\ \\ cross \: multiplying \\ \\ 4x \: \times 12 = - 6 \\ \\ 48x = - 6 \\ dividing \: bothsides \: by \: 48 \\ \frac{48x}{48} = \frac{ - 6}{48} \\ \\ x = - \frac{1}{8} [/tex]

[tex]12 \frac{2}{5}=\frac{62}{5}\\\\\frac{62/5}{1/4}=4\left(\frac{62}{5} \right)=\frac{248}{5}=\boxed{49 \frac{3}{5}}[/tex]