Suppose you make the following deposits into an account earning 2.1%: $12,000 today followed by $6,000 each year for the next 7 years (so the last cash flow is at year 7). How much will you have in the account after 10 years? Round to the nearest dollar.

Answer: A: substitution method

Step-by-step explanation:

The substitution method is one way of solving systems of equations. To use the substitution method, use one equation to find an expression for one of the variables in terms of the other variable. Then substitute that expression in place of that variable in the second equation.

The hash of the given message is 135.

In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.

Here, it is given the message m = 23  

The formula to calculate hash is him) - (m*7;2 MOD 7793.

So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793

⇒ (8*23) - (49 MOD 7793)

⇒ 184 - 49= 135.

So, the hash of the given message is 135.

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Answer:

15/100 x 10625

Saved: 1593.75 pounds

If rxy = 0.83, we can conclude that x and y have a relatively strong positive linear relationship or correlation.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, in this case, x and y. The value of r ranges between -1 and 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other variable tends to increase as well.

In this case, with rxy = 0.83, the correlation coefficient is close to 1, suggesting a strong positive linear relationship. This means that when x increases, y also tends to increase, and vice versa. The closer the value of r is to 1, the stronger the linear relationship between x and y.

It is important to note that correlation does not imply causation. While a high correlation coefficient indicates a strong linear relationship, it does not provide information about the underlying cause or direction of the relationship between the variables. Other factors and variables may influence the relationship, and further analysis may be required to understand the nature of the relationship between x and y.

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Answer:

1. 6

2. 8

3. 80

4. 11

5. 60

6. 3

7. 30

8. 0.8

9. 5

10. 600

11. 150

12. 110

13. 15

14. 1.1

15. 36

Hope it helps

Step-by-step explanation:

10^2   +    10^6    +   10^1    =    10 ^(2+6+1)  = 10 ^9

Step-by-step explanation:

a) 2x+7= -3

2x = -10

x = -5.

b) 7x-3= 9x+5

7x - 9x = 5 + 3

-2x = 8

x = -4

h) (2x-1)3= -125

6x - 3 = -125

6 x = -128

x = 21.33

c) 6x+7-2x = -x-8

6x -2x -x = -8 -7

3x = -15

x = -5

i) 2 (x+7)2= 242

2x + 14 * 2 = 242

2x + 28 = 242

2x = 242 + 28

2x = 270

x = 135.

d) -9+6x= 15+2x

6x -2x = 15 + 9

4x = 24

x = 6.

j) 1 + √2x + 3 = 6

√2x + 4 = 6

√2x = 6+4

√2x = 10

x = 7.1

e) 4x-8= -4 (2x-3)+4

4x - 8 = -8x +12 + 4

4x -8 = -8x + 16

4x - 8x = 16 - 8

-4x = 8

x = -2.

k) √3x + 22 = 4

√3x = 4 + 22

√3x = 26

x = 15

f) 2x+17 = 5 (x+1)

2x + 17 = 5x + 5

2x - 5x = 5 -17

-3x = -12

x = 4.

g) 7x-5= -3 (-x-9)

7x - 5 = 3x + 27

7x - 3x = 27 + 5

4x = 32

x = 8.

The equation states that the gradient of the natural logarithm of the density of component A, denoted as (∇ ln(ρA)), is equal to the negative divergence of the velocity vector (∇ · V).

To derive equation (25-11), we start with the general form of the conservation of mass equation:

∂(ρA) / ∂t + ∇ · (ρA V) = ṁA_gen Where:

ρA is the density of component A,

t is time,

V is the velocity vector,

∇ is the gradient operator,

ṁA_gen is the net rate of generation of component A within the control volume.

Assuming steady-state conditions (no change with time) and neglecting any mass generation or consumption, we can simplify the equation to:

∇ · (ρA V) = 0

This equation states that the divergence of the mass flux of component A is zero, indicating a steady-state condition.

By applying the divergence theorem, we can rewrite the equation as:

∫(∇ · (ρA V)) dV = 0

Using the product rule of divergence, we have:

∫(∇ρA · V + ρA ∇ · V) dV = 0

Since the control volume is arbitrary, the integral can be simplified to:

∇ρA · V + ρA ∇ · V = 0

Rearranging the equation, we obtain:

∇ρA · V = -ρA ∇ · V

Dividing both sides by ρA, we get:

V · (∇ρA / ρA) = -∇ · V

Finally, recognizing that the left side of the equation is the gradient of the natural logarithm of ρA (i.e., (∇ ln(ρA))), we have:

(∇ ln(ρA)) · V = -∇ · V

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Answer:

+3.16i, -3.16i

Step-by-step explanation:

This has complex roots.

ax² + bx + c = 0

a = 1

b = 0

c = 10

Roots:  +3.16i, -3.16i

Therefore, the AAA test of congruency demonstrated that ABE is Congruence to CDE.

Something that is "exactly equal" in terms of size and shape is referred to as congruent. No matter which way we spin, flip, or rotate the shapes, they remain accurate. For instance, you may draw two circles with the same radius, cut them out, and stack them.

In this case, we are aware that AB ll DC - GIVEN

In light of the characteristic of parallel lines,

Let's recall the property of parallel lines:-

"When the pair of alternating angles equals one another, two straight lines become parallel."

Alternate angles are angle ABE and angle CDB.

angle BAE ≅ angle DCE -{alternate angles}

E is a midway, given that.

According to the midpoint theorem, opposite angles are congruent when angle AES and angle CED are compared.

Here, we may see the congruency test from AAA.

Hence its proved that ∆ABE ≅ ∆CDE by AAA test of congruency.

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Answer:

Top-

11.5 or the square root of 133

Bottom-

15.3 or the square root of 235

Answer:

c) \(x=\sqrt{133}\)

d)\(x=\sqrt{235}\)

Step-by-step explanation:

Pythagorean Theorem: \(a^2+b^2=c^2\)

c) Solve for that side length and then solve for x

\(4^2+y^2=10^2\\y=\sqrt{133} \\(\sqrt{84} )^2+7^2=x^2\\x=\sqrt{133}\)

d) Solve for that side length and then solve for x

\(5^2+y^2=10^2\\y=\sqrt{(16^2-5^2)} \\(\sqrt{231} )^2+7^2=x^2\\x=\sqrt{235}\)

Answer:

C

Step-by-step explanation:

Function

\(f(x) = 1.5x\)

(22, 33) is a valid point in this line, therefore it's (22, 33), aka option C

The roots of the auxiliary equation are 0 (repeated root) and -b, where b is a constant.

To find the roots of the auxiliary equation for a homogeneous linear fourth-order differential equation with constant coefficients, we need to substitute the given solution into the differential equation and solve for the roots.

The given solution is:  \(y = 1 - x + 6x^2 + 3e^x.\)

The general form of a fourth-order homogeneous linear differential equation with constant coefficients is:

ay'''' + by''' + cy'' + dy' + ey = 0.

Let's differentiate y with respect to x to find the first and second derivatives:

\(y' = -1 + 12x + 3e^x,\)

\(y'' = 12 + 3e^x,\)

\(y''' = 3e^x,\)

\(y'''' = 3e^x.\)

Now, substitute these derivatives into the differential equation:

\(a(3e^x) + b(3e^x) + c(12 + 3e^x) + d(-1 + 12x + 3e^x) + e(1 - x + 6x^2 + 3e^x) = 0.\)

Simplifying the equation, we get:

\(3ae^x + 3be^x + 12c + 3ce^x - d + 12dx + 3de^x + e - ex + 6ex^2 + 3e^x = 0.\)

Rearranging the terms, we have:

\((6ex^2 + (12d - e)x + (3a + 3b + 12c + 3d + 3e))e^x + (12c - d + e) = 0.\)

For this equation to hold true for all x, the coefficients of each term must be zero. Therefore, we have the following equations:

6e = 0 ---> e = 0,

12d - e = 0 ---> d = 0,

3a + 3b + 12c + 3d + 3e = 0 ---> a + b + 4c = 0,

12c - d + e = 0 ---> c - e = 0.

From the equations e = 0 and d = 0, we can deduce that the differential equation has a repeated root of 0.

Substituting e = 0 into the equation c - e = 0, we get c = 0.

Finally, substituting d = 0 and c = 0 into the equation a + b + 4c = 0, we have a + b = 0, which implies a = -b.

Therefore, the roots of the auxiliary equation are 0 (repeated root) and -b, where b is a constant.

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Answer:

The fraction is 3/10 = .3

Answer:

Step-by-step explanation:

9x - 1 / 2 + 9/2 x = 0.128886 (43)

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

= x1 + 24 - 3/4 + 8

9/3 - 1 x = /3

The equation that models the amount of time that is left on the cd is 80 - m.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the blank CD can hold 80 minutes of music you have burned m minutes of music onto the cd. The time left will be:

= Total minutes - Time used

= 80 - m

This illustrates the equation.

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There are 147 small coffees and 65 large coffees were sold.

What is equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Let's call the number of small coffees sold "x" and the number of large coffees sold "y".

We know that a small coffee costs $2 and a large coffee costs $3, and that a total of 212 cups of coffee were sold, so we can set up two equations based on the number of cups sold and the amount of money collected:

x + y = 212 (equation 1: total number of cups sold)

2x + 3y = 489 (equation 2: total amount of money collected)

Now we can solve for x and y by using substitution or elimination:

Solve equation 1 for x in terms of y:

x = 212 - y

Substitute this expression for x into equation 2:

2(212 - y) + 3y = 489

Distribute the 2:

424 - 2y + 3y = 489

Simplify:

y = 65

Substitute this value for y into the expression we found for x:

x = 212 - y = 212 - 65 = 147

Therefore, 147 small coffees and 65 large coffees were sold.

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The specific numerical solution will depend on the number of firms in the market and their behavior.

In a Stackelberg version of monopolistic competition, there is a leader firm that sets its output first, and all the other firms in the market act as followers and choose their outputs simultaneously.

Suppose there are "n" firms in the market, with the first firm denoted as the leader. Let's assume that each firm has a constant marginal cost of $10 per unit. Then, the leader firm's profit-maximizing output level can be found by solving the following problem:

max (30-Q1-Q2-...-Qn)Q1 - 10Q1

subject to Q1 >= 0

where Q1 is the output level of the leader firm, and Q2, Q3, ..., Qn are the output levels of the follower firms.

Taking the first-order condition by differentiating with respect to Q1 and setting it equal to zero, we get:

d/dQ1 [(30-Q1-Q2-...-Qn)Q1 - 10Q1] = 0

Simplifying this expression, we get:

30 - Q1 - Q2 - ... - Qn - 2Q1 = 0

Solving for Q1, we get:

Q1 = (30 - Q2 - ... - Qn)/3

This equation gives us the leader firm's profit-maximizing output level as a function of the follower firms' output levels.

Now, let's consider the follower firms' profit-maximizing output levels. Since each follower firm is a price-taker, its profit-maximizing output level can be found by equating marginal cost to market price, which is equal to the market demand curve divided by the total quantity produced by all firms in the market. Therefore, the profit-maximizing output level of the jth follower firm can be expressed as:

Qj* = (1/n) * (30 - Q1 - Q2 - ... - Qj-1 - Qj+1 - ... - Qn - 10)

where Qj* is the follower firm's profit-maximizing output level, and j = 2, 3, ..., n.

Using these expressions for the leader and follower firms' profit-maximizing output levels, we can solve for the equilibrium outputs and profits in the Stackelberg version of monopolistic competition. However, the specific numerical solution will depend on the number of firms in the market and their behavior.

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the correct answer is false

The statement that shows kemi first mistake is that

' Kemi first mistake was in step 2 , instead of multiplying 1.3 with all terms , she added 1.3 to each term instead'. (optionB)

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler. For example;

5( 2x+6) can be simplified by using distributive law. i.e 5× 2x + 5× 6

= 10x + 30

Similar simplifying 1.3 (5+2.3m - 2.4), we use distributive law to simplify.

1.3 × 5 + 1.3 × 2.3m -2.4 × 1.3

= 6.5 + 2.99m - 3.12

The next step is to collect like terms

= 6.5-3.12 + 2.99m

= 3.38 + 2.99m

Instead of using the distributive law, Kami added 1.3 to all the terms in parentheses.

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Answer:

the x axis contains the arithmetic sequence

Answer:

-2, -1/2

Step-by-step explanation:

Step-by-step explanation:

The midpoint of a line segment between two points is given by

\(M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)

where ( x1 , y1) and ( x2 , y2) are the points

From the question

The midpoint of the line segment using points (-5,2) and (1, -3) is

\(M = ( \frac{ - 5 + 1}{2} , \frac{2 - 3}{2} )\)

\(M = ( - \frac{ 4}{2} , - \frac{1}{2} )\)

We have the final answer as

\(M = ( - 2, - \frac{1}{2} )\)

Hope this helps you

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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Answer:

- 7r² + 12r - 8

Step-by-step explanation:

Given

(10 + 7r - r² ) + (- 6r² - 18 + 5r) ← remove parenthesis

= 10 + 7r - r² - 6r² - 18 + 5r ← collect like terms

= - 7r² + 12r - 8

The expression (10 + 7r - r² ) + (- 6r² - 18 + 5r) is equivalent to - 7r² + 12r - 8 after applying the property.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

(10 + 7r - r² ) + (- 6r² - 18 + 5r)

Using distribution property:

After applying the above property the expression can be written as:

10 + 7r - r² - 6r² - 18 + 5r

Adding like terms:

- 7r² + 12r - 8

Thus, the expression (10 + 7r - r² ) + (- 6r² - 18 + 5r) is equivalent to - 7r² + 12r - 8 after applying the property.

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Answer:

The sum of all the possible distinct sum is 128

Step-by-step explanation:

The number of balls in the bag = 3

The ball labels, (the numbers written on the balls) = 2, 4, and 8

The number of balls selected with replacement = 1

Therefore, we have have, the number of ways of selecting 1 ball from 3 = 3 ways

The distinct combination of the selected balls are;

2, 2, 2 with sum 2 + 2 + 2 = 6

2, 2, 4 with sum 2 + 2 + 4 = 8

2, 2, 8 with sum 2 + 2 + 8 = 12

2, 4, 4 with sum 2 + 4 + 4 = 10

2, 4, 8 with sum 2 + 4 + 8 = 14

2, 8, 8 with sum 2 + 8 + 8 = 18

4, 4, 4 with sum 4 + 4 + 4 = 12

4, 4, 8 with sum 4 + 4 + 8 = 16

8, 8, 4 with sum 8 + 8 + 4 = 20

8, 8. 8 with sum 8 + 8 + 8 = 24

The distinct sums are therefore;

6, 8, 12, 10, 14, 18, 16, 20, 24

The sum of the distinct sum is 6 + 8 + 12 + 10 + 14 + 18 + 16 + 20 + 24 = 128.

Answer: 128

Step-by-step explanation:  

Any sum formed by a combination of the numbers 2, 4, 8  and  must be divisible by 2. The smallest possible value of such a sum is equal to 3*2=6 , and the largest possible value of such a sum is equal to 3*8=24 . After testing, we find that

6 = 2+2+2,    8=4+2+2,    10=4+4+2

12 = 4+4+4,    14 = 8+4+2,   16 = 8+4+4

18 = 8+8+2,   20 = 8+8+4,    24 = 8+8+8

 However, we cannot find a combination that will add to be 22: if two of the numbers are not 8, then the maximum possible sum is 4+4+8 = 16. Thus, two of the numbers picked must be 8, but then the third ball must have the number 6, which is not possible. Thus, the answer is the sum of the even numbers from 6 to 24 excluding 22, which is 128 .

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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hello

we need to first convert the values into degrees first

now we can convert the values in degrees to surds form

now let's solve for cosine

Answer: 25 students per teacher and 12 students per tutor. They need 2.4 tutors for the school