Two years ago, Joseph invested $18,200.00. Today, he has $18,700.00. If Joseph earns the same annual rate implied from the past and current values of his invetment, then in how many years from today does he expect to have exactly $20,400.00

Answer:

\(c=2\sqrt{13\)

Step-by-step explanation:

In a right triangle, to find the hypotenuse (c) you use Pythagoras theorem. Which is \(a^2+b^2=c^2\). Once we plug in our variables we get \(6^2+4^2=c^2\), then we solve.

\(36+16=c^2\)

\(52=c^2\)

\(\sqrt{c^2} =\sqrt{52}\)

\(c=\sqrt{52}\)

If we simplify...

\(c=2\sqrt{13}\)

Answer:  see below

Step-by-step explanation:

\(32)\quad \dfrac{3}{5}(x-12)>x-24\)

        3(x - 12) > 5(x - 24)

        3x - 36 > 5x - 120

      -5x         -5x        

        -2x - 36 >      -120

             +36          +36

        -2x        >       -84

     ÷ -2         ↓       ÷ -2  

             x      <       42

Graph:   ←------------o

                             42

34)   6[5y - (3y - 1)] ≥ 4(3y - 7)

        6[5y - 3y + 1] ≥ 4(3y - 7)

        6{2y + 1]        ≥ 4(3y - 7)

         12y + 6        ≥ 12y - 28

        -12y                -12y      

                  6        ≥         -28

                        TRUE  so the solution is All Real Numbers

Graph:   ←-----------------------→

36)   BC  +  AC      > AB

         4    + 8 - AB > AB

                12 - AB  > AB

                    +AB    +AB

                12          > 2AB

              ÷2            ÷2    

                 6           >  AB

                         AB < 6

\(38)\quad \dfrac{1}{2}(y-16)\geq y+2\quad ;\text{claim}\ y\leq 20\)

Check: let y = 16

           then \(\frac{1}{2}\)(16 - 16) ≥ 16 + 2

                            0    ≥ 18

                            FALSE  so the claim is wrong

40) question not provided in the image so I cannot give a solution.

Answer:

From 1846 to 1847 there was a 30% decrease and from 1847 to 1848 it increased by 51.4%

Step-by-step explanation:

How it decreased by 30%

V2-V1/V1x100

V2=3.5 V1=5

=(3.5−5)|5|×100
=−1.55×100

=−0.3×100

=−30%change

=30%decrease
How it increased by 51.4%
V2-V1/V1x100
V2=5.3 V1=3.5

=(5.3−3.5)|3.5|×100

=1.83.5×100

=0.514286×100

=51.4286%change

=51.4%increase

Answer:

$1.10.

Step-by-step explanation:

0.88 * 1.25.

Answer:

$1.10

Step-by-step explanation:

1.25*.88

Answer:

The answer is f(x)=2

Step-by-step explanation:

When the input is given it means that the x is substituted by that number.

so 3x3-7.

3x3-7

9-7=2.

The f of x is equivalent to 2.

I hope this helps :D

Answer:

Neither increasing or descreasing

Step-by-step explanation:

Decreasing - slope of line is negative, e.g. y = -2x

Increasing - slop of line is positive, e.g. y = 2x

Vertical lines have no slope, so they are neither increasing or decreasing

The solutions to the given inequality x² + 3x – 4 > 0 are -6 and 5 which is the correct answer would be options (A) and (D).

To find the solutions to the inequality x² + 3x – 4 > 0, we can start by factoring the quadratic equation on the left side of the inequality:

x² + 3x – 4 = (x - 1)(x + 4)

Since the inequality is strict (i.e., > 0), the solutions are the values of x that make the expression on the left side positive. Therefore, we can find the solutions by looking at the signs of the factors on the right side:

If x < -4, then both factors are negative, so (x - 1)(x + 4) is positive.

If -4 < x < 1, then one factor is negative and the other is positive, so (x - 1)(x + 4) is negative.

If x > 1, then both factors are positive, so (x - 1)(x + 4) is positive.

Therefore, the solutions to the inequality x² + 3x – 4 > 0 are x < -4 or x > 1.

The values that fit this description are -6 and 5, so the solutions to the inequality are -6 and 5.

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so it basically 36.16

Step-by-step explanation:

4x9=36

4x4=16

36.16

The long-run behavior of the given function is approaching negative infinity as x approaches positive or negative infinity.

The given function is f(x) = -4x^5 - 5x^4 + 2x^3 + 3. Now, we will find the long-run behavior of the function. Let's find the degree of the function. Degree of the function = 5. Since the degree of the function is odd and the leading coefficient of the function is negative, therefore, the graph of the function opens downward. The long-run behavior of a function refers to the behavior of the function as x approaches positive infinity or negative infinity. There are three possibilities for the long-run behavior of a function: Approaching positive infinity Approaching negative infinity. Oscillating Let's check the long-run behavior of the function. As x approaches negative infinity (-∞), the function will approach negative infinity, i.e.,f(x) → -∞As x approaches positive infinity (+∞), the function will approach negative infinity, i.e., f(x) → -∞. Therefore, the long-run behavior of the given function is approaching negative infinity as x approaches positive or negative infinity.

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The store pays $842.00 for the crystal sculpture and marks the price up by 29%,  then the amount of the markup is $243.98.

What is the arithmetic operation?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

we have given,

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,

so, the amount of the mark-up can be calculated as follows:

$842.00 * 29% = $842.00 * 0.29 = $243.98

Therefore, the amount of the markup is $243.98.

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Correct question:

A store pays $842.00 for a crystal sculpture and mark the price by 29%. What is the amount of the mark-up?

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,  then the amount of the markup is $243.98.

A subfield of mathematics known as arithmetic operations deals with the study and manipulation of numbers, which are essential to all other subfields of mathematics. Basic operations like addition, subtraction, multiplication, and division are included in it.

The four mathematical operations are functions that take input values, or numbers, as inputs and turn one number into another. They are: multiplication, division, addition, and subtraction.

According to contemporary mathematicians, the Riemann Hypothesis is possibly the most significant open problem in all of mathematics. One million dollars will be awarded to the person who can solve it, which is one of the seven Millennium Prize Problems.

we have given,

The store pays $842.00 for the crystal sculpture and marks the price up by 29%,

so, the amount of the mark-up can be calculated as follows:

\(842.00 \times 29% \\= $ 842.00 \times 0.29 \\= $243.98\)

Therefore, the amount of the markup is $243.98.

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Correct question:

A store pays $842.00 for a crystal sculpture and mark the price by 29%. What is the amount of the mark-up?

a) Chocolate Candy Bars  Total Utility (utils)  Marginal Utility (utils)

           1                                         28                               20

           2                                         63                               35

          3                                         81                               18

b) Marginal utility of the two additional candy bars is = 38.

a. Chocolate Candy Bars and Marco's Utility

Chocolate Candy Bars  Total Utility (utils)  Marginal Utility (utils)

           1                                         28                               20

           2                                         63                               35

           3                                         81                               18

b. To determine which option Marco is likely to prefer, we need to compare the marginal utility of the soda to the marginal utility of the two additional candy bars.

Since we don't have the marginal utility for the third candy bar, we can estimate it by taking the difference between the total utility of the third candy bar and the total utility of the second candy bar, which is:

Marginal Utility of Third Candy Bar = Total Utility of Third Candy Bar - Total Utility of Second Candy Bar

= 81 - 63

= 18

So the marginal utility of the two additional candy bars is 18 + 20 = 38.

Since the marginal utility of the soda is 24, and the marginal utility of the two additional candy bars is 38, Marco is likely to prefer the two additional candy bars

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The probability of selecting a green marble from a jar containing 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles is 0.1875 or 18.75%.

To find p(g), we need to first determine the total number of marbles in the jar, and then determine the number of green marbles in the jar.

Total number of marbles = 4 blue marbles + 3 green marbles + 7 red marbles + 2 white marbles = 16 marbles.

Number of green marbles = 3.

So p(g) = number of green marbles / total number of marbles = 3 / 16.

Therefore, p(g) = 0.1875 or 18.75%.

Therefore, Choosing a green marble from a container holding 4 blue marbles, 3 green marbles, 7 red marbles, and 2 white marbles has a probability of 0.1875 or 18.75%.

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Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.

A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.

Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:

\(P(t) = K / (1 + Ae^{-rt})\)

where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.

Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: \(P(1) = 500\), \(K = 2000\), and \(P(0) = 200\).

\(500 = 2000 / (1 + Ae^{-r(1)})\)

Now, solve for A by dividing both sides by 2000 / (1 + A):

\(1 + A = 4A = 3\)

Substitute the value of A back into the logistic model equation:

\(P(t) = 2000 / (1 + 3e^{-rt})\)

Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):

\(P(1) = 500 = 2000 / (1 + 3e^{-r(1)})\)

\(P(4) = ? = 2000 / (1 + 3e^{-r(4)})\)

Solve the first equation for r:

\(500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e\)

Solve for e using the quadratic formula to get:

e = 0.4274 and e = 1.1713

Let e = 0.4274:

\(1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r\)

Take the natural logarithm of both sides:

\(ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr\)

Use a graphing calculator to solve for r:

\(ln(1 + 0.5746^r) = rln(1.7166) - lnr\);  -0.1568 < r < 0.7534

Solve for r using the second year’s data:

\(2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78\)

Thus, the population will be 852.78 after another three years.

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The way to write the rule is

(x, y) is  (x – 3, y + 5).

A triangle which is on a coordinated plane is translated to the rule

Two lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line.

The original rule x and y coordinates

that are being moved to the left-hand side of the equation by

decreased by 3 units and rise up by 5 units.

Based on the information given,

we can come to the conclusion that other way to

write the given rule is

(x, y) is (x – 3, y + 5).

Hence, the other rule which are given are incorrect.

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(x, y) → (x – 3, y + 5)

The given rule is t–3, 5(x, y). This means that the triangle plane is translated 3 units to the left, and 5 units up. This can be written in another way as (x, y) → (x – 3, y + 5).

The given rule t–3, 5(x, y) states that the triangle is translated 3 units to the left, and 5 units up on the coordinate plane. This can be rewritten as (x, y) → (x – 3, y + 5). This means that for each point (x, y), the new point after the translation will be (x – 3, y + 5). In other words, the x-coordinate of the new point will be three units less than the original x-coordinate, and the y-coordinate of the new point will be five units more than the original y-coordinate. This translation of the triangle can also be visualized as moving the triangle three units to the left and five units up on the coordinate plane.

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Answer:

It is the first one

Hope this helps!

Answer:

I believe it is 4x+10y=200, x+y=38

Explanation:

Applying the perpendicular bisector theorem, the values of the measures are:

y = 12

x = 7

PQ = 29

SR = 32

PT = 18

PR = 36

The perpendicular bisector theorem states that if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the line segment.

In other words, if a point P is the perpendicular bisector of line segment AB, then the distances from P to points A and B are equal. This is true no matter where point P is located on the perpendicular bisector.

Since QT is the perpendicular bisector of PR, we would therefore have the following based on the above stated theorem:

PQ = QR

Substitute:

5y - 31 = 2y + 5

5y - 2y = 31 + 5

3y = 36

3y/3 = 36/3

y = 12

SP = SR

Substitute:

4x + 4 = 7x - 17 [congruent segments]

4x - 7x = -4 - 17

-3x = -21

x = 7

PQ = 5y - 31 = 5(12) - 31 = 29

SR = 7x - 17 = 7(7) - 17 = 32

PT = 6x - 2y = 6(7) - 2(12)

PT = 18

PR = 2(PT)

PR = 2(18)

PR = 36

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Write the first ten terms of a sequence whose first term is -10 and whose common difference is -2.

\( - 10 - ( - 2) = \boxed{ - 8}\)

\( - 8 - ( - 2) = \boxed{ - 6}\)

\( - 6 - ( - 2) = \boxed{ - 4}\)

\( - 4 - ( - 2) = \boxed{ - 2}\)

\( - 2 - ( - 2) = \boxed{0}\)

\(0 - ( - 2) = \boxed{2}\)

\(2 - ( - 2) = \boxed{4}\)

\(4 - ( - 2) = \boxed{6}\)

\(6 - ( - 2) = \boxed{8}\)

-10, -8, -6, -4, -2, 0, 2, 4, 6, 8

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That the equation of the line is y = 7x - 50.

The equation of a line with slope m passing through the point (x1, y1) is given by: y - y1 = m(x - x1).

In this case, the line has a slope of 7 and passes through (8, 6). Therefore, we can plug in the values for m, x1, and y1 into the equation above to find the desired equation.

Substituting in 7 for m, 8 for x1, and 6 for y1, we can rewrite the equation as: y - 6 = 7(x - 8).

Simplifying, we find that the equation of the line is y = 7x - 50.

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Answer:

The surfacearea of the box would 140 length (14 times 10), 125 width (12.5 times 10), and 10 height(1 times 10). Therefore2ﾗ(140ﾗ125 + 140ﾗ10 + 125ﾗ10) = 40,300 centimeters^2

We are given the function;

The input of this function as it is, is x. To evaluate the function at any given output we would simply replace/substitute the value of x with the value provided.

If for example, we are given the function and we have to evaluate its value at f(3), what we will simply do is replace x with two in the function. This is shown below;

Therefore, the value of the function at f(3) is -9.

This is basically the procedure we shall use when evaluating a function at any given output value.

Answer:

6, 2, 6, 2, 6, 6, 1

Step-by-step explanation:

a = 6

b = 2

c = 6

d = 2

e = 6

f = 6

g = 1

Answer: 6, 2, 6, 2, 6, 6, 1

Step-by-step explanation:

Step-by-step explanation:

the formula for the circumference of a circle is

2×pi×r

well, does this look familiar ?

our given circumference is

2×pi×sqrt(2)

so, clearly, r (radius) = sqrt(2).

the area of a circle is

pi×r²

so, for our circle that means

pi×sqrt(2)² = 2pi ft²

Answer:

see below

Step-by-step explanation:

5) 4n + 6 - 2n = (2n + 3)

6)  6m - 8 = 2 + 9m - 1

7)  -v + 5 + 6v = 1 + 5v + 3

8)  2(3b - 4) = 8b - 11

You can rent time on computers at the local copy center for 35 minutes with $25.

To find out how much time you can rent for $25 at the local copy center, follow these steps:

1. Subtract the $10 setup charge from the total amount you have: $25 - $10 = $15.
2. Now you have $15 left for renting time on the computers. Since it costs $2 for every 5 minutes, you need to find out how many 5-minute increments can be covered by $15.
3. Divide the remaining amount by the cost per 5-minute increment: $15 / $2 = 7.5. Since you can't have half an increment, round down to 7.
4. Multiply the number of 5-minute increments by the time per increment: 7 * 5 = 35 minutes.

So, you can rent time on computers at the local copy center for 35 minutes with $25.

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Suppose Z follows the standard normal distribution, then the value of c is approximately 0.83.

For the value of c such that P(-0.69 < Z < c) = 0.7947, we can use the standard normal distribution table or a calculator.

Using a standard normal distribution table, we look for the area corresponding to the probability 0.7947. We find that the closest value is 0.7945, which corresponds to a z-score of approximately 0.83.

Therefore, the value of c is approximately 0.83.

Alternatively, you can use a calculator with the cumulative distribution function (CDF) of the standard normal distribution. By calculating P(Z < c) - P(Z < -0.69) = 0.7947, you can solve for c.

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Answer:

I hope that is useful for you :)

Step-by-step explanation:

\(15 - 1.5y + 7.5 - 7.5 \\ 15 - 1.5y \\ 1.5(10 - y)\)