Mike invests $1,778 in a retirement
account with a fixed annual interest rate of
3% compounded 2 times
per year.
What
will the account balance be after 15 years?

Answer:

an estimate would be 2000/4 so it would be 500

Step-by-step explanation:

hope this helped <3

Answer:

\(R = \$903.125\)

Step-by-step explanation:

Given

\(Selling\ Price = \$289\)

\(Rate = 32\%\)

Required

Determine the regular price (R)

From the question, we understand that:

\(R * 32\% = \$289\)

So, we have:

\(R * 0.32 = \$289\)

\(R = \frac{\$289}{0.32}\)

\(R = \$903.125\)

Hence, the regular price is $903.125

Answer:

x² - 7x + 6

Step-by-step explanation:

(x - 6)(x - 1)

each term in the second factor is multiplied by each term in the first factor , that is

x(x - 1) - 6(x - 1) ← distribute both parenthesis

= x² - x - 6x + 6 ← collect like terms

= x² - 7x + 6

Answer:

We have 4 triangles with base 3 and height 4 and a square with side length 3 so:

Triangles:

The area for a triangle is calculated by \(\frac{bh}{2}\) where b is the base and h is the height so we have \(\frac{12}{2}\cdot 4\) so we have a total area of 24.

[b]Square:[/b]

The area of a square is calculated by \(s^{2}\) where s is the side length so we have the area is 9.

Now we put them together for the surface area so we get 24 + 9 = \(\boxed{33}\)

Hope this helped!

(sorry for taking so long, TeX takes so long to type out(Math typesetting software))

Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

The coordinates of the final point after the reflections across the x-axis twice is (6, -4)

Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.

So reflecting (6,-4) across the x-axis gives us the point (6,4).

Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.

So reflecting (6,4) across the x-axis gives us the point (6,-4).

Therefore, the final point after both reflections is (6, -4).

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Answer:

The polynomial is:

\(p(x) = x^3 + 2x^2 - 3x + 20\)

Step-by-step explanation:

A third degree polynomial can be written in function of it's zeros \(x_1, x_2, x_3\) the following way:

\(p(x) = a(x - x_1)(x - x_2)(x - x_3)\)

In which a is the leading coefficient.

Integer coefficient that have zeros: 1+2i, 1-2i, -4

Leading coefficient: 1

So

\(p(x) = 1(x - (1+2i))(x - (1-2i))(x - (-4))\)

\(p(x) = (x - 1 -2i)(x - 1 + 2i)(x + 4)\)

\(p(x) = ((x-1)^2 - (2i)^2)(x + 4)\)

\(p(x) = (x^2 - 2x + 1 - 4i^2)(x + 4)\)

Since \(i^2 = -1\)

\(p(x) = (x^2 - 2x + 1 + 4)(x + 4)\)

\(p(x) = (x^2 - 2x + 5)(x + 4)\)

\(p(x) = x^3 + 4x^2 - 2x^2 - 8x + 5x + 20\)

\(p(x) = x^3 + 2x^2 - 3x + 20\)

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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According to the given data the equation of the new function is (D) f(x) = 2x - 4.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.

If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:

f(x) = h(x) + 5

Substituting the definition of h(x) into this equation, we get:

f(x) = 2x - 9 + 5

Simplifying, we have:

f(x) = 2x - 4

Therefore, the equation of the new function is (D) f(x) = 2x - 4.

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Answer:

32 ft tall

Step-by-step explanation:

24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32

Answer:

\(f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.\)

Step-by-step explanation:

So if we first graph the given equation, we'll see the graph I've attached below.

Remember that piecewise functions are functions that change based on the circumstances. I know that sounds super confusing, but it's actually really simple!

In this case, for example, we see the line increasing from -∞ to \(0\), and then suddenly going downwards and decreasing. That's a good spot for us to notice because that indicates a change. We notice that the function looks different when \(x<0\) or \(x>0\). If you break the function into those two parts, you see that they are just linear equations, but they're only visible when x is either greater than or less than 0.

Now that we notice this pattern, we can find the equation of the lines for both lines.

The points (-3,-8) and (-1,-2) are points on the first line, the one that increases (on the left). We can use those points to find the slope of the first line. Remember the slope equation:

\(m=\frac{y2-y1}{x2-x1}\)

Plug in your points:

\(m=\frac{-2-(-8)}{-1-(-3)}\)

\(m=\frac{6}{2}\)

\(m=3\)

So, the slope of the first line is 3. The y-intercept, looking at the graph, is 1. The equation of the first line is \(y=3x+1\). We'll need this later.

Let's do the same thing for the second line. Just looking at the graph, we can see that this is the same exact line, just with a negative slope. So, the equation for the second line is \(y=-3x+1\).

So now we can set up a piecewise function.

\(f(x)\left \{ {{3x+1} \atop {-3x+1}} \right.\)

The two functions in the bracket are the two different functions used in this graph. Now we need to figure out where each function is effective. Well, they share a y-intercept. Remember that a true function cannot have two points with the same x value. So the first function is effective to the left of x=0, while the second is effective to the right of x=0. In other words, when \(x\leq 0\), \(f(x)=3x+1\). But, when \(x>0\), \(f(x)=-3x+1\). Now our piecewise function looks like this:

\(f(x)\left \{ {{3x+1 if x\leq 0} \atop {-3x+1 if x>0}} \right.\)

And that is our piecewise function for the original function.

I know this is confusing, so please let me know if you have any questions! I hope this helps!

Answer:

The answer would be, you have 3 hours to use the canoe

Step-by-step explanation:

Improper fractions have a numerator that is larger than the denominator

1 = 6/6

 so  1  1/6  = 7/6

Answer:

C ( 7, -3 )

Step-by-step explanation:

Question:

which point is 8 units away from ( 7, 5 ) ?

Choices:

A : (0,-3 )B (15,13) C ( 7, -3 ) D ( 1, 5 )

Solution:

(7, 5) and (7, 3) have the same x-coordinate, 7.

They are both on a vertical line that passes through point (7, 0).

(7, 5) is 5 units above the x-axis.

(7, -3) is 3 units below the x-axis.

5 + 3 = 8

(7, 5) and (7, 3) are 8 units apart.

Answer: C ( 7, -3 )

Answer:

\(10^3=1,000\)

Step-by-step explanation:

The expression 10=1,000 is obviously false, but we can make it true by rewriting it with an exponent.

Note that 1,000=10*10*10

Or, equivalently:

\(1,000=10^3\)

Thus, if we modify the original false expression and add an exponent 3 to the base 10, then it would be true:

Original:

10=1,000 => false

Rewritten true:

\(\boxed{10^3=1,000}\)

Answer:

\(\sqrt[\\]{40}\)

Step-by-step explanation:

\(2^{2} =4\\6^{2} =36\\4+36=40\)

The measure of the angles in bold are as follows;

25. 90° and 90°

26. 60° and 60°

When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.

Therefore,

x + 96 + x + 96 = 180

2x  = 180 - 192

2x = -12

x = -6

Hence, the angles are 90 and 90 degrees.

6x = 5x + 10(corresponding angles)

6x - 5x = 10

x = 10

Therefore, the angles are 60 degrees and 60 degrees

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Answer

a. (4, 3)

Step-by-step explanation

The translation of a point (x, y) a units to the right and b units up transforms the point into (x + a, y + b).

Considering point B(2, 5), translating it 4 units to the right and 3 units up, we get:

B(2, 5) → (2+4, 5+3) → B'(6, 8)

The translation of a point (x, y) c units to the left and d units down transforms the point into (x - c, y - d).

Considering point B'(6, 8), translating it 2 units to the left and 5 units down, we get:

B'(6, 8) → (6 - 2, 8 - 5) → B''(4, 3)

Answer: The answer would be (4,3)

Step-by-step explanation: because if you started with (2,5), which would be (x,y) x goes left and right, and y goes up and down, and the questions says that you have to go 4 to the right and 3 up, then add 4 to 2, which is 6, and 3 to 5, which is 8, so now you have the point (6,8), then the second translation would be 2 to the left, and down 5, this is negative so you subtract this time, so subtract 2 from 6, which is 4, and 5 from 8, which is 3, so your final answer is (4,3).

Answer:

less than -4

Step-by-step explanation:

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Answer:

The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)

I hope this helps you!

Check the picture below.

\(3x+5=\cfrac{260-100}{2}\implies 6x+10=160\implies 6x=150 \\\\\\ x=\cfrac{150}{6}\implies x=25\hspace{9em}\stackrel{\measuredangle ABC}{3(25)+5}\implies 80^o\)

The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.

1. We have a triangle with two known side lengths: 43 and 67 units.

2. The angle included between these sides measures 27 degrees.

3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.

4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).

5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.

6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.

7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.

8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.

9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.

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A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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Answer:

9*9 or 9 with the 2 at the top

Step-by-step explanation:

The equation with a solution of x = -3 is7x-(x - 9) = 2x - 3

From the question, we have the following parameters that can be used in our computation:

7x-(x - 9) = 2x -

Rewrite as

7x-(x - 9) = 2x - [ ]

Replace the blank with y

So, we have

7x-(x - 9) = 2x - y

The solution is x = -3

So, we have

7(-3) - (-3 - 9) = 2(-3) - y

Evaluate the expression

-9 = -6 - y

Make y the subject

y = 9 - 6

Evaluate

y = 3

Hence, the equation is 7x-(x - 9) = 2x - 3

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In the experiment, the response variable is the dependent variable, or the measured variable.

Reasons:

The study Leonard conducts is a study to determine if the number of

hawks located in the park affects the number of squirrels in the park.

The response variable is the variable of the experimental result, which is

the dependent or output variable obtained by manipulating the input

variable.

In the experiment conducted by Leonard, the variable that is being

manipulated, which is the input variable is the number of hawks in the park

The variable that is being measured, which is the output variable or the

response variable, is; B. the number squirrels in the park.

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