Your company has a plan that matches your retirement contributions up to 2% of your salary. Your annual salary is $22,000. You are paid bi-weekly (26 times per year). How much should you contribute to the retirement account each pay period to take full advantage of the company match

Answer:

Multiply the original points by the fraction or ratio of the dilution needed

Step-by-step explanation:

I'm less confident in this answer, but Scale factor is the ration between two geometric figures, like 1:2 is for every one unit on one figure is two on the other, so to dilute a figure, you multiply the points by 1/2 to make a smaller figure, or by 2 to get a bigger one. Plot the given answers and you have diluted :) Hope this helps!

she was 111 minutes over what her plan allowed.

Answer:

9,150,625.

Step-by-step explanation:

Any  one of the 55 numbers can be combined with any one of the 55 in the other cylinders.

So the number of different combinations are 55^4

= 9,150,625.

The total number of different combinations that can be made with a four-cylinder combination lock that has 55 numbers on each cylinder is 9,150,625. This is calculated using the multiplication principle of counting.

This question involves the principle of counting or combinatorics in mathematics. Specifically, it relates to the multiplication principle, which says that if event A can occur in m ways, and after it happens, event B can occur in n independent ways, then the total number of ways in which both events can occur is calculated as m times n.

In the case of the four-cylinder combination lock with 55 possible numbers for each cylinder, there are 55 ways to choose a number for the first cylinder. Since repetitions are allowed and each choice is independent, there are also 55 ways to choose a number for the second cylinder, 55 ways for the third cylinder, and 55 ways for the fourth cylinder. Using the multiplication principle, we can find the total number of possible lock combinations by calculating 55 * 55 * 55 * 55 = 9,150,625 possible combinations.

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Answer:

It's the first choice.

Step-by-step explanation:

The common ratio is -6/2 = 18/-6 = -3.

2*(-3)^0 = 2*1 = 2.

2*(-3)^1 = -6

2*(-3)^2 = 18

2*(-3)^3 = -54.

So in summation notation is

∞

∑ 2(-3)^n

n=0

The sum using summation notation is given by:

Summation of two times negative three to the power of n from n equals zero to infinity.

i.e. numerically it is given by:

        [tex]\sum_{n=0}^{\infty} 2(-3)^n[/tex]

The alternating series is given by:

                       [tex]2-6+18-54+........[/tex]

The series could also be written in the form:

[tex]=2+(2\times (-3))+(2\times (-3)\times (-3))+(2\times (-3)\times (-3)\times (-3))+....\\\\i.e.\\\\=2\times (-3)^0+2\times (-3)^1+2\times (-3)^2+2\times (-3)^3+.....\\\\i.e.\\\\=\sum_{n=0}^{\infty} 2(-3)^n[/tex]

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

Look at the picture.

The graph of F(x) shifted 1 unit to the right and 3 units down.

Therefore the equation of the function G(x) is

[tex]G(x)=(x-1)^2-3[/tex]

➷ 25,000 - 2500 = 22500

22500 + 10,000 = 32,500

The correct answer would be option D. $32,500

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

Step-by-step explanation:

I would have to go with D. The 25,000 is what you start with minus the 2,500 she withdrew which would leave her at 22,500. She then receives 10,000 for the business leaving her with 32,500

Answer:

0 degrees

Step-by-step explanation:

when it is hour 12 and 0 minutes, the hour and minute hand will be on top of each other, so therefore it does not form an angle

Answer:

The speeds are 34 mph for the slower car and 68 mph for the faster car.

Step-by-step explanation:

speed = distance/time

Using s for speed, d for distance, and t for time, we have the equation for speed:

s = d/t

Solve for distance, d, by multiplying both sides by t.

d = st

Now we use the given information.

Speed of slower car: s

Speed of faster car: 2s

Distance traveled by faster car: d

Distance traveled by slower car: d - 204

time traveled by faster car = time traveled by slower car = 6

Distance equation for faster car:

d = st

d = 2s * 6

d = 12s     <---- equation 1

Distance equation for slower car:

d = st

d - 204 = s * 6

d - 204 = 6s

d = 6s + 204    <----- equation 2

Now, using equations 1 and 2, we have a system of two equations in two unknowns.

d = 12s

d = 6s + 204

Since the first equation is already solved for d, we can use the substitution method. Substitute 12s for d in the second equation:

12s = 6s + 204

6s = 204

s = 34

The speed of the slower car is 34 mph.

The speed of the faster car is

2s = 2(34) = 68

The speed of the faster care is 68 mph.

Two cars started moving simultaneously where one was twice as fast as the other. After setting x as the speed of the slower car, the equations showed the slower car traveled at 34 mph and the faster car at 68 mph, based on being 204 miles apart after 6 hours.

Two cars started moving at the same time and direction where one car's speed was twice as fast as the other. After 6 hours, they were 204 miles apart. To solve for the speed of each car, let's set up an equation where the speed of the slower car is x miles per hour and the faster car is 2x miles per hour.

The distance covered by each car after 6 hours would then be:

Since the cars are 204 miles apart after 6 hours, the equation can be set up as:

12x - 6x = 204

So the distance difference is:

6x = 204

Divide both sides by 6 to find the speed of the slower car:

x = 34

Therefore, the slower car travels at 34 mph and the faster car travels at 68 mph (twice the speed of the slow car).

Answer:

Step-by-step explanation:

z1 = -3

z2 = 5i

z1·z2 = (-3)(5i) = -15i = 0 + (-15)i

Then the real and imaginary parts are a = 0, b = -15.

Answer:   7

Step-by-step explanation:

[tex]\dfrac{\overline{CD}+\overline{A F}}{2}=\overline{BE}\\\\\\\dfrac{(18)+(6x-12)}{2}=2x+10\\\\\\(18)+(6x-12)=2(2x+10)\\\\\\6x +6 = 4x +20\\\\2x+6=20\\\\2x=14\\\\\large \boxed{x=7}[/tex]

Answer:

9.09%

Step-by-step explanation:

You over estimated by 2 feet.  Find out how much 2 feet of 22 is by dividing 2 by 22...

2/22 = 0.090909090909

To convert a decimal to a percent, multiply the decimal by 100%

0.0909090909(100%) = 9.0909090909% or 9.09%

Final answer:

The percent error in the student's estimate of the board's length is approximately 9.09%. The exercise demonstrates the value of precise calculations over rough estimates, although some thoughtful guesses can be quite close.

Explanation:

To find the percent error of the student's estimate, we'll use the following formula:

Percent Error = |(Actual Value - Estimated Value) / Actual Value| × 100%

The actual length of the board is 22 feet, and the estimated length is 24 feet. So we can calculate the percent error as follows:

|(22 - 24) / 22| × 100% = |(-2) / 22| × 100% = (2 / 22) × 100% ≈ 9.09%

The percent error in the student's estimate is approximately 9.09%. This calculation underscores the importance of making careful calculations rather than relying on rough guesstimates, which can lead to significant errors in certain situations. However, it can also show that even guesses made with some thought, like the example of 10 feet versus an actual of 12 feet, can sometimes be surprisingly close.

Answer:

  2

Step-by-step explanation:

The rule for secants from an external point is that the product of the near and far distance to the intersection with the circle is a constant.

  EA·EB = EC·ED

  (x+12)·(x+1) = (x+4)·(x+5)

  x^2 +13x +12 = x^2 +9x +20 . . . . . . eliminate parentheses

  4x = 8 . . . . . . . . . . . . subtract x^2+9x+12 from both sides

  x = 2 . . . . . . . . . . . . . divide by 4

The value of x is 2.

Answer:

k = -2

Step-by-step explanation:

x     -1   0   2     5

f(x)  2   0  -4  -10

ƒ(x) = kx

Substitute a pair of values for x and ƒ(x)

-10 = k×5

Divide each side by 5

k = -2

The constant of variation k = -2.

Answer:

l = 4, w = 14

Step-by-step explanation:

[tex]A_r = 56 = l * w[/tex]

l - length;

w - width;

l = w - 10;

We substitute the 'l' using the previous formula =>

[tex][tex]A_r = (w -10) \cdot w = w^2 - 10w = 56 =>\\w^2 - 10w - 56 = 0\\[/tex]

By the quadratic formula we solve for 'w':(we will use the positive value, because we're talking about lengths of planes in a Euclidean space)

[tex]w = \frac{10 + \sqrt{100+224} }{2} =  \frac{10+18}{2} = \frac{28}{2} = 14[/tex]

l = w - 10 = 14 -10 = 4

Use the rule to change the base

[tex]\log_a(b) = \dfrac{\log_c(b)}{\log_c(a)}[/tex]

To express both logarithms in terms of the natural logarithm (for example, any common base would be fine:

[tex]\log_c(x) = \dfrac{\ln(x)}{\ln(c)},\quad \log_d(x) = \dfrac{\ln(x)}{\ln(d)}[/tex]

Since the natural logarithm is an increasing function, we have

[tex]c<d\implies \ln(c)>\ln(d)[/tex]

which implies

[tex]\dfrac{\ln(x)}{\ln(c)}=\log_c(x)<\log_d(x)=\dfrac{\ln(x)}{\ln(d)}[/tex]

Explanation:

For each exponent inside the radical, you will divide it over the root index. The root index is the small number to the left and above the radical symbol. So the root index is 6 in this case.

Divide each exponent over 6

3/6 = 1/2 is the final exponent for x

18/6 = 3 is the final exponent for y

which is how we get to x^(1/2)*y^3

--------------------

note: x^(1/2) is the same as the square root of x

[tex]x^{1/2} = \sqrt{x}[/tex]

The more general rule is

[tex]x^{m/n} = \sqrt[n]{x^m}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

it is B

Step-by-step explanation:

1st of all, this makes my brain hurt

2nd of all, which one was the first marble?

Answer:

35/12 cups

Step-by-step explanation:

Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.

To find the total number of cups of fruit salad Brett's recipe will make, we add the amounts of each fruit together:

1. Apples: 1 1/2 cups

2. Oranges: 3/4 cup

3. Grapes: 2/3 cup

To add these fractions, we need a common denominator. The least common denominator (LCD) of 2, 4, and 3 is 12.

[tex]1. Apples: \(1 \frac{1}{2} = \frac{3}{2}\) cups[/tex]

[tex]2. Oranges: \(\frac{3}{4}\) cup[/tex]

[tex]3. Grapes: \(\frac{2}{3}\) cup[/tex]

Now, we convert each fraction to have a denominator of 12:

[tex]1. Apples: \(\frac{3}{2} \times \frac{6}{6} = \frac{9}{6}\) cups[/tex]

[tex]2. Oranges: \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\) cups[/tex]

[tex]3. Grapes: \(\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}\) cups[/tex]

Now, we add these amounts:

[tex]\(\frac{9}{6} + \frac{9}{12} + \frac{8}{12} = \frac{18}{12} + \frac{9}{12} + \frac{8}{12} = \frac{35}{12}\) cups[/tex]

So, Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.

(132°-x)+(6x-12°) = 180°(Co-interior Angles)

132°-12°-x+6x = 180°

120° + 5x = 180°

5x = 180° - 120°

5x = 60°

x = 12°

(132°-x)+(6y+18°) = 180°(Co-interior Angles)

132°-x+6y+18°=180°

132°-12°+18°+6y=180°

138°+6y=180°

6y=180°-138°

6y=42°

y = 7°

HOPE THIS WILL HELP YOU

Answer:

B

Step-by-step explanation:

Since a quadrilateral has an angle sum of 360 degrees you just add the three angle measures together and subtract them from 360 leaving you with 108.

The angle which is outside is supplementary which means it adds to 180 degrees. All you have to do here is subtract 71 from 180 which gives you 109.

It’s B) x=108,y=109

Es la respuesta

Answer:

g(-12) = -7

Step-by-step explanation:

Answer: g(-12)=-7

Step-by-step explanation:

g(x)= 3/4x+2

g(-12)= 3/4(-12)+2

g(-12)=-9+2

g(-12)=-7

Total Outcomes = {1,2,3,4,5,5}

Less than 5 = {1,2,3,4}

P(less than 5) = 4/6 = 2/3

Answer:

Step-by-step explanation:

Since n < 30, we will find the t-score and compare that to the t-score of a significance level of 1%.    

Since they are asking if the difference is significant, we will have a two tailed test, with degree of freedom being 22, so our critical values are

t < -2.704 and t > 2.704

Our t-value for this situation is

t = ([µ + 5.8] - µ)/(1.4/√23)

It's µ + 5.8 because the problem told us that their levels are 5.8 mm higher than the average, so it's the average, plus 5.8

Simplify the equation...

t = 5.8/(1.4/√23)

t = 19.868

19.868 > 2.704, the evidence supports that there is significant difference between the sample and the population

There is a significant difference between the sample and the population.

A standard deviation (or σ) indicates how dispersed the data is in relation to the mean.

The t-distribution indicates the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

A t-score is the number of standard deviations away from the mean of the t-distribution.

Here the degree of freedom is 22 and so the critical values are:

t < -2.704 and t > 2.704

∴ The t-value for this situation is

t = ([µ + 5.8] - µ)/(1.4/√23)

⇒ t = 5.8/(1.4/√23)

⇒t = 19.868

So, we can say that there is significant difference between the sample and the population.

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Answer:

The answer is vertical translation down 9 units  ⇒ answer (d)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) - k

* Lets study the problem

- The basic function is y = csc(x)

∵ y = csc(x) - 9

- That means the function translated vertically 9 units down

* Vertical translation 9 units down

* Look to the graph

-The red graph is y = csc(x)

- The green graph is y = csc(x) - 9

Answer:

A line graph

Step-by-step explanation:

A line graph will be the best option because it can show the exact height based on time as a data point. Connecting each data point will then reveal the trend in how the sapling grows and average growth rate among other information can be found.

Final answer:

A line graph is the best choice for displaying the continuous growth of a sapling tree over a period of several weeks, as it shows trends over time effectively.

Explanation:

The best type of graph for showing the height of a sapling tree over several weeks is a line graph. A line graph is designed to show trends over time and is particularly useful when you want to display changes in a variable continuously, such as the growth of a tree's height. The line graph will clearly depict the gradual increase in height with each passing week, allowing for an easy visual interpretation of the data. Other graphs such as a bar graph, circle graph (or pie chart), or a histogram are not as suitable for representing data over time in the same continuous and clear manner as a line graph.

Answer:

[tex]\large\boxed{x=3\ and\ y=2\to(3,\ 2)}[/tex]

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}x+2y=7\\x-2y=-1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=6\qquad\text{ivide both sides by 2}\\.\qquad x=3\\\\\text{Put the value of x to the first equation:}\\\\3+2y=7\qquad\text{subtract 3 from both sides}\\\\2y=4\qquad\text{divide both side by 2}\\\\y=2[/tex]

The solution to the given system of linear equations is (3, 2), which is found by eliminating y and solving for x, then substituting back to find y.

Given the system of equations:

x + 2y = 7
x - 2y = -1

To find the solution to the system, we can add the two equations to eliminate y:

(x + 2y) + (x - 2y) = 7 + (-1)
2x = 6
x = 3

Substituting x = 3 into the first equation:

3 + 2y = 7
2y = 4
y = 2

So, the solution to the system of equations is (3, 2). None of the other provided options, {(-8, -12)} or {(-4, 6)}, match this solution.

Let's start with the formula for the area of a triangle

[tex] \frac{1}{2} bh[/tex]

And for the first one, insert the numbers

[tex] \frac{1}{2} 3 \times 6[/tex]

To make this easier, 3×6=18, 1/2 of 18 is 9, so the answer is 9 square feet. There's all you need to complete the rest, good luck .

Answer:

5π/2 it is not a solution for the equation 2sin²x - sinx - 1 = 0

Step-by-step explanation:

∵ 2sin²x - sin x - 1 = 0

* Lets factorize it as a quadratic equation

∴ ( 2sinx + 1)(sinx - 1) = 0

∴ 2sinx + 1 = 0 ⇒ 2sinx = -1 ⇒ sinx = -1/2

* ∵ The value of sinx is -ve

  ∴ x is in the 3rd or 4th quadrant ⇒ According to ASTC Rule

- ASTC Rule:  1st all +ve , 2nd sin only +ve ,

                      3rd tan only +ve , 4th cos only +ve

* Let sinα = 1/2 where α is an acute angle

∴ α = π/6

∵ x is in 3rd or 4th quadrant

∴ x = π + α = π + π/6 = 7π/6 or

∴ x = 2π - π/6 = 11π/6

OR

∴ sinx - 1 = 0 ⇒ sinx = 1

∴ x = π/2

∴ ALL values of x are π/2 , 7π/2 , 11π/2 if 0 ≤ x ≤ 2π

∴ 5π/2 it is not a solution for the given equation

Answer:

5pi/2 is a solution for the equation 2sin²x -sin x -1=0

Step-by-step explanation:

We need to check 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.

Substituting 5pi/2 in equation

       [tex]2sin^2x-sin x-1=2sin^2\left (\frac{5\pi}{2} \right )-sin\left (\frac{5\pi}{2} \right )-1\\\\=2sin^2\left (2\pi +\frac{\pi}{2} \right )-sin\left (2\pi +\frac{\pi}{2} \right )-1\\\\=2sin^2\left (\frac{\pi}{2} \right )-sin\left (\frac{\pi}{2} \right )-1\\\\=2\times 1-1-1=0[/tex]

So 5pi/2 is a solution for the equation 2sin²x -sin x -1=0.

Answer:

(-2, 0)

Step-by-step explanation:

Because both equations are to find Y, set them equal to each other to solve:

3x+6 = x+2

Subtract x from both sides:

2x + 6 = 2

Subtract 6 from both sides:

2x = -4

Divide both sides by 2:

x = -4 /2

x = -2

Now you have a value for x, replace X with -2 in one of the equations and solve for y:

y = 3x +6 = 3(-2) +6 = -6 +6 = 0

X = -2 and Y = 0

(-2,0)