If John has pairs of red, orange, yellow, blue, green, white and black socks, how many orders can he wear them in over 7 days? Repetition is allowed because John is alright with wearing dirty socks.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]

The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.

This can be achieved using the future value and present value formulas or factors.

We can also use an online finance calculator, as follows:

Future value = $5,000

Investment period = 3 years

Annual compound interest = 5%

N (# of periods) = 3 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $5,000 ($4,531.56 + $468.44)

Results:

PMT = $1,510.52

Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)

Total Interest = $468.44

Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

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Answer:

31 3/4 %

Step-by-step explanation:

There are 100 squares so each square is a percent.  There at 31 full squares colored and it looks like 3/4 of 1 square.

The critical points of the function graphed are given as follows:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In a graph, they are turning points, and are classified as follows:

Looking at the graph, the turning points are approximately:

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The area of the triangle which is formed as described is; 60.

According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).

It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.

Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.

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From the line theorems explained below and when we apply it to the given image, we have; X║Y, A║B, Z ⊥ A

The perpendicular transversal theorem states that in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Now, since we are told that Line X is perpendicular to Line A, then it means that Line X is also perpendicular to line B.

The inverse of perpendicular transversal theorem states that if there are two perpendicular lines to a straight line, they're parallel to each other. Thus, it means that Line X is parallel to Line Y and similarly, line A is parallel to Line B.

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The ordered pair (2,-1) is a solution the inequality.

Given the inequality is 3x-4y<12.

An inequality is a statement that compares two quantities and claims that one is greater or less than the other (the equation may also be included). These inequalities are linear if the variables are only linear.

By substituting each of the given option in the given inequality we will check which ordered pair satisfy the inequality.

1. (4,0)

Here x=4 and y=0

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(0)<12

12<12

This is not true

2. (0,-3)

Here x=3 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(0)-4(-3)<12

12<12

This is not true.

3. (2,-1)

Here x=2 and y=-1

Substitute this in the inequality 3x-4y<12, we get

3(2)-4(-1)<12

6+4<12

10<12

This is true.

4. (4,-3)

Here x=4 and y=-3

Substitute this in the inequality 3x-4y<12, we get

3(4)-4(-3)<12

12+12<12

24<12

This is not true.

Hence, the ordered pair that satisfy the given inequality 3x-4y<12 is (2,-1).

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Answer:

Vertex: (0,0)

Left 2 points: (-1,1) , (-2,4)

Right 2 points: (1,1) , (2,4)

Step-by-step explanation:

Answer:

[tex]x^4-20x^3 +175x^2 -750x+1250[/tex]

Step-by-step explanation:

By the conjugate root theorem, 5+5i is also a root.

[tex]f(x)=a(x-5)^2 (x-5-5i)(x-5+5i) \\ \\

= a(x^2 - 10x+25)((x-5)^2 - (5i)^2) \\ \\

= a(x^2 - 10x+25)(x^2 - 10x+25+25) \\ \\

= a(x^2-10x+25)(x^2-10x+50) \\ \\

= a(x^4- 10x^3 + 50x^2 - 10x^3 + 100x^2 - 500x + 25x^2 - 250x+1250) \\ \\

= a(x^4-20x^3 +175x^2 -750x+1250) \\ \\ [/tex]

Answer: 5

Step-by-step explanation: 2 + 5 = 7,  7 + 5 = 12,  12 + 5 = 17,  17 + 5 = 22

The steps you have are correct. I'll fill in the gap between step 2 and step 3.

[tex]0.4245 = \frac{2.5}{\text{x}}\\\\0.4245\text{x} = 2.5\\\\\text{x} = \frac{2.5}{0.4245}\\\\\text{x} = 5.8892815\\\\\text{x} = 5.9\\\\[/tex]

I multiplied both sides by x, then divided both sides by 0.4245 to isolate the variable.

With the exception of 2.5, every other decimal value mentioned is approximate.

Answer:

Step-by-step explanation:

Okay, so first of all, when a slope is negative, the line goes down from left to right, not up from left to right. Then, plot the Y intercept as -2. Finally, either go up 2 and left 3 or down 2 and right 3.

Answer:

Graph attached.

Step-by-step explanation:

As we have been given the slope and the y-intercept, we can create a linear equation using the slope-intercept form.

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Substitute the given values into the formula to create an equation for the line:

[tex]\implies y=-\dfrac{2}{3}x-2[/tex]

Now we have an equation for the line, find at least two points on the line by inputting values of x into the found equation:

[tex]x=0 \implies y=-\dfrac{2}{3}(0)-2=-2 \implies (0,-2)[/tex]

[tex]x=3 \implies y=-\dfrac{2}{3}(3)-2=-4 \implies (3,-4)[/tex]

[tex]x=-6 \implies y=-\dfrac{2}{3}(-6)-2=2 \implies (-6,2)[/tex]

Plot the found points and draw a straight line through them (see attachment).

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The area of the equilateral triangle is 110.9 cm

area of a triangle = 1 / 2 bh

where

Therefore,

tan 60 = opposite / adjacent

tan 60 = 8√3 / x

x =  8√3 / √3

x = 8

hence,

b = 8 + 8 = 16

Therefore,

area of a triangle =  1 / 2 × 16 × 8√3

area of a triangle = 64√3

area of a triangle = 110.851251684

area of a triangle = 110.9 cm

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Answer:

0.4

Step-by-step explanation:

4+3+2+1 =10

5m÷10 =0.5

(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)

2 : 1.5 : 1 : 0.5

longest piece= 2 (2m)

4+1= 5

2÷5= 0.4

(0.4×4=1.6, 0.4×1=0.4)

1.6 : 0.4

so the shortest piece is 0.4!

You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.

The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.

let

x + y = 54

4x + 3y = 200

From equation (1)

x = 54 - y

4x + 3y = 200

4(54 - y) + 3y = 200

216 - 4y + 3y = 200

216 - y = 200

- y = 200 - 216

-y = -16

y = 16

x + y = 54

x + 16 = 54

x = 54 - 16

x = 38

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When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

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For the circular cover we have:

A) The area is 379.94 ft²

B) The length of the rope must be 68.2 ft

Remember that the area of a circle of radius R is given by the formula:

[tex]A = pi*R^2[/tex]

Where pi = 3.14

In this case, the diameter of the pool is 20ft, then the radius is:

R = 20ft/2 = 10ft

And it must extend 12 inches beyond, then the radius of the cover must be:

R = 10ft + 12in

Now, we know that 1ft = 12 in, then we can rewrite the radius as:

R = 10ft +1ft = 11ft

Then the area of the cover is:

[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]

B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.

Remember that the circumference of a circle of radius R is:

[tex]C = 2*pi*R[/tex]

Then the length of the rope will be:

[tex]C = 2*3.14*11ft = 68.2ft[/tex]

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Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°

Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).

Measure of one of the intercepted arcs = 250°

The second intercepted arc = 360 - 250 = 110°

Positive difference of the intercepted arcs = 250 - 110 = 140°

Measure of angle A = 1/2(140)

Measure of angle A = 70°

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Answer:

the answer is 70. hope this helps <3

Step-by-step explanation:

a. [tex]I = 6. 1[/tex] × [tex]10^-4[/tex] A

b. [tex]I = 2. 6[/tex] × [tex]10^-3[/tex] A

c. [tex]I = 0. 04[/tex] A

The LED which would glow brightest is LED C with the greatest current and voltage

The LED which would be the most dim is LED B with low voltage and consequently low current.

The formula for finding current

I = V/R

Where v = voltage

R = resistance

A. V = 12V

R = 4. 7 + 15 = 19. 7 kΩ = 19700 Ω in series

[tex]I = \frac{12}{19700}[/tex]

[tex]I = 6. 1[/tex] × [tex]10^-4[/tex] A

B. V = 9V

R = 4. 7 + 1 = 4. 7 kΩ = 4700Ω in series

[tex]I = \frac{12}{4700}[/tex]

[tex]I = 2. 6[/tex] × [tex]10^-3[/tex] A

C.  V=  12V

1/R = [tex]\frac{1}{750} + \frac{1}{1200} + \frac{1}{950 }[/tex] = [tex]3. 22[/tex] × [tex]10^-3[/tex]

R = [tex]\frac{1}{3. 22 * 10 ^-3}[/tex] = 310. 56 Ω

[tex]I = \frac{12}{310. 56}[/tex]

[tex]I = 0. 04[/tex] A

It is important to note that the brightness of a bulb depends on both current and voltage depending on whether the bulb it is in parallel or series.

The LED which would glow brightest is LED C with the greatest current and voltage

The LED which would be the most dim is LED B with low voltage and consequently low current.

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Claire's measuring stick would make a more precise measurement

The given parameters are:

Claire = 1 cm

Martin = 0.1 cm

The 0.1 cm marking would make a more accurate measurement.

This is so because the length of a slug would most likely be in decimal centimeters

However, this doesn't translate to a precise measurement.

Hence, Claire's measuring stick would make a more precise measurement

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The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point (x, y) is rotated 270° counter-clockwise about the origin, the new point is (y, -x)

The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]

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Answer: graph c

Hope I was able to help

The chart that best represents the student results from a class assignment is B. Histogram or bar graph.

Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.

The frequencies are depicted on the Y-axis (vertical axis).

The X-axis (horizontal axis) represents the measured variable.

A. Frequency table

B. Histogram or bar graph

C. Pareto chart

D. Pictogram

E. Pie chart

Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.

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The area of the enclosed figure is 4 square units.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

The triangle's area can be described as,

Area = 1/2 x base x height.

To find the area of the enclosed figure, we need to first plot the given points and then determine the shape of the figure.

Plotting the points A, B, and C on a coordinate grid, we get:

The image is given below.

Connecting points A, B, and C, we can see that the figure formed is a right triangle with legs of lengths 4 and 2.

Therefore, the area of the enclosed figure is:

Area = (1/2) x base x height

= (1/2) x 4 x 2

= 4 square units

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The complete question:

Maria plots the following points on a coordinate grid. Then, she connects each plotted point to the previous one in the order shown to form a figure. What is the area, in square units, of the enclosed figure?

Point A (1, 3)

Point B  (5, 7)

Point C(5, 3)

Point A (1, 3)

The coordinates of A exist (11, 0).

Let, the point A (-5, -2) exists reflected over the line y = -1, and then stand reflected over the line x = 3.

The distance between the y value exists -1 - (-2)= 1

We move 1 unit beyond the line y = -1

After reflection over the line y = -1 the coordinates of A becomes (-5, 1-1) is (-5, 0)

It exists reflected over the line x = 3

The distance between -5 and 3 exists 3 - (-5) = 8

We move 8 units out from the line x = 3

The Point (-5, 0) becomes (3 + 8, 0) exists (11, 0).

Therefore, the coordinates of A exist (11, 0).

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The complete question:

The point A (-5, -2) is reflected over the line y = -1, and then is reflected over the line x = 3. What are the coordinates of A.

Using the probability concept, the number of blue balls you need to add is:

D) 5.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A probability of 0.5 is reached if the number of red balls is the same as the number of blue balls. Current the difference is of 7 - 2 = 5, hence 5 blue balls must be added.

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Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

The answer is 14.

First, we need to find X using the first statement.

Now, we have to substitute this in the required expression.

Answer:

2635

Step-by-step explanation:

the first two stand for 1000

so

2000

is the first part

the second numeral stands for 100

there are 6 of them

so

600

is the second part

the third numeral stands for 10 and there are 3 of them

thus

30

is the third part

there are 5 lines so the last part is 5

so your answer is 2635