Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.

Answer:

C) 3.2

Step-by-step explanation:

[tex]\text{Mean}=\frac{2(0)+1(1)+3(2)+6(3)+2(4)+3(5)+2(6)}{19}\approx3.2[/tex]

Answer:

2.7

Step-by-step explanation:

the hockey score is 2.7

Answer:

(a) 27°

(b) 17.9m

Step-by-step explanation:

According to the attachment

⠀

let AB be the ladder

BC be the distance between the ladder and wall

⠀

(a) We have to find ∠A by trigonometry formula

[tex] \sf \sin A = \frac{perpendicular}{hypotenuse} [/tex]

Here angle A is facing BC so it is perpendicular

and AB is the longest side so it is hypotenuse

[tex] \sf \implies \sin A = \frac{BC}{AB} \\ \\ \\ \sf \implies \sin A = \frac{9}{20} \\ \\ \\ \sf \implies \sin A = 0.45 \\ \\ \\ \sf \implies \sin A = \sin27{ \degree} \\ \\ \\ \sf \purple {A = 27{ \degree}}[/tex]

(b)

AC is the distance from the upper end of the ladder to ground

we will find it by Pythagoras theorem

[tex] \sf {hypotenuse}^{2} = {perpendicular}^{2} + {base}^{2} \\ \\ \\ \sf \implies {AB}^{2} = {BC}^{2} + {AC}^{2} \\ \\ \\ \sf \implies {20}^{2} = {9}^{2} + {AC}^{2} \\ \\ \\ \sf \implies 400 = 81 + {AC}^{2} \\ \\ \\ \sf \implies 400 - 81 = {AC}^{2} \\ \\ \\ \sf \implies 319 = {AC}^{2} \\ \\ \\ \sf \implies \sqrt{319} = AC \\ \\ \\ \sf \blue{\implies 17.86 = AC}[/tex]

Answer:

See below

Step-by-step explanation:

(36 - 2x) * (17-2x) = 700      I think, given the info

4x^2 - 106x + 612 = 700     expanded....

Answer:

180 square yards

Step-by-step explanation:

there are 3 shapes that create the total area :

a large right-angled triangle to the right. its baseline is 16 yd. the left side is a bit complicated, we get to it.

a small middle rectangle with length 6 yd. it's width is 3 yd.

is area is 6×3 = 18 yd²

a large rectangle at the bottom left with length 11 yd and width 6yd.

its area is 11×6 = 66 yd²

now, how long is the left side of the triangle ? we need it as the height of the triangle to get the area

baseline × height / 2

we see that a part of the left side is 8 yd.

then the width of the middle rectangle is also a part of that left side : 3 yd.

and then we notice that the triangle goes a little bit below the top length side of the large rectangle. how much ? well the actual width of the large rectangle is 6 yd, but the side under the triangle says only 5 yd. so, the missing piece is 6-5 = 1 yd.

so, the full left side is

8 + 3 + 1 = 12 yd

and the area of the triangle is

16×12 / 2 = 16×6 = 96 yd²

so, the total area of the figure is

18 + 66 + 96 = 180 yd²

Answer:

this cannot be factored since nothing shares factorable groups/values

Step-by-step explanation:

hope this helps:)

Answer:

76 unit^2

Step-by-step explanation:

Total area: (0.5  * base * height) +( length * breadth ) + (0.5 * base * height)

= (0.5 * 8 * 2) + ( 7*8) +( 0.5 * 8 * 3) = 8 + 56 + 12 = 76

Answer:

There was a 50% chance that the goldfish would swim to the left

Step-by-step explanation:

Percentage means "amount in one hundred".

[tex]\textsf{one in two}=\sf \dfrac{1}{2}=\sf \dfrac{1\times 50}{2 \times 50}=\dfrac{50}{100}=50\%[/tex]

Newspaper headline:

There was a 50% chance that the goldfish would swim to the left.

Answer:

I did the work and uploaded the answer as a picture for you

I hope it was helpful!!

Step-by-step explanation:

Answer:

5/(8+4+5) = 5/17

Step-by-step explanation:

total has (8 red +4 white+5 blue）= 17

we looking for blue , so is 5.

5/17

Answer:

Below.

Step-by-step explanation:

k / 22 = -66

k = 22*-66

= -1452.

Answer:

1. 2

2. 5

Step-by-step explanation:

1. write 5% as

[tex] \frac{5}{100} [/tex]

Then,

[tex] \frac{5}{100} \: of \: \: 40 = \frac{5}{100} \times 40[/tex]

Therefore, the answer is 2

If you are using a calculator, simply enter 5 divided by 100 times 40 which will give you 2 as the answer.

2. Write 20% as 20/100

[tex] \frac{20}{100} \: of \: 25 = \frac{20}{100} \times 25[/tex]

Therefore, the answer is 5

If you are using a calculator, simply enter 20 divided by 100 times 25 which will give you 5 as the answer.

Answer:

true

Step-by-step explanation:

Examples :

180 = 5 × 2² × 3²

Then

The number 180 has perfect square factors which are 2 and 3

Then

The number √180 can be simplified because:

[tex]\sqrt{180} =\sqrt{5\times 2^{2}\times 3^{2}}[/tex]

        [tex]=\sqrt{5\times \left( 2\times 3\right)^{2} }[/tex]

        [tex]=\sqrt{5\times \left( 6\right)^{2} }[/tex]

        [tex]=\sqrt{5} \times \sqrt{6^{2}}[/tex]

        [tex]=6\sqrt{5}[/tex]

On the other hand :

10 = 5 × 2

Then

The number 10 has no perfect square factors

Then

The number √10 cannot be simplified because:

[tex]\sqrt{10} =\sqrt{5\times 2} =\sqrt{5} \times \sqrt{2}[/tex]

[tex]\text{and} \ \sqrt{5} \times \sqrt{2} \ \text{is not a simplified expression of} \ \sqrt{10} \ \\\text{,in fact it is more complicated than} \ \sqrt{10}[/tex]

To solve this problem, we have to understand that the parallel lines cut will form two alternate angles which are equal to each other. The value of x is equal to -8/5

In the given question, we have two alternate angles fixed at opposite end to each other.

Data;

Since we've established that alternate angles are equal to each other, we can proceed to equate the two angles and solve for x

[tex]8x -1 = 3x - 9\\8x - 3x = - 9 + 1\\5x = - 8\\x =-\frac{-8}{5}[/tex]

The value of x is equal to -8/5

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Answer:

no

Step-by-step explanation:

Answer:

number 2

Step-by-step explanation:

im not that sure but i think it's that one

The plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the plumber spend x hours to fixing the sink.

Then we can frame a linear equation in one variable:

55 + 45x = 190

45x = 135

x = 3 hours

Thus, the plumber spend 3 hours to fixing the sink if the plumber fixed a leaky sink and charged $55 for parts and $45 per hour for labour.

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Answer:

0.778 to the nearest thousandth.

Step-by-step explanation:

Dividing 7 by 9:    

9) 7.000000

   0.7777777 ....   <--    quotient

So it is 0.778 to the nearest thousandth.

Answer:

d)The midline is y=1.5

Step-by-step explanation:

Because you can see in the graph that the midline is 1. So only c is no correct.

The amplitude is measured between the midline and the pik(highest or lowest value) of the function. This case is 2. True

The period is the distance between “equivalent” points. pi in this case. True.

The phase shift occur when the function is shifted on the x-axis. There is no phase shift. True.

The graph is showing the equation of circle x²+y²=4

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.

The equation will be as follows:-

x²+y²=4

Hence the graph is showing the equation of circle x²+y²=4

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The simplification of √75+ √48 -2√675 is -21√3.

Surds are irrational numbers.

To simplify the surd in the question above, we use the addition and subtraction of surds.

Two or more surds can be added or subtracted if they are in the same basic form.

E.g

Using the above example,

Given:

Express the surds to the same basic form

Hence, the simplification of √75+ √48 -2√675 is -21√3.

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Answer:

a = √3 * r

a = √3 * 10

a = 10√3 cm

Step-by-step explanation:

Answer:

B and C are both in slope-intercept-form.

Step-by-step explanation:

Slope Intercept Form is --> y = mx + b, where m is the slope, and b is the y-intercept.

Both B and C have a slope (-6/4 for B, -3/2 for C) and both have a y-intercept (8/4 or 2).

I hope this helps. Please mark me brainliest!

Answer:

a 230 metera 230 metersa 230 metersa 230 metersa 230 metersa 230 meters

The best investment option for this couple is the Food and Beverage industry because it is the one that gives them the highest profits within 11 years compared to the other alternatives.

To calculate the pair's gain in each alternative we must perform the following mathematical operations:

Food and beverage (FNB) industry

Clothing and textiles industry

Current Bank

Based on the foregoing, it can be inferred that the best investment option for the couple is the Food and Beverage (FNB) industry because it is the one that leaves the highest profits despite the decrease in profits during the second year.

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Answer:

C.

Step-by-step explanation:

-3 7/8 rounds down to -4

4.63 rounds up to 5

-4 x 6 + 5

-24 + 5

-19

her answer (-19.14) also rounds to -19

So yes, it is reasonable and the correct response is C.

Answer:

621.72

Step-by-step explanation:

The explanation is that the formula is V=2HπR

Multiply all of that and you get your answer of 621.72

Answer:

B. Unlikely

Step-by-step explanation:

Generally speaking, a probability of 0.11 to 0.40 is unlikely. 1/5 is 0.2, which falls in this range.

Answer:

X=80

Step-by-step explanation:

Angle OAB=50(Properties of isosceles traingle)

X+50+50=180(sum of the interior angles of the traingle)

X=180-100

X=80