) If the pattern shown continues, how many black keys appear on a portable keyboard with 49 white keys? Suggestion: use equivalent ratios or a rate table to confirm your answer.

Answer:

Number of tile need = 300 tiles

Step-by-step explanation:

Given:

Dimensions of floor = 3 m by 4 m

Perimeter of square tile = 80 cm

Find:

Number of tile need

Computation:

Perimeter of square tile = 4(Side)

80 = 4(Side of tile)

Side of tile = 80 / 4

Side of tile = 20 cm

Side of tile = 0.2 meter

Area of tile = 0.2 x 0.2

Area of tile = 0.04

Area of floor = 3 x 4

Side of tile = 12 square meter

Number of tile need = 12 / 0.04

Number of tile need = 300 tiles

Answer:

Step-by-step explanation:

(a) We will prove by induction that if n is a multiple of 3 then Bob has a winning strategy.

Let n=3

It is given that Alice always plays first.

Then, for the first move, Alice has a choice of removing 1 or 2 stones.

Case 1:

Alice removes 1 stone. Then it is now Bob's turn. There are 2 stones left. Bob has the choice of removing 1 or 2 stones. Then Bob's winning strategy should be to remove 2 stones. Then Bob removes the last stone and wins.

Case 2:

Alice removes 2 stones. Then it is Bob's turn. There is exactly 1 stone left, which Bob removes in his turn. Since he removes the last stone, he wins.

Thus, in either case, for n=3, Bob has a winning strategy. ____ (A)

Now, let us assume that Bob has a winning strategy for n=3p.

We will now check if Bob has a winning strategy for n=3p+3

It is given that Alice plays first.

Case 1:

Alice starts the game by removing 1 stone. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 2 stones, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case Bob has a winning strategy.

Case 2:

Alice starts the game by removing 2 stones. Then, Bob has a choice of removing 1 or 2 stones. If he chooses to remove 1 stone, then the number of stones left is 3p+3-3=3p and it is now Alice's turn to play. This is again exactly the game when n=3p and we have already assumed that Bob has a winning strategy for n=3p. Thus, in this case also, Bob has a winning strategy.

Thus, in either case Bob has a winning strategy for n=3p+3 if he has a winning strategy for n=3p. _______ (B)

Thus, from (A) & (B), using induction, we can say that Bob has a winning strategy if n is a multiple of 3.

(b) We will now prove that if n is not a multiple of 3, then Alice has a winning strategy.

If n is not a multiple of 3, then n can have either of the forms of 3m+1 or 3m+2, m ∈ W.

We will prove the given fact for both the forms simultaneously

Let m=0, i.e., n=1 or n=2

Since Alice starts first, she removes 1 stone, if n=1 or 2 stones if n=2 and thus wins. Thus Alice has a winning strategy if m=0. ______ (A)

Let us assume that Alice has a winning strategy for m=k, i.e., for n=3k+1 & n=3k+2

Now, we will check if Alice has a winning strategy for m=k+1, i.e., for n=3(k+1)+1=3k+4 or n=3(k+1)+2=3k+5

Let n=3k+4

Since Alice plays first, she has a choice to remove 1 or 2 stones.

Note that, if Alice removes 2 stones and in turn Bob removes 2 stones, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.

Then, Alice should remove 1 stone. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.

Case 1:

Bob removes 1 stone. Then there are 3k+4-1-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.

Case 2:

Bob removes 2 stones. Then there are 3k+4-1-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.

Thus, in either case, Alice has a winning strategy.

Let n=3k+5

Since Alice plays first, she has a choice to remove 1 or 2 stones.

Note that, if Alice removes 1 stone and in turn Bob removes 1 stone, then the number of stones becomes a multiple of 3 such that it is Alice's turn to play. In that case, Bob will have a winning strategy as shown in the previous part.

Then, Alice should remove 2 stones. Then, it is now Bob's turn and he has a choice of removing 1 or 2 stones.

Case 1:

Bob removes 1 stone. Then there are 3k+5-2-1=3k+2 stones remaining and it is Alice's turn. This is identical to the game where n=3k+2. We have already assumed that Alice has a winning strategy in this case.

Case 2:

Bob removes 2 stones. Then there are 3k+5-2-2=3k+1 stones remaining and it is Alice's turn. This is identical to the game where n=3k+1. We have already assumed that Alice has a winning strategy in this case.

Thus, in either case, Alice has a winning strategy.

Then, we can say that Alice has a winning strategy for m=k+1 if she has a winning strategy for m=k. _____ (B)

Then, by induction, from (A) & (B), we can say that if n is not a multiple of 3, then Alice has a winning strategy.

Answer:

n=-17

Step-by-step explanation:

8(2n-5)=3(6n-2)

1) Distributive property

16x-40=18x-6

16x−40=18x−6

2) Subtract 16x16x from both sides.

-40=18x-6-16x

−40=18x−6−16x

3) Simplify 18x-6-16x18x−6−16x to 2x-62x−6.

-40=2x-6

−40=2x−6

4) Add 66 to both sides.

-40+6=2x

−40+6=2x

5) Simplify -40+6−40+6 to -34−34.

-34=2x

−34=2x

6) Divide both sides by 22.

-\frac{34}{2}=x

−

2

34

=x

7) Simplify \frac{34}{2}

2

34

to 17

−17=x

8) Switch sides.

x=−17

Answer:

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

Step-by-step explanation:

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.

This means that the consumption after t years is given by the following differential equation:

[tex]\frac{dC}{dt} = kC[/tex]

In which k is the growth rate.

The solution is, applying separation of variables:

[tex]C(t) = C(0)e^{kt}[/tex]

In which C(0) is the initial consumption.

The town consumed 4.4 trillion British thermal units (BTUs) initially.

This means that [tex]C(0) = 4.4[/tex]

So

[tex]C(t) = C(0)e^{kt}[/tex]

[tex]C(t) = 4.4e^{kt}[/tex]

5.5 trillion BTUs annually after 5 years.

This means that [tex]C(5) = 5.5[/tex]. We use this to find k. So

[tex]C(t) = 4.4e^{kt}[/tex]

[tex]5.5 = 4.4e^{5k}[/tex]

[tex]e^{5k} = \frac{5.5}{4.4}[/tex]

[tex]e^{5k} = 1.25[/tex]

[tex]\ln{e^{5k}} = \ln{1.25}[/tex]

[tex]5k = \ln{1.25}[/tex]

[tex]k = \frac{\ln{1.25}}{5}[/tex]

[tex]k = 0.0446[/tex]

So

[tex]C(t) = 4.4e^{0.0446t}[/tex]

After 9 years?

This is C(9). So

[tex]C(9) = 4.4e^{0.0446*9} = 6.57[/tex]

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

Answer:

The answer is C

Step-by-step explanation:

there is no explanation

Answer:

Area of a square garden = 2, 500 m².

Length of the side of the garden =  √2,500 = 50 m.

Width of the path = 2.5 m.

Path is inside the garden.

Width of the garden that is inside (enclosed) by the path:

        50 - 2 * 2.5 = 45 m.

Length of the garden inside by the path :  = 45 m.

So the area of garden inside the path = 45 * 45 m²

     = 2, 025 m².

Area of the path = 2, 500 - 2, 025  

    = 475 m².

Cost of laying the path = Rs 25 /m² * 475 m²

   = Rs 11, 875.

Step-by-step explanation:

Answer:

Value of the test statistic for this problem = -3.74

Step-by-step explanation:

Here

the sample size n = 1263

and the x = 565

So, the p' -value = 565/1263 = 0.4473

As per the test statistics formula, z value will be evaluated

z = (0.4473-p)/sqrt {p(1-p)/n}

Let us say that p = 0.5

Substituting the given value in above equation, we get -

z = (0.4473-0.5)/sqrt {0.5(1-0.5)/1263}

z = -3.74

The test statistic of the question is; z = -3.74

We are given;

Sample size; n = 1263

Number of people that said yes; x = 565

Sample proportion is; p'= 565/1263 = 0.4473

Formula for the test statistic of proportion is;

z = (p' - p)/(√(p(1 - p)/n)

We will assume that population proportion p = 0.5. Thus;

z = (0.4473 - 0.5)/(√(0.5(1 - 0.5)/1263)

z = -3.74

Read more about test statistic at; https://brainly.com/question/4621112

Answer:

Step-by-step explanation:

A, D and F

1. 40°

2. 50°

3. 45°

4. a. draw a line from angle P to downward but make it so it can cut angle OPQ from the half

b. 70°

c. angle TPQ = angle OPQ ÷2

angle TPQ = 140÷2= 70°

Answer:

Step-by-step explanation:

Jan >> Feb >> Mar >> Apr

       x2        x2       x2

$10 >> $20 >> $40 >> $80

Answer:

y = -2/3 x + 6

Step-by-step explanation:

Using the coordinates (1, 16/3) and (3,4)

Slope m = 4-16/3/3-1

Slope m = -4/3 * 1/2

Slope m = -2/3

For the y-intercept

Substitute (3,4) and m = -2/3 into y  =mx+b

4 = -2/3(3) + b

4 = -2 + b

b = 4 + 2

b = 6

Get the required equaton;

Recall that y = mx+b

y = -2/3 x + 6

Answer:

$54

Step-by-step explanation:

first find 1/4 of $80 and then take that answer and find 10% of that to get your answer

Answer:

a^2

Step-by-step explanation:

Ia^2I if a<0

Since a^2 is always positive, we can remove the absolute value sign and nothing will change

a^2

Answer:

MINIMUM WAGE does not increase much over time

Step-by-step explanation:

Based on the information given the conclusion you can draw from this is that MINIMUM WAGE DOES NOT INCREASE OR TEND TO GO UP MUCH OVER TIME Since the MINIMUM WAGES of the poverty threshold of whom TWO were related children was the amount of $21,027 and the poverty threshold of whom THREE were related children was the amount of $21,100 indicating that the minimum wages only increase from $21,027 to $21,100 given us the amount of $73 ($21,027 -$21,100) which is less than the amount of $100 as the difference between these TWO THRESHOLDS for each of the preceeding year.

Answer:

0.057

Step-by-step explanation:

To obtain the p value, we need to obtain the test statistic :

For a one sample test :

Test statistic is given by :

(xbar - μ) ÷ (σ/√(n))

(185 - 175) ÷ (20/√(10))

10 ÷ 6.3245553

Test statistic = 1.581

Qe used the Z distribution because we are working with the population standard deviation.

Using the Pvalue from test statistic calculator :

Pvalue obtained using the Pvalue from Z statistic calculator, we obtain ;

Pvalue = 0.0569

Answer:

0.1354 = 13.54% probability that exactly one of these three blue ray players is defective.

Step-by-step explanation:

For each player, there are only two possible outcomes. Either it is defective, or it is not. The probability of a player being defective is independent of any other ray. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Five percent of all blue ray players manufactured by a large electronics company are defective.

This means that [tex]p = 0.05[/tex]

A quality control inspector randomly selects three players from the production line.

This means that [tex]n = 3[/tex]

What is the probability that exactly one of these three blue ray players is defective?

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.05)^{1}.(0.95)^{2} = 0.1354[/tex]

0.1354 = 13.54% probability that exactly one of these three blue ray players is defective.

Answer:

x = 5

Step-by-step explanation:

According to triangle angle bisector theorem, the ray divides the opposites side of the triangle into segments that are proportional to the other two sides.

So,

      [tex]\frac{x-1}{x-2} = \frac{12}{9}\\\\\frac{x-1}{x-2} = \frac{4}{3}\\\\3(x-1) = 4(x-2)\\\\3x - 3 = 4x - 8\\\\4x - 3x = -3 +8 \\\\x = 5[/tex]

Answer:

1. AC = EC

Step-by-step explanation:

As it says that the figure has to be proved by SAS postulate. We know that, SAS stands for Side - Angle - Side, so we need to prove that any two sides and one angle of two triangles are equal/proportional or not.

Given, BC = CD, and angle ACB = angle DCE.

Therefore, the answer is 1. AC = EC.

Answer:

9901 / 2000

Step-by-step explanation:

might be wrong

Answer:

Step-by-step explanation:

Properties

Center:(7,0)

The center of a circle is a point from which all points on a circle are the same distance.

Radius:4

The radius of a circle is the length of a line segment from its center to its perimeter.

The radius is typically denoted as "r" or "R".

Diameter:8

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.

Circumference or (or Permieter) = 2*π*R = 2*3.14*4 = 25.1327412287183

The circumference of a circle is the distance around it.

Area:50.2654824574367

Area of a Circle is the amount of space occupied by the circle.The area of a circle is p times the radius squared, which is written: A = π*R2.

Equation

Standard Form

The standard form for the equation oif a circle is

(x-a)2+(y-b)2=r2

And in our particular case:

(x-7)2+(y-0)2=42

(x-7)2+(y-0)2=16

General Form

The general form for the equation of a circle is

x2 + y2 + Ax + By + c = 0

We can get the general form by expanding the equation of the standard form

(x-a)2+(y-b)2=r2

(x-7)2+(y-0)2=42

(x-7)2+(y-0)2=16

x2-14x+49+y20y+0=16

x2+y2-14x+0y+33=0 Referenced definitions

Chord A chord of a circle a line segment that joins two points on the circumference of a circle.

π The ratio of a circle's circumference to its diameter. Equal to 3.1415926535... (the digits go on indefinitely without repeating)

Circle a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre).

The required equation of a circle will be (x - 7)² + y² = 16 with a center at (7, 0) and a radius of 4.

The equation of a circle with center (h,k) and radius r is :

r² = (x−h)² + (y−k)²

The center of the circle is given as (h,k) = (7, 0) which is given in the question

And radius r = 4

Substituting the given values into this equation gives us an equation of a circle with a center at (7, 0) and a radius 4:

(x - 7)² + (y - 0)²  = 4²

Simplifying this equation gives us:

(x - 7)² + y² = 16

This is the equation of a circle with a center at (7, 0) and a radius of 4.

Learn more about the equation of a circle here:

brainly.com/question/1554214

#SPJ2

Answer:59

Step-by-step explanation:

beacause you need to added them all together

Answer:

[tex]21^{\circ}[/tex]

Step-by-step explanation:

The Law of Sines is given by [tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex] and works for every triangle.

Substituting given values, we have the following equation:

[tex]\frac{\sin 68^{\circ}}{18}=\frac{\sin C}{7}, \\\\\sin C=\frac{7\sin 68^{\circ}}{18},\\\\C=\sin^{-1}(0.36057149899),\\\\C\approx \boxed{21^{\circ}}[/tex]

*Note that because [tex]\sin \theta=\sin(180-\theta)[/tex], when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.

Answer:

A 70°

Step-by-step explanation:

Angle of the triangle

=180-60-60

=60°

x= 180-60-50

=120-50

=70°

Answer:

they might not be the same numbers but you can do it with all of the step-by-step explanations I gave you just with the numbers you have

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine tan m∠A, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan A = √32/2 = (√16 × √2)/2

Tan A = (4√2)/2

Tan A = 2√2

Answer:

1200*0.70=840

840*0.70=588

588*0.70=411.60

411.60*0.70=288.12

Answer:

10xyz + 20xy - 15x

Step-by-step explanation:

5 x ( 2yz + 4 y - 3)

using the Distributive property multiply the each term by 5x

5x × 2yz + 5x × 4y - 5x × -3

calculate the product

10xyz + 20xy - 15x

Answer:

10xyz+20xy-15

Step-by-step explanation:

Hi there! Use the difference of two squares formula below:

[tex] \large \boxed{ {x}^{2} - {y}^{2} = (x + y)(x - y)}[/tex]

You need to know that what number times itself and get 16. 16 comes from 4×4 or 4².

Then,

[tex] \large{ {x}^{2} - 16 = (x + 4)(x - 4)}[/tex]

[tex] \large{(x + 4)(x - 4) = 0}[/tex]

Solve the equation for all real values of x.

[tex] \large{x = 4, - 4}[/tex]

If you don't like using a formula. You can do this:

[tex] \large{ {x}^{2} - 16 = 0} \\ \large{ {x}^{2} = 16} \\ \large{x = \pm \sqrt{16} } \\ \large{x = \pm 4}[/tex]

If you remember the square root well, the square root of 16 is 4×4. Pull out the two 4's and thus the square root of 16 is 4.

For the square both sides method above (second method), we can define that:

[tex] \large \boxed{ \large{ {x}^{2} = a \longrightarrow x = \pm a }}[/tex]

Answer