Let's suppose someone flips a fair coin three times. 1. How many outcomes are possible? [a] 2. What is the probability of getting exactly one tail? Give as a fraction [b] 3. What is the probability of getting at most two tails? Give asa fraction [c]​

Answer:

your mom fat as he'll that way you are adopted

Answer:

Step-by-step explanation:

15) let T1 be the event : “get a tail in the first flip”

    let T2 be the event : “get a tail in the second flip”

p(T1 ∩ T2) = 1/4

p(T1) = 1/2

p(T2) = 1/2

Then

p(T1) × p(T2) = (1/2)(1/2 = 1/4

Since ,p(T1 ∩ T2) = 1/4 = p(T1) × p(T2)

Then the events are independent.

16) These events are dependent since we don’t  replace the Queen before the second draw.

The two Events are dependent because the probability that we draw a Queen  in the first draw affect the probability that we draw a Queen in the second draw.

Step-by-step explanation:

the missing side is given by sqrt(16² - 8²)

hence,

the number that belongs in the green box is 192

Answer: Both diagonals bisect each other.

Answer:

2,3,7,2,5

Step-by-step explanation:

When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.

42 is equal to 6 and 7 and 6 is 2 times 3

2,3,7 is prime

10 is 2 times 5

2 and 5 is prime

Answer:

420 = 2² × 3 × 5 × 7

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:

⇒ 420 ÷ 2 = 210

As 210 is not a prime number, we need to divide again.  Let's try dividing by 2 again:

⇒ 210 ÷ 2 = 105

As 105 is not a prime number, we need to divide again.  105 is not divisible by 2, so let's try dividing it by the next prime number, 3:

⇒ 105 ÷ 3 = 35

As 35 is not a prime number, we need to divide again.  35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:

⇒ 35 ÷ 5 = 7

As 7 is a prime number, we can stop.

Therefore, 420 is the product of all the prime numbers we found together with the final one:

⇒ 420 = 2 × 2 × 3 × 5 × 7

As 2 appears twice, we can write this using exponents:

⇒ 420 = 2² × 3 × 5 × 7

Answer:

B.  51.7699^2

Step-by-step explanation:

Last 2 wrong because it is positive.

101.... is not the definite integral for the curve

51... purrfecto

Answer:

Ans=...334832 can be your questions answer

The true equation will be f(6) = 0. Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given by the set of ordered pairs.

{(1,0), (–10,2), (0,6), (3,17), (–2,–1)}

Then the function can be written as

f(abscissa) = ordinate

Then the function will be

f(0) = 6

Then the correct option is C.

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Answer:

f of 0 = 6

Step-by-step explanation:

Edge

Done!

Answer:

[tex](f+g)(x)=3x^3-2x^2+10x-12[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=3x^3-2x^2+4x-5\\g(x)=6x-7 \end{cases}[/tex]

[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (3x^3-2x^2+4x-5)+(6x-7)\\& = 3x^3-2x^2+4x-5+6x-7\\& = 3x^3-2x^2+4x+6x-5-7\\& = 3x^3-2x^2+10x-12\end{aligned}[/tex]

Answer:

B

Step-by-step explanation:

First, we have to find the rate of change for this problem. To do this, we subtract any two numbers of days and the coordinating two total questions. Let's just use the first two rows. 8-4=4, and 40-20=20. For every 4 days, he answers 20 questions. We can further simplify this by dividing both sides by 4. 4/4=1, and 20/4=5. For every 1 day, he answers 5 questions. Now, to find 16 days, we just multiply both sides by 16. 16*1=16 and 16*5=80. For every 16 days, he answers 80 questions. 80 is our answer.

Hope this helps!

0.45° in minutes is 27.36 minutes and in seconds is 21.6 seconds.

Why is it necessary to divide decimal degrees by 60 to obtain minutes and seconds?

How 0.45° is converted to equal minutes and seconds?

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The correct answer is option D which is f(x) is decreasing for all the values of x < 3.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The value of the function [tex]f(x) = \dfrac{x+6}{x^2-9x+18}[/tex] is represented on the graph in the graph we can see that at x>6 the value of the function is decreasing and at x<3 the value of the function is increasing.

Therefore the correct answer is option D which is f(x) is decreasing for all the values of x < 3.

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a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

Answer:

a=2

Step-by-step explanation:

[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]

[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]

the curve is a right parabola.

here b=0,and a=4a for x

we are finding the area between x-axis and x from 0 t0 4a.

curve is symmetrical about x-axis so we multiply by 2.

If the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Area bounded by the curve  [tex]=\int\limits^a_b {x} \, dx[/tex]

We have,

[tex]y^2 =4ax[/tex]  

⇒ [tex]y=\sqrt{4ax}[/tex]

[tex]x= 4a[/tex],

Area of the region  [tex]=\frac{256}{3}[/tex]  Sq units

Now comparing both given equation to get the intersection between points;

[tex]y^2=16a^2[/tex]

[tex]y=4a[/tex]

So,

Area bounded by the curve  [tex]= \[ \int_{0}^{4a} y \,dx \][/tex] ​

 [tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]

[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]

 [tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]                                            

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]

On applying the limits we get;

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]

[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]

⇒ [tex]a^{3} =8[/tex]

[tex]a=2[/tex]

Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

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The age of the bird skeleton is 6539.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, N =[tex]N_{0}.e^{-0.0001t}[/tex]

             = 52% N₀

[tex]e^{-0.0001t}[/tex] = 0.52

-0.0001 t = ln 0.52

t = -10000 ln 0.52

t = 6539

Thus, the age of the bird skeleton is 6539.

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Answer:

Step-by-step explanation:

Functions are written in terms of variables. The value of the function when x  is -8 is 124

Functions are written in terms of variables. Given the function below;

g(x) = 2x^2 - 4

If the value of x is -8, substiute

g(-8) = 2(-8)^2 -4

g(-8) = 2(64) - 4

g(-8) = 124

Hence the value of the function when x  is -8 is 124

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The residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

The regression equation is given as:

y = 0.005x + 3.111

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.005 * 4 + 3.111 = 3.131

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 5 + 3.111 = 3.136

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 8 + 3.111 = 3.151

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 10 + 3.111 = 3.161

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 6 + 3.111 = 3.141

y = 0.005 * 6 + 3.111 = 3.141

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

y = 3.46 - 3.131 = 0.329

y = 2.78 - 3.126 = -0.346

y = 3.2 - 3.136 = 0.064

y = 2.8 - 3.126 = -0.326

y = 3.2 - 3.151 = 0.049

y = 2.9 - 3.186 = -0.286

y = 3 - 3.161 = --0.161

y = 3.4 - 3.186 = 0.214

y = 3.57 - 3.141 = 0.429

y = 3.2 - 3.141 = 0.059

Hence, the residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

See attachment for the residual plot.

The residual plot shows that the linear model from the regression calculator is a good model because the points are not on a straight line

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Answer:

11- B

moving left 90 degrees from a

because clockwise is the right direction in a circle and counterclockwise is the left direction in a circle

12- C

moving 180 degrees left from a

13- B

moving 270 degrees right from a

14- d

moving 270 degrees left from a

hope this helps! message me if you have any further questions :)

Answer:

y = 1/40x + 20

Step-by-step explanation:

Slope-intercept equation format:

y = mx + b

m = slope/ gradient/ constant of variation/ rate of change

b = y-intercept

To find the slope, use the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Find  two random points:

1 - (0.5, 40) , 2 - (1, 60)

Plug in:

[tex]\frac{60-40}{1-0.5}[/tex]

Solve:

[tex]\frac{20}{0.5}[/tex]

Divide:

[tex]\frac{1}{40}[/tex]

The y-intercept is when the x-coordinate is equal to 0.

The y-intercept is always the beginning.

So observing the graph, the first point is (0, 20)

The x-coordinate is 0.

Y intercept = 20.

Plug in both slope and y-intercept:

y = 1/40x + 20

Answer:

D)

Step-by-step explanation:

[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]

Step-by-step explanation:

in a management information system, the quality of information is determined by its usefulness to users, and its usefulness determines the success of the information system.

Answer:

squares: 204

rectangle: 1,296

Step-by-step explanation:

Board Size: 8 x 8

The total number of squares is thus:

[tex]1^{2} + 2^{2} + ... + n^{2}[/tex]

sum = [tex]\frac{n(n + 1)(2n + 1)}{6}[/tex]

For a chess board, with n = 8,

sum = [tex]\frac{(8)((8) + 1)(2(8) + 1)}{6}[/tex]

sum = 204

the number of rectangles on a chess board,

to make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. There are 36 distinct pairs and the same number of vertical pairs, so the answer is 36 × 36 = 1,296.

Answer:The result follows from manipulating the conditional probability. By definition,

By the law of total probability,

So we have

Step-by-step explanation:

P(A|B) = P(B|A)×P(A)/P(B)

so, in our case

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)

I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.

so,

P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =

= 0.25 + 0.05 + 0.1 = 0.4

therefore,

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1

The points on the line are points B and D

The equation is given as:

y = x + 4

The above means that the output value is 4 more than the input value

Using the above rule, the points that satisfy the equation are:

B) 2, 6 and D) 2, 4

This is so because:

6 = 2 + 4

4 = 2 + 2

Hence, the points on the line are points B and D

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Answer:

3, 2, 4, 1

Step-by-step explanation:

A particle moves along line segments from the origin to the points, work done is mathematically given as

W=184.5units

Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force

Generally,  the equation for force is mathematically given as

F = z2i + 5xyj + 2y2k

Therefore, Considering u*v

[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]

[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]

Where

[tex]i * i = j *j=k * k=0[/tex]

Hence

[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]

[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]

The normal equation formed

-2y + 15z = 0

z= (1/5)y

Considering the level surface and differential surface area

h(x,y,z) = -y + 5z =0

[tex]dS = |grad(h)| dA[/tex]

In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have

[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]

Using strokes theorem to evaluate

[tex]F = z2i + 5xyj + 2y2k[/tex]

[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]

[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]

In conclusion, The work done is

[tex]W=\int _CF *dr[/tex]

[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]

[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]

[tex]\int _C F * dr = \frac{123*3}{2}[/tex]

W= 184.5units

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Answer:

294[tex]m^2[/tex]

Step-by-step explanation:

The area of one face of the cube would be 7 x 7 = 49 [tex]m^2[/tex]

Since there are 6 faces on a cube, the total surface area would therefore be 49 x 6 = [tex]294m^2[/tex]

Based on this construction, the value of m∠ABC is 64°.

From the point, E and D, two arcs are made which are intersecting each other at point P.

It means, that line BP is the bisector of angle ABC. ABC will be:

= 2 * 32=64

Therefore, based on this construction, the value of m∠ABC is 64°.

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