Nisha collects comic books, and she convinced her friend Hakim to start collecting as well. Every week, they go to the store together, and they each buy a new comic book. This table shows how many books they each have:

Expanding the desired form, we have

[tex]A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)[/tex]

and matching it up with the given expression, we see that

[tex]\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}[/tex]

A natural choice for one of the symbols is [tex]\omega = 4\pi[/tex]. Then

[tex]\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}[/tex]

Use the Pythagorean identity to eliminate [tex]\phi[/tex].

[tex](A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2[/tex]

so that

[tex]A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}[/tex]

Use the definition of tangent to eliminate [tex]A[/tex].

[tex]\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}[/tex]

so that

[tex]\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)[/tex]

We end up with

[tex]y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}[/tex]

where

• amplitude:

[tex]|A| = \boxed{\sqrt{29}}[/tex]

• angular frequency:

[tex]\boxed{4\pi}[/tex]

• phase shift:

[tex]4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)[/tex]

I don't know what you mean by g. and h., so I'll just skip that part.

I'm assuming you're asking about some arbitrary finite set [tex]A[/tex].

a. If [tex]A[/tex] has 64 subsets, then [tex]A[/tex] has [tex]\log_2(64) = \boxed{6}[/tex] elements. This is because a set of [tex]n[/tex] elements has [tex]2^n[/tex] subsets/elements in its power set.

b. A proper subset is a subset that doesn't contain all the elements of the parent set. This means we exclude the set [tex]A[/tex] from its power set. The power set itself would have 32 elements, so [tex]A[/tex] would have [tex]\log_2(32) = \boxed{5}[/tex] elements.

c. The empty set is a proper subset of any non-empty set. However, if [tex]A=\emptyset[/tex], then it has no proper subsets. So [tex]A[/tex] must be the empty set and have [tex]\boxed{0}[/tex] elements.

d. By the same reasoning as in part (b), if [tex]A[/tex] has 255 proper subsets, then it has a total of 256 subsets, and [tex]\log_2(256) = \boxed{8}[/tex].

Answer:

Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope

So the easiest way to do so is to put the said equation in y-intercept form

y=mx +b
m= slope

b= y intercept

so 1. 3x + 4y = 12

=

4y = 12-3x

divide that by 4 to get only y

y=3-3/4x

-3/4 is our slope

y=-3/4x+b

than we have a point -2, -2

if we put -2 for y

-2=-3/4x+b

and then we put our -2 for x
-2 = -3/4 * -2 + b

=

-2  = -1.5 +b
b=-0.5

Answer : y=-3/4x-0.5

Step-by-step explanation: Given that the graph shows the side view of a water slide with dimensions in feet.

We are to find the rate of change between the points (0, ?) and (?, 40).

From the graph, we note that

the y co-ordinate for the x co-ordinate 0 is 80 and the x co-ordinate for the y co-ordinate 40 is 5.

So, the given two points are (0, 80) and (5, 40).

The rate of change for a function f(x) between the points (a, b) and (c, d) is given by

Therefore, the rate of change for the given function between the points (0, 80) and (5, 40) is

Thus, the required rate of change is -8.

Answer:

Step-by-step explanation:

why is it so hard omg

Answer:9

Step-by-step explanation:1+2=3 6/2=3

3x3=9

Answer:

92 degrees

Step-by-step explanation:

The sum of the exterior angles will be 360.  

67 x 4 = 268.  That means that the last angles must be 92 (360 - 268)

The dependent variable here is task performance. The independent variable in the question is musical genres.

This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.

The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.

The task performance is what we want to know here. To do so we want to use the genre of music.

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From the 2 selected employees, the probability that they will both be females is; C: 4/15

We are given;

Number of male employees = 7

Number of female employees = 8

Total number of employees = 8 + 7 = 15

Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2

Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15

Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15

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Answer:

Step-by-step explanation:

Equivalent polar coordinates will have the same modulus and some multiple of 360° added to the argument, or the opposite modulus and some odd multiple of 180° added to the argument.

  a∠b° = a∠(b+360n)° = -a∠(b +180 +360n)°

Equivalents will be ...

  (2, (-60 +360n)°) = (2, 300°)

  (-2, (-60 +180 +360n)°) = (-2, -240°) = (-2, 120°)

Equivalents will be ...

  (-2, (240 +360n)°) = (-2, -120°)

  (2, (240 +180 +360n)°) = (2, -300°) = (2, 60°)

Answer:

The area of windowpane is answer.

Answer:

The area of the window pane

Step-by-step explanation:

The area of an object is the width x length of said object.

Ex: A  4 x 4 sized square has an area of 16 ( 4 x 4 = 4 by 4)

P.S. The area of Andrea´s windowpane is 648.

Answer:

Step-by-step explanation:

Option C.

Step-by-step explanation:

Initial number of clients = 18

Number of Increase per week = 4

We need to use an arithmetic sequence to write a function.

So, the required arithmetic sequence for four weeks is

18, 22, 26, 30

Here, first term is 18 and common difference is 4. The range is  [18,30].

The explicit formula of n arithmetic sequence is

where, a is first term and d is common difference.

Substitute a=18 and d=4 in the above formula.

The function notation is

The function is f(x)=4x+14 and the range is  18 ≤ y ≤ 30.

Therefore, the correct option is C.

Answer:

The function is odd because f(-x) = -f(x)

Step-by-step explanation:

[tex]f(x)=8x^3[/tex]
[tex]f(-x)=8(-x)^3[/tex]
[tex]f(-x)=-8x^3[/tex]
[tex]-f(x)=-(8x^3)[/tex]
[tex]-f(x)=-8x^3=f(-x)[/tex]
[tex]f(-x)=-f(x)[/tex], therefore the function is odd

The function is odd because f(-x)=-f(x).

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=8x³.

We need to find which statement would be true in the given options.

Let us find this by taking x as -x.

f(-x)=8(-x)³

We know that when a negative sign is multiplied three times we get negative sign.

f(-x)=-8x³

-f(x)=-(8x³)

-f(x)=-8x³=f(-x)

f(-x)=-f(x)

By the definition of odd function f(-x)=-f(x).

Hence, the function is odd because f(-x)=-f(x).

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Based on the percentage of the first, second, and third acids, the milliliters of each acid that should be used to make 100 ml of 18% are:

Assuming the concentration of the 40% acid is denoted as x, the other acid concentrations would be:

10% acid = 4x

20% = 100 - 5x

The target solution is 100ml of 18%.

Solving gives:

(10% × 4x) + (20% × (100 - 5x)) + (40% × x) = 18% x 100

(80% × x) + 20 - x = 18

(80x - 100x) / 100 = 18 - 20

-20x / 100 = -2

20x = 200

x = 200 / 20

x = 10 ml

The 10% solution:

= 10 x 4

= 40 ml

20% acid:

= 100 - (5 x 10)

= 50 ml

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Step-by-step explanation:

since the sumation of f(x) of a probability is 1

thw probability to win is o.5 and to lose is o.5 so expected value is xf(x

your expected value will b 0.5 multiply by 5 thats is 2.5 thats your expected gain

Answer:

0

Step-by-step explanation:

because 1-0=1*2^3=8

because2^3=8

The point estimate of difference of the sample his will be -20.

Based on the information given, the. following can be depicted:

n1 = 13

x1 = 141

s1 = 13

n2 = 9

x2 = 161

s2 = 12

The point estimate of difference will be:

= 141 - 161

= -20

The margin of error to be used in constructing the confidence interval will be calculated by multiplying the standard error which is 5.467 and the critical value. This will be:

= 5.467 × 2.528

= 13.822

The margin of error is 13.822.

The confidence interval will now be:

= (-20 + 13.822) and (-20 - 13.822)

= -6.178 and -33.822

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The dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

For the pool, we have that;

Let the width = x feet

Length = (x+8) feet

The pool alongside the walkway gives;

Width = x + 5 + 5 = (x + 10) feet

Length = x + 8 + 5 + 5 = (x + 18) feet

Total area of the pool with walkway = 950 square feet

Note that formula for area is given as

Area = length * width = 950

Equate the length and width

(x+18)  × (x + 10) = 950

Using the  FOIL method, we have;

(x × x )+ (x × 10) + (18 × x) + (18 × 10) = 950

x² + 10x + 18x + 180 -950 = 0  

collect like terms

x² + 28x - 770 = 0

Thus, the dimensions of the pool would give a quadratic equation x² + 28x - 770 = 0

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Answer:

A and D

Step-by-step explanation:

Let's find the slope of the functions in all tables.

A. -1/2

B. -1/2

C. -1/2

D. 1

E. -1/2

Option D. is out since it has a different slope.

The answer has to be two tables out of A, B, C, and E.

Start with Table A.

As x goes from 8 to 6, y goes up by 1.

We can create points for x = 0 and x = 2

x = 2, y = 9

x = 8, y = 6

This is exactly table D.

Answer: Tables A and D

Answer:

1/6

Step-by-step explanation:

You have six choices and you want to pick only 1 of those choices.

1/6

[tex]\displaystyle\frac{1}{6}[/tex]

Probability explains the likelihood of an event occurring. The outcome you are finding the probability for is the successful outcome. The sample size is the total number of possible outcomes.

Simple Probability

Simple probability is when there is only one single event. In this situation, the cube is only being rolled once, so it's a simple probability question. To solve this question as a fraction, the numerator should be the number of successful outcomes and the denominator should be the sample size.

Solving for P(B)

Since there are 6 sides with 6 letters, the sample size is 6. So, 6 should be the denominator. We are finding the probability of "B", which means there is 1 successful outcome. Thus, the numerator should be 1.

This means as a fraction the probability is [tex]\frac{1}{6}[/tex].

Answer:

What is the expected value when rolling a fair 12-sided die?

132=6.5

Recall the definition of the expected value:

E[X]=∑ni=1xp(x)

Here, we have 12 possible values the die can take on, and the probability of each one is the same: 1/12. So we can just pull the term p(x), the probability of each outcome, out of the summation:

E[X]=112∑12i=1x

A useful trick here is that the sum of the numbers 1..N=N(N+1)2. So:

E[X]=11212(13)2

E[X]=12(13)12(2)

E[X]=132

Step-by-step explanation:

hope it helps you :)

Answer:

c)  3 units

d)  g(x) - f(x) = x² + 2x

e)  (-∞, -2] ∪ [0, ∞)

Step-by-step explanation:

To calculate the length of FC, first find the coordinates of point C.

The y-value of point C is zero since this is where the function f(x) intercepts the x-axis.  Therefore, set f(x) to zero and solve for x:

[tex]\implies 1-x^2=0[/tex]

[tex]\implies x^2=1[/tex]

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

[tex]\implies x= \pm 1[/tex]

As point C has a positive x-value,  C = (1, 0).

To find point F, substitute the x-value of point C into g(x):

[tex]\implies g(1)=2(1)+1=3[/tex]

⇒ F = (1, 3).

Length FC is the difference in the y-value of points C and F:

[tex]\begin{aligned} \implies \sf FC& = \sf y_F-y_C\\ & = \sf 3-0\\ & =\sf 3\:units \end{aligned}[/tex]

Given functions:

[tex]\begin{cases}f(x)=1-x^2\\ g(x)=2x+1 \end{cases}[/tex]

Therefore:

[tex]\begin{aligned}\implies g(x)-f(x) & = (2x+1) - (1-x^2)\\& = 2x+1-1+x^2\\& = x^2+2x\end{aligned}[/tex]

The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):

Point A is the y-intercept of both functions, therefore the x-value of point A is 0.

To find the x-value of point E, equate the two functions and solve for x:

[tex]\begin{aligned}g(x) & = f(x)\\\implies 2x+1 & = 1-x^2\\x^2+2x & = 0\\x(x+2) & = 0\\\implies x & = 0, -2\end{aligned}[/tex]

As the x-value of point E is negative ⇒ x = -2.

Therefore, the values of x for which g(x) ≥ f(x) are:

Answer:

a)

A = (0, 1)

B = (-1, 0)

C = (1, 0)

D = (-0.5, 0)

b) E = (-2, -3)

c) FC = 3 units

d) x² + 2x

e) x ≤ -2 and x ≥ 0

Explanation:

This question displays one equation of a linear function g(x) = 2x + 1 and a parabolic function f(x) = 1 - x².

a)

A point is where the linear function cuts the y axis.

y = 1 - (0)²

y = 1

A = (0, 1)

B and C point is where the parabolic function cuts the x axis.

1 - x² = 0

-x² = -1

x² = 1

x = ±√1

x = -1, 1

B = (-1, 0), C = (1, 0)

D point is where the linear function cuts x axis.

2x + 1 = 0

2x = -1

x = -1/2 or -0.5

D = (-0.5, 0)

b)

E point is where both equations intersect each other.

y = y

2x + 1 = 1 - x²

x² + 2x = 0

x(x + 2) = 0

x = 0, x = -2

y = 1, y = -3

E = (-2, -3)

c)

C : (1, 0)

To find F point

y = 2(1) + 1

y = 3

F : (1, 3)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]\sf d = \sqrt{(1 - 1)^2 + (3 - 0)^2}[/tex]

[tex]\sf d = \sqrt{0 + 3^2}[/tex]

[tex]\sf d = 3[/tex]

FC length = 3 units

d)

g(x) - f(x)

(2x + 1) - (1 - x²)

2x + 1 - 1 + x²

x² + 2x

e)

g(x) ≥ f(x)

2x + 1 ≥ 1 - x²

x² + 2x ≥ 0

x(x + 2) ≥ 0

[tex]\boxed{If \ x \ \geq \ \pm \ a \ then \ -a \ \leq x \ \ and \ x \ \geq \ a }[/tex]

x ≤ -2 and x ≥ 0

The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is

[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]

The factors of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex]  are x=1, -2, 4/3, -2/5.

Given equation is [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex],

By performing L-division method, we get

[tex]y = (x-1)(15x^{3} +16x^{2} -36x-16)[/tex]

Then again doing the same L-division method to the cubic equation [tex]15x^{3} +16x^{2} -36x-16[/tex], we get

[tex]15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)[/tex]

Therefore, [tex]y = (x-1)(x+2)(15x^{2}-14x-8)[/tex]

Then finally the roots of the quadratic equation [tex]15x^{2}-14x-8[/tex] are (x-(4/3)) and (x+(2/5))

Hence, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )[/tex]

Therefore, the roots of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.

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According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

According to the statement

we have given that the mean of 7 hours per day watching TV, and a standard deviation of 1.8 hours.

And we have to find that the At least how many hours of daily TV watching are necessary for a person to be eligible for the interview.

So, For this purpose,

The confidence interval is is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level.

Let us Assume x is the amount of hours that 5% of the persons exceeds.

Then P(z<(x-7)/1.8) = 0.95

From a standard normal table, we know that:

(x-7)/1.8 = 1.6449

x-7 = 2.9607

x = 9.9607

So, According to the confidence interval only persons who watch at least 9.9 hours TV per day are eligible.

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The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Given that:

d = rt

Hence:

t = d/r

For d = 40, r = 8:

t = 40 / 8

t = 5

The formula that shows the relationship between the distance, rate and time is t = d/r and t = 5.

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the area of the minor segment is 0. 29 cm^2

From the information given, we have the following parameters;

It is important to note the formula for area of a sector is given as;

Area = πr² + θ/360° - 1/ 2 r² sin θ

The value for π = 3.142

θ = 30°

Now, let's substitute the values

Area = 3. 142 × 5² × 30/ 360 - 1/ 2 × 5² × sin 30

Find the difference

Area = 3. 142 × 25 × 1/ 12 - 1/ 2 × 25 × 1/2

Multiply through

Area = 6. 54 - 6. 25

Area = 0. 29 cm^2

The area of the minor segment is given as 0. 29 cm^2

Thus, the area of the minor segment is 0. 29 cm^2

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Answer:

135

Step-by-step explanation:

Then add the first and last number i.e.

433+107===> 540

divide 540 by 4

540/4

= 135

Answer:

134

Step-by-step explanation:

-107/4 = -26.75

429/4 = 107.25

107.25 - (-26.75)

107.25 + 26.75 = 134