PLEASE HELP
4. The table shows the probabilities of a response chocolate or vanilla when asking a child or adult. Use the formula for conditional probability to determine independence.

Chocolate | Vanilla | Total
Adults 0.21 0.39 0.60

Children 0.14 0.26 0.40

Total 0.35 0.65 1.00


a. Are the events “Chocolate” and “Adults” independent? Why or why not?
b. Are the events “Children” and “Chocolate” independent? Why or why not?
c. Are the events “Vanilla” and “Children” independent? Why or why not?

Answer:

30 and 38

Step-by-step explanation:

If x is the smaller number and y is the larger number:

x + y = 68

x = y - 8

Solve with substitution:

y - 8 + y = 68

2y = 76

y = 38

x = 30

So the two numbers are 30 and 38.

Answer:

Smaller number = 30

Larger number = 38

Step-by-step explanation:

68 = (x+8) + x

68 = 2x - 8

60 = 2x

30 = x

and

68 = (x-8) + x

68 = 2x - 8

76 = 2x

38 = x

Answer:

[tex]x =26\°[/tex]

Step-by-step explanation:

For this case we have 2 secant lines and an exterior angle x.

Then by definition the measure of the outer angle is equal to half the difference of the arcs formed by the sides.

This means that the angle x is equal to:

[tex]x =\frac{66\°-14\°}{2}\\\\x =26\°[/tex]

the answer is:

[tex]x =26\°[/tex]

For this case we must factor the following expression:

[tex]4x ^ 3 + x ^ 2-8x-2[/tex]

We group the first two and the last two terms:

[tex](4x ^ 3 + x ^ 2) + (- 8x-2)[/tex]

We factor the highest common denominator of each group:

[tex]x ^ 2 (4x + 1) -2 (4x + 1)[/tex]

We take the common factor[tex]4x + 1:[/tex]

[tex](4x + 1) (x ^ 2-2)[/tex]

Answer:

[tex](4x + 1) (x ^ 2-2)[/tex]

Following are the description on the function behavior:

Given:  

[tex]\bold{f(x) = -3x^4 + 7x^2 - 12x + 13}[/tex]

To find:

Function behavior=?

Solution:

We use Power and Polynomial Functions features in the absence of technology. As the function [tex]\bold{f(x) = -3x^4 + 7x^2 -12x + 13}[/tex]

For final behaviour of power functions of such form[tex]\bold{f(x)=ax^n}[/tex] wherein n is a non-negative integer depends on the power and the constant.

 So, the leading term, [tex]\bold{f(x)=-3x^4}[/tex]

When the negative constant and even power are:  

[tex]\to x \to \infty\\\\\to f(x) \to -\infty[/tex]

At  

[tex]x \to -\infty\\\\f(x) \to -\infty[/tex]

 Therefore, the final answer is "Down on the left down on the right "

Learn more:

brainly.com/question/13821048

The end behavior of [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] is described as "Down on the left, down on the right," The correct answer is option a) Down on the left, down on the right.

To determine the end behavior of the polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] without using technology, we analyze the leading term, which dominates the behavior of the function as x approaches positive or negative infinity.

1. Identify the leading term: The leading term of [tex]\( f(x) \) is \( -3x^4 \)[/tex].

2. Consider the degree and leading coefficient:

  - The degree of the polynomial is 4.

  - The leading coefficient (coefficient of the term with the highest power of [tex]\( x \)) is \( -3 \)[/tex].

3. Determine the end behavior:

  - As [tex]\( x \to +\infty \), \( -3x^4 \)[/tex] approaches [tex]\( -\infty \)[/tex] because [tex]\( x^4 \)[/tex] grows much faster than the negative coefficient affects it. Therefore, [tex]\( f(x) \to -\infty \)[/tex].

  - As [tex]\( x \to -\infty \)[/tex], [tex]\( -3x^4 \)[/tex] also approaches [tex]\( -\infty \)[/tex] for the same reason. Hence, [tex]\( f(x) \to -\infty \)[/tex].

4. Conclusion: Based on the analysis:

  - The polynomial [tex]\( f(x) = -3x^4 + 7x^2 - 12x + 13 \)[/tex] decreases to [tex]\( -\infty \)[/tex] as x goes to both positive and negative infinity.

Therefore, the end behavior of [tex]\( f(x) \)[/tex] is described as "Down on the left, down on the right", which corresponds to option a). This indicates that the graph of [tex]\( f(x) \)[/tex] starts high on the left and continues downward indefinitely in both directions.

Complete question : Without using technology, describe the end behavior of f(x) = −3x4 + 7x2 − 12x + 13.

a Down on the left, down on the right

b Down on the left, up on the right

c Up on the left, down on the right

d Up on the left, up on the right

Answer:

Vertical A @ x=3 and x=1

Horizontal A nowhere since degree on top is higher than degree on bottom

Slant A @ y=x-1  

Step-by-step explanation:

I'm going to look for vertical first:

I'm going to factor the bottom first:  (x-3)(x-1)

So we have possible vertical asymptotes at x=3 and at x=1

To check I'm going to see if (x-3) is a factor of the top by plugging in 3 and seeing if I receive 0 (If I receive 0 then x=3 gives me a hole)

3^3-5(3)^2+4(3)-25=-31 so it isn't a factor of the top so you have a vertical asymptote at x=3

Let's check x=1

1^3-5(1)^2+4(1)-25=-25 so we have a vertical asymptote at x=1 also

There is no horizontal asymptote because degree of top is bigger than degree of bottom

There is a slant asympote because the degree of top is one more than degree of bottom (We can find this by doing long division)

                       x   -1

                --------------------------------------------------

x^2-4x+3 |      x^3-5x^2+4x-25

                  - ( x^3-4x^2+3x)

                   --------------------------------

                            -x^2 +x  -25

                       -   (-x^2+4x-3)

                          ---------------------

                                   -3x-22

So the slant asymptote is to x-1

Answer: D

Step-by-step explanation:

EDGE 2021

Answer:

Option B. [tex]F(x)=x^{2}+1[/tex]

Step-by-step explanation:

we know that

[tex]G(x)=x^{2}[/tex]

This is the equation of a vertical parabola open upward wit vertex at (0,0)

The rule of the translation of G(x) to F(x) is equal to

(x,y) ----> (x,y+1)

therefore

The vertex of the function f(x) is the point (0,1) and the equation is equal to

[tex]F(x)=x^{2}+1[/tex]

Answer:

  2π ≈ 6.283

Step-by-step explanation:

The average value of the function is the area under it, divided by the base. This function describes a semicircle of radius 8, so its area is ...

  A = 1/2πr² = 1/2π·8² = 32π

The width of the base is the diameter of the semicircle, so is 16. Then the average value is ...

  32π/16 = 2π . . . . . average value of y

Answer:

  3

Step-by-step explanation:

Fill in the known values in the vertex form equation and solve for the coefficient.

  y = a(x -h)^2 +k

  -1 = a(3 -2)^2 -4 = a -4 . . . . fill in the values and simplify

  3 = a . . . . . . . . . . . . . . . . . . .add 4

The coefficient of the squared expression is 3.

Final answer:

The coefficient of the squared term in the parabola's equation, given the vertex (2, -4) and a point (3, -1) on the parabola, is found to be 3 by substituting these values into the vertex form of a parabola's equation.

Explanation:

The student is asking how to determine the coefficient of the squared term in a parabola's equation, given the vertex and a point on the parabola. The standard form of a parabola's equation with vertex (h, k) is  [tex]y = a(x - h)^2 + k,[/tex] where a is the coefficient in question. Knowing the vertex at (2, -4) and a point (3, -1) on the parabola, we can substitute these into the equation to find a.

Substituting the vertex into the equation gives us the form [tex]y = a(x - 2)^2 - 4.[/tex] Then we substitute the point (3, -1):

[tex]-1 = a(3 - 2)^2 - 4[/tex]

[tex]-1 = a(1)^2 - 4[/tex]

-1 + 4 = a · 1

a = 3

Therefore, the coefficient of the squared expression in the parabola's equation is 3.

Answer:

c(x) = –8x^2 + 3x – 5 is a quadratic function.

Step-by-step explanation:

At first, we will define what a quadratic function is.

A quadratic function is a polynomial with one or more variables with degree 2.

So, from the given functions

a(x) = -2x^3+ 2x – 6 has highest degree 3. So it is not a quadratic function.

b(x)=5x^3 + 8x^2 + 3 has highest degree 3. So it is not a quadratic function.

c(x) = –8x^2 + 3x – 5 has highest degree 2. So it is a quadratic function.

d(x) = 6x^4 + 2x – 3 has highest degree 4. So it is not a quadratic function.

Answer:

Step-by-step explanation:

Answer:

  = (x +4)(x -7)(x^2 +25)

  roots are -4, 7, ±5i

Step-by-step explanation:

You have not said what "solve" means in this context. An expression by itself doesn't have a solution. We have assumed you want to find the factoring and/or roots of it.

I like to use a graphing calculator to find the real roots. For this expression, there are two of them, one positive and one negative. (You know there will be one positive real root, and at least one negative real root, from Descartes's rule of signs.)

Then those roots can be factored out and the solution to the remaining quadratic determined. That factoring can occur by polynomial long division, synthetic division, or other means.

I like to see what happens when I plot the graph of the function divided by the known factors. (We expect a parabola that doesn't cross the x-axis.) The vertex of that parabola can be used to find the remaining roots.

The x-intercepts of the given expression are -4 and +7, so two of the factors are (x+4) and (x-7). Dividing these from the given expression (by synthetic division or other means) gives (x^2 +25). This only has imaginary roots (±5i).

____

If you're constrained to doing this "by hand" with only a scientific calculator, Descartes's rule of signs tells you there is one positive real root. (Only one sign change in the sequence of coefficient signs: +----.)

The rational root theorem tells you it will be a divisor of 700. Various estimates of the maximum magnitude of it will tell you it is probably less than 14 (easily checked). So, the numbers you can test as roots would be 1, 2, 4, 5, 7, 10, 14. You will find that 7 is a root, and then you can reduce the problem to the cubic x^3 +4x^2 +25x +100.

When odd-degree term signs are changed, there will be 3 sign changes (-+-+), hence at least one negative real root. The rational root theorem tells you it is a divisor of 100, so possible choices are -1, -2, -4, -5. By trial and error or other means, you can find the root to be -4. Then the problem reduces to the quadratic x^2 +25.

Roots of that are ±√(-25) = ±5i.

This process generally entails a fair amount of trial-and-error work, which is why I prefer one that makes some use of technology.

_____

We have presumed you have some familiarity with ...

This will usually be the case when you're presented with problems like this. If you need additional information on any of these, it is readily available on the internet (and probably also in your reference material).

Answer:

3%

Step-by-step explanation:

We are given the data of number of cars observed waiting in line at the beginning of 2 minute intervals between 3 and 5 p.m. on Friday.

We are to find the probability (in percent) that there is no one in line.

Sum of frequencies = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60

Frequency of no car in line = 2

P (no car in line) = 2 / 60 × 100 = 3.3% ≈ 3%

Answer:

(10, −13); (15, −20)

Step-by-step explanation:

Answer:

center at (6, -4) r = √7

Step-by-step explanation:

(x – 6)^2 + (y + 4)^2 = 7

This is in the form

(x – h)^2 + (y - k)^2 = r^2

Where (h,k) is the center of the circle and r is the radius of the circle

Rearranging the equation to match this form

(x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2

The center is at (6, -4) and the radius is the sqrt(7)

Answer:

center at (6, -4) r = √7

Step-by-step explanation:

(x – 6)^2 + (y + 4)^2 = 7 This is in the form (x – h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius of the circle Rearranging the equation to match this form (x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2 The center is at (6, -4) and the radius is the sqrt(7)

Answer:

see explanation

Step-by-step explanation:

1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{1}{4}[/tex], hence

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (8, - 1) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - [tex]\frac{1}{4}[/tex] x + 1 ← in slope- intercept form

2

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 1 and (a, b) = (- 2, 5), hence

y - 5 = - (x - (- 2)), that is

y - 5 = - (x + 2)

Step-by-step explanation:

49-30=19, then add 19+16, then you get the answer of 35!

Hope this helps!

See the attached picture for the answer.

Answer:

  a) see the plots below

  b) f(x) is exponential; g(x) is linear (see below for explanation)

  c) the function values are never equal

Step-by-step explanation:

a) a graph of the two function values is attached

__

b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).

__

c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.

In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.

Answer:

b. The function f(x) appears exponential because its graph approaches but does not cross the negative x-axis, while growing at a faster and faster rate to the right (or precisely: as x increases by 1, the value gets multiplied by the same constant, 3.) The function g(x) is linear since g(x) increases by the same amount as x increases in steps of one unit.

c. The graph appears to show that the functions do not intersect, so the function values will not be equal. The function f is already above the function g and it is growing at a faster rate, so they cannot ever be equal.

Step-by-step explanation:

used the answer above just changed a few words and all

Answer:

D

Step-by-step explanation:

3 and 7 are the main factors so you add them and get 10 but since it’s two equilateral trapezoids then you get another 10 being 20 square feet.

Answer:

D) 20 square feet

Step-by-step explanation:

We are given two congruent isosceles trapezoids and placed together formed to make a corner of the desk.

We need to find the area.

We know that the area of a trapezoid = [tex]\frac{h}{2} [base 1+ base 2][/tex]

Where "h" is the height of the trapezoid.

Given: h = 2 ft, base 1 = 7ft and base 2 = 3ft

Now plug in these values in the above formula, we get

Area of a 1 trapezoid = [tex]\frac{2}{2} [7 + 3][/tex]

= 10 square feet

The two trapezoids are congruent.

So the area of the given figure = 2(10) = 20 square feet.

Answer:

  $227.64

Step-by-step explanation:

The relevant relations are ...

  sales + tax = total

  tax = 7% × sales

Using the second equation, we can write sales in terms of the tax as ...

  sales = tax/0.07

Substituting this into the first equation gives ...

  tax/.07 + tax = total . . . . . substitute for sales

  tax(1/0.07 + 1) = total . . . . factor out tax

  tax ((1 +.07)/.07) = total . . . simplify to a single fraction

Multiply by the inverse of this fraction:

  tax = .07/1.07 × total = (7/107)($3479.64)

  tax = $227.64

Answer:

  3

Step-by-step explanation:

Solving the inequality gives ...

  x/9 < 2/5

  x < 18/5 . . . . multiply by 9

Applying the problem restrictions, we have ...

  0 < x < 3.6 . . . . . x is an integer

Solutions are {1, 2, 3}. There are 3 distinct possible values for x.

Answer:

  (d -21) is the number of days the book is late

Step-by-step explanation:

There is no fee if the book is returned within 21 days, so d-21 represents the number of "late days" for which a fee is charged.

Answer:

(d -21) is the number of days the book is late

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The only possible answer if 12 because all of the other choices come to the conclusion that 8h ≤ 64

if h=12 then 8h= 8 * 12 = 96 > 64

The value of h is 12.

Multiply the length, width, and height of a rectangular prism to determine its volume. Cubic measurements are used to express volume.

Given,

The only possible answer is 12 because all of the other choices come to the conclusion that 8h ≤ 64

if h=12 then 8h= [tex]8 * 12[/tex] = 96 > 64

To know more about rectangular prism  refer to :

https://brainly.com/question/477459

#SPJ2

Answer:

5

Step-by-step explanation:

Blue: when x = - 3, y = 5

Green: when x = -3, y = 0

The difference between the two graphs at X = -3 : 5 - 0 = 5

Answer

5

Answer:

r=4ft

h=8ft

Area of cyclender=?

by using formula,

A=πr²h

=22/7×4²×8

=402.28ft²Ans.

ANSWER

301.6 ft²

EXPLANATION

The surface area of a cylinder is calculated using the formula;

[tex]S.A = 2\pi \: r(r + h)[/tex]

From the diagram the height of the cylinder is 8 feet and the radius is 4 feet.

We substitute the values into the formula to obtain,

[tex]S.A = 2\pi \: 4(4+ 8)[/tex]

This simplifies to:

[tex]S.A = 8\pi \: (12)[/tex]

[tex]S.A = 96\pi[/tex]

Or

[tex]S.A = 301.6 {ft}^{2} [/tex]

to the nearest tenth.

Amplitude = 2; period T = π; midline y = 1.

This sinusoidal wave is a even function which means that it has a positive half-cycle and a negative half-circle of equal size, from the image we can see that the midline is y = 1 which is the point where the function is centered.

The amplitude is the measure from the midline to the positive half-cycle, and the midline to the negative half-cycle which is 2.

The period corresponds to a complete cycle of the function or the repetition of the wave seen from a point. In this case, we can see that the wave, starting from π/2 it repeat in 3π/2. So, to calculate the period just substract 3π/2 by π/2

T = 3π/2 - π/2 = (3π - π)/2

T = 2π/2

T = π

ANSWER

[tex]f(x) = 2 ({x - 1)}^{2} - 1[/tex]

EXPLANATION

The vertex form of a parabola has equation:

[tex]f(x) = a ({x - h)}^{2} + k[/tex]

where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.

From the question, we have that, the vertex is

[tex](1,-1)[/tex]

and the leading coefficient is

[tex]a= 2[/tex]

We substitute the vertex and the leading coefficient into the vertex form to get:

[tex]f(x) = 2 ({x - 1)}^{2} + - 1[/tex]

We simplify to get:

[tex]f(x) = 2 ({x - 1)}^{2} - 1[/tex]

The graph of this function is shown in the attachment.

The graph that has a vertex of (1,-1) and a leading coefficient of a=2 is a parabola.

The graph that has a vertex of (1,-1) and a leading coefficient of a=2 is a parabola. The leading coefficient, which is the coefficient of the squared term, determines the nature of the parabola.

Since the leading coefficient is positive, the parabola opens upward. The equation of the parabola can be written in the form y = ax^2 + bx + c, where a represents the leading coefficient.

Therefore, the equation of the graph is y = 2x^2 - 4x + 1.

For this case we have that by definition, the area of the trapezoid is given by:

[tex]A = \frac {1} {2} (B + b) * h[/tex]

Where:

B: It is the major base

b: It is the minor base

h: It's the height

Substituting the values according to the data of the figure:

[tex]A = \frac {1} {2} (2.1 + 0.9) * 1.3\\A = \frac {1} {2} (3) * 1.3\\A = \frac {1} {2} * 3.9\\A = 1.95[/tex]

Thus, the area of the trapezoid is[tex]1.95 m ^ 2[/tex]

ANswer:

Option B

Answer:

vertex (-3,5) and another pt (-2,4)

Step-by-step explanation:

It is in vertex form so the vertex is (-3,5)...

Now just plug in a value for x say like -2...

f(-2)=-(-2+3)^2+5

f(-2)=-(1)^2+5

f(-2)=-1+5

f(-2)=4

So another point is (-2,4)

Answer:

y-int = 5

roots: sqrt(5)-3 or -3 - sqrt(5)

TP @ (-3,5)

Step-by-step explanation:

y intercept = 5 (when x = 0)

Roots:

When y = 0

5 - (x + 3)^2 = 0

(x+3)^2 = 5

Square both sides:

x + 3 = Sqrt[5] or x + 3 = - Sqrt[5]

x = Sqrt[5] - 3 or x= - 3 - Sqrt[5]

Turning point (Critical Point):

dy/dx (5-(x+3)^2) = - 2 (x+3)

Solve -2 (x+3) = 0

x = - 3

y = 5

Max point at (-3,5)

Answer:

  A = 4π(7)^2

Step-by-step explanation:

The formula for the area of a sphere is ...

  A = 4πr^2 . . . . . . for radius r

When the radius is 7 feet, the value 7 goes where r is in the formula:

  A = 4π·7^2 . . . . . square feet

Answer:

  3520 ft/min

Step-by-step explanation:

40 mi/h = (40 mi/h)×(5280 ft/mi)×(1 h)/(60 min) = 3520 ft/min

_____

Each conversion factor has a value of 1 (numerator = denominator), so changes the units without changing the speed.

Final answer:

To convert 40 mi/h to feet per minute, multiply by 5280 feet per mile and then divide by 60 minutes per hour, resulting in a speed of 2400 ft/min. So the correct option is a. 2,400 ft/min.

Explanation:

To convert the speed of a car from miles per hour (mi/h) to feet per minute (ft/min), we need to know the following conversions:

1 hour = 60 minutes

Now, we can use these conversions to calculate the speed:

40 mi/h
40 mi/h = 40
(5280 ft/mi)
(60 min/hour) = 2,400 ft/min.

The car is driving at a speed of  2,400 ft/min.