Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (Enter your probability as a fraction.) (b) On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased

Answer:

The expected number of offspring is 2

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]

Required

The expected number of offspring

This implies that we calculate the expected value of the function.

So, we have:

[tex]E(x) = \sum x * P(x)[/tex]

Substitute known values

[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]

Using a calculator, we have:

[tex]E(x) = 1.74[/tex]

[tex]E(x) = 2[/tex] --- approximated

Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

2(3x - 7) = 16

Step 2: Solve for x

Answer:

X=5

Step-by-step explanation:

divide by 2 on both sides first then you have

3x-7 = 8

take 7 to the other side so that you have an X factor on one side, thus

3x =15

then divide by 3 to remain with X

X = 5

Area of shaded region = 1/2(πr²)

= 1/2(22/7×3×3)

= 99/7

= 99/7×2

= 198/7 cm^2

Thats the total area of the shaded region

Must click thanks and mark brainliest

Answer:

see below

Step-by-step explanation:

a x (b+c) = a x b + a x c

Let A= -35 , B = 10 , C= -5

-35 * ( 10 -5) = -35 *10 + -35 * -5

-35 *(5) = -350 + 175

-175 = -175

Answer: [tex]x=12[/tex]

Step-by-step explanation:

[tex]f(x)=16x-30\\g(x)=14x-6[/tex]  are the equations that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

[tex]16x-30[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]16(12)-30[/tex]

Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.

[tex]192-30[/tex]

Step 4: Subtract 192 from 30. Which gives us 162.

[tex]162[/tex]

The right side of the equal sign:

Step 1: Write the equation down:

[tex]14x-6[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]14(12)-6[/tex]

Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.

[tex]168-6[/tex]

Step 4: Subtract 168 from 6. Which gives us 162.

[tex]162[/tex]

We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.

[tex]162=162[/tex]

Solve all of the equations below and add all of the solutions to those equations to get your answer.

10x4x2=

8x4x2=

10x8=

(10x8)-(7x6)=

7x2x2=

6x2x2=

7x6=

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

Part A) y=1,100x + 4,500

Part B) 14,400

Step-by-step explanation:

Part A)

There is a base fee of $4,500, meaning that the line begins at y=4500 (i.e. The y-intercept is [0,4500], so 'b' in y=mx+b is 4,500). There is a $1,100 hourly rate, which is proportional to the value of x, the amount of hours filmed. Therefore, 'm' in y=mx+b is $1,100.

Thus, the final equation looks like:

y= 1,100x + 4,500

Part B)

x=9

y=1,100x+4,500

y=1,100(9)+4,500

y=9,900+4,500

y=14,400

Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.

The percentage that is over 50 is 15.6%:

The data on the bar graph can be represented as:

Under 17 [tex]\to[/tex] 25

18 - 24 [tex]\to[/tex] 35

25 - 34 [tex]\to[/tex] 40

35 - 50 [tex]\to[/tex] 35

Over 50 [tex]\to[/tex] 25

So, the total customer surveyed are:

[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]

[tex]Total = 160[/tex]

The percentage over 50 are:

[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]

[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]

[tex]\%Over\ 50 = 0.15625* 100\%[/tex]

[tex]\%Over\ 50 = 15.625\%[/tex]

Approximate

[tex]\%Over\ 50 = 15.6\%[/tex]

Read more at:

https://brainly.com/question/10440833

Answer:

ytre

Step-by-step explanation:

Answer:

1320 m^2

Step-by-step explanation:

area of ground = π r ^2

= (22/7) × (137/2)^2

= 14,747.0714286 m^2

area of ground and path

=( 22/7)(143/2)^2

= 16,067.0714286 m^2

area of path

=16,067.0714286 -14,747.0714286

= 1320 m^2

note :

r = radius = diameter /2

area of a circle = π r^2

diameter of circle created with path and ground = 137 + 2 × width of path

= 137 + 2× 3 = 143 m

Answer:

b)  [tex]c=1[/tex]

Step-by-step explanation:

From the question, we are told that:

Function

[tex]F(x)=2x^2-4x+9[/tex]

Given

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Generally, the Function above is a polynomial that can be Differentiated and it is continuous

Where

-F(x) is continuous at (-1,3)

-F(x) Can be differentiated at (-1.3)

-And F(-1)=F(3)

Therefore

F(x) has Satisfied all the Requirements for Rolle's Theorem

Differentiating F(x) we have

[tex]F'(x)=4x-4[/tex]

Equating F(c) we have

[tex]F'(c)=0[/tex]

[tex]4(c)-4=0[/tex]

Therefore

[tex]c=1[/tex]

0.08 cm/min

Step-by-step explanation:

Given:

[tex]\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}[/tex]

Find [tex]\frac{dr}{dt}[/tex] when diameter D = 20 cm.

We know that the volume of a sphere is given by

[tex]V = \dfrac{4\pi}{3}r^3[/tex]

Taking the time derivative of V, we get

[tex]\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}[/tex]

Solving for [tex]\frac{dr}{dt}[/tex], we get

[tex]\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})[/tex]

[tex]\:\:\:\:\:\:\:= 0.08\:\text{cm/min}[/tex]

Answer:

1130

Step-by-step explanation:

1109+7 = 1116

1116+7 = 1123

Adding 7 each time

1123+7 = 1130

Answer:

a. P = 30

b. Y = 40

Step-by-step explanation:

Given the following data;

P = 1.2

Y = 100

First of all, we would have to determine the constant of proportionality;

P = k/Y (inverse proportion or relationship)

1.2 = k/100

k = 1.2 * 100

k = 120

a. To find the value of p when y = 4;

P = k/Y

P = 120/4

P = 30

b. To find the value of y when p = 3;​

P = k/Y

Y = k/P

Y = 120/3

Y = 40

Answer:

A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample​ and/or if the population of differences in winning times for all years is normal.

Step-by-step explanation:

In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.

Answer:

total = 2.8 + 3x

x is the price of the candy bars

Answer:

95

Step-by-step explanation:

300-20=280

280+100=380

380÷4=95

There you go...

Answer:

y=-1/2x+-1

Step-by-step explanation:

try desmos with this equation.

y=mx+b

m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.

b=y-intercept meaning the point which the line crosses the line y .-1

Answer:

[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Step-by-step explanation:

Given

Shapes: cylinder and hemisphere

[tex]h = 101[/tex] --- height of cylinder

Required

The volume of the silo

The volume is calculated as:

Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)

So, we have:

[tex]V_1 = \pi r^2h[/tex]

[tex]V_1 = \pi r^2 * 101[/tex]

[tex]V_1 = 101\pi r^2[/tex] --- cylinder

[tex]V_2 = \frac{2}{3}\pi r^3[/tex] ---- hemisphere

So, the volume of the silo is:

[tex]V =V_1 + V_2[/tex]

[tex]V =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Write as a function

[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Where: [tex]\pi = \frac{22}{7}[/tex]

Answer:

The nonresponse rate is 52 percent.

Step-by-step explanation:

150 sampled:

72 returned and 150 - 72 = 78

The nonresponse rate is

Percentage that 78 is out of 150, that is:

78*100%/150 = 52%

The nonresponse rate is 52 percent.

Answer:

C - 136

(115+157)/2

Step-by-step explanation:

Answer:

The answer is C

.91

ED2021

Answer:

540 miles/hr and 50 miles/hr respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50

Answer:

152 / 370

Step-by-step explanation:

Total number of people

152+218 = 370

P( own a dog) = people said yes / total

                       = 152 / 370

Step-by-step explanation:

you cannot just put the actual numbers in and calculate ?

and you can't provide the correct problem statement, as it seems.

I assume you mean

an = 3n² - 1

a sequence starts with a1, so, n>=1

a1 = 3×1² - 1 = 3-1 = 2

a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11

a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26

a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47

a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74

there, that is all there is to it. you really needed help with that ?

Answer:

A.

Step-by-step explanation:

Start with

7y + 5 - 3

Combine like terms:

7y + 2

By combining like terms in 7y + 5 - 3, we end up with 7y + 2 which is the second expression.

Therefore, the expressions are equivalent because they evaluate to equal values for every value of y.

Answer: A.