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

Answers

Answer 1

Answer:

Here both probabilities are not equal.

Therefore the die is not fair and biased.

Step-by-step explanation:

Now n= 1200 times and x = 419 times.

a) Empirical Probability:

         [tex]=\frac{x}{n} \\\\= \frac{419}{1200}\\ \\=0.349[/tex]

Probability = 0.349

b) Theoretical Probability:

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

Here both probabilities are not equal.

Therefore the die is not fair and biased.


Related Questions

I need help to fine the statement that is true

Answers

Answer:

option A

Step-by-step explanation:

wx and zy making 90 angle with each other therefore they are perpendicular.

wx and ab making 0 angle with each other therefore they are parallel

The central angle in a circle of radius 6 meters has an intercepted arc length of 10 meters. Find the measure of the angle in radians and in degrees

Answers

Answer:

The central angle is 5/3 radians or approximately 95.4930°.

Step-by-step explanation:

Recall that arc-length is given by the formula:

[tex]\displaystyle s = r\theta[/tex]

Where s is the arc-length, r is the radius of the circle, and θ is the measure of the central angle, in radians.

Since the intercepted arc-length is 10 meters and the radius is 6 meters:

[tex]\displaystyle (10) = (6)\theta[/tex]

Solve for θ:

[tex]\displaystyle \theta = \frac{5}{3}\text{ rad}[/tex]

The central angle measures 5/3 radians.

Recall that to convert from radians to degrees, we can multiply by 180°/π. Hence:

[tex]\displaystyle \frac{5\text{ rad}}{3} \cdot \frac{180^\circ}{\pi \text{ rad}} = \frac{300}{\pi}^\circ\approx 95.4930^\circ[/tex]

So, the central angle is approximately 95.4930°

f(x) = - 2x
g(x) = 8x^2 - 5x + 7
Find (f • g)(x).

Answers

9514 1404 393

Answer:

  (f•g)(x) = -16x^3 +10x^2 -14x

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)

Use the distributive property:

  (f•g)(x) = -16x^3 +10x^2 -14x

If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?​

Answers

Answer:

16 cm^2/min

Step-by-step explanation:

dV/dt=24

V=a^3, differentiate with respect to t

dV/dt=3a^2*da/dt, a^2*da/dt=8

S=6a^2, 216=6a^2. a=6. da/dt=(8/36)

dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min

What is the surface area of this figure in square centimeters?

A.96
B.75
C.84
D.60

Answers

9514 1404 393

Answer:

  A.  96

Step-by-step explanation:

The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.

  A = 2(1/2)bh + PH

where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.

  A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²

  A = 96 cm²

The surface area of the triangular prism is 96 square cm.

2/5 = 6/ = 10/30 = 14/


Please tell asap

Answers

Answer:

6/15.

14/42.

Step-by-step explanation:

2/5 = 6/x

Cross multiply:

2x = 5*6

x = 15

Similarly:

10/30 = 14/x

10x = 30*14

x = 420/10

x = 42.

find the supplement of 158 degrees and 17 minutes

Answers

Answer:

supplement of 158 degree

x+158=180

x=180-158

x=22 degree.

Step-by-step explanation:

Solve for x.
–5(–2x – 5) – 2 – 1= -12

Answers

Answer:

x=-17/5

Step-by-step explanation:

–5(–2x – 5) – 2 – 1= -12

+10x+25-2-1=-12

10x+22=-12

10x=-12-22

10x=-34

x=-34/10

x=-17/5

Step-by-step explanation:

Open the brackets

10x +25 -2 - 1= -12

Collect the like terms

10x = -12-25+2+1

10x = -34

Divide both sides by 10

Therefore,x = -34/10 = -3.4

There is 60% chance of making $12,000, 10% chance of breaking even and 30% chance of losing $6,200. What is the expected value of the purchase?

Answers

Answer:

$5,340

Step-by-step explanation:

Given :

Making a probability distribution :

X : ___12000 ____0 _____-6200

P(X) __ 0.6 _____ 0.1 _____ 0.3

Tge expected value of the purchase si equal to the expected value or average, E(X) :

E(X) = ΣX*p(X)

E(X) = (12000 * 0.6) + (0 * 0.1) + (-6200 * 0.3)

E(X) = 7200 + 0 - 1860

E(X) = $5,340

Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)

Answers

Answer:

Test statistic = 0.63

Pvalue = 0.555

A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.

Step-by-step explanation:

Given :

Before 13 22 65 123 56 63

After_ 14 21 43 84 75 72

To perform a paired t test :

H0 : μd = 0

H1 : μd ≠ 0

We obtain the difference between the two dependent sample readings ;

Difference, d = -1, 1, 22, 39, -19, -9

The mean of difference, Xd = Σd/ n = 33/6 = 5.5

The standard deviation, Sd = 21.296 (calculator).

The test statistic :

T = Xd ÷ (Sd/√n) ; where n = 6

T = 5.5 ÷ (21.296/√6)

T = 5.5 ÷ 8.6940555

T = 0.6326

The Pvalue : Using a Pvalue calculator ;

df = n - 1 = 6 - 1 = 5

Pvalue(0.6326, 5) = 0.5548

Decision region :

Reject H0 ; If Pvalue < α; α = 0.05

Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.

Which expression is equivalent to (3 squared) Superscript negative 2?

Answers

Answer:

–81

Step-by-step explanation:

WILL GIVE BRAINLIEST
Combine like terms.
2x – 3 – 5x + 8 = [ ? ]x + [ ]

Answers

Answer:

-3x + 5

Step-by-step explanation:

like terms are the ones that have x and the ones that don't.

hope this makes sense

Answer:

-3x + 5

Step-by-step explanation:

2x - 3 - 5x + 8 can also be written as 2x - 5x - 3 + 8

→ Using the rewritten method collect the x terms

-3x - 3 + 8

→ Now collect the integers

-3x + 5

Solve the equation for x 11x=110

Answers

Answer:

x = 10

Step-by-step explanation:

11x = 110

Divide both sides by 11

11x/11 = 110/11

x = 10

How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155

Answers

9514 1404 393

Answer:

  10

Step-by-step explanation:

The sum of terms of an arithmetic series is ...

  Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2

For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...

  155 = (3n^2 +n(2·2 -3))/2

Multiplying by 2, we have ...

  3n^2 +n -310 = 0 . . . . . arranged in standard form

Using the quadratic formula, the positive solution is ...

  n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10

10 terms of the series will have a sum of 155.

Answer: 10 terms

Step-by-step explanation:

[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]

Devy likes to learn! Could someone please tell me how to answer this question?

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).

On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).

On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).

On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).

Answers

Answer:

B

Step-by-step explanation:

Recall that if two functions, f and g, are inverses, then by definition:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

Hence, the graph of f(g(x)) should be simply y = x.

Therefore, our answer is B, as both coordinates are equivalent for all three points.

Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. SAS Postulate

Answers

Answer:

HJ = FG

Step-by-step explanation:

SAS means side - (included) angle - side.

we have one angle confirmed (at H and at G).

we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.

so, we need the confirmation of the second side enclosing the confirmed angle.

Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? O a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. O d) She will have a hard time focusing.

Answers

Option C

Customers will think she is very busy

A messy desk indicates that the person is very busy.

Must click thanks and mark brainliest

PLEASE HELP

-1/2m=-9

Show your work in details if you can, I have a hard time understanding this.

Answers

[tex] \begin{cases} \\ \large\bf{\green{ \implies}} \tt \: - \: \frac{1}{2} \: m \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{1 \: m}{2} \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 9 \: \times \: 2 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 18 \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{ \cancel- 18}{ \cancel - 1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{18}{1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: 18 \: \\ \end{cases}[/tex]

Please help quicklyyy!!!

Answers

Answer:

Its the 3 one

Step-by-step explanation:

2. What is the length of AB? Round your
answer to the nearest hundredth.

Answers

Answer:

The required length of AB is 7.28 units.

To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used

Answers

Answer:

Cluster Sampling

Step-by-step explanation:

Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.

An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?

Answers

Answer:

The standard deviation of your weight over a day is of 1.1547 pounds.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b, and the standard deviation is:

[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.

This means that [tex]a = -2, b = 2[/tex]

What is the standard deviation of your weight over a day?

[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]

The standard deviation of your weight over a day is of 1.1547 pounds.

the line parallel to 2x – 3y = 6 and containing (2,6)
what is the equation of the line ?

Answers

First, write out the equation in slope intercept form.

-3y= -2x+6

y= 2/3x -2

The slope of the equation is 2/3, m.

Substitute the slope and coordinate into y=mx+b. Since it’s parallel, the slope remains the same.

6= 2/3(2)+b

6= 4/3+b

14/3=b

y= 2/3x + 14/3

What is the measure of x?

Answers

Answer:

22

Step-by-step explanation:

This is a right angle so the sum of those would be equal to 90 degrees

x + 7 + 3x - 5 = 90 add like terms

4x + 2 = 90 subtract 2 from both sides

4x = 88 divide both sides by 4

x = 22

Which equation is represented by the graph?

Answers

Answer:

I don't knowledge bro sorry

Find the unit rate.
1/3 kilometer in 1/3hour

Answers

Answer:

1 kilometer in 1 hour

Step-by-step explanation:

unit rate is km(kilometer) per hour(hr)

1/3 km = 1/3 hr

multiply both sides by 3

1 km in 1 hour

I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4

Answers

9514 1404 393

Answer:

  yes

Step-by-step explanation:

No x-value is repeated, so these ordered pairs do represent a function.

A worker in the automobile industry works an average of 43.7 hours per week. Assume the distribution is normal with a standard deviation of 1.6 hours.


(i) What is the probability that a randomly selected automobile worker works less than 40 hours per week?


(ii) If 15 automobile workers are randomly selected, what is the probability that the sample mean of working time is more than 45 hours per week?

Answers

Answer:

The solution is:

(1) 0.0104

(2) 0.0008

Step-by-step explanation:

Given:

Mean,

[tex]\mu = 43.7[/tex]

Standard deviation,

[tex]\sigma = 1.6[/tex]

(1)

⇒ [tex]P(X<40) = P(\frac{x-\mu}{\sigma}<\frac{40-43.7}{1.6} )[/tex]

                      [tex]=P(z< - 2.3125)[/tex]

                      [tex]=P(z<-2.31)[/tex]

                      [tex]=0.0104[/tex]

(2)

As we know,

n = 15

⇒ [tex]P(\bar X > 45)= P(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } } >\frac{45-43.7}{\frac{1.6}{\sqrt{15} } } )[/tex]

                      [tex]=P(z> 3.15)[/tex]

                      [tex]=1-P(z<3.15)[/tex]

                      [tex]=1-0.9992[/tex]

                      [tex]=0.0008[/tex]

trig..experts...help! Will give brainly!

Answers

Answer:

Step-by-step explanation:

189² = 215² + 123² - 2(215)(123)cos x°

35,721 = 46,225 + 15,129 - 52,890 cos x°

35,721 = 61,354 - 52,890 cos x°

52,890 (cos x° ) = 25,633

cos x° = 25,633 ÷ 52,890 ≈ 0.4846

x° ≈ 61.01°

Four people share a taxi to the airport the fare was $36 and they gave the driver a tip equal to 25% of the fair. If they equally share the cost of the fair tip, how How much did each person pay?

Answers

Answer:

$11.25

Step-by-step explanation:

Total money given to the taxi driver=36+25% of 36=45

Each person will pay (45/4)=11.25

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