A table is made using the following two patterns.
Pattern 3: Starting number: 5, Rule: add 1
Pattern y: Starting number: 10, Rule: add 2
Complete the table for the given patterns.

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4  for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

[tex]P(6)=\dfrac{1}{6}[/tex]

The probability of getting a 5 is:

[tex]P(5)=\dfrac{1}{6}[/tex]

The probability of getting a 4 is:

[tex]P(4)=\dfrac{1}{6}[/tex]

The probability of getting other numbers (1,2,3) is:

[tex]P(\text{Otherwise})=\dfrac{3}{6}[/tex]

[tex]P(\text{Otherwise})=\dfrac{1}{2}[/tex]

We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

[tex]E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})[/tex]

[tex]E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}[/tex]

[tex]E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0[/tex]

[tex]E(x)=\dfrac{10+7+4}{6}[/tex]

[tex]E(x)=\dfrac{21}{6}[/tex]

[tex]E(x)=3.5[/tex]

Therefore, the expected winnings for this game are $3.50.

Answer:

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.

This means that [tex]\mu = 100, \sigma = 15[/tex]

Sample of 3

This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]

Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?

We have to find the z-score.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]

[tex]Z = 1.73[/tex]

|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.

Step-by-step explanation:

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Answer:

a)89

b)89.45

Step-by-step explanation:

Answer:

C.4/9

Step-by-step explanation:

You add the black marbles, blue marbles, and the white marbles together, which equal 18. Out of the 18 marbles, 8 of them are white so it would be 8/18.

but you have to simplify it. 8 and 18 have 2 as the greatest common factor. 8 divided by 2 is 4 and 18 divided by 2 is 9. Finally its 4/9 since you cant simplify it even more.

Answer:

34 cm

Step-by-step explanation:

The radius is half of the diameter, so 17 cm is half of 34 cm.

Diameter = 34 cm

Answer:

True.

Step-by-step explana

-4/5 + 4/5 is 0

Answer:

The Third one

Step-by-step explanation:

Your Welcome :)

Graph of the function is attached below.

Correct option is D.

As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:

Definition of exponential function

In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant  called the base of the function, which must be greater than 0.

Given, exponential function

f(x) = (1/4)4ˣ

exponential function is defined for x∈R

Putting x = 0

f(0) = (1/4)4⁰

f(0) = 1/4

Point on curve is (0,1/4)

Putting x = 1

f(1) = (1/4)4¹

f(1) = (1/4)4

f(1) = 1

Point on curve is (1,1)

Putting x = 2

f(2) = (1/4)4²

f(2) = (1/4)16

f(2) = 4

Point on curve is (2,4)

Putting x = 3

f(3) = (1/4)4³

f(3) = (1/4)64

f(3) = 16

Point on curve is (3,16)

Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.

Hence, graph of the function is drawn as follows.

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9514 1404 393

Answer:

  A, C

Step-by-step explanation:

A: -3 -(-8) = -3 +8 = 5

B: -2 -3 = -5

C: 1 -(-4) = 1 +4 = 5

D: 7 -(-2) = 7 +2 = 9

__

Differences A and C are 5.

Answer: A: -3- (-8)

B:1 -(-4)

Step-by-step explanation:

in A your subtracting them in B your adding them

9514 1404 393

Answer:

  it depends on the accuracy and resolution required of the answer

Step-by-step explanation:

The shaded portion appears to be about half the length of the unshaded portion, suggesting the shaded amount is 1/3.

__

Using a pair of dividers, one could determine the number of times the shaded portion fits into the whole bar. Depending on how much is left over, the process could repeat to determine the approximate size of the remaining fraction relative to the bar or to the shaded portion. (Alternatively, one could replicate the length of the bar to see what integer number of shaded lengths fit into what integer number of whole lengths.)

One could measure the shaded part and the whole bar with a ruler, then determine the relative size of the shaded part by dividing the first measurement by the second. The finer the divisions on the ruler, the better the approximation will be.

Answer:

— Ang salitang entrepreneur ay hango sa salitang French na entrepende na nangangahulugang?

Answer:

a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.

b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.

c) Expected number of acceptable specimens among the ten is 7.938.

d) Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

Step-by-step explanation:

a )

[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]

b )

[tex]c = 1.96 * 3 = 5.88[/tex]                    { Since Z = 1.96 for 95% CI refer table.}

c )

Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]

d )

Binomial with n = 10 and p = P(X < 73.84)

[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]

The values of variables, such as the height of the table can be found by writing equations of their relationships

The height of the table is 105 cm

The reason the above height value is correct is as follows;

Known parameters:

The diagram shows a table, a cat and a mice

Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice

From the given diagram, we have;

Height of the table + Height of the cat - Height of the mice  = 120 cm

∴ x + y - z = 120...(1)

Height of the table + Height of the mice - Height of the cat   = 90 cm

∴ x + z - y = 90...(2)

Adding equation (1) to equation (2) gives;

x + y - z + (x + z - y) = 120 + 90 = 210

x + y - z + (x + z - y) = 210

However;

x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x

∴ x + y - z + (x + z - y) = 2·x = 210

x = 210/2 = 105

Therefore;

The height of the table, x = 105 cm

Learn more about word problems leading on simultaneous equations here:

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Answer:25

Step-by-step explanation:

Answer:

se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.

Answer: The coefficient before x^4 is 60

Step-by-step explanation:

Hey! So I am not an expert at this, but you have to use the binomial theorem

I have attached of the Pascals Triangle (one shows the row numbering as well)

Basically in a pascal triangle, you add the two numbers above it to get the next number below

As you can see, the rows start from 0 instead of 1

The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms

NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)

Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)

It would be 15 × 2^4 × (1/2)^2 = 60

The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power

Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)

Answer:

B: A systematic random sample

Step-by-step explanation:

Systematic sampling is a type of probability sampling in which members of a larger population are chosen at random from a larger population but at a fixed, periodic interval. This interval, also known as the sampling interval, is calculated by dividing the population size by the sample size desired. Despite the fact that the sample population is chosen in advance, systematic sampling is still considered random if the periodic interval is set in advance and the starting point is chosen at random.

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

Answer: 3) R(n) = 1200(1.002)n - 100n

Step-by-step explanation:

After n months, which function represents Chet’s net worth, R(n)?

(1) R(n) = 1200(1.002)n + 100n

(2) R(n) = 1200(1.002)12n + 100n

(3) R(n) = 1200(1.002)n - 100n

(4) R(n) = 1200(1.002)12n - 100n

Answer: 3) R(n) = 1200(1.002)n - 100n

Net worth is the amount of his savings minus his debt,

Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.

Answer: B ACE is similar to DCB

Step-by-step explanation:

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean, ayy

What you know about rollin' down in the deep?

When your brain goes numb, you can call that mental freeze

When these people talk too much, put that sh*t in slow motion, yeah

I feel like an astronaut in the ocean

Answer:

Interest Earned ₹ 1,800

Principal Amount ₹ 10,000

Total Value ₹ 11,800

The cost of the loan for Mandy will be $11800 and the total interest for 3 years will be $1800.

Simple interest is a predetermined proportion of the principal amount borrowed or lent that is paid or received over a set period of time.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.

In another word, if the principle amount is the same in each time period then the interest will also same for every time period.

Given that

Principle amount = $ 10000

Time period = 3 years

Rate of interest = 6%

Rate of interest at the end of 1st year

10000 × 6/100 ⇒ $600

Since in simple interest rate of interest remain same so

Rate of interest for 3 years

3 × 600 = $ 1800 hence rate of interest will be $1800.

Cost of the loan = principle amount + total interest

Cost of the loan = 10000 + 1800 ⇒ $11800 will be the cost of the loan.

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Answer:

observational study

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = 2x-8

2x = y+8

x = 0.5y+4

inverse function: y = 0.5x+4

Answer:

x=41

Step-by-step explanation:

LM =JM

154=4x-10

154+10=4x

164=4x

164/4=4x/4

41=x

hope this is helpful

Answer:

10.9 %

Step-by-step explanation:

46 - 41 = 5

5/46 * 100% = 10.8695652174%

Rounded

10.9 %

first and last one i think

Answer:

The equation of the new function is [tex]g(x) = 7x + 9[/tex]

Step-by-step explanation:

Vertically compress by a factor of 7.

Vertically compressing a function by a units is the same as:

[tex]g(x) = f(ax)[/tex]

In this question:

[tex]f(x) = x, a = 7[/tex]. So

[tex]g(x) = f(7x) = 7x[/tex]

Shift up 9 units.

Shifting a function up a units is the same thing as adding a to the function. In this case, [tex]a = 9[/tex], and then:

[tex]g(x) = 7x + 9[/tex]

The equation of the new function is [tex]g(x) = 7x + 9[/tex]