Two cards are drawn one at a time from a full deck of cards. a) What’s the probability they are an ace or a heart? b) What’s the probability they are neither ace nor a heart?

Answer:7

Step-by-step explanation:

Vectors u, v, and w are represented graphically in ℝ². Scalars λ₁ and λ₂ for w = λ₁u + λ₂v are found as λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

a) Vector Representation:

To draw vectors u, v, and w in ℝ², we can use their respective components. Vector u = (1, 2) starts at the origin and extends to the point (1, 2). Vector v = (-3, 4) starts at the origin and extends to the point (-3, 4). Vector w = (5, 0) starts at the origin and extends to the point (5, 0).

b) Scalar Representation:

We want to find scalars λ₁ and λ₂ such that w = λ₁u + λ₂v. This can be expressed as a system of equations:

w₁ = λ₁u₁ + λ₂v₁

w₂ = λ₁u₂ + λ₂v₂

Substitute the values:

5 = λ₁(1) + λ₂(-3)

0 = λ₁(2) + λ₂(4)

Solve the system of equations to find λ₁ and λ₂. Multiplying the first equation by 2 and adding it to the second equation:

10 = 2λ₁ - 3λ₂ + 0

10 = 2λ₁ - 3λ₂

Solving for λ₁:

2λ₁ = 3λ₂ + 10

λ₁ = 3/2λ₂ + 5

Now, let λ₂ = t, then λ₁ = 3/2t + 5.

So, the scalars λ₁ and λ₂ are λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.

Answer:

$2743.66

Step-by-step explanation:

Data provided in the question:

Interest rate = 5%

Future value = $55,000

Time, t = 4.5 years

Now,

Since the interest is compounded quarterly

therefore,

Number of periods in a year = 4

Interest rate per period = 5% ÷ 4 = 1.25% = 0.0125

Total number of periods in 4.5 years = 4.5 × 4 = 18

also,

PMT = Future value × [ r × (( 1 + r )ⁿ - 1)⁻¹ ]

therefore,

PMT = $55,000 × [ 0.125 × ( ( 1 + 0.0125 )¹⁸ - 1 )⁻¹ ]

or

PMT = $55,000 × 0.0498

or

PMT = $2743.66

Answer:

a.

Step-by-step explanation:

A and B both are greater than mean and so A and B lies on the right side of mean. Further it is stated that A is more away from the mean than B. It means that A is greater than B. So, in order to find the area between A and B we have to subtract the area of mean to B from area of mean to A. It can be explain in the notations as

P(B<X<A)=P((B-μ)/σ<z<(A-μ)/σ)

P(B<X<A)=P(z<(A-μ)/σ)-P(z<(B-μ)/σ)

Hence, we find the area from mean to A and subtract the area from mean to B.

Answer:

  (a) 4.00×10^7 m

  (b) 5.10×10^14 m^2

  (c) 1.083×10^21 m^3

Step-by-step explanation:

Put the given value of radius into the various formulas and do the arithmetic. Your scientific calculator can show you the results in scientific notation.

  C = 2πr = 2π·6.37×10^6 m ≈ 4.00×10^7 m* . . . circumference

  A = 4πr^2 = 4π(6.37×10^6 m)^2 ≈ 5.10×10^14 m^2 . . . area

  V = (4/3)πr^3 = (4/3)π(6.37×10^6 m)^3 ≈ 1.083×10^21 m^3 . . . volume

_____

* An early definition of the meter was 10^-7 times the distance from the North Pole to the Equator as measured through Paris, France.

Finding the z-value in a standard normal distribution for certain proportions involves using a standard normal (Z-score) table. For (a) the z-value is -0.36, and for (b), the z-value is 0.36.

To find the value of z that allows for a proportion of observations less or greater than it in a standard normal distribution, you need to use a standard normal (Z-score) table, or use an online calculator that allows you to find the Z-score associated with a specific proportion.

(a) For the proportion of observations that are less than z = 0.36, you would look up this proportion in the body of a standard normal table to find the associated Z-score. Alternatively, using a Z-score calculator, the z value is approximately -0.36.

(b) For the proportion of observations that are greater than Z = 0.36, it would be equivalent to looking for the proportion that is less than Z = 1 - 0.36 = 0.64 in the standard normal table. The z value here is approximately 0.36.

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Answer:

B. stratified random sample.

Step-by-step explanation:

The Stratified sampling is a type of sampling method in which the observer divides the whole sample population in the different or the separate groups.

These separated different groups are known as strata.

And from these, probability sample also called as simple random sample is taken out from each group.

The sampling method used in this scenario is defined as stratified random sampling, where the population is divided into groups (or strata) and random samples are taken from each group.

The technique described in your question is an example of a stratified random sample. This sampling method is characterized by dividing a population into smaller groups, known as 'strata', and then selecting a simple random sample from each group. In your example, the population is first divided into men and women, these are your strata. Then, a simple random sample is chosen from each group: 500 men and 700 women. This method ensures representation from all sections of the population and can often lead to more accurate results compared to a simple random sample.

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Answer:

L.A. = 80 + 16√13

Step-by-step explanation:

the lateral area is the area of the vertical faces.

So, for the given prism = The sum of the area of the vertical rectangles.

                                      = height * perimeter of the right triangle.

The hypotenuse of the right triangle = [tex]\sqrt{6^2+4^2} = \sqrt{36+16} =\sqrt{52} =\sqrt{4*13} =2\sqrt{13}[/tex]

So, the sides of the triangle are 4 , 6 and 2√13

The perimeter of the right triangle = 4 + 6 + 2√13 = 10 + 2√13

Height = 8

The lateral area for the prism = 8 * ( 10 + 2√13 ) = 80 + 16√13

Answer:

The correct answer is 80 + 16√13 feet²

Step-by-step explanation:

Like we can see in the plot, the prism has three rectangular sides, that are its lateral area. For calculating the area, we need to add up the three sides, this way:

Height of the prism (h) = 8 ' or 8 feet

Area of the first side = 8 * 4 = 32 feet²

Area of the third side = 8 * 6 = 48 feet²

Area of the third side = 8 * Hypotenuse of the triangle

Hypotenuse of the triangle² = 4² + 6² = 52

Hypotenuse of the triangle =√52 = √13 * 4 = 2√13 feet

Area of the third side = 8 * 2√13 feet = 16√13 feet²

Area lateral of the prism = 32 + 48 + 16√13 = 80 +  16√13 feet²

Answer:

Step-by-step explanation:

Hello!

Missing Questions:

1) The probabylity of P(121 < X ≤ 129) is:

You can rewrite it as:

P(X ≤ 129) - P(X < 121)

Now the expression " P(X < 121)" does not include 121 so to calculate this interval you have to substract the cummulative probability to the previoous value of the variable " P(X ≤ 120)"

Then the interval is

P(X ≤ 129) - P(X ≤ 120)= 0.978 - 0.533= 0.445

2) The approximation to normal (without correction of continuity) of P(121 < X ≤ 129) is:

To use the normal approximation you have to calculate the mean and variance of the variable.

E(X)= np= 150*0.8= 120

V(X)= np(1-p)= 150*0.8*0.2= 24

Now you can standardize the given interval:

P(X ≤ 129) - P(X < 121)= P(Z ≤ (129-120)/√24) - P(Z < (121-120)/√24)

P(Z ≤ 1.84) - P(Z < 0.20) = 0.967 - 0.579= 0.388

3) The approximation to normal (with correction of continuity) of P(121 < X ≤ 129) is:

P(121 < X ≤ 129)

Applying the correction of continuity:

For X ≤ n + 0.5

For X > n + 0.5

P(121.5 < X ≤ 129.5) = P(X ≤ 129.5) - P(X < 121.5)

P(Z ≤ (129.5-120)/√24) - P(Z < (121.5-120)/√24)

P(Z ≤ 1.94) - P(Z < 0.31) = 0.974 - 0.622= 0.352

4) The approximation of poisson of P(121 < X ≤ 129) is:

First define the rate of successes of the distribution λ= np= 150*0.8= 120

Then you look at the individual cummulative probabilities using the tables of the distribution:

P(X ≤ 129;  λ= 120)= 0.808

P(X < 121;  λ= 120)= P(X ≤ 120;  λ= 120)= 0.524

P(121 < X ≤ 129) =  P(120 ≤ X ≤ 129)= P(X ≤ 129) - ≤ 129)= 0.808 - 0.524= 0.284

I hope it helps!

Answer:

[22.57 ± 2.776]

Step-by-step explanation:

Hello!

You have the 95% Confidence Z-interval (21.182;23.958), the mean X[bar]= 22.57 and the sample size n=25.

The formula for the Z interval is

[X[bar] ± [tex]Z_{1-\alpha /2} *( \frac{Sigma}{\sqrt{n} } )[/tex]]

The value of Z comes from tha standard normal table:

[tex]Z_{1-\alpha /2} = Z_{0.975}= 1.96[/tex]

The semiamplitude (d) or margin of error (E) of the interval is:

E or d= (Upperbond- Lowerbond)/2 = (23.958-21.182)/2 = 2.776

[X[bar] ± E]

[22.57 ± 2.776]

I hope it helps!

Answer:

The equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Step-by-step explanation:

Considering the logarithmic function

[tex]f(x)=log(x)[/tex]

As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.

So,

[tex]g(x)=log(x)+4[/tex] is basically the shift up by 4 units, and the graph also showing the same situation.

Therefore, the equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]

Also, the graphs of both [tex]f(x)=log(x)[/tex] and  [tex]g(x)=log(x)+4[/tex] is attached where black mark graph represents  [tex]f(x)=log(x)[/tex] and red mark graph represents [tex]g(x)=log(x)+4[/tex].

Keywords: transformation, vertical shift, graph

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Answer:

D. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

Step-by-step explanation:

0.21 + 0.28 + 0.02 + 0.28 + 0.21 = 1

All individual data are between 0 and 1. Data added up = 1

The true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

For a distribution to be a discrete probability distribution, the following must be true

[tex]\sum P(x) =1[/tex]

So, we have:

[tex]\sum P(x) = 0.21 + 0.28 + 0.02 + 0.28 + 0.21[/tex]

Evaluate the sum

[tex]\sum P(x) =1[/tex]

The above statement shows that the distribution is a discrete probability distribution

Hence, the true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

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Answer:

there a bad football team probably the raiders  

Step-by-step explanation:

but take 72.5 and take away 13.5

                     72.5

                  -  13.5

                   -----------

                      59

Answer: [tex]5\frac{4}{5}[/tex]

Step-by-step explanation:

The first step is to make 7&2/5 a improper fraction, using the rule [tex]a\frac{b}{c}= \frac{ac+b}{c}[/tex].

Answer:

a) The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b) The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Step-by-step explanation:

This is a common statistic method.

If you want to estimate something about a big population, you select a random sample of the population, and estimate for the entire population.

For example, if you want to estimate the proportion of residents of Buffalo, New York, that are Buffalo Bills fans, you are going to ask, for example, 1000 Buffalo residents. The population is all the residents of Buffalo, New York. and the sample are the 1000 Buffalo residents.

However, if you send a Bills player to ask this question, people will try to make him happy, which could lead to a biased answer.

So, for this question

a. What are the population and the sample?

The population is all the Hispanic residents of Denver.

The sample is 300 adults which very visited by the officer.

b. Why are the results likely to be biased even though the sample is an SRS?

The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.

Answer:

16/52 or 4/13 when reduced.

Step-by-step explanation:

4/52 is for the Jack card since there are 4 jack cards out of a total of 52 cards.

12/52 is for the face cards since there are 12 face cards out of a total of 52 cards.

Since the problem says OR, this means one or the other, so you will be adding those two fractions together. If the problem said AND, this would mean that you have to multiply since both would have to occur.

The probability of selecting a heart or a face card from a standard deck of cards is 22/52.

To calculate the probability of selecting a heart or a face card from a standard deck of cards, we must consider the total number of heart cards and face cards in the deck, mindful not to double-count any cards that are both. A standard deck has 52 cards, 12 of which are face cards (3 face cards per suit, and there are 4 suits in total). Besides these 12 face cards, there are 13 heart cards, but since three of them are face cards, which we have already counted, we subtract those, leaving us with 10 additional heart cards. Thus, the total number of favorable outcomes is 12 (face cards) + 10 (non-face-card hearts) = 22.

The probability of drawing a heart or face card is then 22 favorable outcomes divided by 52 possible outcomes, which simplifies to 11/26 or about 42.31%.

To understand if this outcome is more or less likely than selecting a heart suit face card, we consider that there are only 3 face cards in the hearts suit. Hence, the probability of drawing a heart suit face card is 3/52 or about 5.77%. Clearly, drawing a heart or a face card is more likely than drawing a heart suit face card alone, as 42.31% > 5.77%.

Answer:

160/100+60+0/one hundred sixty

OR JUST 160 LIKE YOU ASKED

The product of thirty-two and five will be equal to 160.

A product is the result of multiplication or an expression that indicates factors that are to be multiplied, in mathematics.

The multiplication will be given as:-

32  x  5  =  160

Or we can also do it like the addition of 32 five times:-

32  +  32  + 32  +  32  +  32 = 160

Therefore products of thirty-two and five will be equal to 160.

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Answer:

∫(x+25x)dx=13x²

Step-by-step explanation:

From Exercise, we want  calculate integral for x + 25 x dx.  

But this not required  a substitution to express the integrand as a rational function. We can calculte integral, and we get

∫(x+25x)dx= ∫x dx+25∫x dx=x²/2+ \frac{25}{2} · x^2=\frac{26}{2}·x^2=13x²

Therefore, we get that is  

∫(x+25x)dx=13x².

Answer:

We calculate that is CD=4.

Step-by-step explanation:

From Exercise we have that

AB=AC=3

BC=6

BD=2

AD=1.  

From Axioms D-1 and D-3, we have  

D-1: ∀ A, B∈ S,  there is a unique AB ∈ R

D-3: ∀ A, B∈ S, AB=BA.

We use the  Axioms D-1 and D-3, and we get that

AC=CA=3

AD=1

because are the points is collinear, we get

CA+AD=CD

3+1=CD

CD=4

We calculate that is CD=4.

Final answer:

To find the length of segment CD, we assume points on a collinear path as A-D-B-C, and subtract the length of BD from BC, resulting in CD = 4 units.

Explanation:

The student has asked for the length of segment CD when given a set of collinear points A, B, C, and D, with various distances between them. Since we have point B between points A and C, and points A and D, and knowing AB, AC, BC, and BD, we can determine the length of AD by subtracting from AC the length of BC, since AB equals AC. Therefore, AD = AC - BC = 3 - 6 = -3, which does not make sense geometrically since lengths cannot be negative. This might imply a typo or a misinterpretation of the points' arrangement. If assuming points in a line segment: A-D-B-C, CD can be found by subtracting BD from BC, CD = BC - BD = 6 - 2 = 4.

Answer:

Mean of the 11th observations = 46.809

Step-by-step explanation:

The step by step explanations is given in the attached file.

What is appled is mean or average which is the total number of observation divided by the sum of the frequencies of each observaton .

Answer:

x+2a-b=5x+5a-2*3a+2*b

x+2a-b=5x+5a-6a+2b

x+2a-b=5x-a+2b

5x-x=2a-b+a-2b

4x=3a-3b

4 x=3(a-b)

x=3/4(a-b)

The answer of the vector x in the form of a and b is 3/4(a-b).

"A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head."

Here,

[tex]x + 2a - b = 5(x + a) - 2(3a - b) x[/tex]

[tex]x+2a-b=5x+5a-6a+2b\\\\x+2a-b=5x-a+2b\\\\5x-x=2a-b+a-2b\\\\4x=3a-3b\\\\4 x=3(a-b)\\\\x=3/4(a-b)\\[/tex]

Hence the vector x = 3/4(a-b)

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Answer:

a) 25446.90 ft²

b) 101787.60 ft²

c) 407150.41 ft²

d) 2025πt²

Step-by-step explanation:

Data provided in the question:

Rate of spread radially = 45 feet per day

a) Radius of spread after 2 days

= 45 × 2

= 90 feet

Therefore,

Area affected = πr²

= π(90)²

= 25446.90 ft²

b) Radius of spread after 2 days

= 45 × 4

= 180 feet

Therefore,

Area affected = πr²

= π(180)²

= 101787.60 ft²

c) Radius of spread after 2 days

= 45 × 8

= 360 feet

Therefore,

Area affected = πr²

= π(360)²

= 407150.41 ft²

a) Radius of spread after t days

= 45 × t ft

Therefore,

Area affected = πr²

= π(45t)²

= 2025πt²

The area affected by the fungal disease, which spreads radially at a constant speed, can be calculated by using the formula for the area of a circle, where the radius is the product of the spread speed and time. After 2, 4, and 8 days, the areas affected are 25,446 square feet, 101,784 square feet, and 407,150 square feet, respectively.

The given scenario represents a real-world application of the mathematical concept involving growth in a circular pattern where the growth happens at a constant rate. Here, the representation of the disease spread through the farm is in form of a circle increasing in radius over time. To calculate the area affected on any given day (t), we apply the formula for the area of a circle (πr^2) where the radius is the rate of spread multiplied by the number of days.

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Answer:

Each unit cost $800

Step-by-step explanation:

Annual compensation = $48,000

Annual number of units sold = 2000

Commission on each item sold = 3%

Compensation for 2000 units = $48,000

Compensation for 1 unit = $48,000/2000 = $24

Cost of one unit = compensation for one unit ÷ commission on one unit = $24 ÷ 3% = $24 ÷ 0.03 = $800

Answer: cost of one unit = $280

Question:

A salesman has a base salary $2600 per month and makes 3% commission on each unit sold. If his total annual compensation is $48,000 and he sold 2000 units, how much does each unit cost

Step-by-step explanation:

Given;

base salary = $2600 per month

Total annual compensation = $48,000 per annum

Number of units sold = 2000

Commission = 3% per unit

Salesman's Salary per annum = $2600 × 12 = $31,200

Total commission earned = total compensation - total yearly salary

Total commission = $48,000 - $31,200 = $16,800

Commission on each unit = total commission/number of units

Unit commission = $16800/2000 = $8.4

Given that the commission per unit is 3% per unit

That is $8.4 is 3% of the cost of each unit.

Cost of each unit = $8.4/3% = $8.4/0.03 = $280

Answer:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240

Hence proved Conjecture is correct

L.H.S=R.H.S

Step-by-step explanation:

Consider the pattern:

8(5)=10(5-1)=40

8(5) + 8(25) = 10(25 - 1) =240

8(5) + 8(25) + 8(125) = 10(125 - 1) =1240

8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)=6240

According to inductive reasoning next term of pattern will become:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240

Checking whether conjecture is correct or not:

Consider L.H.S:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)

40+200+1000+5000+25000

31240

R.H.S:

31240

Hence proved Conjecture is correct

L.H.S=R.H.S

Final answer:

The wind chill table can be used to determine how cold it feels at different combinations of temperature and wind speed.

Explanation:

Wind chill is a measure of how cold it feels when the temperature is combined with wind speed. To determine how cold it feels when the temperature is 0°F and the wind speed is 10 mph, we can look at the table provided. At 0°F and 10 mph wind speed, the temperature adjusted for wind chill is -10°F.

If the temperature is 35°F and we want to know the wind speed that makes it feel like 25°F, we can look at the table and find that at 35°F, a wind speed of 15 mph makes it feel like 25°F.

If the wind speed is 10 mph and we want to know the approximate temperature that feels like 0°F, we can look at the table and find that at 10 mph wind speed, a temperature of 5°F feels like 0°F.

(a) At 0°F with a wind speed of 10 mph, it feels like -11°F.

(b) To make 35°F feel like 25°F, a wind speed of 15 mph is needed.

(c) With a wind speed of 10 mph, a temperature of 5°F feels like 0°F.

To find the adjusted temperature for wind-chill, we can use the given table which provides adjustments based on both temperature and wind speed.

(a) If the temperature is 0°F and the wind speed is 10 mph, we can find the adjusted temperature from the table:

Temperature: 0°F

Wind speed: 10 mph

From the table:

Adjusted temperature: -11°F

So, it feels like -11°F when the temperature is 0°F with a wind speed of 10 mph.

(b) If the temperature is 35°F, and we want it to feel like 25°F, we need to find the wind speed that corresponds to this adjusted temperature from the table:

Temperature: 35°F

Adjusted temperature desired: 25°F

From the table, look for the entry where the adjusted temperature is 25°F:

Adjusted temperature: 25°F

Wind speed corresponding to this adjusted temperature: 15 mph

So, a wind speed of 15 mph would make a temperature of 35°F feel like 25°F.

(c) If the wind speed is 10 mph and we want to find the temperature that feels like 0°F, we can find this from the table:

Wind speed: 10 mph

Adjusted temperature desired: 0°F

From the table, look for the entry where the adjusted temperature is 0°F:

Adjusted temperature: 0°F

Corresponding temperature: 5°F

So, approximately, a temperature of 5°F would feel like 0°F with a wind speed of 10 mph.

Answer:

a) Permutations

b) combination

Step-by-step explanation:

a)

Since the order of 15 most important artwork pieces matter, with most popular at first and then at N0.2, 3,4, and so on. Whenever we are dealing with "order of placement" the question at hand is of permutations.

b)

Out of 320 pieces, 125 pieces are to be "selected" and displayed, the process of selection incurs Combinations in which the order in which we select does not matter.  

Scenario a) represents a permutation and the 15 popular pieces can be arranged in 15! ways.

Scenario b) represents a combination and the 125 pieces can be selected in 320 choose 125 ways.

a) This scenario is an example of a permutation. In a permutation, the order of the items matters. In this case, the 15 popular pieces can be arranged in 15! (15 factorial) ways.
b) This scenario is an example of a combination. In a combination, the order of the items does not matter. In this case, the 125 pieces can be selected from the total of 320 pieces in a total of 320 choose 125 ways.

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Answer:

36

Step-by-step explanation:

We have been given that you have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. We are asked to find the number of choices if 2 of the friends are feuding and will not attend together.

We can choose 5 friends from 8 friends in [tex]^8C_5[/tex] ways.

[tex]^8C_5=\frac{8!}{5!(8-5)!}=\frac{8!}{5!(3)!}=\frac{8*7*6*5!}{5!*3*2*1}=8*7=56[/tex]

Therefore, we can choose 5 friends from 8 friends in 56 ways.

Since two friends are feuding, so we need to choose 3 friends from 6 friends and subtract them from total ways.

We can choose 3 friends from 6 friends in [tex]^6C_3[/tex] ways.

[tex]^6C_3=\frac{6!}{3!(6-3)!}=\frac{6!}{3!(3)!}=\frac{6*5*4*3!}{3!*3*2*1}=5*4=20[/tex]

[tex]56-20=36[/tex]

Therefore, we have 36 choices, if 2 of the friends are feuding and will not attend together.

Final answer:

The number of different choices for inviting friends to the party without the feuding friends attending together is 41 different choices.

Explanation:

The student's question deals with a combinatorial problem where they have 8 friends but can only invite 5 to a party. However, there is a constraint: 2 of the friends are feuding and cannot attend together. To solve this, we calculate the number of ways to choose 5 friends out of 8 without the feuding friends both attending.

Calculating Combinations with Restrictions

First, we find the total number of ways to invite 5 friends out of 8 without any restrictions, which is calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of friends and k is the number of friends to be invited.

C(8, 5) = 8! / (5!(8 - 5)!) = (8 × 7 × 6) / (3 × 2 × 1) = 56 ways.

Next, we calculate the number of combinations where the feuding friends would attend together. We treat them as a single entity and find combinations of the remaining 6 friends to invite 4 plus the 'unit' of feuding friends.

C(6, 4) = 6! / (4!(6 - 4)!) = (6 × 5) / (2 × 1) = 15 ways.

To get the total number of combinations without the feuding friends attending together, we subtract the 15 'restricted' combinations from the total 56 combinations.

56 - 15 = 41.

Therefore, there are 41 different choices for inviting friends to the party without the feuding friends attending together.

Answer:

a number produced from a subset of the group of interest.

Step-by-step explanation:

This problems is, basically, about the difference of concepts between a statistic and a parameter.

When something is taken from a sample and estimated to the entire population, it is a statistic. For example, if you survey 200 Central New York residents, an 60% of them say they are Buffalo Bills fans, the 60% is a statistic.

When something is true to the entire population, it is a parameter. If i study the voting preference of all 53 players on the Buffalo Bills active roster, and 83% are Democrats, the 83% is an parameter.

So the correct answer is:

a number produced from a subset of the group of interest.

This subset is the sample, for example, and the group of interest is the population.

Answer:

The best option is to phone a friend which will yield a total earnings of $ 806,400

Step-by-step explanation:

From the analysis of the question, there is the probability of success and failure.

if he choose not to answer which is the probability of success, his earnings = $500,000.

if he he answers the question correctly, his earnings = $1,000,000 which in the end, is still a success for him

if he answers the question wrongly, his earnings = $32,000

the last option is to phone a friend and he will either choose option a or option b

Probability of choosing option A = 0.6

Probability of choosing option B = 0.4

expected earnings = P(choosing A) x his earnings if correct +  P(choosing B) x his earnings if wrong

= 0.6 x 1,000,000 + 0.4 x 32,000

= $612,000 will be his earning by second option

if he picks the option b = P (choosing B) x his earnings if correct + P(choosing A) x earnings if wrong = 0.4 x 1,000,000 + 0.6 x 32,000

= $419,000

from the P(success) + P( failure) =1

His earnings = Probability of success x earnings if correct + Probability of failure x earnings if incorrect = 0.8 x 1,000,000 + 0.2 x 32,000

= $806,400

from the calculation done, it is apparent that his best option is to go by phoning a friend since that will yield more earnings for him which is greater than his earnings by going for the second options hence the best option is phoning a friend as this will accrue his expected earning to be $ 806,400

The best strategy is to select an answer (a or b). The expected payout for this option is $600,000.

To find the best strategy, we can create a decision tree. The decision tree will consider the options of not answering, selecting an answer, and phoning a friend. The expected payout for each option can be calculated by multiplying the probability of that option with the payout associated with that outcome. After calculating the expected payout for each option, we can compare them to determine the best strategy.

The decision tree shows that the best strategy is to Select an answer (a or b).

The expected payout for this option is calculated by multiplying the probability of choosing (a) and winning with the payout of $1,000,000, and adding it to the probability of choosing (b) and winning with the payout of $32,000.

The expected payout for this option is $600,000.

Therefore, by selecting an answer, you can expect to win $600,000 on average.

Answer:

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=21-1=20[/tex]  

Since is a one side left tailed test the p value would be:  

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation  

[tex]\bar X[/tex] represent the mean

[tex]s[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t=-0.024 would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 140[/tex]  

Alternative hypothesis:[tex]\mu < 140[/tex]  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

The statistic is given by: [tex] t = -0.024[/tex]

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=21-1=20[/tex]  

Since is a one side left tailed test the p value would be:  

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected [tex]\alpah=0.01,0.05,0.1[/tex]

Answer:

28

Step-by-step explanation:

People he interviewed on that day (x)

1.50x + 10 = 52

1.50x = 42

x = 42/1.50

x = 28

The number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

Let's suppose the people he interviewed on that day x

The linear equation can be framed as per the question:

1.50x + 10 = 52

After solving:

x = 42/1.50

x = 28

Thus, the number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.

Learn more about the linear equation here:

brainly.com/question/11897796

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