A neighborhood in Shiloh is building a treehouse. It has a rectangle floor of 6 ft by 4 ft. What is the area of the tree house floor?

a) The probability of drawing all kings from a shuffled deck of cards without replacement is approximately 0.0000014, or 1.4 in 1 million.

b) The probability of drawing all red cards from a shuffled deck without replacement is approximately 0.000000103, or 1.03 in 10 million.

a) Probability of drawing all kings:

To calculate the probability of drawing all kings, we need to determine the total number of possible outcomes and the number of favorable outcomes. Let's break it down step by step:

Step 1: Total number of possible outcomes

In a standard deck of 52 playing cards, there are four kings. When we draw one card, there are 52 cards to choose from. For the second draw, only 51 cards remain, and so on. Therefore, the total number of possible outcomes for drawing four cards without replacement is:

52 × 51 × 50 × 49 = 649,740

Step 2: Number of favorable outcomes

Since we want all four cards to be kings, there are only four kings in the deck. When we draw the first card, there is a 4/52 chance of it being a king. For the second card, the probability reduces to 3/51 since there are three kings remaining out of 51 cards. Similarly, for the third and fourth cards, the probabilities become 2/50 and 1/49, respectively. Therefore, the number of favorable outcomes is:

(4/52) × (3/51) × (2/50) × (1/49) = 1/270,725

Step 3: Calculating the probability

Finally, we can calculate the probability of drawing all kings by dividing the number of favorable outcomes by the total number of possible outcomes:

P(all kings) = (1/270,725) / (649,740) ≈ 0.0000014

b) Probability of drawing all red cards:

Similarly, let's calculate the probability of drawing all red cards from the deck. We follow the same steps:

Step 1: Total number of possible outcomes

When we draw the first card, there are 26 red cards in a deck of 52. For the second draw, there are 25 red cards remaining out of 51, and so on. Hence, the total number of possible outcomes for drawing four cards without replacement is:

26 × 25 × 24 × 23 = 358,800

Step 2: Number of favorable outcomes

Since we want all four cards to be red, there are 26 red cards in the deck. The probability of drawing a red card for the first draw is 26/52. For the second draw, the probability becomes 25/51, for the third draw it is 24/50, and for the fourth draw, it is 23/49. Thus, the number of favorable outcomes is:

(26/52) × (25/51) × (24/50) × (23/49) ≈ 0.037

Step 3: Calculating the probability

The probability of drawing all red cards is the ratio of the number of favorable outcomes to the total number of possible outcomes:

P(all red cards) = (0.037) / (358,800) ≈ 0.000000103

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The integrate is W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt.

To find the work done by the force field F in moving an object from point A to point B, we can use the line integral of the force field along the path connecting A and B. The line integral is given by the formula:

W = ∫[C] F · dr

where C represents the curve connecting points A and B, F is the force field, dr is the differential displacement vector along the curve, and · denotes the dot product.

First, let's calculate the differential displacement vector dr. Since we are moving from point A(1, 1) to point B(3, 4), the differential displacement vector dr can be expressed as:

dr = dx i + dy j

Now, let's determine the curve C connecting A and B. The curve can be parametrized as follows:

x(t) = 1 + 2t

y(t) = 1 + 3t

where t varies from 0 to 1.

Differentiating these parametric equations, we obtain:

dx = 2 dt

dy = 3 dt

Substituting these values into the differential displacement vector dr, we have:

dr = 2 dt i + 3 dt j

Next, let's calculate the force field F at each point along the curve C. Given that F(x, y) = 6y^(3/2) i + 9x √y j, we can substitute the parametric equations for x and y into F:

F = 6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j

Now, let's evaluate the line integral by substituting the values of F and dr into the integral expression:

W = ∫[0 to 1] (6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j) · (2 dt i + 3 dt j)

Expanding the dot product, we have:

W = ∫[0 to 1] (12(1 + 3t)^(3/2) dt + 27(1 + 2t) √(1 + 3t) dt)

Now, we can simplify and integrate each term separately:

W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt

To evaluate these integrals, we can use appropriate substitution or integration techniques. After integrating both terms, we will have the value of the work done by the force field F in moving the object from A to B along the curve C.

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Answer:

hi!

Step-by-step explanation:

The equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.

To find the equation of a line that is parallel to the line 2x - 5y = 10, we need to determine the slope of the given line first. The equation is in the form of Ax + By = C, where A = 2, B = -5, and C = 10.

To find the slope, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope.

2x - 5y = 10

-5y = -2x + 10

y = (2/5)x - 2

From this equation, we can see that the slope of the given line is 2/5.

A line that is parallel to this line will have the same slope. Therefore, the equation of the parallel line can be determined using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) represents the coordinates of the given point (-5, 1).

Using the slope of 2/5 and the point (-5, 1), we can now check the options to see which ones satisfy the conditions:

A. y = -x - 1: This equation has a slope of -1, not 2/5. It is not parallel to the given line.

B. 2x - 5y = -5: This equation has the same slope of 2/5 and passes through the point (-5, 1). It satisfies the conditions and is parallel to the given line.

C. y = -x - 3: This equation has a slope of -1, not 2/5. It is not parallel to the given line.

D. 2x - 5y = -15y: This equation has a slope of 2/20, which simplifies to 1/10. It is not parallel to the given line.

E. -1 = -(x - 5): This equation does not represent a line. It is not a valid option.

Therefore, the equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.

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Answer:

D. A = 3n + 15

Step-by-step explanation:

3 should be beside the n variable because n represents each ride that was purchased.

As 15 represents the fee

The A variable represents the total amount spent

Therefore your answer is D.

Your Welcome.

Answer:

7.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance "D" = rate × time

or d = r × t.

Tad and his buddies drove to the orange bowl(while going) -50mph

Tad and his buddies while returning from a trip -75mph

Total round trip = 12 hours

Distance while going = 50 x t

Distance while returning = 75 (12 - t)

50t = 75(12 -t)

50t = 900 -75t

50t + 75t = 900

125t = 900

t = 900/125

t= 7.2

The total number of hours it takes Tad and his buddies to drive to the orange bowl is 7.2 hours.

Answer:

50

Step-by-step explanation:

180-(65+65)

Answer:

<C = 50

Step-by-step explanation:

<c = x

x + 65 + 65 = 180

x + 130 = 180

x = 50

Answer:

Step-by-step explanation:

1/5 + 1/5 = 2/5

1/7 + 1/7 = 2/7

1/3 + 1/3 = 2/3

There are an infinite number of these fractions. They must be 1 and 1 in the numerator, and the denominator must be relatively prime  to 2. The examples I have picked are prime in the denominator, but the rule is not without many exceptions. For example

1/9 + 1/9 = 2/9

I don't think you can pick an even denominator because it will reduce when put with two.  Oh wait 2/18 + 2/18 = 4/18 = 2/9 But these could be reduced before adding. Still, it might count. It depends on who is marking the question.

What about an odd and even denominator?

1/9 + 1/18 = 3/18 = 1/6  There must be something that works, but I can't come up with an example.

Answer: 829.44 ft²

Step-by-step explanation:

Correction - The walkway is 31.2 feet wide.

To solve this, first find the area of the fountain:

Area of a square = Length * Width

= 12 * 12

= 144 ft²

The find the area of the walkway including the fountain:

= 31.2 * 31.2

= ‭973.44‬ ft²

To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:

= 973.44 - 144

= 829.44 ft²

For the goodness-of-fit test with data collected from 55 subjects, the degrees of freedom for the chi-square distribution will be 4.

In a goodness-of-fit test, the degrees of freedom for the chi-square distribution determine the critical values and the interpretation of the test statistic. For a multinomial distribution with k categories, the degrees of freedom are calculated as (k - 1).

In this specific case, we have a multinomial distribution with 5 categories. Therefore, the degrees of freedom for the chi-square distribution will be (5 - 1) = 4.

Having 4 degrees of freedom means that the chi-square test statistic will be evaluated against the chi-square distribution with 4 degrees of freedom to determine the p-value and assess the significance of the test. The critical values at the chosen significance level will also depend on these degrees of freedom.

In summary, when conducting a goodness-of-fit test for a multinomial distribution with 5 categories and collecting data from 55 subjects, the chi-square test will have 4 degrees of freedom. These degrees of freedom play a crucial role in determining the validity and interpretation of the test results.

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Answer:

Triangle P' Q' R' is half the size of the original triangle.

-The scale factor is probably 1/3.

Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).

Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.

Step-by-step explanation:

:)

Answer:

B because it does not contain an = sign

Answer:

162 caps.

Step-by-step explanation:

Let x be the number of caps.

We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.

We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges ().

Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000. We can represent this information in an equation as:

Now let us solve for x.

Let us divide both sides of our inequality by 6.

Answer:

0 slope

Step-by-step explanation:

flat horizantal line

no increase in y-value

Answer:

40

Step-by-step explanation:

This rhombus is divided into 4 triangles. UL= upper left LL= lower left UR= upper right LR= Lower Right

UL: ½bh = ½(5)(4)=10

LL: ½bh = ½(5)(4)=10

UR: ½bh = ½(5)(4)=10

LR: ½bh = ½(5)(4)=10

Add up all the areas of each individual triangle (10+10+10+10 =40) and that's your final answer.

Answer:

I am guessing it is 67 as for maybe the whole thing is 180 degrees. So 180 subtracted by 67 and 46 equals 67!!!

67+46+?=180

113+?=180

?=180-113

?=67

Using the inverse matrix, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.

To solve the system of equations using the inverse matrix, we can represent the equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The system of equations can be written as:

Equation 1: -3X₁ + 2X₂ = -3

Equation 2: 3X₁ + 5X₂ = 1

Equation 3: 3X₁ - 2X₂ = 4

Equation 4: -4X₁ + 3X₂ = -5

Rewriting the equations in matrix form, we have:

[tex]\left[\begin{array}{ccc}-3&2\\3 &5\\3 &-2\\-4 &3\end{array}\right] \left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]

To find the solution, we need to calculate the inverse of the coefficient matrix A. Let's call it A^(-1).

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right][/tex]

Now, we can solve for X by multiplying A^(-1) with B:

[tex]\left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right]\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]

Performing the matrix multiplication and Simplifying the results, we have:

X₁ = -7/25

X₂ = -2/25

Therefore, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.

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a) The probability that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg=0.016

b) The expected value of N=86.6

c) The probability that Day N is also Sunday=1/7.

Explanation:

a)

For 1 day, 1 tray must contain no spoiled eggs: 0.999^12,

1 tray must have at least 1 spoiled egg: 1 - 0.999^12,

and the probability that Miss Ang has 2 trays, each containing at least 1 spoiled egg in one day:

(1 - 0.999^12) * (1 - (0.999^12 + 11 * 0.001 * 0.999^11)) = 0.00245

For 7 days, the probability that Miss Ang has at most 2 trays, each containing at least 1 spoiled egg:

= 0.00245 * C(7,0) * 1^0 * (1 - 1)^7 + 0.00245 * C(7,1) * 1^1 * (1 - 1)^6 + 0.00245 * C(7,2) * 1^2 * (1 - 1)^5

= 0.01622 ≈ 0.016

b)

Let X be the number of trays that Miss Ang has to buy to get the first tray containing at least 1 spoiled egg. Then X follows a geometric distribution with parameter

p = 1 - 0.999^12 and

E(X) = 1/p = 1/0.011543 ≈ 86.6 (rounded to the nearest 0.1).

c)

Since Miss Ang buys one tray of eggs a day, the probability that Day N is Sunday is 1/7. Therefore, the probability that Day N is Sunday given that it is the first day that Miss Ang bought a tray of eggs containing at least one spoiled is also 1/7.

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a) The probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg:

              P(X ≤ 2) = 0.2966763801

b) The expected value of N = 83.8059327318 days

c) The probability that Day N is also Sunday= 0.1406909760

(a)

For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled. Therefore, the probability that an egg is not spoiled is

1-0.001 = 0.999.

Since Miss Ang buys one dozen eggs every day, the probability that all 12 eggs in a tray are not spoiled is

(0.999)¹² = 0.98806738389.

Therefore, the probability that there is at least one spoiled egg in a tray is

1 - 0.98806738389 = 0.01193261611.

The probability that Miss Ang buys at most 2 trays of eggs with each having at least one spoiled egg in one week (7 days) can be found using the Poisson distribution with a mean of λ = 1.19574793916.

Therefore,

P(X ≤ 2) = 0.2966763801

(b)

Let N be the first day that Miss Ang bought a tray of eggs containing at least one spoiled.

Since Miss Ang buys one tray of eggs every day, the probability that N = n is the probability that the tray she buys on day n has at least one spoiled egg, and all the trays she buys on days 1, 2, ..., n - 1 have no spoiled eggs.

This probability is given by

[tex]P(N = n) = (0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

The expected value of N can then be found by taking the sum of nP(N = n) over all possible values of n.

This gives

[tex]E(N) = Σn=1∞nP(N = n)[/tex]

[tex]= Σn=1∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

n= 83.8059327318 days.

(c)

Suppose Day 1 is Sunday. Since Miss Ang buys one tray of eggs every day, Day N is also Sunday if and only if N ≡ 1 (mod 7).

Using the same method as in part (b), we get

[tex]P(N ≡ 1 (mod 7)) = Σk=0∞P(N = 7k + 1)[/tex]

                         =[tex]Σk=0∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]

                         = 0.1406909760

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Answer:

option A

Step-by-step explanation:

thats the answer!!!

Answer:

This theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. ' This is kind of like the SAS, or side-angle-side postulate. But SAS requires you to know two sides and the included angle.

Step-by-step explanation:

Two particles are traveling along space curves defined by the equations r₁(t) = (t, t², t³) and r₂(t) = (1/6t, 1/30t, 1/126t). We need to find the points at which their paths intersect.

To find the points of intersection, we need to solve the system of equations formed by equating the components of the two space curves.

Comparing the x-components, we have:

t = 1/(6t) => t² = 1/6 => t = ±√(1/6).

Comparing the y-components, we have:

t² = 1/(30t) => t³ = 1/30 => t = ±∛(1/30).

Comparing the z-components, we have:

t³ = 1/(126t) => t⁴ = 1/126 => t = ±∜(1/126).

Combining all the solutions, we have four possible values for t: √(1/6), -√(1/6), ∛(1/30), and -∛(1/30). However, we need to check if these values are valid for all components of the curves.

By substituting these values of t into the equations, we find that only the value t = √(1/6) yields valid points of intersection: (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).

Therefore, the points at which the paths of the particles intersect are (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).

Please note that the other values of t do not yield valid points of intersection, so they are not considered as solutions in this case.

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Answer:B

Step-by-step explanation:

The approximated value of f'(0) using the 2-point forward difference formula with h = 0.2 is -0.21385. So, first option is the correct answer.

To calculate an approximate value of f'(0) using the 2-point forward difference formula with h = 0.2, we can use the given function values:

f(-0.2) = -0.91736

f(0) = -1

f(0.2) = -1.04277

Using the 2-point forward difference formula, we have:

f'(0) ≈ (f(h) - f(0)) / h

Substituting the values:

f'(0) ≈ (f(0.2) - f(0)) / 0.2

f'(0) ≈ (-1.04277 - (-1)) / 0.2

f'(0) ≈ (-0.04277) / 0.2

f'(0) ≈ -0.21385

Therefore, the approximated value of f'(0) using the 2-point forward difference formula with h = 0.2 is -0.21385. Therefore, the correct answer is first option: f'(0) ≈ -0.21385.

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Answer:7

+

7

(

5

)

+

7

5

(

2

)

+

7

5

(

3

)

+

7

5

(

4

)

Step-by-step explanation:

Answer: 5473+7x^5

Step-by-step explanation:

Try Photo Math! Gives step by step explanations!

Hope this helps!!

Answer:

y = 2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

y² = ([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{2}[/tex] )² = 2 + 2 = 4 ( take the square root of both sides )

y = [tex]\sqrt{4}[/tex] = 2

a) The odds of surviving is 1/4

b) The odds of not surviving is 4.

c) You would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.

a) The odds of surviving the zombie apocalypse can be calculated by taking the probability of survival (20%) and dividing it by the probability of not surviving

100% - 20% = 80%

So the odds of surviving would be,

20%/80% = 1/4

This means that for every one chance of surviving, there are four chances of not surviving.

b) The odds of not surviving the zombie apocalypse can be calculated by taking the probability of not surviving (80%) and dividing it by the probability of survival (20%).

So the odds of not surviving would be

80%/20% = 4/1

This means that for every four chances of not surviving, there is one chance of surviving.

c) If you bet $25 on surviving and you do survive, based on the odds of 1/4, you would win the bet. The payout can be calculated by multiplying the bet amount by the odds of surviving.

So the payout would be

$25 * 1/4 = $6.25

Therefore, based on the odds, you would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.

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Answer:

67

Step-by-step explanation:

no

Answer:

25

Step-by-step explanation:

Given the expression x^2 - 10x + 8 = 0.

According to completing the square method

Subtract 8 from both sides

x^2 - 10x + 8 - 8 = 0 - 8

x^2 - 10x = -8

Complete the square

Add the square of half of coefficient of x to both sides

Coefficient of x = -10

Half of Coefficient of x = -10/2

Half of Coefficient of x = -5

Square of Half of Coefficient of x = (-5)^2

Square of Half of Coefficient of x = 25

Add (-5)^2 to both sides

x^2 - 10x + (-5)^2 = -8 + (-5)^2

(x-5)^2 = -8 + 25

(x-5)^2 = 17

Hence the required constant that was added is 25