Write the following number in standard form: 3.471 x 10 to the power of negative 3

A random 9-card hand is dealt from a standard deck of cards. The probability that the hand contains at least 2 cards of every suit is approximately 0.6699 or 67%.

There are four different suits in a standard deck of cards, which are clubs, diamonds, hearts, and spades. There are 13 cards in each suit in a standard deck of cards, making a total of 52 cards.Therefore, the total possible ways to draw a 9-card hand from a standard deck of cards is: 52C9 = 45,057,474.To get the probability that the hand contains at least 2 cards of every suit, we can consider different scenarios:i) All four suits appear in the hand:There are 4 different suits in the deck, and we need to choose 2 cards from each suit to get a total of 8 cards, as shown below: 13C2 × 13C2 × 13C2 × 13C2 = 2,637,312.Next, we need to choose the remaining 1 card from any of the four suits, which gives us 4 ways to do that.Next, we need to choose 5 cards from the remaining 2 suits, which gives us: 26C5 = 65,780.Therefore, the total ways to choose 9 cards with 2 cards from two suits and 5 cards from the remaining suits is: 338,800 × 65,780 = 22,295,144.Finally, the probability that the hand contains at least 2 cards of every suit is the sum of the probabilities from i, ii, and iii divided by the total number of ways to draw a 9-card hand:Probability = (10,549,248 + 471,846,120 + 22,295,144)/45,057,474= 504,690,512/45,057,474= 0.6699, which is approximately 0.67 or 67%.Therefore, the probability that a random 9-card hand contains at least 2 cards of every suit is approximately 0.6699 or 67%.

There are 52 cards in a standard deck of cards, and there are four different suits in the deck: clubs, diamonds, hearts, and spades. Each suit has 13 cards, which are numbered from 2 to 10, and then have face cards (Jack, Queen, King, and Ace).To find the probability that a random 9-card hand contains at least 2 cards of every suit, we need to consider different scenarios. Therefore, the total number of ways to choose 9 cards with 2 cards from three suits and 3 cards from one suit is 1,647,420 × 286 = 471,846,120.The third scenario is when two suits appear in the hand. We need to choose 2 cards from each of the two suits, which gives us 13C2 × 13C2 ways, which is approximately 338,800. Next, we need to choose 5 cards from the remaining two suits, which gives us 26C5 ways, which is 65,780. Therefore, the total number of ways to choose 9 cards with 2 cards from two suits and 5 cards from the remaining suits is 338,800 × 65,780 = 22,295,144.The probability that a random 9-card hand contains at least 2 cards of every suit is the sum of the probabilities from the three scenarios divided by the total number of ways to draw a 9-card hand. Therefore, the probability is:Probability = (10,549,248 + 471,846,120 + 22,295,144)/45,057,474= 504,690,512/45,057,474= 0.6699, which is approximately 0.67 or 67%.Therefore, the probability that a random 9-card hand contains at least 2 cards of every suit is approximately 0.6699 or 67%.

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Answer:

Step-by-step explanation:

(a) To find the vertical (x-) nullcline, we set dy/dx = 0, which gives y = 0 or 4-x-5y = 0. Solving for y in the second equation gives y = (4-x)/5. Therefore, the vertical nullcline is x = 4/5.

To find the horizontal (y-) nullcline, we set dx/dy = 0, which gives x = 0 or 1-4x = 0. Solving for x in the second equation gives x = 1/4. Therefore, the horizontal nullcline is y = 0.

(b) To find the equilibrium points, we need to solve the system dx/dt = 0 and dy/dt = 0. From dx/dt = 0, we have x(4-x-5y) = 0, which gives x = 0 or x = 4-5y. Substituting x = 4-5y into dy/dt = 0 gives y(1-4(4-5y)) = 0, which gives y = 0 or y = 4/5. Therefore, the equilibrium points are (0,0) and (4/5,1/4).

(c) If we start at the initial position (1/4, ), trajectories approach the point (4/5,1/4). This can be seen from the phase plane plot, where the trajectories move towards the equilibrium point (4/5,1/4) from all directions except the x-axis, where they move towards the equilibrium point (0,0) (since the horizontal nullcline is y = 0).

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Answer: x = 9.42 in

Step-by-step explanation:

Area = (4x+9) x

440 = 4x²+9x

4x²+9x-440=0

x = 9+√9²-4x4x(-440)/2x4

x = 9.42 in

Brainliest? <33

Answer:

B

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

\(\frac{32}{x}\) = \(\frac{20}{30}\) = \(\frac{2}{3}\) ( cross- multiply )

2x = 3 × 32 = 96 ( divide both sides by 2 )

x = 48

The correct answer is one-half. The probability is one-half because the area of the triangle is half of the area of the rectangle.

The probability that a point chosen at random in the rectangle is also in the blue triangle can be found by dividing the area of the triangle by the area of the rectangle. The area of the triangle is given by: A = (1/2)bh = (1/2)(5)(4) = 10 square inches.

The area of the rectangle is given by: A = bh = (5)(4) = 20 square inches

Therefore, the probability that a point chosen at random in the rectangle is also in the blue triangle is: P = A(triangle) / A(rectangle) = 10/20 = 1/2

Hence, the answer is one-half.

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Answer:

step 2

Step-by-step explanation:

Gary didn't multiply the 2.5 and 4 correctly. The product isn't 8, it is 10.

We would expect approximately 56 cups to contain less than the amount stated by the vending machine.

We would expect approximately 379 students to leave the exam before the end.

We have,

To calculate the number of cups that would contain less than the amount stated by the vending machine, we need to find the probability of a cup containing less than 200 ml of coffee.

Using the normal distribution, we can calculate the z-score for the value of 200 ml using the mean and standard deviation:

z = (200 - 208) / 9 = -8/9 ≈ -0.889

Next, we need to find the probability corresponding to this z-score using a standard normal distribution table or a calculator.

The probability of a cup containing less than 200 ml can be found as:

P(Z < -0.889).

Assuming a normal distribution, we can use the z-score to find the corresponding probability.

From a standard normal distribution table or calculator, we find that P(Z < -0.889) is approximately 0.1867.

To calculate the expected number of cups containing less than the stated amount, we multiply this probability by the total number of cups used, which is 300:

Expected number of cups containing less than the stated amount.

= 0.1867 x 300

= 56

So,

We would expect approximately 56 cups to contain less than the amount stated by the vending machine.

For the second question, we need to calculate the number of students expected to leave the exam before the end.

We can find this by calculating the probability of a student taking less than 110 minutes to finish the exam (10 minutes before the end).

Using the normal distribution, we calculate the z-score for the value of 110 minutes:

z = (110 - 96) / 20 = 14/20 = 0.7

Next, we find the probability corresponding to this z-score using a standard normal distribution table or calculator.

The probability of a student finishing in less than 110 minutes can be found as P(Z < 0.7).

From the standard normal distribution table or calculator, we find that P(Z < 0.7) is approximately 0.7580.

To calculate the expected number of students leaving before the end, we multiply this probability by the total number of students taking the exam, which is 500:

Expected number of students leaving before the end

= 0.7580 x 500 ≈ 379

Therefore,

We would expect approximately 56 cups to contain less than the amount stated by the vending machine.

We would expect approximately 379 students to leave the exam before the end.

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Answer: Y axis

Step-by-step explanation: The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y-axis.

Answer:

m= \(\frac{y-b}{x}\)

Step-by-step explanation:

(a) The length of wire that should be used for the square in order to maximize the total area is 9 meters.

(b) Using the same 9 meters of wire for the square will result in the minimum total area as well as the maximum total area.

(a) To maximize the total area, we need to use as much wire as possible for the square and as little as possible for the triangle. Let x be the length of wire used for the square, then the length of wire used for the triangle is 9 - x.

For the square, we have:

4s = x, where s is the side length of the square.

For the equilateral triangle, we have:

3t = 9 - x, where t is the side length of the equilateral triangle.

Solving for x in terms of s and t, we get:

x = 4s and x = 9 - 3t/2.

Substituting x = 4s into x = 9 - 3t/2, we get:

4s = 9 - 3t/2

8s = 18 - 3t

t = (18 - 8s)/3

The area of the square is given by A = s^2, and the area of the equilateral triangle is given by A = (\(\sqrt{3}\)/4)t^2.

Substituting t = (18 - 8s)/3, we get:

A = (\(\sqrt{3}\)/4)((18 - 8s)/3)^2

To maximize the total area, we need to maximize A, which is a function of s. Taking the derivative of A with respect to s, we get:

dA/ds = -4\(\sqrt{3}\)(4s-9)/27

Setting dA/ds = 0, we get:

4s - 9 = 0

Solving for s, we get:

s = 9/4

Therefore, the length of wire that should be used for the square in order to maximize the total area is:

x = 4s = 9 meters.

(b) To minimize the total area, we need to use as little wire as possible for the square and as much as possible for the triangle. Let x be the length of wire used for the square, then the length of wire used for the triangle is 9 - x.

Using the same equations as in part (a), we get:

t = (18 - 8s)/3

A = (\(\sqrt{3}\)/4)((18 - 8s)/3)^2

Taking the derivative of A with respect to s, we get:

\(dA/ds = -4\sqrt{3}(4s-9)/27\)

Setting dA/ds = 0, we get:

4s - 9 = 0

Solving for s, we get:

s = 9/4

This is the same value as in part (a), which means that using 9 meters of wire for the square will result in the minimum total area as well as the maximum total area.

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Answer:

Should be 5^16

Step-by-step explanation:

24-8=16

then keep the 5

Answer:

4 ( x ) + ( y )

Step-by-step explanation:

.........

hmm yeah

Answer:

4*(4 + y)

Step-by-step explanation:

4*4 + 4y

16 + 4y

highest common factor is 4

4*(4+y)

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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The one-time administration fee is (d) $60

From the question, we have the following parameters that can be used in our computation:

12 months costs $660.

15 months costs $810.

This means that

(x, y) = (12, 660) and (15, 810)

For the one-time administration fee, we have

(x, y) = (0, y)

So, we calculate the slope using

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)

This gives

(660 - y)/12 = 50

So, we have

660 - y=600

This gives

y = 60

Hence, the administration fee is $60

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Answer:

The time might be 1.13 sec

Step-by-step explanation:

Angle relationships, where we're given a diagram containing 2+ parallel lines and a transversal, can tell us a lot about the angles.

The two angles indicated in the diagram measure 4x + 19 degrees and 6x + 7 degrees.

These two angles form a "Z" pattern, meaning they are on opposite sides of the transversal and opposite sides of the two parallel lines. They are alternate angles.

Alternate angles are always equal. Therefore, we can set up the following equation and solve for x:

\(4x + 19 = 6x + 7\\19 = 2x + 7\\12 = 2x\\x = 6\)

x = 6

We can expect 76 teenagers to say yes whether they  preferred watching shows over the internet, rather than through cable.

To calculate the expected number of teenagers who would prefer watching shows over the internet, rather than through cable:

73%, which is equivalent to 0.73 prefer watching shows over the internet. (Given)

Total number of teenagers surveyed is 104. (Given)

Expected number of teenagers who prefer watching shows over the internet =

= 0.73  × 104

= 75.92

Since it is a discrete variable we cannot have a fractional part of a teenager, we need to round the solution to the nearest whole number. Rounding 75.92 to the nearest whole number gives us 76.

Therefore, we can expect 76 out of the 104 teenagers surveyed to say yes, they prefer watching shows over the internet, rather than through cable.

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Answer:

yo

Step-by-step explanation:

Answer:

71.55

Step-by-step explanation:

a2 + b2 = c2

c=square route (a2+b2)

Answer:

Irrational

Step-by-step explanation:

The square root of 16.45 would be a number that will never end, making it irrational.

Answer:

irrational

Step-by-step explanation:

4.05585995813

does not terminate or repeat

not an integer

Answer: 4/9 or 0.4 with a reapeating 4.

Step-by-step explanation:

The volume will be 9 times increased if she triples the dimension of the square. So, yes, he is right because 3 is 2 times in the formula.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Given

Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base 8.

The side of the square is 8.

The height of the prism is 11.

Volume = Area of square × height.

The volume of the original prism will be.

\(\rm V_1 = 8 * 8 * 11\\\\V_1 = 704\)

If she triples the side of the square.

Then dimensions will be

The side of the square is 24.

The height of the prism is 11.

The volume of the modified prism will be.

\(\rm V_2 = 24 * 24* 11\\\\V_2 = 9*704\\\\V_2 = 9 \ Times \ of \ V_1\)

Thus, the volume will be 9 times bigger. So, yes, he is right because 3 is 2 times in the formula.

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Answer:

follow the statement below

Step-by-step explanation:

The question you presented here has multiple (un-limited) solutions unless you have another condition to solve for a single solution.

Equation: y = ax² + bx + c

y intercept (0 , 3): c = 3

axis of symmetry x=-5, therefore a corresponding point (-10,3) on the curve

3 = a*(-10)² + b*(-10) + 3

100a - 10b = 0

b = 10a  .... any pair like a=0.5 b=5; a=1 b=10 0r a=2 b=20 ..... all fit the function

y = 0.5x² + 5x +3

y = x² + 10x + 3

y = 2x² + 20x +3

........................

Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).

This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.

Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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The dimensions of the rectangle are 7 cm (width) and 13 cm (length).

Let's assume the width of the rectangle is x cm. According to the given information, the length of the rectangle would be x + 6 cm.

The area of a rectangle is calculated by multiplying its length and width. Therefore, we can set up the following equation:

Area = Length × Width

91 cm² = (x + 6 cm) × x cm

To solve this equation, we can expand it and rearrange it:

91 cm² = x² + 6x cm

Now, let's rearrange it to a quadratic equation form:

x² + 6x - 91 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In the given equation, a = 1, b = 6, and c = -91. Substituting these values into the quadratic formula, we get:

x = (-6 ± √(6² - 4(1)(-91))) / (2(1))

Simplifying further:

x = (-6 ± √(36 + 364)) / 2

x = (-6 ± √400) / 2

x = (-6 ± 20) / 2

Now, we have two possible solutions for x:

x = (-6 + 20) / 2 = 14 / 2 = 7

x = (-6 - 20) / 2 = -26 / 2 = -13

Since a negative value doesn't make sense for the width of a rectangle, we discard the second solution.

Therefore, the width of the rectangle is 7 cm.

Using this information, we can find the length:

Length = Width + 6 = 7 cm + 6 cm = 13 cm

So, the dimensions of the rectangle are 7 cm (width) and 13 cm (length).

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Free samples or product trials as a type of sales promotion can be both beneficial and detrimental. They encourage consumers to try a product at reduced risk, but they can also reduce the perception of value for the product or service.

Offering free samples or product trials is a common sales promotion strategy to attract customers and encourage them to try a product or service. This approach has several benefits. Firstly, it lowers the perceived risk for consumers as they can experience the product without making a financial commitment upfront. This can be especially effective for new or unfamiliar products, as it allows potential customers to test the product's quality and functionality.

However, there can be drawbacks to this sales promotion technique. Providing free samples or trials can create the perception that the product or service has less value or is of lower quality. Consumers may develop a mindset of expecting free or discounted offerings, and it can undermine the willingness to pay the full price in the future. Additionally, if the free samples or trials are not managed effectively, it may attract individuals who are not genuinely interested in the product, leading to wastage of resources and potentially diluting the brand image.

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