a 4 card hand is dealt from a deck of 52 playing cards. assuming that each hand is equally likely, what is the probability that the hand contains cards from exactly one suit

Answer:

  a) 22e^-0.01t kilograms

  b) about 19.906 kilograms

Step-by-step explanation:

You want an equation for the amount of salt in a 15 kL brine tank initially containing 22 kg of salt if 150 L/min of the contents is replaced by pure water.

The quantity of salt s(t) in kilograms can be described by the differential equation ...

  s(0) = 22; s'(t) = -150/15000·s(t)

The solution can be found by separation of variables.

  [tex]\displaystyle\dfrac{ds}{dt}=-0.01s\\\\\int{\dfrac{1}{s}}\,ds=-0.01\int{}\,dt\\\\\ln{s}=-0.01t+c_1\\\\s=c_2\cdot e^{-0.01t}\qquad\text{where $c_2$ is $s(0)=22$}\\\\\boxed{s(t)=22e^{-0.01t}}[/tex]

The amount of salt remaining after 10 minutes is ...

  s(10) = 22·e^(-0.01·10) = 22·e^-0.1

  s(10) ≈ 19.906 . . . . kilograms

There is about 19.906 kg of salt in the tank after 10 minutes.

__

Additional comment

The initial rate of change of the amount of salt is -22/100 kg/min, so after 10 minutes, we expect an approximate reduction by 2.2 kg to 19.8 kg. Since the rate slows as salt is removed, the value 19.9 kg after 10 minutes is reasonable.

There are a couple of places where the integration constant can be put in the equation for the salt quantity. As a multiplier of the exponential function, its value is found in a straightforward way.

The reaction of ammonium hydroxide and aluminium chloride will form a white precipitate.

The presence of sodium, potassium, calcium, or aluminium chloride can be tested using a combination of physical and chemical methods. For sodium chloride, the flame test is the most common and effective way to confirm its presence. The sodium chloride compound will emit a yellowish-orange flame when exposed to heat. To test for the presence of potassium chloride, the chloride test is used. The presence of potassium chloride will cause a violet or purple color in the reaction when it is added to a silver nitrate solution. To test for the presence of calcium chloride, aqueous ammonia is added.

The formation of a white precipitate confirms the presence of calcium chloride. Lastly, to test for the presence of aluminium chloride, ammonium hydroxide is used.

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The cost of one avacado is equal to 0.5$ and it is found by the use of division method.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. an a person who knows what I mean by just calling it what they do when they just want to go to the store. Just call it what they call it, whatever ites. Really, whatever it is, these are the same people. It is a mathematical operation used for equal distribution and equal grouping.
One of the fundamental mathematical operations is division, which involves breaking a larger number into smaller groups with the same number of items.
We are given the cost of 8 avacados= $4.

The cost of 1 avacado= 1/8 * 4 = 1/2 = 0.5.

Hence, the cost of one avacado is equal to $0.5.

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Answer:

7/4

Step-by-step explanation:

if you divide 7/4, you will get 1.75 which is greater than 1.43.

Answer:

Hi, your answer is 7/4

Step-by-step explanation:

Hope this helps :D

Answer:

=(x+9)(x+5)

Step-by-step explanation:

Answer:

Angle 4 and angle 8 are corresponding angles because they are the same angle on the same side.

A discrete data random variable is a random variable that can only take on a finite or countable number of values.

Out of the options given, the number of cars finished in a factory each day is a discrete data random variable. This is because the number of cars finished can only take on a finite number of values, such as 0, 1, 2, 3, and so on. It cannot take on any value between these integers, and there are only a finite number of possible values.

In contrast, a person's height and weight are continuous data random variables, as they can take on any value within a certain range (for example, a person's height can take on any value between 4 feet and 7 feet).

Similarly, the volume of water in a swimming pool can take on any value within a certain range, and is also a continuous data random variable.

Therefore, the only discrete data random variable out of the options given is the number of cars finished in a factory each day.

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There isn't a way we get a fractional number or cones, we roll down to the closest full amount: 28 cones. The great majority of cone boxes that Higgins Shop can fill to the brim by one ice cream tub is 28.

or as one number followed by the other number inside a line of text, as in: 3/4. 3 out of 4 components are represented by the fraction 3/4, or three quarters. The term "numerator" refers to the higher number, 3, whereas the term "denominator" refers to the lower number, 4.

Its radius is 2.5/2 ≈ 1.25 inches because the cone container's diameter is specified as 2.5 inches. It states that the height is 6 inches.

Thus, one cone container has a volume of: V = (1/3)(1.25)2(6)V 7.35 cubic inches.

We must now determine which of these cone-shaped containers one tub of cream can fit into.

First, we must convert 1 tub of ice cream's volume from inches to cubic centimeters.

211.2 cubic inches from 384 ounces divided by 0.55 cubic inches per ounce.

Secondly, we divide a volume of a cone container by volume of an ice cream tub:

28.77 cones out of 28.12 cubic inches at 7.35 cubic inches each

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The solution of the system of equations is (2, 1).

Here we have the system of equations:

y = 2x - 3

y = -x + 3

To solve the system of equations graphically, we need to graph both of these lines in the same coordinate axis and then find the point where the lines intersect.

That point will be the solution of the system.

On the image at the end you can see the graph of the system of equations, there we can see that the solution is (2, 1).

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Around 0.13% or 0.0013 of children find relief for less than four hours.

The percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution is determined as follows:

Step 1: Define the parameters of the problem. Assume that relief times are normally distributed with a mean of μ = 5.5 hours and a standard deviation of σ = 0.5 hours. We want to find the percentage of children who experience relief for less than four hours.

Step 2: Convert the normal distribution to the standard normal distribution using the formula: z = (x - μ) / σwhere x is the relief time in hours.

Step 3: Find the z-score corresponding to the value of x = 4:z = (4 - 5.5) / 0.5 = -3

Step 4: Use a standard normal distribution table to find the percentage of the area under the curve to the left of z = -3. This is equivalent to the percentage of children who experience relief for less than four hours.

Using the standard normal distribution table or calculator, we get that the percentage of children who experience relief for less than four hours is approximately 0.13% or 0.0013.


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Philip puts 8 ounces of snack mix in each bag. To get this answer, we found the total weight of the mix by adding the weights of the three ingredients and converted it to ounces.

First, we need to find the total weight of the mix. Since Philip mixes 2 pounds of each ingredient and he has three ingredients, the total weight of the mix is:

2 pounds + 2 pounds + 2 pounds = 6 pounds

Since there are 16 ounces in a pound, the total weight of the mix in ounces is:

[6 pounds] 16 ounces/pound = 96 ounces

To find how many ounces of mix Philip puts in each bag, we divide the total weight of the mix by the number of bags:

96 ounces / 12 bags = 8 ounces per bag

Therefore, Philip puts 8 ounces of snack mix in each bag.

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the nationwide coffee chain is downsizing its branches in six states, and has already informed the store managers. The process should involve analyzing the reasons for downsizing, identifying the branches to be downsized, developing a transition plan, implementing the plan, and monitoring the progress and results.

The question asks about a nationwide coffee chain that is downsizing its branches in six states and has informed the store managers.
To answer this question, we can discuss the process of downsizing branches and the possible reasons behind it.
Analyze the reasons for downsizing
The coffee chain may be downsizing due to financial challenges, declining sales, or a shift in strategic focus. Understanding the reasons for downsizing will help in determining the best approach to manage the process.
Identify the branches to be downsized
The coffee chain must have a clear plan for which branches in the six states will be downsized. This can be based on factors such as sales performance, location, and overall profitability of each branch.
Inform the store managers
The coffee chain has already taken this step by informing the store managers about the downsizing. This is important to ensure that they are aware of the changes and can communicate this information to their employees.
Develop a transition plan
The coffee chain should develop a comprehensive plan to manage the downsizing process. This could involve offering support to affected employees, such as providing severance packages, job placement assistance, or opportunities to transfer to other branches.
Implement the downsizing plan
Once the plan has been developed, the coffee chain can begin the process of downsizing the identified branches. This may involve closing or merging some locations, reducing staff, and reallocating resources.
Monitor the progress and results
After the downsizing process is complete, the coffee chain should closely monitor the outcomes and make any necessary adjustments to ensure the desired results are achieved.

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Answer:

about 169.65

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]\pi r^2h[/tex].

All you have to do is plug the numbers in.

[tex]V=\pi (3)^2(6)[/tex]

Then use a calculator to evaluate.

The volume of the cylinder is approximately 169.56 cubic units.

The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius of the base, and h is the height.

Substituting the given values, we get:

V = π(3)^2(6)

V = π(9)(6)

V = 54π

Therefore, the volume of the cylinder is 54π cubic units. If you need an approximate numerical value, you can use the approximation 3.14 for π and calculate:

V ≈ 54 x 3.14

V ≈ 169.56

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The correct question is :

What is the volume of a cylinder with a base radius of 3 units and height of 6 units?

The Height of the toy box is 7 feet.

The height of the toy box in the shape of a rectangular prism is calculated using the following formula:

Volume = Length * Width * Height.

In this case, Volume = 36 cubic feet, Length = 2 * Width, and Height = Width - 1.
Therefore, we can solve for the Width by substituting the values into the formula:
36 = (2 * Width) * (Width - 1)
36 = 2 * Width^2 - Width
2 * Width^2 - Width - 36 = 0

By using the quadratic formula, Width = 8.
Therefore, the Height of the toy box is 7 feet.

To summarize, the toy box in the shape of a rectangular prism has a Width of 8 feet, a Length of 16 feet, and a Height of 7 feet to hold a total of 36 cubic feet.

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The length of altitude CD is 133/25 units.

What is the length if altitude?

To find the length of altitude CD, we need to find the length of the line segment CD, which is perpendicular to AB and passes through the point C.

First, let's find the equation of the line AB. We can use the two-point form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. Using points A and B, we get:

m = (0 - 6)/(8 - 0) = -3/4

y - 6 = (-3/4)(x - 0)

y = (-3/4)x + 6

Next, let's find the slope of the line CD, which is the negative reciprocal of the slope of AB. This is because perpendicular lines have slopes that are negative reciprocals of each other. Therefore:

m_CD = 4/3

Now we can use the point-slope form to find the equation of line CD. We know that the line passes through point C (5, 8), so:

y - 8 = (4/3)(x - 5)

Simplifying, we get:

y = (4/3)x - 4/3 + 8

y = (4/3)x + 20/3

Now we need to find the intersection of line CD with line AB. We can solve the system of equations:

y = (-3/4)x + 6

y = (4/3)x + 20/3

Setting the two expressions for y equal to each other, we get:

(-3/4)x + 6 = (4/3)x + 20/3

Multiplying both sides by 12, we get:

-9x + 72 = 16x + 80

25x = -8

x = -8/25

Substituting this value of x into either equation, we get:

y = (-3/4)(-8/25) + 6 = 57/25

Therefore, the point of intersection is (-8/25, 57/25).

Finally, we can use the distance formula to find the length of CD, which is the distance between C and the point of intersection:

d = √[(5 - (-8/25))² + (8 - 57/25)²]

d = √[(125/25 + 8/25)² + (200/25 - 57/25)²]

d = √[(133/25)² + (143/25)²]

d = √(17689/625)

d = 133/25

Therefore, the length of altitude CD is 133/25 units.

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Two samples are matched pairs because there are two samples and each pair in the two samples have about the same GPA indicating they have similar characteristics. Correct option is A.

This is because the paired t-test is used when we have two related samples or when the same sample is measured twice, such as before and after a treatment.

In this case, the two samples being compared are students' GPAs before and after a particular intervention or treatment. Since the same group of students are being measured twice, they are matched pairs and the paired t-test is appropriate to use.

Option B is not a suitable answer because the fact that the samples are both MBA majors does not necessarily make them matched pairs. Option C is also not a suitable answer because having equal numbers of data does not necessarily make the samples matched pairs.

Option D is not a suitable answer because it does not provide any explanation as to why the paired t-test is being used.

Therefore, correct option is A.

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Complete question is:

Why do we use the paired t test for these data? In other words, why these two samples are matched pairs? Select the most suitable answer. A. There are two samples and each pair in the two samples have about the same GPA indicating they have similar characteristics.

B. There two samples of MBA majors.

C. There are two samples with equal number of data.

D. None of these.  

Rent-A-Reck Incorporated should charge $95 to maximize its revenue and the company will rent 45 cars at a price of $95.

To determine the price that will maximize Rent-A-Reck Incorporated's revenue, we need to consider the relationship between the price of renting a car and the number of cars that are rented.

Based on the information provided, we know that the demand for rental cars decreases as the price increases. Specifically, for each $5 increase in price, two fewer cars will be rented.

Let's denote the price of renting a car as P and the number of cars rented as Q. Then we can express the relationship between price and quantity as:

Q = 60 - 2(P - 80)/5

This equation tells us that as the price P increases, the number of cars rented Q decreases. We can also use this equation to find the price that will maximize revenue. Revenue is calculated by multiplying the price by the number of cars rented, so we can write the revenue function as:

R = P(Q) * Q

= P * (60 - 2(P - 80)/5)

To find the price that maximizes revenue, we need to find the value of P that makes R as large as possible. One way to do this is to take the derivative of R with respect to P and set it equal to zero:

dR/dP = (60 - 2(P - 80)/5) - 2P/5 = 0

Solving for P, we get:

P = $95

To find the number of cars that will be rented at this price, we can substitute P = $95 into the demand equation:

Q = 60 - 2($95 - $80)/5

= 45

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Complete question is:

Rent-A-Reck Incorporated finds that it can rent 60 cars if it charges $80 for a weekend. It estimates that for each $5 price increase it will rent two fewer cars. What price should it charge to maximize its revenue? How many cars will it rent at this price?

Answer:

I disagree with the statement that a temperature of -11 degrees Fahrenheit is warmer than a temperature of -15 degrees Fahrenheit.

Temperatures are usually compared in terms of their absolute values. In the case of Fahrenheit, the absolute value of a temperature can be obtained by adding 459.67 to the Fahrenheit temperature. Using this conversion, we can see that:

 •A temperature of -11 degrees Fahrenheit is equal to 471.47 degrees  absolute.

•A temperature of -15 degrees Fahrenheit is equal to 456.67 degrees  absolute.

Since 471.47 is greater than 456.67, we can conclude that a temperature of -11 degrees Fahrenheit is colder than a temperature of -15 degrees Fahrenheit in terms of their absolute values. Therefore, a temperature of -15 degrees Fahrenheit is actually warmer than a temperature of -11 degrees Fahrenheit.

Answer: 20:21 or 20 to 21

Step-by-step explanation:

Answer:

If 20 out of 21 students want pancakes, then only 1 student wants waffles.

The ratio of the number of students who want waffles to the total number of students is therefore:

1 waffle student : 21 total students

or simplified as:

1 : 21

So the ratio is 1 to 21

Answer:

Step-by-step explanation:

We can claim that after answering the above question, the Therefore, equation there were 3624 fans wearing red at the hockey game.

In mathematics, an equation is a statement that states the equality of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the sentence "2x + 3" equals the value "9". The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complex equations, regular or nonlinear, with one or more factors are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.  

Let's start by setting up a proportion:

[tex]60/100 = x/6040\\100x = 60 * 6040\\x = (60 * 6040) / 100\\x = 3624[/tex]

Therefore, there were 3624 fans wearing red at the hockey game.

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The height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

According to the Pythagorean Theorem, for any triangle which is a right triangle, the squares of the legs added together equal the square of the hypotenuse.

In the given triangle ABC.

AB = BC = 6 cm

So, ∠A = ∠C  (by isosceles triangle)

Then, AD = DC = 8.5/2

So, in right angles triangle ABD, applying Pythagorean theorem:

AB² = AD² + BD²

6² = (8.5/2)² + BD²

36 - 18.0625 = BD²

BD = √17.9375

BD =  4.23

Thus, the height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

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Answer:

The polynomial expression x^4 + 4x - 21 cannot be factored into linear factors with rational coefficients. This can be shown using the rational root theorem, which states that any rational roots (zeros) of the polynomial must be of the form p/q, where p is a factor of the constant term (in this case, 21) and q is a factor of the leading coefficient (1). The only possible rational roots of this polynomial are ±1, ±3, ±7, and ±21. However, plugging in each of these values does not give a zero of the polynomial, meaning it has no rational roots. Therefore, it cannot be factored into linear factors with rational coefficients. It may still be factorable using complex numbers, but it is not factorable using only real numbers.

Thus, the area of the given shape of trapezoid is obtained as: 120 sq. ft.

Rectangle, rhombus, and square are the names given to parallelograms with particular characteristics like right angles as well as all congruent sides (or both).

Area of trapezoid = 1/2 * (sum of parallel sides) * height

Area of trapezoid = 1/2 * (21 + 9) *8

Area of trapezoid = 120 sq. ft.

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The mean absolute deviation (MAD) of the given set of data is 3.875.

To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:

Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8

Mean = 8

Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:

|12 - 8| = 4

|10 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|8 - 8| = 0

|4 - 8| = 4

|2 - 8| = 6

|12 - 8| = 4

Then, we find the mean of the absolute deviations:

Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8

Mean absolute deviation = 26 / 8

Mean absolute deviation = 3.875

Therefore, the mean absolute deviation of the given set of data is 3.875.

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Complete Question:

what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.

Answer: 5% Of Tape

there is going to be 5% of tape for the coaster

The angle of elevation from the base to the top of the mountain is 26.56°.

Given, The vertical height of a mountain = 1200 feet

The distance from the top of the mountain to the base = 2400 feet

Now, we need to find the angle of elevation from the base to the top of the mountain.

Hence, we can find the angle of elevation by using the formula

tanθ = Perpendicular/Base

Now, let's apply the formula,

tanθ = Perpendicular/Base 1200/2400= 0.5 tanθ = 0.5

Now, we need to find the value of θθ = tan⁻¹ 0.5θ = 26.56°

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There are 25 feet in 300.0 inches.

Conversion is a numerical quantity that enables you to convert one unit to another. There are various units for measurements such as length, weight, mass, and so on.

The conversion factor between inches and feet is important to understand when performing this type of calculation. As I mentioned earlier, there are 12 inches in one foot, which can be expressed as:

1 foot = 12 inches

This means that to convert a measurement in inches to feet, we need to divide the number of inches by 12.

300.0/12 = 25

Therefore, 300.0 inches is equivalent to 25 feet.

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Answer:

The answer to your problem is, A. 60%

Step-by-step explanation:

54 of 90 can be written as: [tex]\frac{54}{90}[/tex]

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

[tex]\frac{54}{90} * \frac{100}{100}[/tex]

= [tex]\frac{( 54 * 100)}{90} * \frac{1}{100} = \frac{60}{100}[/tex]

Thus the answer to your problem is, A. 60%

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Answer:

x = 60%

Step-by-step explanation:

Let the unknown percentage be x.

We can make an expression using the given information.

[tex]\sf90*\frac{x}{100} =54[/tex]

Solve for x to find the percentage.

[tex]\sf\frac{90x}{100} =54\\90x=54*100\\\\90x=5400\\\\\frac{90x}{90}=\frac{5400}{90}\\\\ x=60[/tex]