Use the contingency table to the right to determine the probability of events. a. What is the probability of event A? b. What is the probability of event A'? c. What is the probability of event A and B? d. What is the probability of event A or B? A A B 90 30 В' 60 70

The probability that each player has a 5-card hand an ace when the 52 cards is 5/13.

Given is 52 cards of a standard deck, we need to find the probability of picking an ace,

so,

There are 4 aces in the 52-card deck so the probability of dealing an ace is 4/52 = 1/13.

In a 5-card hand, each card is equally likely to be an ace with probability 1/13. So together, the expected number of aces in a 5-card hand is 5 * 1/13 = 5/13.

Hence the probability that each player has a 5-card hand an ace when the 52 cards is 5/13.

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(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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Answer:

Step-by-step explanation:

From the given information:

The ratio of the limiting floor area to lot area is 0.60 to 1

i.e.

= 0.60 : 1

For instance, let's take that the remodel size as p sq.ft on 1140 sq.ft

Then, the ratio = \(\dfrac{p}{11400}\)

The proportion of these equations is as follows:

\(\dfrac{p}{11400} = \dfrac{0.60}{1}\)

\(p \times 1 = 11400 \times 0.60\)

\(p = 11400 \times \dfrac{60}{100}\)

\(p =\dfrac{ 11400 \times 60}{100}\)

\(p =\dfrac{ 114 \times 100 \times 60}{100}\)

\(p = 114 \times 60\)

p = 6840 sq ft

Thus, the maximum allowable size of a remodeled house is 6840 sq.ft

b.

Recall that, the size of the home remodeled by limiting floor to lot area is

0.60:1

Then the proportion equation form is as follows:

\(\dfrac{0.60}{1}= \dfrac{5040}{x}\)

By cross multiplying

\(0.60 \times x = 5040 \times 1\)

\(x = \dfrac{5040 \times 1}{0.60 }\)

\(x = \dfrac{5040 \times 100}{60 }\)

\(x = \dfrac{84 \times 60 \times 100}{60 }\)

\(x =84 \times 100\)

x = 8400 sq.ft

Hence, the size of lot area is 8,400 sq.ft

The free cash flow (FCF) for year 1 can be calculated by subtracting the investment in fixed assets and the investment in net working capital from the profit after taxes and adding back the depreciation. In this case, the free cash flow for year 1 is $2 million

Free cash flow (FCF) is a measure of the cash generated by a company after accounting for its expenses and investments in fixed assets and working capital. It represents the amount of cash available to the company for distribution to its shareholders, reinvestment in the business, or debt reduction.

In this case, the given data states that the profit after taxes is $5 million, the depreciation is $2 million, the investment in fixed assets is $4 million, and the investment in net working capital is $1 million.

The free cash flow (FCF) for year 1 can be calculated as follows:

FCF = Profit after taxes + Depreciation - Investment in fixed assets - Investment in net working capital

FCF = $5 million + $2 million - $4 million - $1 million

FCF = $2 million

Therefore, the free cash flow for year 1 is $2 million. This means that after accounting for investments and expenses, the company has $2 million of cash available for other purposes such as expansion, dividends, or debt repayment.

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If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.

we first find the side length of the cube and the radius of the sphere.

The volume of the cube is 512 cubic units,

We have,

⇒ side³ = 512,

⇒ side = 8

So, the side length of the cube is 8 units.

Volume of sphere is also 512 cubic units,

We have,

⇒ (4/3)πr³ = 512,

On Simplifying,

We get,

⇒ r = 4.96 units.

So, radius of sphere is = 4.96 units.

Next we can find the surface area of each solid.

The surface-area of cube is = 6×(side)²,

⇒ 6(side²) = 6(8²) = 384 square units,

The surface area of the sphere is = 4πr²,

⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.

Therefore, the Cube has a greater surface area than the sphere.

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The angle between the acceleration and velocity vectors at t=1 is  46.6°. Hence the answer is (a) 46.6°.

To obtain the angle between the acceleration and velocity vectors at t=1, we need to differentiate the position equations to obtain the velocity and acceleration equations.

We have:

x(t) = 2t³ - 3t

y(t) = t² + 4

To calculate the velocity, we take the derivatives of x(t) and y(t) with respect to time (t):

\(\[ v_x(t) = \frac{d}{dt} \left(2t^3 - 3t\right) = 6t^2 - 3 \]\)

\(\[v_y(t) = \frac{{d}}{{dt}} \left(t^2 + 4\right) = 2t\]\)

So the velocity vector at any time t is: \(\[ v(t) = (v_x(t), v_y(t)) = (6t^2 - 3, 2t) \]\)

To calculate the acceleration, we differentiate the velocity equations:

\(\[a_x(t) = \frac{{d}}{{dt}} \left[6t^2 - 3\right] = 12t\]\)

\(\[a_y(t) = \frac{{d}}{{dt}} \left[2t\right] = 2\]\)

So the acceleration vector at any time t is: \(\[a(t) = (a_x(t), a_y(t)) = (12t, 2)\]\)

Now, we can calculate the acceleration and velocity vectors at t=1:

v(1) = (6(1)² - 3, 2(1)) = (3, 2)

a(1) = (12(1), 2) = (12, 2)

To obtain the angle between two vectors, we can use the dot product and the formula:

\(\[\theta = \arccos\left(\frac{{\mathbf{a} \cdot \mathbf{v}}}{{\|\mathbf{a}\| \cdot \|\mathbf{v}\|}}\right)\]\)

Let's calculate the angle:

\(\(|a| = \sqrt{{(12)^2 + 2^2}} = \sqrt{{144 + 4}} = \sqrt{{148}} \approx 12.166\)\\\(|v| = \sqrt{{3^2 + 2^2}} = \sqrt{{9 + 4}} = \sqrt{{13}} \approx 3.606\)\)

(a⋅v) = (12)(3) + (2)(2) = 36 + 4 = 40

\(\\\[\theta = \arccos\left[\frac{40}{12.166 \times 3.606}\right]\]\)

θ ≈ arccos(1.091)

Using a calculator, we obtain that the angle is approximately 46.6°.

Therefore, the closest answer is (a) 46.6°.

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Answer:

tanC

Step-by-step explanation:

tanC = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{6}{10}\)

Answer:

3-y/3

The slope is -2/5

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

Answer:

Sally's soccer team won 68% of the games they played.

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

The expression for dw/dt is \(e^(^t^-^1^)\)- (ln t + 1)cos(t ln t).

To find dw/dt, we need to use the chain rule of differentiation and differentiate each term with respect to t.

First, we can substitute the given expressions for x, y, and z into the expression for w:

w = z - sin(xy) = \(e^(^t^-^1^)\) - sin(t ln t)

Now we can differentiate w with respect to t using the chain rule:

dw/dt = d/dt(\(e^(^t^-^1^)\)) - d/dt(sin(t ln t))

To find d/dt(\(e^(^t^-^1^)\)), we can use the chain rule:

d/dt(\(e^(^t^-^1^)\)) = d/dt(\(e^u\)) where u = t-1

= d/dt(u) * d/du(\(e^u\)) = 1 *\(e^(^t^-^1^)\) = \(e^(^t^-^1^)\)

To find d/dt(sin(t ln t)), we can also use the chain rule:

d/dt(sin(t ln t)) = d/dt(sin(u)) where u = t ln t

= d/dt(u) * d/du(sin(u)) = (ln t + 1) * cos(t ln t)

Putting it all together, we have:

dw/dt = \(e^(^t^-^1^)\) - (ln t + 1)cos(t ln t)

Therefore, the expression for dw/dt is \(e^(^t^-^1^)\) - (ln t + 1)cos(t ln t).

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Answer:

Below.

Step-by-step explanation:

False for all isosceles triangles except:

This is only true for a 45-45-90 triangle.

a. The scalar projection of b onto a is -6.50

b.  the vector b into a component parallel to a and a component orthogonal to a. Parallel component: (-1.67, 2.77, -5.24) and Orthogonal Component  [9, -5, 1]

(A) The scalar projection of b onto a is given by:

proj_a(b) = (b . a) / ||a||

where "·" denotes the dot product and "|| ||" denotes the norm (magnitude) of a.

So, we have:

b . a = (-3)(9) + (5)(-5) + (-9)(1) = -78

||a|| = √[(-3)^2 + 5^2 + (-9)^2] = √[115]

Therefore:

proj_a(b) = (-78) / √[115] ≈ -6.50

(B) To find the component of b parallel to a, we can use the scalar projection we just found and multiply it by the unit vector in the direction of a. The unit vector in the direction of a is given by:

u_a = a / ||a||

So, we have:

comp_parallel = proj_a(b) * u_a

= (-6.50) * [(-3)/sqrt[115], 5/√[115], (-9)/sqrt[115]]

≈ (-1.67, 2.77, -5.24)

To find the component of b orthogonal to a, we can subtract the parallel component from b:

comp_orthogonal = b - comp_parallel

= [9, -5, 1] - (-1.67, 2.77, -5.24)

≈ (10.67, -7.77, 6.24)

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Answer: Ok, so the tree would start with the ten marbles going to 1 of the reds, 1 of the black , and get till you used up all the black, then do 2/10 and 8/10 to 12 and repeat the 1 part step, and then do 4/12 and 8/12 and add it all up and place the probability out of 22.

Step-by-step explanation:

The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

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The baseball clears the 3.00 m high fence by a distance of 42.3 m. This can be calculated using the equations of projectile motion. The initial velocity of the baseball is 31.4 m/s, and it is launched at an angle of 32.5° above the horizontal. The time it takes the baseball to reach the fence is 3.10 s.

The horizontal distance traveled by the baseball in this time is 104 m. The vertical distance traveled by the baseball in this time is 3.10 m. Therefore, the baseball clears the fence by a distance of 104 m - 3.10 m - 3.00 m = 42.3 m.

The equations of projectile motion can be used to calculate the horizontal and vertical displacements of a projectile. The horizontal displacement of a projectile is given by the equation x = v0x * t, where v0x is the initial horizontal velocity of the projectile, and t is the time of flight. The vertical displacement of a projectile is given by the equation y = v0y * t - 1/2 * g * t^2, where v0y is the initial vertical velocity of the projectile, g is the acceleration due to gravity, and t is the time of flight.

In this case, the initial horizontal velocity of the baseball is v0x = v0 * cos(32.5°) = 31.4 m/s. The initial vertical velocity of the baseball is v0y = v0 * sin(32.5°) = 17.5 m/s. The time of flight of the baseball is t = 3.10 s.

The horizontal displacement of the baseball is x = v0x * t = 31.4 m/s * 3.10 s = 104 m. The vertical displacement of the baseball is y = v0y * t - 1/2 * g * t^2 = 17.5 m/s * 3.10 s - 1/2 * 9.8 m/s^2 * 3.10 s^2 = 3.10 m.

Therefore, the baseball clears the 3.00 m high fence by a distance of 104 m - 3.10 m - 3.00 m = 42.3 m.

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Answer:

C) \(\sf \sqrt{45}\)

Step-by-step explanation:

Pythagorean theorem:

               AB = 6 units

              BC = 3 units

AC is hypotenuse and AB is the base and BC is the altitude.

Hypotenuse² = base² + altitude²

               AC² = AB² + BC²

                      \(\sf = 6^2 + 3^2\\\\ = 36 + 9\\\\ = 45\)

               \(\sf AC= \sqrt{45}\)

Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.

The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.

Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.

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Main Answer: The slope of a steep upward-sloping line will be a positive.

Supporting Question and Answer:

How is the slope of a line calculated?

The slope of a line is calculated by dividing the change in the y-coordinate (vertical change) between any two points on the line by the change in the x-coordinate(horizontal change)between the same two points.This is represented by the formula:

slope= \(\frac{(y_2-y_1)}{(x_2-x_1)}\) ,where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Body of the Solution:In mathematics, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. A positive slope indicates that the line is increasing in the y-direction as the x-coordinate increases.

A steep upward-sloping line means that the line is increasing rapidly in the y-direction as the x-coordinate increases, and therefore the slope of the line will be a large positive number. Conversely, a steep downward-sloping line will have a large negative slope, indicating that the line is decreasing rapidly in the y-direction as the x-coordinate increases.

Therefore, the slope of a steep upward-sloping line will be a positive.

Final Answer:The slope of a steep upward-sloping line will be a positive.

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Answer:

1/5

Step-by-step explanation:

Total Frequency is 14+21+70 = 105

Sewing has frequency of 21

21/105 = 0.2 = 1/5

Answer:

They both will meet each other when they both have been running for 10 seconds

Lauren will run \(x=80\ \text{ft}\) and Clara will run \(40\ \text{ft}\)

Step-by-step explanation:

Velocity of Lauren

\(v_l=\dfrac{24}{3}\\\Rightarrow v_l=8\ \text{ft/s}\)

Velocity of Clara

\(v_c=\dfrac{20}{5}\\\Rightarrow v_c=4\ \text{ft/s}\)

Let distance traveled by Lauren be \(x\)

As Clara has a 40 feet head start distance she will travel is \(x-40\)

\(\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}\)

The time that will have passed when they both will meet will be the same for both of them so

\(\dfrac{x-40}{4}=\dfrac{x}{8}\\\Rightarrow 8x-320=4x\\\Rightarrow 8x-4x=320\\\Rightarrow 4x=320\\\Rightarrow x=\dfrac{320}{4}\\\Rightarrow x=80\ \text{ft}\)

Time they will meet is \(\dfrac{80-40}{4}=\dfrac{80}{8}=10\ \text{s}\).

So, Lauren will run \(x=80\ \text{ft}\) and Clara will run \(x-40=80-40=40\ \text{ft}\).

Answer: 3 toys

Step-by-step explanation:

Equation: 60-5t=45

Solving: 5t=60-45

5t=15

t=3

Answer:

The unit of measure appropriate is cubic metre or cubic meter (m³)

Step-by-step Explanation:

we know that

The volume of a cube is equal to

V = b^3

where b is the length side of the cube

In this problem we have

b = 2m

substitute in the formula of volume

V = 2^3

V = 8 m^3

therefore

The unit of measure appropriate is cubic metre (m³)

Answer:

y = -2x+7

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = -2x+b

Using the point

3 = -2(2)+b

3 = -4+b

3+4 = b

7=b

y = -2x+7

\(4x+7=6x+4\\\\\implies 6x -4x = 7-4\\\\\implies 2x = 3\\\\\implies x =\dfrac 32\)

Answer:

x= 3/2

Step-by-step explanation:

4x+7=6x+4

Step 1: Subtract 6x from both sides.

4x+7−6x=6x+4−6x

−2x+7=4

Step 2: Subtract 7 from both sides.

−2x+7−7=4−7

−2x=−3

Step 3: Divide both sides by -2.

-2x=-3

-2    -2

=

3/2

One number is six times another number and their difference is thirty. The smaller number is 6 and the larger number is 36.

Let x be the smaller number and y be the larger number.

According to the problem, y = 6x and y - x = 30. We can substitute the first equation into the second equation to get: 6x - x = 30

Simplifying, we get: 5x = 30

Dividing both sides by 5, we get: x = 6

Now that we know the value of x, we can substitute it into the first equation to find y: y = 6x = 6(6) = 36

Therefore, the smaller number is 6 and the larger number is 36.

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Given:

A standard deck is made up of cards from 4 suit clubs, hearts, diamonds, and spades.

Required:

Find the fewest number of cards that you need to draw so that you are certain that you have at least two cards of the same suit.

Explanation:

The total number of cards = 52

The number of cards with the same suit = 13

The probability of an event is given by the formula:

The probability of drawing two cards with the same suit is:

Final Answer:

The probability of