Suppose that A and B are independent events. If P(A) = 9⁄10 and P(B) = 7⁄10 , find P(A ∩ B).
a) 0.07
b) 0.16
c) 1.00
d) 0.09
e) 0.63
f) None of the above.

Answer:

1) 28

2) 28

B) 1 and 1/2 hr

Answer:

that is a great question, could u explain more? im serious

Step-by-step explanation:

Answer:

The large squares represent X squared, and had two sides, blue and red, to determine whether it is positive or negative (blue = positive, red = negative). There is also the long rectangles that represent X, with the positive side being green and the negative red. The side length of X is the same side length of X squared, which makes sense because X multiplied by X equals X squared. The smallest square pieces represent the number 1. The colours are yellow for positive and red for negative. These are the basic pieces used in algebra tiles. Hope this helps

Step-by-step explanation:

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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ANSWER

Option D

EXPLANATION

Given:

Total number of investors = 998

Number of investors tracking daily stock = 235

Determine the probability

The range of a function is the complete set of all possible resulting values of the dependent variable (usually, y.)

From the graph given, the set of values of y that satisfy the given graph is from 1 to 5 (inclusive)

So we will have:

These documents suggest that the Cold War significantly influenced discussions of freedom in the early 1950s.

The tensions between the United States and the Soviet Union led to contrasting ideas of what freedom meant, with both sides promoting their political, economic, and social systems. This often resulted in increased scrutiny, propaganda, and a focus on national security.


1. During the early 1950s, the Cold War was at its peak, with both the United States and the Soviet Union vying for global influence.

2. The United States emphasized individual liberties, capitalism, and democracy, while the Soviet Union promoted communism, state control, and collective rights.

3. Discussions of freedom were heavily affected by these contrasting ideologies, with each side claiming to offer the true form of freedom.

4. Additionally, concerns over espionage, subversion, and the spread of communism led to a heightened sense of national security in the United States, impacting how freedom was discussed and viewed.

5. Propaganda played a significant role in shaping discussions of freedom, with both sides attempting to portray their respective systems as superior and more liberating than the other.

6. Overall, the Cold War led to a complex and polarized debate over the meaning of freedom in the early 1950s, as both superpowers sought to advance their own agendas and influence global perceptions of liberty and justice.

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(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Reports that compare performances of different business units or time periods are commonly referred to as comparative performance reports.

Comparative performance reports are analytical tools used to assess and compare the performances of different business units, departments, or time periods within an organization. These reports provide valuable insights into the relative strengths, weaknesses, and trends among the entities or time periods being evaluated.

By comparing key performance indicators (KPIs) such as revenue, profit, cost, market share, or productivity metrics, organizations can gain a deeper understanding of the factors driving success or underperformance.

Comparative performance reports allow decision-makers to identify areas of improvement, allocate resources effectively, and make data-driven strategic decisions.

These reports can be presented in various formats, including tables, graphs, or visual dashboards, making it easier for stakeholders to interpret and comprehend the performance data.

Comparative performance reports are instrumental in evaluating the effectiveness of strategies, identifying best practices, and fostering a culture of continuous improvement within an organization.

Therefore, comparative performance reports are commonly used to compare the performances of different business units or time periods, providing insights for evaluating strengths, weaknesses, and trends within an organization.

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The area of the triangle with base 2x and height (x - 7) in simplified form is x² - 7x

Area of a triangle = ½ × base × height

Base = 2x

Height = (x - 7)

Area of a triangle = ½ × base × height

= ½ × 2x × (x - 7)

= (2x² - 14x) / 2

= x² - 7x

Hence, the triangle given the dimensions has an area of x² - 7x

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Answer:

Step-by-step explanation:

He can drive 81 miles in 3 hours

The ratio 40 minutes to 70 minutes can be written as 4/7 in lowest terms.

To understand how we arrived at the fraction 4/7, let's break down the process of simplifying the given ratio.

Step 1: Write the ratio as a fraction

The ratio 40 minutes to 70 minutes can be expressed as a fraction: 40/70.

Step 2: Find the greatest common divisor (GCD)

To simplify the fraction, we need to determine the GCD of the numerator (40) and the denominator (70). The GCD is the largest number that evenly divides both numbers. In this case, the GCD of 40 and 70 is 10.

Step 3: Divide by the GCD

We divide both the numerator and denominator of the fraction by the GCD (10). Dividing 40 by 10 gives us 4, and dividing 70 by 10 gives us 7.

Therefore, the simplified fraction is 4/7, which represents the ratio of 40 minutes to 70 minutes in its lowest terms.

Simplifying fractions is a fundamental concept in mathematics that involves reducing fractions to their simplest form. By dividing both the numerator and denominator by their GCD, we eliminate any common factors and obtain a fraction that cannot be further simplified.

This process allows us to express ratios and proportions in their most concise and understandable form.

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Answer:

0.60 :D

Step-by-step explanation:

Pls mark me brainliest ty :D

Answer:

0.60

Step-by-step explanation:

if 4 apples are $0.40 and 4+2 is 6 add 0.20

therefor 6 apples cost $0.60

Answer:

y = 5/9x + 19/3

Step-by-step explanation:

slope: 10 - 5 / 6 - (-3) = 5/9

point-slope form:

y - 5 = 5/9(x + 3)

y -5 = 5/9x + 4/3

y = 5/9x + 6 1/3

Answer:

1 solution

Step-by-step explanation:

There is only one solution as it is not a quadratic

Only one solution x =  0 and y = 11 of the system of the equations possible.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

4x + y = 11    {equation 1}

-6x + y = 11    {equation 2}.

Subtracting equation 1 to the equation 2,

x = 0

Then y = 11.

Therefore, only one solution possible.

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Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

We are given the following picture

We are given the following statements

- Line BA is congruent to line OC

- Line ON is congruent to line DA

- Angle A is congruent to angle O

If we highlight the congruencies we get

where the matching colors indicate congruency. As we can see, we have a pair of sides that are congruent and the included angle are also congruent. This is the condition for the SAS theorem to apply. Hence both triangles are congruent by the SAS theorem

Answer:

1 1/3 chapters per hour

Step-by-step explanation:

eplaination is in the picture

Answer:

*selects all tables*

Answer:

Problem 1 all you need to do is move the decimal place over four times as it says in your text book. Start out by making the decimal point visible by doing this 58,927. right there then move it over four times like this 5,892.7 one 589.27 two 58.927 three 5.8927 four. When they say move it over four places that's what it means. Now you should be able to do the rest on your own. GOOD LUCK!!!

Answer:

y= x2+x-3

Step-by-step explanation: i think this is the answer

Answer:

A

Step-by-step explanation:

Commenter is right cause I graphed it to doublecheck

The centre and radius of the circle is (2, 3) and 6 units respectively

The standard equation of a circle is expressed as:

(x – a)² + (y – b)² = r²

where:

Given the equation

(x – 2)² + (y – 3)² = 36

Compare

(a, b) = (2, 3)

r² = 36

r = 6 units

Hence the centre and radius of the circle is (2, 3) and 6 units respectively

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The function that represent reflection of f(x) is given by g(x) = Negative two-fifths(10)x

Similar to reflections regarding the y-axis, the x-axis reflections are fundamentally the same. The only distinction is that the points are mirrored from above the x-axis to below the x-axis, and vice versa, rather than along the y-axis.

Make sure you have studied how to perform basic vertical and horizontal translations before we move on to reflections across the y-axis.

The reflection across the co-ordinate axis which is x-axis is as follows;

Reflection about the x-axis

Pre-image point before reflection = (x, y)

Point of image after reflection = ((x, -y)

Therefore, the x coordinate remains the same while the y coordinate changes sign

For which given that f(x) = y = 2/5(10)x and g(x) = Reflection of f(x) across the x-axis, we have

Reflection about the x-axis

Pre-image point before reflection = (x, f(x))

cordinate of image after the reflection = (x, g(x))

Hence g(x) = -f(x) = -2/5(10)x.

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Complete question:

Which function represents g(x), a reflection of f(x) = Two-fifths (10)x across the x-axis? g(x) = Negative two-fifths(10)x g(x) = Negative two-fifths (one-tenth) Superscript x g(x) = Two-fifths (one-tenth) Superscript negative x g(x) = Two-fifths(10)-x

To balance the equation, the right side of the equation must also change by 4%.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equals sign (=)

To balance the exchange equation, the percentage change on the left side of the equation \((\% \triangle M + \% \triangle V)\) must equal the percentage change on the right side of the equation \((\% \triangle P + \% \triangle Q)\).

Given that there has been a 3% change in the money supply \((\% \triangle M)\) and a 1% change in velocity \((\% \triangle V)\), the left side of the equation can be written as:

\(\%\triangle M + \%\triangle V = 3\% + 1\% = 4\%\)

To balance the equation, the right side of the equation must also change by 4%. Therefore, the correct answer is:

B. 4%

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Answer:

About 5.5% decrease

Step-by-step explanation:

Here, we want to calculate the percentage increase or decrease and its value.

The first thing to do here is to check if we are going to have a decrease or an increase.

since the value before the change is higher than the value after the change, then what we have is a decrease.

Mathematically, the percentage decrease is calculated as follows;

% decrease = (old value - new value)/old value * 100%

old value = 163 feet

new value = 154 feet

% decrease = (154-163)/163 * 100%

% decrease = -9/163 * 100%

% decrease = -5.52%

Thus the best answer is about 5.5% decrease

The general solution for the given trigonometric equation is:

θ = 0.568 + 2πn or θ = 32.59° + 360°n, where n is an integer representing all possible solutions.

To find the general solution for the trigonometric equation sin(θ) + 18tan(θ) + 37 = 130 + 66cos(θ), we'll work on simplifying and rearranging the equation.

Starting with the given equation:

sin(θ) + 18tan(θ) + 37 = 130 + 66cos(θ)

We can rewrite tan(θ) as sin(θ)/cos(θ):

sin(θ) + 18sin(θ)/cos(θ) + 37 = 130 + 66cos(θ)

Now, let's multiply through by cos(θ) to eliminate the denominator:

sin(θ)cos(θ) + 18sin(θ) + 37cos(θ) = 130cos(θ) + 66cos^2(θ)

Using the identity sin(θ)cos(θ) = (1/2)sin(2θ), we have:

(1/2)sin(2θ) + 18sin(θ) + 37cos(θ) = 130cos(θ) + 66cos^2(θ)

Rearranging the equation to have zero on one side:

66cos^2(θ) - 93cos(θ) + (1/2)sin(2θ) - 18sin(θ) - 37 = 0

This equation is a quadratic equation in terms of cos(θ). We can solve it by using the quadratic formula:

cos(θ) = [-b ± √(b^2 - 4ac)] / (2a)

Applying the formula, we get:

cos(θ) = [93 ± √(93^2 - 4(66)(-37))] / (2(66))

cos(θ) = [93 ± √(8649 + 9732)] / 132

cos(θ) = [93 ± √(18381)] / 132

cos(θ) = [93 ± 135.604] / 132

cos(θ) = [93 + 135.604] / 132 or cos(θ) = [93 - 135.604] / 132

cos(θ) = 1.586 or cos(θ) = -0.643

Since the cosine values are limited to the range [-1, 1], the second solution, cos(θ) = -0.643, is not valid.

Now, we can solve for θ using the inverse cosine function:

θ = cos^(-1)(1.586)

Using a calculator, we find that cos^(-1)(1.586) is approximately 0.568 radians or approximately 32.59 degrees.

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As the odds of the poorest shooter missing both shots are higher, intentionally fouling them (56 percentage) is a better tactic than fouling the 94% free throw shooter.

a. A player has a 0.8836 chance of making both free throws if they convert 94% of their attempts (to 4 decimals).

b. There is a 0.9972 percent chance that a player who makes 94% of his free throws will also make at least one (to 4 decimals).

c. There is a 0.0028 percent chance that a player who makes 94% of his free throw attempts will miss both attempts (to 4 decimals).

It is better to intentionally foul the guy who makes 94% of his free throw attempts than it is to intentionally foul the player with the poorest free throw shooting percentage. The likelihood that a player will make both free throws when he makes 56% of his attempts is 0.3136. (to 4 decimals). The odds that a player will make at least one free throw with a 56% success rate are 0.8232. (to 4 decimals). The likelihood that a player will miss two of his free throw attempts when he makes 56% of them is 0.1768. (to 4 decimals). Intentionally fouling the poorest free throw shooter would be the more successful tactic since the odds of the worst free throw shooter missing both shots are higher than the odds of the 94% free throw shooter missing both shots.

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Answer:

k=-13...............

7×50×5 = 1750 minutes

1750minutes/60minutes = 29.161 hours

Step-by-step explanation:

Starting with the equation x^2 + y^2 = 25, we can implicitly differentiate with respect to t using the chain rule:

2x dx/dt + 2y dy/dt = 0

Now we can plug in the given values for dy/dt, x, and y:

2(3) dx/dt + 2(4) (3) = 0

Simplifying:

6 dx/dt + 24 = 0

Subtracting 24 from both sides:

6 dx/dt = -24

Dividing by 6:

dx/dt = -4

Therefore, dx/dt = -4 when dy/dt = 3, x = 3, and y = 4.

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The value of the derivative, dx/dt is -4, when x^2 + y^2 = 25, dy/dt = 3, x = 3, and y = 4.

1. Differentiate both sides of the equation x^2 + y^2 = 25 with respect to t. Use the chain rule for differentiating y^2 with respect to t.
  d(x^2)/dt + d(y^2)/dt = d(25)/dt

2. Apply the chain rule,
  2x(dx/dt) + 2y(dy/dt) = 0

3. Plug in the given values for x, y, and dy/dt,
  2(3)(dx/dt) + 2(4)(3) = 0

4. Simplifying the equation,
  6(dx/dt) + 24 = 0

5. Solve for dx/dt,
  6(dx/dt) = -24
  dx/dt = -24/6
  dx/dt = -4

So, when x^2 + y^2 = 25, dy/dt = 3, x = 3, and y = 4, the value of the derivative, dx/dt is -4.

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