Given that P(A)=0.450 and P(B)=0.680 and P( A U B)=0.824. Find the probability

Answer:

The system of linear inequalities represented by the graph is:

y > x - 2 and y < x + 1

This system of inequalities indicates that y is greater than x - 2, which represents the upper boundary of the shaded region in the graph. Additionally, y is less than x + 1, which represents the lower boundary of the shaded region. The intersection of these two conditions is the region between the lines, satisfying both inequalities.

Step-by-step explanation:

When we simplify the expression, we get:

0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)

Using a calculator to evaluate the two fractions separately, we get:

0.0048 / 0.027 ≈ 0.1778

0.81 / 0.04 = 20.25

Substituting these values back into the original expression, we get:

(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25

Multiplying these two values together, we get:

0.1778 * 20.25 ≈ 3.59715

To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:

3.59715 ≈ 3.59715 × 10^(-3)

Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).

Answer:

Step-by-step explanation:

To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.

Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.

Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.

From the bar graph, we can see the following:

The bar representing 4+ children has a height of 4.

The bar representing 3- children has a height of 3.5.

The bar representing 2- children has a height of 2.5.

The bar representing 1- children has a height of 1.5.

The bar representing 1 child has a height of 1.

The bar representing 0.5- children has a height of 0.5.

The bar representing 0 children has a height of 0.

To find the total number of adults questioned (m), we sum up the heights of all the bars:

m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0

m = 18

Therefore, the total number of adults questioned is 18.

To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:

Percentage = (2.5 / 18) * 100

Percentage ≈ 13.9 (rounded to 1 decimal place)

Therefore, approximately 13.9% of the adults questioned had 2 children.

Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

As we know that,

Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.

So, r= (n+1)th term / nth term

where r ⇒ common ratio

          (n+1)th term⇒ succeeding term

          nth term⇒ preceding term

According to the given question, r = (9/8) / (3/4)

                                                       r = (2/3)

We also know,

Any term of a G.P. [nth term] can be obtained by the formula:

Tₙ= a[tex]r^{n-1}[/tex]

where, Tₙ= nth term

            a= first term of G.P.

            r=common ratio

Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.

   Tₙ= a[tex]r^{n-1}[/tex]

⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])

⇒ (64/729)= ([tex]2/3^{n-1}[/tex])

⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])

⇒ n-1 = 6

⇒ n = 7

∴ The total number of terms in G.P. is 7.

Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.

The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.  

So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.

To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.

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The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.

To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.

First, let's find the points of intersection by setting f(x) equal to g(x):

[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]

Rearranging the equation, we get:

[tex]x^3 + 2x^2 - 8x = 0[/tex]

Factoring out an x, we have:

[tex]x(x^2 + 2x - 8) = 0[/tex]

Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).

To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:

Area = ∫[from -4 to 2] (f(x) - g(x)) dx

Evaluating the definite integral, we have:

Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx

= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx

Integrating each term and evaluating the integral, we find:

Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2

= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]

= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]

= 1/3 + 128/3 - 16 + 4 - 128/3 + 64

= 1/3 + 4 + 64

= 69 1/3

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Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

Answer:

2, 4, 10, 20, 50, and 100.

Step-by-step explanation:

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

Answer:

I can't understand the language but try people who can

Answer:

the effective tax rate for a taxable income of $175,000 is approximately 21.02%.

Step-by-step explanation:

Let's break down the income into the corresponding tax brackets:

The first $10,275 is taxed at a rate of 10%.

Tax on this portion: $10,275 * 0.10 = $1,027.50

The income between $10,276 and $41,175 is taxed at a rate of 12%.

Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88

The income between $41,176 and $89,075 is taxed at a rate of 22%.

Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98

The income between $89,076 and $170,050 is taxed at a rate of 24%.

Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88

The income between $170,051 and $175,000 is taxed at a rate of 32%.

Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44

Now, sum up all the taxes paid:

$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68

The effective tax rate is calculated by dividing the total tax paid by the taxable income:

Effective tax rate = Total tax paid / Taxable income

Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)

Answer:

(fg)(x)= (x²+6)(x²-x+9)

multiply the terms:

(fg)(x)= x²(x²-x+9) +6(x²-x+9)

add the like terms:

(fg)(x)= (x⁴-x³+9x²)+(6x²-6x+54)

and you get your final answer:

(fg)(x)= x⁴-x³+15x²-6x+54

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The polynomial [tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex] simplifies to [tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18.[/tex]

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It is defined as a sum of terms, where each term consists of a variable raised to a non-negative integer exponent, multiplied by a coefficient.

The general form of a polynomial is:

P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a₀

To simplify the expression[tex](x^2 + 3x + 3) * (-2x^2 - x + 6)[/tex], we need to perform the multiplication and combine like terms.

First, we multiply each term in the first polynomial by each term in the second polynomial:

[tex](x^2 + 3x + 3) * (-2x^2 - x + 6) = x^2 * (-2x^2 - x + 6) + 3x * (-2x^2 - x + 6) + 3 * (-2x^2 - x + 6)[/tex]

Expanding each term, we get:

=[tex](-2x^4 - x^3 + 6x^2) + (-6x^3 - 3x^2 + 18x) + (-6x^2 - 3x + 18)[/tex]

Now, we combine like terms:

=[tex]-2x^4 + (-x^3 - 6x^3) + (6x^2 - 3x^2 - 6x^2) + (18x + 18x - 3x) + 18[/tex]

Simplifying further:

=[tex]-2x^4 - 7x^3 - 3x^2 + 33x + 18[/tex]

The simplified expression in polynomial standard form is:

-2x^4 - 7x^3 - 3x^2 + 33x + 18

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It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:

                          1             2           3            4          5          6

                   1    ( 1 , 1 )   ( 1 , 2 )   ( 1 , 3 )   ( 1 , 4 )   ( 1 , 5 )   ( 1 , 6 )

                   2   ( 2 , 1 )  ( 2, 2 )   ( 2 , 3 )  ( 2 , 4 )  ( 2 , 5 )  ( 2 , 6 )

                   3   ( 3 , 1 )  ( 3 , 2 )  ( 3 , 3 )   ( 3 , 4 )  ( 3 , 5 )  ( 3 , 6 )

                   4   ( 4 , 1 )  ( 4 , 2 )  ( 4 , 3 )   ( 4 , 4 )  ( 4 , 5 )  ( 4 , 6 )

                   5   ( 5 , 1 )  ( 5 , 2 )  ( 5 , 3 )  ( 5 , 4 )  ( 5 , 5 )  ( 5 , 6 )

                   6   ( 6 , 1 )  ( 6 , 2 )  ( 6 , 3 )  ( 6 , 4 )  ( 6 , 5 )  ( 6 , 6 )

- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.

- Now locate and highlight all the even pairs shown in bold.

- The total number of even pairs outcomes are = 9.

- The total possibilities are = 36.

- The probability of getting even pairs as favorable outcome can be expressed as:

                 P ( Even pairs ) = Favorable outcomes / Total outcomes

                 P ( Even pairs ) = 9 / 36

                 P ( Even pairs ) = 1 / 4.

- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4

(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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Answer:

Step-by-step explanation:

To determine if the point (4,1) is a solution for the system of equations, we need to substitute the values of x and y from the point into both equations and check if the equations hold true.

For the first equation, y = -x + 5, we substitute x = 4 and y = 1:

1 = -(4) + 5

1 = -4 + 5

1 = 1

The equation holds true for the first equation.

For the second equation, y = 2x - 7, we substitute x = 4 and y = 1:

1 = 2(4) - 7

1 = 8 - 7

1 = 1

The equation also holds true for the second equation.

Since the point (4,1) satisfies both equations, it is indeed a solution to the system of equations.

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

number is 16

Step-by-step explanation:

let n be the number , then 7 more than the number is n + 7 and 9 less than twice the number is 2n - 9

equating the 2 expressions

2n - 9 = n + 7 ( subtract n from both sides )

n - 9 = 7 ( add 9 to both sides )

n = 16

the required number is 16

The answer is:

Work/explanation:

Let's call the number n.

Seven more than n = n + 7

Nine less than twice n = 2n - 9

Put the expressions together :           n + 7 = 2n - 9

Now, we have an equation that we can solve for n.

First, flop the equation

2n - 9 = n + 7

Subtract n from each side

n - 9 = 7

Add 9 to each side

n = 16

Based on the quadratic function, an 18 year old would spend 3 hours watching television.

Using the quadratic function given :

The age is represented as the variable , 'z'

substitute z = 18 into the equation

y = (0.004*18²) - 0.314(18) + 7.5

y = 3.144

y = 3 hours approximately

Hence, an 18 year old spend approximately 18 hours watching television.

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The probability that a flight has 100 or more passengers and arrives on time is approximately 0.12 or 12%.

Let A be the event that a flight has 100 or more passengers, and B be the event that the flight arrives on time. We want to find the probability of the intersection of these two events, P(A ∩ B).

We are given:

- P(B) = 0.80, the probability that any given flight arrives on time

- P(A) = 0.30, the probability that any given flight has 100 or more passengers

- P(B | A) = 0.40, the conditional probability that a flight arrives on time given that it has 100 or more passengers (since 60% of such flights are late)

We can use the formula for conditional probability to find P(A ∩ B):

P(A ∩ B) = P(B | A) * P(A)

         = 0.40 * 0.30

         = 0.12

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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

Answer:

16

Step-by-step explanation:

the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then

32 → [tex]\frac{1}{2}[/tex] (32)

32 → 16

In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

Answer:

(r q)(-3) = -3

(q r)(-3) = -3

Step-by-step explanation:

let x = 1

q(1) = -1 +2 = 1

r(1) = 1² = 1

(r q)(-3) = ?

(1×1)(-3) = -3

(q r)(-3) = ?

(1×1)(-3) = -3