Call a household prosperous if its income exceeds $100,000. call the household educated if the householder completed college. select an american household at random, and let a be the event that the selected household is prosperous and b the event that it is educated. according to a survey, p(a) = 0.132, p(b) = 0.227, and the probability that a household is both prosperous and educated is p(a and
b.= 0.082. what is the conditional probability that a household is prosperous, given that it is educated? (round your answer to four decimal places.) .3612 explain why your result shows that events a and b are not independent. if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the sum p(a) + p(b). if a and b were independent, then p(a|b) would equal p(a and b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the sum p(a) + p(b). submit answer save progress

Answer:

Option A - 0.5 pounds

Step-by-step explanation:

Given : Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds.

To find : What was the greatest possible error for her actual measurement?  

Solution :

To find the margin of error first we find the median of the given numbers.

Median of 23.5 and 24.5

[tex]M=\frac{23.5+24.5}{2}=\frac{48}{2}=24[/tex]    

So, the Greatest possible error is 24.5-24 = 0.5 pounds

Therefore, option A is correct.                                  

Answer:

  7.25%

Step-by-step explanation:

You want the effective rate of interest on a $12,000 Treasury bill with a nominal interest rate of 7% and maturity in 15 weeks.

The Treasury computes the selling price of the bill by subtracting the interest from the face value. The interest is computed as "ordinary interest" using a 360-day year. 15 weeks is 105 days.

  I = Prt

  I = $12000·0.07·(105/360) = $245

Then the cost of the bill is $12,000 -245 = $11,755.

Using the formula for the maturity value with a 365-day year, we have ...

  A = P(1 +rt)

  12000 = 11755(1 +r(105/365))

Solving for r gives ...

  [tex]r=\left(\dfrac{12000}{11755}-1\right)\cdot\left(\dfrac{365}{105}\right)\approx0.0724514\approx\boxed{7.25\%}[/tex]

The effective rate of interest is about 7.25%.

76 is the correct answer

The price of the jersey before the mark-up = $76

"A number that can be expressed as a fraction of 100."

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

For given question,

A basketball jersey has been marked up by 25% and is now selling for $95.00

Let 'm' be the price of the jersey before the mark-up.

So, we get an equation,

⇒ m + (25 percent of m) = 95

25 percent of m

= [tex]\frac{25}{100}\times m[/tex]

= 0.25 m

so, the equation becomes,

⇒ m + 0.25 m = 95

⇒ 1.25 m = 95

⇒ m = 76

Therefore, the price of the jersey before the mark-up = $76

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What is the standard deviation for the data set?

212, 249, 212, 248, 239, 212, 216, 234, 248Answer:16.9

Step-by-step explanation:

Answer:

13.2 cm

Step-by-step explanation:

b = [tex]\sqrt{c^{2} - a\\^{2} }[/tex]

b = [tex]\sqrt{20^{2} - 15\\^{2} }[/tex]

b = [tex]\sqrt{400-225\\} \\[/tex]

b = [tex]\sqrt{175}[/tex]

b = 13.228

b= 13.2 cm

:) good luck on the rest!

Answer:

The correct option is a.

Step-by-step explanation:

Given information: radius r =2.7 meters, arc length s = 4.32 meters.

The formula of arc length is

[tex]s=r\theta[/tex]

where, r is radius and θ is central angle in radians.

Using the above formula we get

[tex]4.32=2.7\times \theta[/tex]

Divide both sides by 2.7.

[tex]\frac{4.32}{2.7}=\theta[/tex]

[tex]1.6=\theta[/tex]

The value of the central angle is 1.6 radians. Therefore option a is correct.

Grass can grow up to six inches in a week depending on temperature, humidity, and time of year

We have to calculate how tall will grass grow in 24 days

we know there are seven days in a week

so in one day grass can grow up to 6/7 inches

therefore we could say that grass can grow up to 24*6/7 inches

so the answer is 20.57 inches

so in 24 days grass can grow up to 20.57 inches

Grass can grow approximately 20.58 inches in 24 days.

To calculate the height that grass will grow in 24 days, we need to find out how much it grows in 1 week, and then multiply that by the number of weeks in 24 days. If grass can grow up to six inches in a week, we can calculate the height it will grow in 24 days as follows:

Therefore, grass will grow approximately 20.58 inches in 24 days.

The roots of the Given quadratic equation are x₁ = -2 and x₂ = -12.

ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given a quadratic equation, x² + 24 = 14 x

Simplifying the equation using the factorization method,

=> x² + 24 = 14 x

=> x² +14 x +24 = 0

factorize the "x term"

=> x² +12x + 2x +24 = 0

=> x(x +12)+2(x + 12) = 0

=>(x + 2)(x + 12) = 0

x = -2, -12

thus,

the value of x will be either -12 or -2

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Final answer:

The secant of an angle is the reciprocal of its cosine. Given cos θ = 2/3 for an acute angle in a right triangle, the sec θ equals 3/2.

Explanation:

In the context of trigonometry, the secant (sec) of an angle is the reciprocal of the cosine (cos) of that angle.

Given that cos θ = 2/3 for an acute angle in a right triangle, we can find the value of sec θ by taking the reciprocal of the cosine value. Hence, the value of sec θ is simply the reciprocal of 2/3, which is 3/2.

24 is the  largest number of identical sets can be made of these crayons and pictures

A number system is defined as a system of writing to express numbers.

To find out the largest number of identical sets that can be made, we need to determine the common factors of the total number of crayons and pictures.

The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and since all three colors have the same number of crayons, we can say that there are 48 x 3 = 144 crayons in total.

The prime factorization of 72 is 2 x 2 x 2 x 3 x 3, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.

The common factors of 144, 72, and 120 are 2 x 2 x 2 x 3 = 24. This means that we can make 24 identical sets.

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Solution: The missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].

Explanation:

The given steps are used to prove the formula for law of cosines.

From step 5 it is noticed that our equation is

[tex]a^2=b^2-2bx+c^2[/tex]      ..... (1)

From step 7 it is noticed that the value of [tex]x[/tex] is [tex]c\cos (A)[/tex].

So by substituting [tex]c\cos (A)[/tex] for [tex]x[/tex] in equation (1) we get the equation of step 8, i.e.,

[tex]a^2=b^2-2bc\cos (A)+c^2[/tex]

Hence, the missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].

The missing reason in Step 8 of the proof for the Law of Cosines is substitution, where x is replaced with cc cos(A) in the expression.

The missing reason in Step 8 of the proof that shows how the Law of Cosines is derived, a2 = b2 + c2 – 2bc cos(A), is the substitution property. In Step 7, we established that c cos(A) is equal to x. Thus, for Step 8, when we replace x with cc cos(A) in the expression b2 – 2bx + c2, we effectively utilize substitution to arrive at the expression a2 = b2 – 2bccos(A) + c2.

To find the area enclosed between two functions, we calculate the definite integral of the absolute difference between the functions over the given interval. The area is equal to the integral of ∣f(x) - g(x)∣, split into two parts where g(x) ≥ f(x) and g(x) < f(x), then added together. The enclosed area for the given functions is 82.26 square units.

To find the area enclosed between the functions f(x) = 0.3x^2+7 and g(x) = x from x = -4 to x = 8, we need to calculate the definite integral of the absolute difference between the two functions over the given interval.

The area is equal to the integral of ∣f(x) - g(x)∣ from x = -4 to x = 8. We can split the integral into two parts where g(x) ≥ f(x) and g(x) < f(x), then evaluate each separately. Finally, we add the two areas together.

After evaluating the integrals, we find that the area enclosed between the two functions is 82.26 square units.

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The first three iterates of the function f(z) = 2z + (3 - 2i) with z0 = 5i are 3 + 8i, 9 + 14i, and 21 + 26i after consecutive substitutions. The first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with the initial value z0 = 5i, we perform successive substitutions into the function.

Thus, the first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.

Final answer:

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, substitute the initial value into the function to get the first iterate. Then, substitute the first result back into the function to find the second iterate. Finally, substitute the second result back into the function to find the third iterate.

Explanation:

To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, we substitute the initial value into the function:

f(z0) = 2(5i) + (3 - 2i) = 10i + 3 - 2i = 3 + 8i.

Then, we substitute the result back into the function to find the second iterate:

f(3 + 8i) = 2(3 + 8i) + (3 - 2i) = 6 + 16i + 3 - 2i = 9 + 14i.

Finally, we substitute the second result back into the function to find the third iterate:

f(9 + 14i) = 2(9 + 14i) + (3 - 2i) = 18 + 28i + 3 - 2i = 21 + 26i.