Alice gave Bob as many dollars as Bob had. Bob then gave Alice as many dollars Alice then had. At this point, each had 24 dollars. How much did Alice have at the beginning?

Please answer it step-by-step, and explained it very detailed. Thx.

The probability that the entire batch will be accepted will be 9339

4000-90 = 3910 (non-defective) (non-defective)

If P(first not defective) = 3910/4000 and it is not changed (1 less to choose from and 1 less not defective)

P(second is not flawed if first is flawed) = 3909/3999 If the item is also not replaced (a total of 2 less to choose from and 2 less not defective)

P

(1st and 2nd are not defective, so the third is also not defective)) = 3908/3998

Simply multiply these three fractions to get the answer: 3910(3909>)(3908)) / (4000(3999)(3998)).

=9339

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Answer:

The solution set is (1, 4)
There are a finite number of solutions.

Step-by-step explanation:

We have 2x+y=6 and y=4x.

Let's write the first equation into y=mx+b form.

We get: y=-2x+6

Now, we just set the equations equal to each other.

-2x+6=4x Add 2x to both sides.

6=6x Divide both sides by 6

x=1

Now, plug x back into either of the equations given to us.

y=4(1)

y=4

The solution set is (1, 4)

Answer: 1.55

Step-by-step explanation:70 percent sure, might be .155

Answer:

D) y= -2X+1

Step-by-step explanation:

All of the lines are perpendicular to the line 2x+y=6 except for D) y= -2X+1.

The regression equation for predicting y from x in the given set of data is y = 1.909x + 2.227. This equation represents the line of best fit that minimizes the sum of squared residuals between the predicted values and the actual values of y based on the corresponding values of x.

To find the regression equation, we use the method of least squares to fit a line to the data points. The equation takes the form of y = mx + b, where m is the slope (coefficient of x) and b is the y-intercept. Using the given set of data, we calculate the slope (m) and the y-intercept (b) to determine the regression equation.

By applying the formulas for m and b:

m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)

b = (Σy - mΣx) / n

where n is the number of data points, Σxy is the sum of the products of x and y, Σx and Σy are the sums of x and y respectively, and Σx² is the sum of the squares of x.

By substituting the values from the given data set into these formulas, we obtain the values for m and b. The resulting regression equation for predicting y from x in this case is y = 1.909x + 2.227. This equation represents the line that best fits the data points and can be used to estimate or predict the value of y for any given x within the range of the data.

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Answer:A:

If two lines intersect at right angles, then the two lines are perpendicular.

Hypothesis: Two lines are perpendicular.

Conclusion: Two lines intersect at right angles.

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

AB to B is 16 units, so it's reasonable to assume that A to AB is 16 units as well.

The length of the other leg to the nearest tenth of a foot is 5.7 feet.

What is Pythagorean theorem?

We can use the Pythagorean Theorem to find the length of the other leg

\(a^{2} + b^{2} = c^{2}\)

"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.

So,

      \(b^{2} = c^{2} - a^{2}\)

        =  7² - 4²

  b = \(\sqrt{49 - 16}\)

  \(b = \sqrt{33}\) ⇒ 5.7 feet

Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.

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There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.

To choose a president, a vice-president, and a secretary from a committee of 20 members,

We will use the formula for combinations,

which is: C(n, k) = n! / (k! (n - k)!)

where n is the total number of members and k is the number of members being chosen.

So, for n = 20 and k = 1, we have:

C(20, 1) = 20! / (1! (20 - 1)!) = 20

This gives us 20 choices for the president.

For the vice president,

We need to choose 1 member from the remaining 19 members.

So, for n = 19 and k = 1,

we have:

C(19, 1) = 19! / (1! (19 - 1)!) = 19

This gives us 19 choices for the vice president.

Finally, for the secretary,

We need to choose 1 member from the remaining 18 members.

So, for n = 18 and k = 1,

we have:

C(18, 1) = 18! / (1! (18 - 1)!) = 18

This gives us 18 choices for the secretary.

Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:

So, the required number of ways will be 20 * 19 * 18 = 6840

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A z-score of 23.9 years must be located in the gorillas' lifespans in a specific zoo's typical normal distribution.

The equation can be used to determine the z score.

z = (x - μ)/σ

In which,

Then,

z = (23.9 - 20.8)/3.1

z = 1

According to the empirical rule, 68% of lifespans are within one standard deviation of the mean.

Half of it, 68/2 = 34% %, is on the right side of the mean's standard deviation.

Given that the likelihood of a gorilla lasting less than 23.9 years is 50%.

A gorilla's lifespan being less than the norm means is;

50% + 34% = 84% sits below z-score 1.

Thus, the probability of a gorilla living less than 23.9 years is 84%.

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The correct question is-

The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the

standard deviation is 3.1 years.

Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a gorilla living less than 23.9 years.

A and B are mutually exclusive, with P(A) is 0.7 and P(B) is 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

To find the probability of B given A, we can use the formula:

P(B|A) = P(A and B) / P(A)

Given:

P(A) = 0.5

P(B) = 0.1

P(A and B) = 0.3

P(B|A) = 0.3 / 0.5

= 0.6

Therefore, the probability that B will occur if A occurs is 0.6.

Given:

P(A) = 0.3

P(B) = 0.4

Since A happening guarantees that B must also happen, the events A and B are not independent. In this case, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.3 + 0.4 - 0.3

= 0.4

Therefore, the probability of A or B occurring is 0.4.

Given:

P(A) = 0.7

P(B) = 0.2

Since A and B are mutually exclusive events, they cannot occur together. In this case, we have:

P(A and B) = 0

Therefore, P(B|A) = P(BIA)

= 0.

P(BIA) = P(B)

= 0.2.

So, P(BIA) < P(B) is true.

When events A and B are mutually exclusive, with P(A) = 0.7 and P(B)

= 0.2, the probability of event B given event A (P(B|A)) and the probability of event B given event A (P(BIA)) are both 0.2.

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Answer: The equation that represents the graph is y=4x.

Step-by-step explanation: If you plug in just one coordinate in each equation, you will find that these are the following outcomes no matter which coordinate you pick(but I'm picking (2,8) for your view):

y=x   ,    8=2

y=x   ,    8=2

y=2x    ,     8=4

y=4x   ,   8=8(ONLY CORRECT STATEMENT)

Answer:

y= 4x

Step-by-step explanation:

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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the formulam of the volume is

where r is the radius and h the height

r=3/5 because is the half of diameter

h=10

so replacing

the volume of the cone is 3.78 square millimeters

the red multiplication is the numerator and green the denomintor

simplify by 15

and then add the pi

The measure of angle x is 80 degrees, which is statement (4) x = 118 because 180 − 147 + 85 = 33 + 85 = 118.

Based on the given information, statement (4) x = 118 because 180 − 147 + 85 = 33 + 85 = 118 is true.

In a triangle, the measures of the three angles add up to 180 degrees. In this triangle, one of the angles measures 85 degrees, and another angle measures 147 degrees. Therefore, the measure of the third angle must be 180 - 85 - 147 = 48 degrees.

Since the measure of the third angle is 48 degrees, and the measure of one of the other angles is 33 degrees, the measure of the remaining angle must be 48 - 33 = 15 degrees.

Finally, since the measure of one angle is 85 degrees and another angle is 15 degrees, the measure of the third angle must be 180 - 85 - 15 = 80 degrees.

Therefore, the measure of angle x is 80 degrees, which is statement (4) x = 118 because 180 − 147 + 85 = 33 + 85 = 118.

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The root mean square speed of a carbon dioxide molecule at mentioned average kinetic energy is 1.57× \( {10}^{-11} \).

The formula to find root mean square speed of carbon dioxide molecule using average kinetic energy is as follows -

c = ✓2KE/m, where c is root mean square speed, KE is kinetic energy and m is molecular mass

Keep the values in formula to find the root mean square speed.

c = ✓2×5.44×\( {10}^{-21} \)/44

Performing multiplication and division on Right Hand Side of the equation

c = ✓2.47×\( {10}^{-22} \)

Taking square root on Right Hand Side of the equation

c = 1.57× \( {10}^{-11} \)

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Answer:

20 22 28 32 33 65 159

median =32

mean= 51.285714285

Answer:

-5x - 24

Step-by-step explanation:

3(2x − 8) – 11x =

Distribute the 3.

= 6x - 24 - 11x

Combine like terms.

= -5x - 24

1. n = 37

isolate n by dividing both sides by 5

2. y = 83

isolate y by dividing both sides by 3

3. w = -118

isolate w by dividing both sides by -6

a. There are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The value of parameter α for  P(|X| < 1) = P(|X| > 2) is 4

a. We know that for a uniform distribution over (−α,α), the probability density function is given by f(x) = 1/(2α) for −α ≤ x ≤ α and zero otherwise. Thus, the probability of the event (-1 < X < 2) can be computed as:

P(-1 < X < 2) = ∫(-1)²/(2α) dx + ∫2²/(2α) dx

= (1/2α) ∫(-1)² dx + (1/2α) ∫2² dx

= (1/2α) [x]₋₁¹ + (1/2α) [x]²₂

= (1/2α) (2α - 1) + (1/2α) (4 - α²)

= (3 + α²)/(4α)

We want this probability to be 0.75. So, we solve the equation (3 + α²)/(4α) = 0.75 for α:

(3 + α²)/(4α) = 0.75

=> 3 + α² = 3α

=> α² - 3α + 3 = 0

This is a quadratic equation in α with discriminant:

Δ = b² - 4ac

= (-3)² - 4(1)(3)

= 9 - 12

= -3

Since Δ is negative, there are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The pdf of a uniform distribution is given by:

f(x) = 1/(b-a), for a ≤ x ≤ b

In this case, a = -α and b = α. Therefore,

f(x) = 1/(2α), for -α ≤ x ≤ α

Now we can calculate the probabilities as follows:

P(|X| < 1) = P(-1 < X < 1) = ∫(-1 to 1) f(x) dx = ∫(-1 to 1) 1/(2α) dx = 1/(2α) * [x]_(-1 to 1) = 1/α

P(|X| > 2) = P(X < -2 or X > 2) = P(X > 2) + P(X < -2) = ∫(2 to α) f(x) dx + ∫(-α to -2) f(x) dx = ∫(2 to α) 1/(2α) dx + ∫(-α to -2) 1/(2α) dx = 1/4

Therefore, we need to find α such that P(|X| < 1) = P(|X| > 2) = 1/4.

From P(|X| < 1) = 1/α, we get α = 1/P(|X| < 1) = 1/(1/4) = 4.

From P(|X| > 2) = 1/4, we get the same value of α = 4.

Hence, α = 4 satisfies both conditions.

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The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

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The total exposed surface area of the birdbath, including the pillar and pedestal, is therefore 942 cm² + 300 cm² + 600 cm² = 1842 cm².

Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.


The exposed surface area of the birdbath including the pillar and pedestal can be determined by calculating the surface area of the cylinder and adding the surface area of the pillar and pedestal.

The formula for the surface area of a cylinder is 2πr² + 2πrh, where r is the radius of the cylinder and h is the height. In this case, the radius of the birdbath is 15 cm (half of the diameter of 30 cm) and the height is 10 cm. Therefore, the surface area of the cylinder is 2π(15 cm)² + 2π(15 cm)(10 cm) = 942 cm².

The surface area of the pillar and pedestal can be calculated by multiplying the height and circumference of each. The height of the pillar is 10 cm and the circumference is 30 cm, so the surface area of the pillar is 300 cm². The height of the pedestal is 20 cm and the circumference is 30 cm, so the surface area of the pedestal is 600 cm².

The total exposed surface area of the birdbath, including the pillar and pedestal, is therefore 942 cm² + 300 cm² + 600 cm² = 1842 cm².

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Answer:

180 - 35 - 45= 100

Step-by-step explanation:

Answer:

x= -2.5

Step-by-step explanation:

Combine like terms, add 12 to both sides, then divide by the coefficient.

-2x-10x+12= 18

-12x+12=18

-12x=30

x=-2.5

Answer:

The answer would be -7/12

Step-by-step explanation:

Use math.way itll help you tremendously :)

Answer:

There are many times in algebra when you need to simplify an expression. The properties of real numbers provide tools to help you take a complicated expression and simplify it.

The associative, commutative, and distributive properties of algebra are the properties most often used to simplify algebraic expressions. You will want to have a good understanding of these properties to make the problems in algebra easier to work.

Step-by-step explanation:

Commutative Property of Multiplication

For any real numbers a and b, a · b = b · aOrder does not matter as long as the two quantities are being multiplied together. This property works for real numbers and for variables that represent real numbers.

just as subtraction is not commutative, neither is division commutative. 4 ÷ 2 does not have the same quotient as 2 ÷ 4.Associative Property of Addition

For any real numbers a, b, and c, (a + b) + c = a + (b + c).

Associative Property of Multiplication

For any real numbers a, b, and c, (a • b) • c = a • (b • c).Multiplication has an associative property that works exactly the same as the one for addition. The associative property of multiplication states that numbers in a multiplication expression can be regrouped using parentheses. For example, the expression below can be rewritten in two different ways using the associative property.

The parentheses do not affect the product, the product is the same regardless of where the parentheses are.

The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of products, in this case, 6(5) – 6(2).

   6(5 – 2) = 6(3) = 18

 65) – 6(2) = 30 – 12 = 18

The distributive property of multiplication can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.3(10 + 2) = ?

According to this property, you can add the numbers 10 and 2 first and then multiply by 3, as shown here: 3(10 + 2) = 3(12) = 36. Alternatively, you can first multiply each addend by the 3 (this is called distributing the 3), and then you can add the products. This process is shown here.

3 (10 + 2) = 3(12) = 36

3(10) + 3(2) = 30 + 6 = 36

The products are the same.

since multiplication is commutative, you can use the distributive property regardless of the order of the factors.