what does a transformation mean?

The number of favorable outcomes for events A and B would be: (1,2,3,4)

The sample space that is used to determine the probability of A given B is  (2, 4.6)

The probability for event A and B occurring would be: 1/6

The probability of event A given event B will be 2/3

The sample space refers to the collection of all the outcomes that can be expected from a set of randome experiments. Probability refers to the number of favorable outcomes divided by the number of tottal outcocmes.

From the data given, the probability of getting an even number and a number less than 5 will be 5/6 amd this is in the same ratio as 2/3. The probability of event A and B occurring will be 1/6.

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Considering a discrete distribution, the expected values for each case are given by:

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Without insurance, the distribution is given by:

Hence:

E(X) = 0.32 x 1050 + 0.45 x 225 = $437.25.

With insurance, the distribution is given by:

Adding to the cost of insurance, we have that:

E(X) = 1580 + 75 x 0.32 + 72 x 0.45 = $1,636.40.

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Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

6-18=-12

\(` u`)/

Answer:

X-18

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 6-x-(-12)=0

Solve  :    -x+18 = 0

Subtract  18  from both sides of the equation : -x=-18

Multiply both sides of the equation by (-1) :  x = 18

if i understand the question it's 25

Step-by-step explanation:

6/21 equal 10/10+x

info x is GJ

6x=150

x=25

i used the similarity in trangle formula because he sayed that FG is parelel to HJ

α & β are the zeroes of 2x² - 5x + 7.

polynomial whose zeroes are 2α + 3β , 2β + 3α .

On comparing with the standard form of a quadratic equation,

Let,

a = 2

b = - 5

c = 7.

We know that,

Sum of the zeroes = - b/a

⟹ α + β = - ( - 5)/2

⟹ α + β = 5/2 -- equation (1)

Product of the zeroes = c/a

⟹ αβ = 7/2 -- equation (2)

Now,

General form of a Quadratic equation is x² - (sum of the zeroes)x + product of the zeroes = 0.

★ Sum of the zeroes = 2α + 3β + 2β + 3α

⟹ Sum of the zeroes = 5α + 5β

⟹ Sum of the zeroes = 5(α + β)

Putting the value from equation (1).

⟹ Sum of the zeroes = 5(5/2)

⟹ Sum of the zeroes = 25/2

Similarly,

★ Product of the zeroes = (2α + 3β)*(2β + 3α)

⟹ Product of the zeroes = 2α( 2β + 3α) + 3β( 2β + 3α )

⟹ Product of the zeroes = 4αβ + 6α² + 6β² + 9αβ

⟹ Product of the zeroes = 13αβ + 6(α² + β²)

a² + b² = (a + b)² - 2ab → α² + β² = (α + β)² - 2αβ

⟹ Product of the zeroes = 13αβ + 6[ (α + β)² - 2αβ ]

Putting the values from equations (1) & (2) we get,

⟹ Product of the zeroes = 13(7/2) + 6 [ (5/2)² - 2(7/2) ]

⟹ Product of the zeroes = 91/2 + 6 ( 25/4 - 14/2 )

Taking LCM we get,

⟹ Product of the zeroes = ( 2 * 91 + 6 * 25 + 2 * 14 ) /2

⟹ Product of the zeroes = (182 + 150 + 28 )/2

⟹ Product of the zeroes = 180

Hence,

New quadratic equation = x² - (25/2) * x + 180 = 0

⟹ New quadratic equation = (2x² - 25x + 360)/2 = 0

⟹ New quadratic equation = 2x² - 25x + 360 = 0

∴ The required quadratic equation is 2x² - 25x + 360 = 0.

I hope it will help you.

Regards.

Answer:

if $15.98----> 2kg

$x --------> 7kg

cross multiply

$x= (15.98 x 7)/2

x = $55.93

Answer:

x ≥ 2 4/9 days

Step-by-step explanation:

Rosa runs 3 1/3 miles on Monday. Each day after that, she runs the same 1 1/2 mile route every morning. Her goal is to run at least 7 miles by the end of the week. Which inequality represents the least number of days after Monday that Rosa needs to run to reach her goal?

Let the number of days left after Monday to run = x

At least 7 miles = Greater than or equal to

Hence:

Our inequality equation is given as:

3 1/3 + 1 1/2x ≥ 7

1 1/2x ≥ 7 - 3 1/3

1 1/2x ≥ 3 2/3

x ≥ 3 2/3 ÷ 1 1/2

x ≥ 11/3 ÷ 3/2

x ≥ 11/3 × 2/3

x ≥ 22/9

x ≥ 2 4/9 days

Therefore, the inequality that represents the least number of days after Monday that Rosa needs to run to reach her goal is

x ≥ 2 4/9 days

Answer:

28+12x

Step-by-step explanation:

Multiply 7 with 4

Multiply 3x with 4

Answer:

28+12x

im pretty sure that is right

Answer:

i believe its false good Sir

Answer:

It is False

Step-by-step explanation:

The line of this graph isn’t linear so it isn’t proportional

Answer:

16

Step-by-step explanation:

First, let's find 64% of 25. We do this and get:

\(\frac{64}{100}\cdot25=\frac{1600}{100}=16. \text{ so our answer is \boxed{16 \text{ problems are true}}}\)

Answer:

After 7 weeks, Mia's office will have recycled 21 pounds.

Step-by-step explanation:

With the information provided, you can use a rule of three to find the pounds of paper that Mia's office will have recycled after 7 weeks given that they recycled 9 pounds over 3 weeks.

3 weeks  →  9 pounds

7 weeks  →         x

x=(7*9)/3

x=21

According this, the answer is that after 7 weeks, Mia's office will have recycled 21 pounds.

The probability that at least one of the students solves the problem correctly is 0.9978.

We can approach this problem using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So, the probability that none of the students solve the problem correctly is:

(1 - 0.95) x (1 - 0.85) x (1 - 0.80) = 0.0027

Therefore, the probability that at least one of the students solves the problem correctly is:

1 - 0.0027 = 0.9978

We can also approach this problem using the addition rule for mutually exclusive events. Since the three students are working independently, we can consider their events as mutually exclusive.

So, the probability that at least one of the students solves the problem correctly is:

0.95 + 0.85 + 0.80 - 0.95 x 0.85 - 0.95 x 0.80 - 0.85 x 0.80 + 0.95 x 0.85 x 0.80 = 0.9978

Therefore, the probability that at least one of the students solves the problem correctly is 0.9978, which is a very high probability.

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Answer:

Son is 20

Step-by-step explanation:

*3 - 10 y ago

20 y age diff

Answer:

polynomial is one. Because the zeros of a polynomial can be determined from the factors of a polynomial, the factors can be created from the zeros. For the zero which occurs at 2, 3 x x = -2/3, the factor which produced that zero is 2. 3 x §· ¨¸ ©¹ The multiplicity represents how many times that zero occurs, in other words, the degree of ...

Step-by-step explanation:

The proportion null hypothesis is a specific type of hypothesis that tests for significant differences in proportions between two groups.

In statistics, a hypothesis is a statement that is being tested through data analysis. The null hypothesis is a specific type of hypothesis that assumes there is no significant difference or relationship between two variables being studied. The proportion null hypothesis specifically applies to situations where the variable being studied is a proportion or percentage.

The proportion null hypothesis states that there is no significant difference in the proportions of two groups being compared. This can be represented mathematically as

H0 => p1 = p2, where H0 represents the null hypothesis, p1 represents the proportion in the first group, and p2 represents the proportion in the second group.

To test this hypothesis, researchers will collect data from both groups and calculate the proportion for each group. They will then use statistical tests to determine whether the difference in proportions is significant or could have occurred by chance. If the difference is not significant, then the null hypothesis is accepted, and it can be concluded that there is no real difference in the proportions of the two groups.

It is important to note that the proportion null hypothesis is just one type of hypothesis that can be tested in statistics.

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Answer:

Step-by-step explanation:

To find the perimeter of the shaded region, we must add all the sides up.

The straight side of the shaded region is 80 meters by 80 meters because the radius of the circle is 80 meters.

The curved side is one half of the semicircle circumference, so the length is:

   length of curved side = \(2\pi r * (\frac{1}{4} )\) = (1/4) * 502. 65482 meters = 125.6637m

Thus the perimeter is the sum of all the side lengths:

  125.6637 + 80 + 80 = 286 meters (approximated)

Hope that helps!

We need to calculate the 4%

The raise will be $1614.44

There are three ways to solve systems of linear equations in two variables:

System of Linear Equations :

A system of linear equations is two or more linear equations that are being solved simultaneously.

Solution of a System :

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common.  So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

A consistent system is a system that has at least one solution.

An inconsistent system is a system that has no solution.

There are three ways to solve systems of linear equations in two variables:

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Answer:4.5

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

EF² + 12² = 19²

EF² + 144 = 361 ( subtract 144 from both sides )

EF² = 217 ( take the square root of both sides )

EF = \(\sqrt{217}\) → F

The length of EF in the right triangle below is √217.

Option F is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Using the Pythagorean theorem,

DE² = EF² + DF²

19² = 12² + EF²

EF² = 361 - 144

EF = √217

Thus,

The length of EF in the right triangle below is √217.

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a least squares linear trend line is just a simple regression line with the years recoded  then it is a true statement

The simple linear regression model is;

y = mx + c

Where,

y = dependent variable

m is the slope

x is the independent variable

c is the y- intercept

The long-term trend only Least-Squares Regression Model also follows the same format except y becomes Yt and x becomes t.

The long-term trend only Least-Squares Regression Model is therefore the same as a simple linear regression only with different variable terms.

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The range of the data 67, 114, 81, 100, 55, 93, 105 is 59.

To find the range of the data 67, 114, 81, 100, 55, 93, 105, follow these steps:

1. Identify the highest and lowest values in the data set.
  - Highest value: 114
  - Lowest value: 55

2. Subtract the lowest value from the highest value.
  - Range = Highest value - The lowest value
  - Range = 114 - 55

3. Calculate the result.
  - Range = 59

So, the range of the data 67, 114, 81, 100, 55, 93, 105 is 59.

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Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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Answer:

47

Step-by-step explanation:

According to the given statement The eighth term in the arithmetic sequence 2/3, 1, 4/3 is 3/1.

To find the eighth term in an arithmetic sequence, we can use the formula:

an = a1 + (n - 1)d

Where:

an represents the nth term,

a1 represents the first term,

n represents the term number,

d represents the common difference.

In this case, the given arithmetic sequence is:

2/3, 1, 4/3, ...

We can observe that the common difference (d) between consecutive terms is 1/3. Therefore, we have:

a1 = 2/3 (first term)

d = 1/3 (common difference)

n = 8 (eighth term)

Now we can substitute these values into the formula to find the eighth term (a8):

a8 = (2/3) + (8 - 1)(1/3)

Simplifying the expression:

a8 = (2/3) + 7(1/3)

a8 = (2/3) + 7/3

Combining the fractions:

a8 = (2 + 7)/3

a8 = 9/3

Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:

a8 = 3/1

Therefore, the eighth term in the arithmetic sequence 2/3, 1, 4/3 is 3/1.

In conclusion, the eighth term is 3/1 or simply 3.

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The complete question is-

What is the eighth term in the arithmetic sequence 2/3, 1, 4/3, ? express your answer in simplest form.

Answer:They do this so they can be safe from predators.

Step-by-step explanation: They make this hard layer so it can help protect the vulnerable soft parts of their body from other fish or mammals.

The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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A histogram with a symmetric distribution looks like this:

Leaving aside the quality of the drawing, the left and the right side of the histogram are identical if we split it by the red line. Is like having a reflexion axis.

Now, we have to discuss what of the 2 data sets may have such an histogram. This means that we must think which of them may have the same number of ocurrences for very short and very long durations, for regular to short and regular to long durations, and so on and so furth.

Pop album tracks:

In the same album we may have arround 12 tracks (small number), all of them with a duration of arround 3 minutes. We could imagine a histogram like the following:

All the songs last between 170 and 190 seconds, and one or two last a little bit more.

Phone talks:

In this case, we can think that there are some calls to say something like "mom, I'm on my way home" and other like "let me tell you the hole movie I saw yesterday night", so very short and very long calls, but they are no so common. There are a lot of "regular" calls that might last for 60 seconds.

Also, in this case, we are taking into account all the calls from people in the school in one day (yesterday), so, may be 1.000 calls? The actual number really doesn't matter, but the fact that the number is very big. Because of the big number, we can expect a symmetric distribution.