FILL IN THE BLANK. If n(E1 and E2​)=3
and
​n(E1​)=12​,
then
​P(E2​|E1​)=​_______.

Using trigonometric relations we can see that:

y = 20

x = 40

Here we can see a right triangle and we want to find the missing side lengths, to do so we need to use trigonometric relations.

Remember that:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing what we know we will get:

tan(60°) = 20√3/y

Solving for x:

y = 20√3/(tan(60°)

y = 20

And for the hypotenuse we can use:

sin(a) = (opposite cathetus)/hypotenuse

sin(60°) = 20√3/x

Solving for y:

x =  20√3/sin(60°)

x  = 2*20 = 40

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Stephanie has 5/8 pounds of birdseed left.

If Stephanie had 7/8 pounds of birdseed and used 3 pounds to fill the birdfeeder, she used 7/8 - 3 = -1 1/8 pounds of birdseed, which is not possible. Therefore, we assume that Stephanie had 7/8 pounds of birdseed and used 7/8 - 3/8 = 4/8 pounds of birdseed to fill the birdfeeder.

Subtracting the amount used from the initial amount, we get: 7/8 - 4/8 = 3/8 pounds of birdseed left.

Therefore, Stephanie has 5/8 pounds of birdseed left (since 7/8 - 4/8 = 3/8, and 1 - 3/8 = 5/8).

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The units of the slope of the linear function are dollars per iPhone per hour, or simply dollars/hour.

The slope of the linear function, to calculate the rate of change of cost with respect to the number of iPhones produced per hour.

Let's call the number of iPhones produced per hour x and the cost y.

To create two points on the line that represents the cost of producing iPhones:

Point 1:

(10, 1900)

Point 2:

(20, 3780)

The slope of the line passing through these two points is:

slope = (y2 - y1) / (x2 - x1)

slope = (3780 - 1900) / (20 - 10)

slope = 1880 / 10

slope = 188

The units of the slope are the change in cost per unit change in the number of iPhones produced per hour.

The cost is given in dollars and the number of iPhones is given in hours, the units of the slope would be dollars per iPhone per hour.

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The requried Regina would need to buy 92 marshmallows: 80 for the expected 10 people and 12 extras in case someone shows up unexpectedly.

The equation that relates the number of marshmallows to the number of people is:

m = 8n + 12

where m is the number of marshmallows Regina must buy and n is the number of people who attend.

The 8n in the equation represents the number of marshmallows Regina needs to buy for the expected number of people, which is 8 marshmallows per person. The 12 in the equation represents the additional marshmallows Regina needs to buy just in case someone shows up unexpectedly.

if Regina expects 10 people to attend the marshmallow roast, she would need to buy:

m = 8n + 12

m = 8(10) + 12

m = 80 + 12

m = 92

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The number of pivot columns in a matrix is equal to the rank of the matrix.

Therefore, A has n pivot columns.

Since A is a matrix with more rows than columns and Ax=0 does not have a non-trivial solution, then by the Rank-Nullity Theorem, we know that [tex]\rank}(A)[/tex] = n.

Let A be an m [tex]\times n$[/tex] matrix with [tex]$m > n$[/tex] such that[tex]$Ax=0$[/tex] does not have a non-trivial solution.

We want to determine the number of pivot columns of A.

Suppose that A has k pivot columns, where [tex]$0 \leq k \leq n$.[/tex]

Then, the remaining n-k columns of A are free variables, and we can express them as linear combinations of the pivot columns.

Since [tex]$m > n$[/tex], there are more rows than columns in [tex]A$.[/tex]

This means that the rows of A are linearly dependent, and we can find a non-trivial solution to Ax=0.

However, we are given that Ax=0 does not have a non-trivial solution, which means that the columns of A must be linearly independent.

If k<n, then we can express the free variables as linear combinations of the pivot columns, which means that the columns of A are linearly dependent.

This is a contradiction, so we must have k=n.

Therefore, A has n pivot columns.

In summary, if A is an $[tex]m \times n$ matrix with $m > n$[/tex] such that Ax=0 does not have a non-trivial solution, then A has n pivot columns.

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The elements of D U E are: 12, 14, 15, 16, 17.

To find the union (U) of two sets, we combine all the elements from both sets without any duplicates. So, to find D U E, we need to list all the elements that are in either set D or set E, or both:

D = {12, 15, 17}

E = {12, 14, 15, 16}

The union of D and E is:

D U E = {12, 14, 15, 16, 17}

Therefore, the elements of D U E are: 12, 14, 15, 16, 17.

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The probability that a patient will have at least one of the two treatments is 0.26. We need to find the probability that a patient will have at least one of the two treatments, surgery (Event A) or obstetric treatment (Event B).

Given probabilities:
P(A) = 0.12 (probability of having surgery)
P(B) = 0.16 (probability of having an obstetric treatment)
P(A ∩ B) = 0.02 (probability of having both treatments)

To find the probability of a patient having at least one of the two treatments, we use the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Plugging in the given probabilities:

P(A ∪ B) = 0.12 + 0.16 - 0.02

Now, perform the calculations:

P(A ∪ B) = 0.26

So, the probability that a patient will have at least one of the two treatments is 0.26.

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[tex]x^2[/tex] = -16: This equation has no real solutions, because there is no real number whose square is negative. We can see this by recognizing that x^2 is always non-negative for any real number x, so it is impossible for x^2 to equal -16.

x(x+2) = 0: This equation has two solutions, namely x=0 and x=-2. We can see this by using the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, we have x(x+2) = 0, so either x=0 or x+2=0, which gives x=-2.

(x-3)(x-3) = 0: This equation has one solution, namely x=3. We can see this by using the zero product property again, which tells us that if the product of two factors is zero, then at least one of the factors must be zero. In this case, we have (x-3)(x-3) = 0, so either x-3=0, which gives x=3.

Thus, since we have the factor (x-3) twice, we only count it once as a solution.

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The smallest universal set U that contains all the listed trees in both Riverside Park and Sleepy Hollow Park is the union of sets R and S. It includes all the trees present in both parks.

To find the smallest universal set, we need to create a set that includes all the unique trees from both parks without any duplicates.

To create the smallest universal set, we need to combine the sets of trees from Riverside Park and Sleepy Hollow Park into one set, removing any duplicate entries.

This will give us a set that includes all the unique trees from both parks, which is the minimum universal set we are looking for. This can be done using the union operation on sets.

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Let's denote the mass of plums produced by each plum tree in 2019 as x kg.

According to the given information, in 2020 each plum tree produced 37.7 kg of plums, which was 16% more than in 2019.

Mathematically, we can express this relationship as:

x + 0.16x = 37.7

Simplifying, we get:

1.16x = 37.7

To solve for x, we can divide both sides of the equation by 1.16:

x = 37.7 / 1.16

Using a calculator, we find:

x ≈ 32.6724

So, the mass of plums produced by each plum tree in 2019 was approximately 32.6724 kg.

A news story with the help of following clues is given below.

Here, we have,

In a shocking incident, the son of the Far West Chief Minister was kidnapped on his way to college. The kidnappers have demanded a ransom of 10,00000/- for his release. The identity of the kidnappers is still unknown, and the police are currently conducting a thorough investigation.

According to sources, there was no specific enmity seen against the Chief Minister's son, and it is unclear why he was targeted. However, the police have stated that they suspect the involvement of a cross-border gang in the kidnapping.

The Chief Minister has appealed for his son's safe return and has assured the kidnappers that the ransom would be paid. Meanwhile, the police have launched a massive search operation to locate and rescue the victim.

The entire state is in shock over the incident, and citizens have expressed their outrage and concern over the safety of their children. The government has assured the public that all measures are being taken to ensure the safe return of the Chief Minister's son.

The investigation is still ongoing, and the police have requested the public to come forward with any information that may help in the case. The entire state is praying for the safe return of the Chief Minister's son, and everyone is hopeful that he will be reunited with his family soon.

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complete question:

Make a news story with the help of following clues. [7] Far West Chief Minister's son kidnapped---Son on the way to college- kidnappers unknown-asking for ransom of 10,00000/- ------no specific enmity seen----investigation continue---suspicion of police is on a gang of cross border.​

Answer:

P= 36

Step-by-step explanation:

P= ns = 2rn sin(180/n)...... formula to find perimeter

p= 2(6)(6)sin(30)

P= 12 ×3

P= 36 ...... is the perimeter of the hexagone.

The point which is marked on the first number line is 0.5 or 1/2.

Given two number lines that Nia drawn.

On the first number line, a point is marked exact in the middle.

Since the end points are 0 and 1, the exact middle point of the line will be the exact middle number between o and 1.

Middle point = (0 + 1) / 2

                     = 1/2

                     = 0.5

Hence the marked point on the first number line is 1/2.

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The complete question is given below.

We can conclude that the triangle with sides 5, 13, and 15 is not a right triangle.

To determine whether the given triangle with sides 5, 13, and 15 is a right triangle or not, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the longest side (hypotenuse).

That is, if a, b, and c are the lengths of the sides of a triangle, with c being the longest side, then:

a² + b² = c²

In this case, we have:

5² + 13² = 25 + 169 = 194

15² = 225

Since 194 is not equal to 225, we can conclude that the triangle with sides 5, 13, and 15 is not a right triangle. Therefore, the angle opposite the longest side (15) is not a right angle (90 degrees).

We can also use the fact that in a right triangle, the longest side (hypotenuse) is always the side opposite the right angle. Therefore, if we can determine that no angle in the triangle is a right angle, we can conclude that it is not a right triangle. In this case, we can use the Law of Cosines to determine the measures of the angles in the triangle:

cos(A) = (b² + c² - a²) / (2bc)

cos(B) = (a² + c² - b²) / (2ac)

cos(C) = (a² + b² - c²) / (2ab)

Using the side lengths 5, 13, and 15, we get:

cos(A) = (13² + 12² - 5²) / (21315) = 0.767

cos(B) = (5² + 15² - 13²) / (2515) = 0.866

cos(C) = (5² + 13² - 15²) / (2513) = 0.258

None of these values is equal to zero, so none of the angles is a right angle. Therefore, we can conclude that the triangle with sides 5, 13, and 15 is not a right triangle.

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The ordered pair are (1, -4), (0, -7), (2, -1).

To find the solution of the equation 3x -y= 7 we have to put the value for x.

let us take x= 1

3(1) -y =7

-y = 7 -3

-y = 4

y= -4

and, x= 0

y= -7

and, x= 2

-y = 1

y= -1

Thus, the ordered pair are (1, -4), (0, -7), (2, -1).

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The answer is A.To find the average value of a function f(x) on a closed interval [a,b], we use the formula:

1/(b-a) ∫[a,b] f(x) dx

In this case, we need to find the average value of the function f(x) = (x² + x) cos(5x) on the closed interval [2,6]. So, we plug in the values of a and b:

1/(6-2) ∫[2,6] (x² + x) cos(5x) dx

Simplifying this expression, we get:

1/4 ∫[2,6] (x² + x) cos(5x) dx

Now, we need to evaluate the integral. We can use integration by parts to do this:

u = (x² + x)   dv = cos(5x) dx
du/dx = 2x + 1   v = (1/5) sin(5x)

∫(x² + x) cos(5x) dx = (x² + x)(1/5) sin(5x) - ∫(2x + 1)(1/5) sin(5x) dx

= (x² + x)(1/5) sin(5x) - (2/25) cos(5x) - (1/25) x sin(5x) + C

Plugging in the limits of integration, we get:

1/4 [(6² + 6)(1/5) sin(30) - (2/25) cos(30) - (1/25) (6) sin(30) - (2² + 2)(1/5) sin(10) + (2/25) cos(10) + (1/25) (2) sin(10)]

Simplifying this expression, we get:

-7.392

So, the average value of f(x) on the closed interval [2,6] is -7.392. Therefore, the answer is A.

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Answer: B

Step-by-step explanation:

y's will eliminate because coefficients have opposite signs and if you added the equations as is the y's would eliminate you would get

2x=8

Answer: 0.95

Step-by-step explanation:

Rule:

Cos ∅ = adjacent/hypotenuse

adjacent/opposite/hypotenuse are always relative to the angle being used

Hypotenuse is always longest and across from the right angle

adjacent is next to the angle that is not the hypotenuse

opposite is across

Here.

cos X = adjacent/hypotenuse

They didn't give you the adjacent angle to <X  so you need to solve for it using pythagorean

9²=(√8)²+x²

x²=81-8

x²=73

x=√73

now we know what adjacent side is

cos x = [tex]\frac{\sqrt{73} }{9}[/tex]

cos x = 0.95

The smallest positive integer x for which the expression [tex]$\log\left(\sin^2{x}-\frac{1}{2}\right)$[/tex] is not defined is x = π/4

We have,

The expression [tex]$\log\left(\sin^2{x}-\frac{1}{2}\right)$[/tex] is defined only when the argument is positive.

Therefore, we must solve the inequality  sin²x - 1/2 > 0

Using the identity sin²x + cos²x =1,

We have,

cos²x = 1/2 and sin²x = 1/2

Therefore,

sin²x - 1/2 = 1/2 - 1/2 = 0

when sin²x = 1/2

So the smallest positive integer x for which the expression [tex]$\log\left(\sin^2{x}-\frac{1}{2}\right)$[/tex]is not defined is the smallest positive integer x for which sin²x = 1/2.

Since sin π/4 = √2/2 and (√2/2)² = 1/2,

We have x = π/4

Therefore,

The smallest positive integer x for which the expression [tex]$\log\left(\sin^2{x}-\frac{1}{2}\right)$[/tex] is not defined is x = π/4

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The significance level, account for multiple testing, and recognize the limitations and context when interpreting p-values.

The p-value is a crucial concept in statistical hypothesis testing. It refers to the probability of observing a test statistic as extreme as or more extreme than the one observed, given that the null hypothesis is true.

In other words, it is the probability of obtaining the observed result by chance, assuming that there is no true effect.
There are several key guidelines that researchers need to keep in mind when interpreting p-values.

This threshold should not be taken as a hard-and-fast rule and other factors such as the study design sample size and effect size should also be considered.
Secondly, the p-value alone cannot determine the validity or importance of a research finding.

It is just one piece of evidence that needs to be considered along with other factors, such as the magnitude of the effect, the precision of the estimates, the plausibility of alternative explanations, and the practical implications of the findings.
Thirdly, the p-value can be influenced by various factors, such as the choice of statistical test, the assumptions made about the data, and the presence of outliers or influential observations.

Therefore,

Researchers should always report the assumptions and limitations of their analyses and consider conducting sensitivity analyses to test the robustness of their results.
In summary,

The key guidelines for interpreting p-values include understanding their meaning and limitations, considering other factors in addition to p-values, and being aware of the factors that can influence their interpretation.

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There were 1.4 pounds of honey in each jar.

Since unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Jasmine extracted 5.6 pounds of honey from a beehive. She divided the honey evenly into 4 jars.

Thus, divided 5.6/4

In each jar there would be; 1.4 pounds.

Now multiplying 1.4 by 4

1.4/4 =  5.6.

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The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).

The difference of two expressions is determined by subtracting one from the other.

Find the difference of each of the expressions given to determine which will give us 5.

-3 - (-8)

= -3 + 8

= 5

-2 - 3 = -5 [this is not the same as 5]

1 - (-4)

= 1 + 4

= 5

7 - (-2)

= 7 + 2

= 9

-3 - (-8) and 1 - (-4) will give us a difference of 5.

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The correct answer when writing 4,050,000 in scientific notation is 4.05 x 10^6.

When a number is too big or too tiny to be comfortably represented in decimal form, scientific notation is used to avoid having to write out an exceptionally long string of digits.

When writing 4,050,000 in scientific notation, certain commonly occurring errors can lead to incorrect results. These include forgetting to shift the decimal point leftwards until only one non-zero digit exists to its left; an elongated six-place movement is necessary here. '

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0.60792 liters x 1000 = 607.92 mL

Multiplying the volume in liters by 1000 converts it to milliliters.

The probability of getting at least one question wrong is approximately 0.999 or 99.9%

The probability of getting all the 10 questions correct would be:

[tex](1/2)^{10} = 0.0009765625[/tex]

Therefore, the probability of getting at least one question wrong would be:

1 - 0.0009765625 = 0.9990234375

So, the probability of getting at least one question wrong is approximately 0.999 or 99.9%

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The answer is that Joan would burn approximately 10.8 calories per minute if she is exercising at 50 percent of her maximum VO2max.


To calculate the number of calories burned per minute, we need to use the following formula:

Calories burned per minute = VO2 x body weight in kg x 5 / 1000

Since Joan's VO2max is given as 3.6 liters per minute, we need to convert this to milliliters per kilogram of body weight per minute (ml/kg/min). To do this, we need to divide Joan's VO2max by her body weight in kilograms. Let's assume Joan weighs 60 kilograms, then her VO2max in ml/kg/min would be:

VO2max = 3.6 L/min / 60 kg = 60 ml/kg/min

Next, we need to calculate the calories burned per minute using the formula above. Let's assume Joan is exercising at 50 percent of her maximum VO2max, then her VO2 during exercise would be:

VO2 during exercise = 0.5 x 60 ml/kg/min = 30 ml/kg/min

Plugging this value into the formula, we get:

Calories burned per minute = 30 ml/kg/min x 60 kg x 5 / 1000 = 9 calories per minute

Rounding this up, we get the final answer of approximately 10.8 calories per minute.


Calories burned per minute = VO2 x body weight in kg x 5 / 1000
VO2max = 3.6 L/min / 60 kg = 60 ml/kg/min
VO2 during exercise = 0.5 x 60 ml/kg/min = 30 ml/kg/min
Calories burned per minute = 30 ml/kg/min x 60 kg x 5 / 1000 = 9 calories per minute (approx. 10.8 calories per minute)

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The measure of the angle m∠CBD between points CD is equal to 495°°

From the question, we observe that the larger angle between AD consists of the two angles between m∠ABC and m∠CBD, so we shall sum the two small angles and equate the result to the larger angle m∠ABD to solve for the value of x as follows:

7x - 9 + 6x + 27 = 96

x + 18 = 96

x = 96 - 18 {collect like terms}

x = 78

put the value of x in m∠CBD;

m∠CBD = 6(78) + 27

m∠CBD = 495

In conclusion, the measure of the angle m∠CBD between points CD is equal to 495°

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The matrix is : [tex]\left[\begin{array}{cc}3&10\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}6\\1\end{array}\right][/tex], using matrix method y = 3.

Calculating y using matrices method,

A single numerical value known as the determinant of a matrix is used to calculate the inverse or to solve systems of linear equations.

Solving the determinant,

D = (3 * 3) - (1 * 10)

D = 9 - 10

D = -1

Replacing the column at the right side of the equality sign with the second column.

 [tex]\left[\begin{array}{cc}3&6\\1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}10\\3\end{array}\right][/tex]

Δ = (3 * 1) - (1 * 6) = 3 - 6 = -3

y = [tex]\frac{\Delta}{D}[/tex]

y = [tex]\frac{-3}{-1}[/tex]

y = 3

Therefore, y = 3

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Complete Question

The matrix equation represents a system of equations. A matrix with 2 rows and 2 columns, where row 1 is 3 and 10 and row 2 is 1 and 3, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 6 and row 2 is 1.

Solve for y using matrices. Show or explain all necessary steps.

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