Suppose that E and F are two events and that P(E and F)=0.1 and P(E)=0.2. What is P(F/E)

The point (if it exists) at which the following plane and line intersect: x=11;r(t)==11; for −[infinity] will be (11, t, 11)

We are given the equation of a plane and a line, but we need more information to determine if and where they intersect. Specifically, we need the equation of the plane in the form Ax + By + Cz = D, and we need the parametric equation of the line in the form x = x0 + at, y = y0 + bt, z = z0 + ct, where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector of the line.

Assuming that the equation of the plane is of the form Ax + By + Cz = D and the parametric equation of the line is of the form x = 11, y = t, z = 11 for all real numbers t, we can proceed as follows:

1. Substitute the parametric equation of the line into the equation of the plane to get an equation in t:

A(11) + B(t) + C(11) = D

2. Solve for t:

t = (D - A(11) - C(11)) / B

3. Substitute the value of t into the parametric equation of the line to get the point of intersection:

(11, t, 11)

This calculation assumes that the line and plane intersect at a single point. If the line is parallel to the plane, it may not intersect at all, or it may intersect in a line or a plane.

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The expression can be written as ⁴√y. The solution has been obtained by solving the radical expressions.

What are radical expressions?

A square root-containing expression is referred to as a radical expression. When a root other than a square root is being represented, the radical sign's 'V'-shaped component will have a superscript number.

We are given expression as y to the three fourths power, all over y to the one half power. This can be written as

[tex]\frac{y^{3/4}}{y^{1/2} }[/tex]

We know that

cᵃ ÷ cᵇ = cᵃ⁻ᵇ

So, using this we get

[tex]y^{3/4 - 1/2[/tex]

[tex]y^{1/4[/tex]

Since, we have to represent this in the radical form, we know that

b[tex]^{1/a}[/tex] = ᵃ√b

So, using this we get

[tex]y^{1/4[/tex] = ⁴√y

Hence, the expression can be written as ⁴√y.

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Answer:

Elimination , $1.79

Step-by-step explanation:

You were correct with elimination! Good job , now to find the cost of fries we have to put elimination in practice. Elimination is subtracting one equation from the other to get the equation of one variable.

4x + 5y = 24.11

-4x + 3y = 20.53

        2y = 3.58

     2y/2 = 3.58/2

           y = 1.79

Answer: x = 3

Step-by-step explanation: 3 + 3 = 6 ; 30 divided by 6 = 5.

Answer:

x = 3

Step-by-step explanation:

[tex]\frac{30}{3+x}[/tex] = 5 ( models the statement )

multiply both sides by 3 + x

30 = 5(3 + x)

30 = 15 + 5x ( subtract 15 from both sides )

15 = 5x ( divide both sides by 5 )

3 = x

Answer:

You selected the correct answer.

Step-by-step explanation:

There are 3 groups of marbles

From the question, we have the following parameters that can be used in our computation:

Blue = 6

Red = 9

Blacks = 12

Factor out the numbers

So, we have the following representation

Blue = 2 * 3

Red = 3 * 3

Blacks = 2 * 2 * 3

Using the above as a guide, we have the following:

GCF = 3

Hence, the number of groups is 3

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Answer:

Plug in the variable (x) in the equation.

Step-by-step explanation:

once you plug it in, multiplied by two, and subtract by 3, and it should equal your y input

With the help of expression 6*33 we found that Mike took a total of 198 baseballs.

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. Mathematical operations include addition, subtraction, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, x. This proposition can be stated mathematically as x/2 + 6. Mathematical expressions are used to answer complex problems.

Now,

Given that Total baseballs=363

Total trash bin=11

baseballs in one trash bin =363/11

=33

Mike took 6 trash bins

then baseballs in 6 trash bins are =6*33

=198

hence,

            Mike took a total of 198 baseballs.

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The conversion method from milimeter to nanometer is Quantity in nanometer = quantity in milimeter × 10⁶.

In the question, the two short forms mm and nm are representative of milimeter and nanometer. As per the known information, the milimeter represents 1/10³ meters and nanometer represents 1/10⁹ meters. So, we see that the difference between the exponents of 10 is 6 (as 9 - 3 = 6).

Therefore, the conversion of milimeter to nanometer will be through the mentioned formula -

Quantity in nanometer = quantity in milimeter × 10⁶

For instance, the quantity 3 mili meters in nanometer will be calculated as follows.

Quantity in nanometer = 3 × 10⁶ nanometer

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Answer: a)

C(x,y) = 25e^(-((x-1)^2 + (y-3)^2))

Czz(x,y) = ∂^2C/∂z^2 = 0 (since C does not depend on z)

Cyy(x,y) = ∂^2C/∂y^2 = 50e^(-((x-1)^2 + (y-3)^2))(2(y-3)^2 - 1)

b)

Cz(x,y) = ∂C/∂z = 0

Cz(1.1, 1.2) = 0

The value of Cz(1.1, 1.2) indicates the rate of change of temperature with respect to z at the point (1.1, 1.2), which is zero. In other words, the temperature does not change with respect to the height (z) at this point.

c)

Cyy(1.1, 1.2) = 50e^(-((1.1-1)^2 + (1.2-3)^2))(2(1.2-3)^2 - 1) ≈ -0.138

The value of Cyy(1.1, 1.2) indicates the rate of change of temperature with respect to y at the point (1.1, 1.2), which is approximately -0.138 °C per inch. In other words, as the ant moves along the line y=1.2, the temperature decreases by approximately 0.138 °C per inch.

d)

Czy(x,y) = ∂^2C/∂z∂y = 100e^(-((x-1)^2 + (y-3)^2))(y-3)

Czy(1.1, 1.2) = 100e^(-((1.1-1)^2 + (1.2-3)^2))(1.2-3) ≈ -43.44

The value of Czy(1.1, 1.2) indicates the rate of change of temperature with respect to both z and y at the point (1.1, 1.2), which is approximately -43.44 °C per inch per unit of height. In other words, as the ant moves along the line z=1.1 and simultaneously moves in the y-direction, the temperature decreases by approximately 43.44 °C per inch per unit of height.

Step-by-step explanation:

The answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

Similar triangles are the triangles that look similar to each other, but their sizes might not be exactly the same.

Given are two pairs of triangles, we need to determine if they are similar or not,

1) Δ ABC and Δ DEF :-

We know that, the sum of the interior angles of a triangle is 180°,

Therefore,

∠ A + ∠ B + ∠ C = 180°

60° + ∠ B + 79° = 180°

∠ B = 180°-139°

∠ B = 41°

In Δ DEF,

∠ F = 79° and ∠ E = 60°

That means,

∠ B ≅ ∠ F and ∠ E ≅ ∠ C

Since, we get two corresponding angles congruent,

Therefore, by the definition of similar triangles,

Δ ABC ~ Δ DEF, By AA rule.

2) Δ RTS and Δ MQP :-

∠ R ≅ ∠ M

RT / MQ = TS / QP = 4 / 5

RS / MP = 20 /26 = 10 / 13

That means,

RT / MQ = TS / QP ≠ RS / MP

Since, we have a condition in similarity, that if, in two triangles two corresponding sides are in equal ratio, and an angle between these sides are congruent then the triangle are similar by SAS rule,

But the angle R and angle M is not in between the sides having equal ratio,

Therefore, Δ RTS and Δ MQP are not similar.

Hence, the answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

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To find the volume of a solid obtained by rotating a region bounded by curves around an axis, we can use the disk or washer method.

Suppose we want to find the volume of a solid obtained by rotating the region bounded by the curves y = f(x), y = g(x), and the lines x = a and x = b around the x-axis.

We can divide the region into vertical slices of width Δx, and rotate each slice around the x-axis to obtain a disk or washer. The volume of each disk or washer can be approximated as the area of the base times the thickness, or π(R² - r²) Δx, where R and r are the outer and inner radii of the disk or washer, respectively.

To find the exact volume, we take the limit as Δx approaches zero and sum up the volumes of all the disks or washers using integration:

V = ∫[a, b] π(R² - r²) dx

where R = f(x) and r = g(x).

Alternatively, if we want to rotate the region around the y-axis, we can divide the region into horizontal slices of width Δy, and rotate each slice around the y-axis to obtain a disk or washer. The volume of each disk or washer can be approximated as π(R² - r²)Δy, where R and r are the outer and inner radii of the disk or washer, respectively.

The exact volume can be found using integration as:

V = ∫[c ,d] π(R² - r²) dy

where R = f(y) and r = g(y), and c and d are the y-coordinates of the endpoints of the region.

In either case, it is important to sketch the region and identify the appropriate radii before setting up the integral.

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To convert milligrams to milliliters for water or a substance with the same density, divide the number of milligrams by 1000.

Converting milligrams (mg) to milliliters (ml) depends on the density of the substance being measured. Density is the amount of mass in a given volume, and different substances have different densities. Therefore, the conversion factor will vary depending on what substance you are trying to convert.

However, if you are working with water or another substance with a density of 1 gram per milliliter, then the conversion is straightforward. One milliliter of water weighs one gram, or 1000 milligrams. So to convert milligrams to milliliters for water or a substance with the same density, you simply divide the number of milligrams by 1000.

However, for other substances with different densities, you need to know the substance's density to convert mg to ml. In this case, you will need to use the formula:

Volume (ml) = Mass (mg) ÷ Density (mg/ml)

It's important to note that for some substances, such as oils or syrups, the density may change depending on the temperature or other factors.

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4 lbs is approximately equal to 1.8143 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

4 lbs = 4 × 0.453592

Multiply the numbers

= 1.8143 kg  ( rounded to four decimal places )

Therefore, 180lbs is 1.81437 kg

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In length 5.4 feet is equivalent to 164.592 centimeters.

Firstly, it is important to understand that length is a physical quantity that describes the size or distance of an object. The unit of length can vary depending on the system of measurement used. The Imperial system, which is commonly used in the United States, measures length in feet, whereas the metric system, which is used worldwide, measures length in centimeters.

Now, to convert 5.4 feet into centimeters, we need to use a conversion factor. One foot is equivalent to 30.48 centimeters, so we can multiply 5.4 feet by 30.48 to get the equivalent length in centimeters.

5.4 feet x 30.48 cm/1 foot = 164.592 cm

It is important to note that when dealing with measurements, it is crucial to use the appropriate unit of length to ensure accuracy and consistency.

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Answer:

22.86

multiple 3.54 to 9

Answer:

6x-5 ≤ 29

Step-by-step explanation:

Let translate each part of the sentence into an equation or expression.

1.  "five subtracted from the product of 6 and a number"

2.  "is less than or equal to 29"

3.  Assemble the two expression into an equation

    Combine parts 1 and 2 into an equation.

       6x-5 ≤ 29

=============

Extra

6x-5 ≤ 29 can be simplified:

6x ≤ 29+5

6x ≤ 36

x ≤ 6

The equation that is used to find the cost of each necktie is (f - 8) = 21 and the cost is $ 29.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

Coefficients, variables, and, constants terms, and the equal to sign are the parts of an equation. Here the variable will represent the unknown quantity or unknown number.

Here we have

Will purchased 7 neckties during the sale.

He paid a total of $147.

The amount paid for 1 necktie = 147/7 = $ 21

Each necktie cost $8 less than its full price.

Here 'f' be the total price of the necktie

The the amount paid by Will = (f - 8)

Since each necktie costs $ 21

=> (f - 8) = 21

=> f = $ 29

Therefore,

The equation that is used to find the cost of each necktie is (f - 8) = 21 and the cost is $ 29.

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Complete Question:

At Trendy Tailor Boutique's annual end-of-season sale, every necktie in the shop gets marked down. Will purchased 7 neckties during the sale. Each necktie cost $8 less than its full price. He paid a total of $147. Which equation can you use to find f, the cost of each necktie at full price?

Answer:

The probability of drawing a red marble then a yellow marble out of the bag is probably 0.48(Decimal) or 12/25(Fraction).

Therefore, there are 21 possible selections of two individuals from a group of seven people.

In mathematics, a combination is a way of selecting a subset of objects from a larger set, where the order of selection does not matter. Combinations are also known as unordered selections or combinations without repetition. The number of combinations of k objects that can be selected from a set of n distinct objects is denoted by "n choose k" and is given by the formula: n choose k = n! / (k! (n - k)!) where n! is the factorial of n, defined as the product of all positive integers up to and including n, and k! and (n-k)! are the factorials of k and n-k, respectively. In words, this formula says that the number of combinations of k objects that can be selected from a set of n objects is equal to the number of ways to arrange k objects out of n, divided by the number of ways to arrange the remaining n-k objects.

Here,

To determine the number of possible selections of two individuals from a group of seven people, we can use the formula for combinations:

nCk = n! / (k! (n - k)!)

where n is the total number of individuals in the group, and k is the number of individuals to be selected. In this case, we want to select 2 individuals from a group of 7, so we have:

n = 7

k = 2

Substituting these values into the formula, we get:

7C2 = 7! / (2! (7 - 2)!)

= 7! / (2! 5!)

= (7 x 6 x 5!) / (2 x 1 x 5!)

= (7 x 6) / (2 x 1)

= 21

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The original expression could be log_2(1/3) / log_10(2).

The change of base formula states that:

log_a(x) = log_b(x) / log_b(a)

where a, b, and x are positive real numbers and a, b ≠ 1.

In the given expression, log1/3 / log2, the denominator is log2, which means that the base of the logarithm in the numerator must be 2 raised to some power.

So we can rewrite the logarithmic expression as:

log1/3 / log2 = log_2(1/3) / log_2(2)

Now we can apply the change of base formula, with a = 2, b = 10, and x = 1/3:

log_2(1/3) / log_2(2) = log_10(1/3) / log_10(2)

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Answer: C

Step-by-step explanation:

In the case of converting 3cm to mm, we find that there are 30mm in 3cm.

Understanding how to convert measurements is a fundamental skill that will serve you well in many areas of study. In this case, we'll focus on how to convert 3cm to mm.

First, it's important to understand that cm and mm are both units of measurement for length or distance. The abbreviation cm stands for centimeters, while mm stands for millimeters. A centimeter is larger than a millimeter, with 1cm equaling 10mm.

To convert 3cm to mm, we need to use this relationship between the two units of measurement. We know that 1cm is equal to 10mm, so we can use multiplication to find out how many millimeters are in 3cm.

We can start by writing out the equation:

3cm x 10mm/1cm

In this equation, we're multiplying 3cm by the conversion factor of 10mm/1cm. This conversion factor tells us that there are 10mm in 1cm. When we multiply 3cm by this conversion factor, we get:

3cm x 10mm/1cm = 30mm

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(a) 27 outcomes in the sample space are : (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3), (2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3), (3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) All outcomes in the event that all three members go to the same station are : (1,1,1), (2,2,2), (3,3,3)

(a) The 27 outcomes in the sample space can be represented as ordered triples, where each element corresponds to the station that each family member is assigned to. The possible values for each element are 1, 2, and 3. Therefore, the sample space consists of the following 27 outcomes:

(1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,2,3), (1,3,1), (1,3,2), (1,3,3),

(2,1,1), (2,1,2), (2,1,3), (2,2,1), (2,2,2), (2,2,3), (2,3,1), (2,3,2), (2,3,3),

(3,1,1), (3,1,2), (3,1,3), (3,2,1), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,3,3)

(b) The outcomes in the event that all three members go to the same station can be found by examining the 27 outcomes in the sample space and selecting those outcomes where all three elements are the same. Therefore, the outcomes in the event that all three members go to the same station are:

(1,1,1), (2,2,2), (3,3,3)

In these outcomes, all three family members are assigned to the same station. There are three such outcomes, since each family member can be assigned to any one of the three stations.

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The third term in the recursive sequence is 9

A recursive sequence is a sequence of numbers where each term is defined by a formula that uses one or more of the previous terms in the sequence. In other words, each term depends on the term(s) that come before it.

Since a₁ = 3 and  [tex]a_{k+1}[/tex]= 2a[tex]_{k}[/tex] - 1

a₂  = 2a₁ - 1  

a₂  = 2(3) - 1 = 6 - 1 = 5

a₃ = 2a₂ - 1  

a₃ = 2(5) - 1 = 10 - 1 = 9  

Thus, the third term in the recursive sequence will be 9

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The conversion of the units 300 meters to miles is equal to 0.1864miles ( round up to four decimal places ) .

Meters and Miles both are units used to measure the length or the distance between any two or more points.

Conversion factor relating meters and miles is equal to

One meter = 0.000621371 miles

To get the value of 300 meters in miles multiply by converting factor we get,

300 meters

= ( 300 ) × ( 0.000621371 ) miles

= ( 0.1864113 ) miles

= ( 0.1864 ) miles ( round up to four decimals places )

Therefore, the conversion distance 300 meters to miles is given by              ( 0.1864 ) miles ( round up to four decimals places ) .

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The volume of cylinder based on the dimensions of radius and height is 1296π m³.

The volume of cylinder can be calculated by the formula -

V = πr²h, where V refers to volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder.

Now, keeping the value of the dimensions in the formula to find the volume of cylinder.

V = π × 12² × 9

Taking square and performing multiplication on Right Hand Side of the equation

V = 1296π m³

Note that we have not kept the value of π in the formula to find the exact correct answer. Thus, the volume of 1296π m³.

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Rounding to the nearest tenth, we get Average rate of change ≈ -27.5

In mathematics, an average is a measure of central tendency that represents the typical or common value of a set of data. There are several types of averages, including:

Arithmetic mean: The arithmetic mean is the most commonly used measure of average. It is calculated by adding up all the values in a dataset and dividing by the total number of values. For example, the arithmetic mean of the numbers 1, 2, 3, 4, and 5 is (1 + 2 + 3 + 4 + 5) / 5 = 3.

Median: The median is the middle value in a dataset when the values are arranged in numerical order. If there is an even number of values, the median is the average of the two middle values. For example, the median of the numbers 1, 3, 4, 6, and 7 is 4.

Mode: The mode is the value that appears most frequently in a dataset. If there are multiple values that appear with the same frequency, the dataset is said to have multiple modes. For example, the mode of the numbers 1, 2, 2, 3, and 4 is 2.

Averages are used in a wide range of applications, including statistics, finance, and science. They can help summarize data, identify trends, and make comparisons between different sets of data. However, it is important to note that averages can be affected by outliers or extreme values in a dataset, so it is important to consider other measures of variability and dispersion when analyzing data.

The average rate of change of the cost from the 6th month to the 8th month is given by the expression:

(Amount of change in cost) / (Amount of change in month)

The amount of change in cost from the 6th to the 8th month is:

c(8) - c(6) = 100 - 155 = -55

The amount of change in month from the 6th to the 8th month is:

8 - 6 = 2

Therefore, the average rate of change of the cost from the 6th month to the 8th month is:

(Amount of change in cost) / (Amount of change in month) = -55 / 2 ≈ -27.5

Rounding to the nearest tenth, we get:

Average rate of change ≈ -27.5

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Answer: 140 dollars

Step-by-step explanation:

0.3x=42   x=140

Anaiah is currently spending $150 on eggplants and kiwis.

Anaiah is behaving irrationally, because

1) He is not spending his entire income

2) He is spending too much on kiwis

3) He is not balancing what he spends on each good

4) His marginal utility per dollar spent is not the same for both goods.

Currently, Anaiah is spending:

On eggplants: 20 x $3 = $60

On kiwis: 30 x $3 = $90

Total spending: $60 + $90 = $150

Therefore, Anaiah is currently spending $150 on these goods.

The reasons that Anaiah is behaving irrationally are:

He is not spending his entire income: Anaiah has $180 to spend but he is only spending $150, which means he is not maximizing his utility by fully utilizing his budget.

He is spending too much on kiwis: Anaiah's marginal utility per dollar spent on kiwis is lower than his marginal utility per dollar spent on eggplants. Therefore, he should be spending more on eggplants and less on kiwis to maximize his utility.

He is not balancing what he spends on each good: Anaiah is consuming 20 eggplants and 30 kiwis, which means he is not allocating his budget efficiently to maximize his total utility. He should be consuming a combination of eggplants and kiwis that gives him the highest total utility within his budget constraint.

His marginal utility per dollar spent is not the same for both goods: Anaiah's marginal utility per dollar spent on eggplants is 160 utils while his marginal utility per dollar spent on kiwis is 190 utils. Therefore, he should be consuming more eggplants and fewer kiwis to maximize his total utility within his budget constraint.

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