Suppose an urn contains 5 blue chips and 3 red chips. Chips are drawn without replacement until either the first red chip is drawn, or until three blue chips are drawn. Let X be the number of blue chips drawn and Y the number of red chips drawn. (a) Find pX,Y , the joint pmf of X and Y . (You might want to make a table.) (b) Find the marginal pmfs pX and pY . (c) Find the conditional pmfs pX|Y (x|0) and pX|Y (x|1).

Thus, a single expression for x(t) that does not involve multiple cases is:

x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)

Using the properties of the unit step function,

we can write:

x(t) = 4t + 4 - u(t-2) - 2u(t-4) + 12u(t-12)

Breaking it down:

For t < 2, the unit step function u(t-2) is 0,

so it does not affect the expression for x(t).

For 2 ≤ t < 4, u(t-2) = 1 and u(t-4) = 0,

so the expression becomes:

x(t) = 4t + 4 - 1 = 4t + 3

For 4 ≤ t < 12, u(t-2) = u(t-4) = 1,

so the expression becomes:

x(t) = 4t + 4 - 2 = 4t + 2

For t ≥ 12, u(t-2) = u(t-4) = 1, and u(t-12) = 1,

so the expression becomes:

x(t) = 4t + 4 - 1 - 2 + 12 = 4t + 13

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D. False. The combined effect of two linear transformations is always linear because multiplying two linear functions together will result in a function which is also linear.

The statement says when two linear transformations are performed one after another, the combined effect may not always be a linear transformation.

This is false,  the combined effect of two linear transformations is always linear because multiplying two linear functions together will result in a function which is also linear.

A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map.

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Morse's monthly budget has a surplus of $3,860 (rounded to the nearest whole number).

From the we are to calculate Morse's monthly budget.

To determine Morse's monthly budget, we need to first calculate his total annual expenses:

Total Annual Expenses = Fixed Expenses + Living Expenses + Annual Expenses

= $2,117 + $489 + $475

= $3,081

Then, we can calculate his monthly budget by dividing his annual net income by 12:

Monthly Budget = Annual Net Income / 12

= $49,397 / 12

= $4,116.42

Now, we can determine Morse's monthly budget by subtracting his total monthly expenses from his monthly net income:

Monthly Budget = Monthly Net Income - Monthly Expenses

Monthly Net Income = Annual Net Income / 12 = $49,397 / 12 = $4,116.42 (rounded to the nearest cent)

Monthly Expenses = Total Annual Expenses / 12 = $3,081 / 12 = $256.75 (rounded to the nearest cent)

Monthly Budget = $4,116.42 - $256.75 = $3,859.67

Hence, Morse's monthly budget has a surplus of $3,860

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Answer:

76 can be written as the product of 2 and 38. It is given as: √ 76 = √ (2 × 38) 2 is not a perfect square. Hence, it stays within the root sign. 38 can be shown as 2 × 19. The simplified radical form of the square root of 76 is 2 √ 19.

Step-by-step explanation:

arrange ff fraction 5/6,8/9,23

The possible combinations made by Enrique are mentioned below:

In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.

Formula for selection of a objects from the n objects,

N = ⁿCₐ

The graph shows a scatter plot of points and does not have the feasible region shaded to show the combinations of wallpaper and paint that Enrique can buy.

In order to graph the feasible region, the budget constraint and minimum requirements constraint need to be plotted as lines on the same graph, and the feasible region would be the region that lies between these lines and below them.

Two possible combinations that Enrique can buy are (30, 100) and (40, 80).

These points represent 30 rolls of wallpaper and 100 cans of paint, or 40 rolls of wallpaper and 80 cans of paint, respectively.

These points lie on the feasible region and satisfy both the budget constraint and the minimum requirements constraint.

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In a transshipment problem (c)  I - O <= S or D. here s is supply and D is demand,

A model that falls within the category of transportation issues is the transshipment model. Transshipment issues come in two different flavors.

Using transient (i.e. intermediate) nodes as sources and destinations

between the sources and the destination with a few temporary nodes

In a transportation issue, the shipment may move from S1 to D1, S1 to D2, S1 to D3, S2 to D1, S2 to D2, and so forth, from one specific source to another specific destination.

In this approach, the shipment travels via one or more intermediary nodes before arriving at the final location. With this technique, the shipment can move back and forth between sources and destinations before arriving at the intended location.

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An equation of the line in fully simplified slope-intercept form is y = -13x - 22.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data points (-2, 4), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (10 - (-3))/(-3 - (-2))(x - (-2))

y - 4 = -13(x + 2)

y = -13x - 26 + 4

y = -13x - 22

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Answer: draw a number line and plot the 0, 1 , and 2

Explanation:

Nancy collected 5 5/6 cans of bags which is 7 times more than her friend.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Nancy collected 7 times as many bags of can and her friend collected 5/6 of a bag.

Therefore, The amount of bags of cans Nancy collected can be obtained by multiplying 7 by the number of bags of can collected by her friend which is,

= (5/6)×7 bags.

= 35/6 bags.

= 5 5/6 can of bags.

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The percentage discount is 95 percent

A percentage discount is a reduction in price that is expressed as a percentage of the original price.  Percentage discounts are commonly used in retail sales and promotions to incentivize customers to make purchases.

To determine the percentage discount of the orange, we can find the original price.

0.75 * 7 = 5.25

This is the cost of orange

The total amount charged = 4.30

The discount = 5.25 - 4.30 = 0.95

The percentage discount will be;

percentage discount = 0.95 * 100 = 95%

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Answer:

x ≤ 1.5

Step-by-step explanation:

Brett can pour at most 1.5 more gallons of water into his fish tank. This is because the fish tank can only hold 10.5 gallons of water and Brett has already poured 9 gallons into the tank. So, the maximum amount of water he can pour is the remaining 1.5 gallons.

Answer:

the value of the original number (n) is 25.

Step-by-step explanation:

Let's use algebra to solve the problem.

We are told that a number (n) is increased by 10 and the result is doubled, which gives:

2(n + 10)

We are also told that this result is 5 less than three times the original number (n), which gives:

2(n + 10) = 3n - 5

Expanding the left side of the equation:

2n + 20 = 3n - 5

Subtracting 2n from both sides:

20 = n - 5

Adding 5 to both sides:

25 = n

Therefore, the value of the original number (n) is 25.

The solution is, their ages are 13 & 39 yrs., when the sum of the ages of a man and his son is equal to twice the difference of that ages, the product of their ages is 507.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The sum of the ages of a man and his son is equal to twice the difference of that ages,

the product of their ages is 507.

let, their ages are, a &b

now, The sum of the ages of a man and his son is equal to twice the difference of that ages,

so, we get,

a+b = 2(a-b)...(1)

and, ab = 507....(2)

we get,

from (1) we get,

solving both side,

2a - a = b + 2b

or, a = 3b

now, putting the value of a in (2),

from (2) we get,

so, 3b^2 = 507

solving we get,

b = 13

a= 39

Hence, The solution is, their ages are 13 & 39 yrs.

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Markup on cost price is 75%

Percent markup on selling price: 25%

Percent markup on cost: ?

Markup is the total profit on a particular commodity or service. It is represented as a percentage over a cost price.

Percent markup on selling price is 25% which means that a product is sold out with 25% profit,

Percent markup on cost price =100-markup on selling price

                                                  = 100-25

                                                  =75

Hence, markup on cost price is 75%

The value of Percent markup on cost nearest to the whole number is,

⇒ 75%.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The value of Percent markup on selling price is,

⇒ 25%

Hence, The value of Percent markup on cost is,

⇒ 100% - selling price

⇒ 100% - 25%

⇒ 75%

Thus, We get;

The value of Percent markup on cost is,

⇒ 75%

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A tree with a height of 6.2 ft exists 3 standard deviations above the mean.

The normal distribution represents a symmetrical display of data around its mean value, with the standard deviation serving as the determinant of the curve's breadth. The "bell curve" is used to visually represent it.

The normal distribution, sometimes referred to as the Gaussian distribution, is a probability distribution that is symmetric about the mean and demonstrates that data that exists closer to the mean exists more likely to even than data that exists farther from the mean. The normal distribution is depicted graphically as a "bell curve."

The majority of data points in a continuous probability distribution known as a "normal distribution" cluster around the middle of the range, while the remaining data points taper off symmetrically toward either extreme. The mean of the distribution is another name for the center of the range.

It exists said that an X value exists found Z standard deviations from the mean if:

[tex]$\frac{X-\mu}{\sigma}=Z$$[/tex]

Given:

[tex]$$\begin{aligned}& \mu=5 \mathrm{ft} \\& \sigma=0.4 \mathrm{ft}\end{aligned}$$[/tex]

We have four different values of X and we must calculate the Z-score for each

For X = 5.4 ft

[tex]$& Z=\frac{X-\mu}{\sigma} \\[/tex]

substitute the values in the above equation, we get

[tex]$ Z=\frac{5.4-5}{0.4}=1\end{aligned}$$[/tex]

A tree with a height of 5.4 ft exists 1 standard deviation above the mean

First Option: False

For X = 4.6 ft

[tex]$Z=\frac{4.6-5}{0.4}=-1\end{aligned}$$[/tex]

A tree with a height of 4.6ft exists 1 standard deviation below the mean

Second Option: False

For X = 5.8 ft

[tex]$Z=\frac{5.8-5}{0.4}=2\end{aligned}$$[/tex]

A tree with a height of 5.8 ft exists  2 standard deviation above the mean

Third Option: False

For X = 6.2 ft

[tex]$ Z=\frac{6.2-5}{0.4}=3\end{aligned}$$[/tex]

A tree with a height of 6.2 ft exists 3 standard deviations above the mean.

Therefore, the correct answer is option d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.

The complete question is;

The heights of a certain type of tree are approximately normally distributed with a mean height y = 5 ft and a standard deviation = 0.4 ft. Which statement must be true?

a) A tree with a height of 5.4 ft is 1 standard deviation below the mean

b) A tree with a height of 4.6 ft is 1 standard deviation above the mean.

c) A tree with a height of 5.8 ft is 2.5 standard deviations above the mean

d) A tree with a height of 6.2 ft is 3 standard deviations above the mean.

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The statement "This door will not open unless a security code is entered" can be expressed in if-then form as "If a security code is not entered, then the door will not open."

This is because the statement "unless" indicates a necessary condition. In other words, the security code must be entered in order for the door to open, and if the security code is not entered, then the door will not open. Therefore, the correct option is: If a security code is not entered, then the door will not open.

The capacity to use numerical data to recognise patterns, solve problems without a pre-existing formula, understand graphs, and reach reasonable conclusions when faced with numerical evidence is known as mathematical reasoning.

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Answer:

x=41,y=15

Step-by-step explanation:

The given system of equations is:

x = 41

x + 2y = 71

We can use substitution to solve for y.

Starting with the first equation:

x = 41

We can substitute the value of x into the second equation:

x + 2y = 71

41 + 2y = 71

2y = 71 - 41

2y = 30

Finally, we can solve for y by dividing both sides of the equation by 2:

y = 30 / 2

y = 15

x=41,y=15.

Answer:

Step-by-step explanation:

To find the price of the NBA ticket in 2017, we need to add 20% to the 2016 price:

Price in 2017 = $1444 + 0.20 x $1444 = $1732.80

To find the price of the NBA ticket in 2020, we need to increase the 2017 price by 20%:

Price in 2020 = $1732.80 + 0.20 x $1732.80 = $2079.36

Rounding this to the nearest dollar, we get:

Price in 2020 = $2079

The distance between the rests in the new map is 0.825 inches.

We know that the original scale is:

2 in = 33mi

or:

1 in = (33mi)/2

1in = 16.5 mi

And on a highway, there are 7 rests in 9 inches.

First, we transform these 9 inches to miles

9 in = 9*(16.5 mi) = 148.5 mi

If the 7 rests are evenly divided in that distance, the distance between each rest is:

148.5mi/6 = 24.75mi

(we divide by 6 because one rest is at each end, so there are 6 even spaces between the two ends)

Now, in the new map the scale is:

1 inch = 30mi

Then the distance between the rests in the new map is:

d = 24.75/30 inches

d = 0.825 inches.

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Since x is less than -6, we use the first equation to calculate h(-6):

h(-6) = 4(-6) - 20 = -24

A function is a mathematical concept that assigns to each input value (or "argument") exactly one output value (or "image"). In other words, a function is a rule that assigns a unique output for each input value. The set of input values is called the domain of the function, and the set of output values is called the range. A function can be represented graphically as a curve, or analytically as a formula. Functions play a central role in many areas of mathematics, science, and engineering.

For x < -6, h(x) = -4x - 20. So, h(-6) = -4(-6) - 20 = 24 - 20 = 4.

For -6 ≤ x < 1, h(x) = x + 5. So, h(0) = 0 + 5 = 5.

For x ≥ 1, h(x) = 1. So, h(1) = h(7) = 1.

So, the values are:

h(-6) = 4, h(0) = 5, h(1) = h(7) = 1.

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The probability that all the guinea pigs selected randomly are pregnant is 1/30 or 0.033

Given, we have 10 guinea pigs out of which 4 are pregnant. We know that probability of an event ⇒ P(E) = (No of favorable outcomes)/(No of all outcomes) . So, The probability of selecting pigs that are pregnant is :

⇒ 4/10

Now, 3 selections are made randomly. The probability that the 1st selected guinea pig will be pregnant = 4/10

The probability that the 2nd selected guinea pig will be pregnant = 3/9

The probability that the 3rd selected guinea pig will be pregnant = 2/8

Therefore, the probability of all the 3 selected guinea pigs being pregnant will be :

⇒  (4/10) x (3/9) x (2/8)

⇒ 1/30

Therefore, The probability of all the selections of pigs being pregnant without replacement rounded to 3 decimal places is 0.033 or 1/30

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The complete question will be :

In a scientific study there are 10 guinea pigs,4 of which are pregnant. if 3are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to 3 decimal places.

a. The subject lies about past illegal drug use: This is a source of nonsampling error, as it is not related to the process of selecting a sample from a population. Rather, it is an error that arises from the behavior or characteristics of the individual being sampled.

b. A typing error is made in recording the data: This is a source of nonsampling error, as it is a mistake that occurs during the process of recording or processing the data, and is not related to the sample selection process.

c. Data are gathered by asking people to go to a website and answer questions online: This is a source of sampling error, as it can potentially lead to a biased sample. Only people who have access to the internet and are willing to answer questions online will be included in the sample, which may not be representative of the population as a whole. This type of bias is known as "self-selection bias" and is a common problem with online surveys.

The measure of each of the angles in the triangle given is 48°, 64° and 68°.

Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b, which means that a parts of a quantity is corresponding to b parts of another quantity.

Given that,

Ratio of measures of two angles of a triangle = 3 : 4

Let x be a number such that,

Measure of smaller angle =3x

Measure of second angle = 4x

Measure of third angle is 20° more than the measure of the smaller of the first two angles.

Measure of third angle = 3x + 20

We know that sum of interior angles of a triangle = 180°

3x + 4x + (3x + 20) = 180

10x + 20 = 180

10x = 160

x = 16

Measure of smaller angle = 3x = 48°

Measure of second angle = 4x = 64°

Measure of third angle = 3x + 20 = 68°

Hence the measures of each of the angle in triangle is 48°, 64° and 68°.

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The cost of each container is $0.18.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given figure we get,

container's length = 6in

width = 2.5in

height = 8in

volume of the container =120 in^3

each container will be made from material that costs $0.0015 per cubic inch.

so, the costs of each container = $0.0015* 120

                                                    = $0.18

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The set S spans R₃ if and only if for any vector (a, b, c) in R₃, there exist scalars x, y, and z such that z is not zero and z/2 is nonzero. This is true for all vectors in R₃, so we conclude that S spans R₃.

To determine if the set S spans R₃, we need to see if any vector in R₃ can be written as a linear combination of the vectors in S.

Let (a, b, c) be an arbitrary vector in R₃. Then we want to see if there exist scalars x, y, and z such that:

x(1, -2, 0) + y(0, 0, 1) + z(-1, 2, 0) = (a, b, c)

This is equivalent to the system of equations:

x - z = a

-2x + 2z = b

y = c

Solving for x, y, and z, we get:

x = (a - z)/2

y = c

z = (b + 2x)/2 = (b + a - z)/2

Substituting these values into the equation for the linear combination, we get:

[(a - z)/2](1, -2, 0) + c(0, 0, 1) + [(b + a - z)/2](-1, 2, 0)

= ((a - z)/2 - (b + a - z)/2, -2(a - z)/2 + 2(b + a - z)/2, 0)

= (-b/2, (3a - b)/2, z/2)

Geometrically, the set S consists of two nonparallel vectors and a vector orthogonal to the xy-plane. Thus, the subspace spanned by S is a plane in R₃ passing through the origin.

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The missing sides of the triangles are given below.

Length is defined as the measurement of distance of an object from one end to the other.

To find the missing sides of the given triangles.

Question 1 :

In the triangle, consider sin 90° = [tex]\frac{opposite side}{hypotenuse side}[/tex]

                                               1 = [tex]\frac{13}{x}[/tex]

                                              ⇒ x = 13

Which is the length of the missing side of the triangle.

Question 2:

In this triangle, consider degree 63° we have to find the  length of hypotenuse side, then,

sin 63° =[tex]\frac{opposite side }{hypotenuse side}[/tex] = [tex]\frac{18}{x}[/tex]

0.89 x = 18

⇒ x = 18/0.22 = 20.22.

Length of the hypotenuse side is 20.22 cm.

Question 4:

In this triangle, consider cos function.

sin 18°= [tex]\frac{opposite side}{hypotenuse}[/tex] = x/11

0.3090*11 = x

x = 3.399 = 3.4 inches.

Question 5:

consider sin angle.

sin 90° = [tex]\frac{opposite side}{hypotenuse}[/tex] = x/21

⇒x = 21 yard.

Question: 6

For this triangle we consider, tan functions.

tan 43° = [tex]\frac{opposite side}{adjacent side}[/tex] = x/23

⇒ x =21.4 mm.

Question 7:

For this triangle , we consider sin function.

sin 33° = 9/x

⇒0.5446 *x=9/0.5446

⇒x = 16.5km

Question 8:

For this triangle we have to choose tan function,

tan67 ° = opposite side/ adjacent side

            = 17/x

⇒x = 7m

Question 9:

For this triangle, we take sin function.

sin 90°= opposite side/hypotenuse

        1   = x/19

⇒x = 19m

Question 10:

For this triangle we consider sin function,

sin 90°= 26/x

⇒x = 26 feet.

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The  answer of this queation :∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where C = C1 + C2 + C3 is the constant of integration for the entire expression.

eparate integrals:

∫ 4 dx + ∫√x dx + ∫ x/x dx

The first two integrals can be easily integrated as follows:

∫ 4 dx = 4x + C1, where C1 is a constant of integration.

∫√x dx = 2/3 x^(3/2) + C2, where C2 is a constant of integration.

For the third integral, note that x/x simplifies to 1 for all nonzero x.

∫ x/x dx = ∫ 1 dx = x + C3, where C3 is a constant of integration.

Putting it all together, we have:

∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where the integration constant for the entire statement is C = C1 + C2 + C3.

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Probability that the selected card bears a Perfect square is 1/10 and the probability that the selected card bears a two digit number is 81/90.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that a box contains cards, number 1 to 90.

A card is drawn at random from the box.

We have to find the the probability that the selected card bears a two-digit number.

In 90 cards, from 1 to 9 are single digit numbers which are 9 in number.

The remaining 81 are two-digit numbers (10 to 90). So the probability of selecting a two-digit number is

81/90

(ii) There are 9 perfect squares between 1 and 90, namely 1, 4, 9, 16, 25, 36, 49, 64, and 81.

So the probability of selecting a perfect square number is:

P(Perfect square) = 9/90 = 1/10

Hence, the probability that the selected card bears a two digit number is 81/90 and probability that the selected card bears a Perfect square is 1/10.

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The right response is C. A has a pivot location in each row if the equation Ax-b has a solution for each b in [tex]R^n[/tex].

The pivots must be on A's diagonal since A is square. Hence, A is a row that is identical to In. A is hence invertible.

If there is an answer to the equation Ax-b for each b in [tex]R^n[/tex], then there is an answer to the equation Ax = b for each b. This indicates that A has complete rank since the column space of A is all of [tex]R^n[/tex].

A must-have n pivot points (one in each row), and the pivots must be on the diagonal of A since A is a square matrix with complete rank.

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