(x + 1) divided by 6y

pls show working out pls thx.

Answer:

Perimeter = 8w

Step-by-step explanation:

Let the width of the rectangular framework be w.

Length = 3w

We know that the perimeter of a rectangular shaped object is given by :

P = 2(l+w)

Substitute all the values in the above formula,

Perimeter = 2(3w+w)

= 2(4w)

= 8w

So, the perimeter of the art be 8w.

Given that the z-score of a student is -2.2, we can use the formula for z-score to find the student's score. The formula is:

z = (x - μ) / σ

where z is the z-score, x is the student's score, μ is the mean, and σ is the standard deviation.

Rearranging the formula, we have:

x = z * σ + μ

Plugging in the values, z = -2.2, μ = 530, and σ = 75, we can calculate the student's score:

x = -2.2 * 75 + 530 = 375 + 530 = 905.

Therefore, the student's score is 905.

To summarize, the student's score is 905 based on a z-score of -2.2, a mean of 530, and a standard deviation of 75.

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1: the total no. of outcomes, which is 16. 2: we sum up the probabilities for each value of Y across all values of X. 3: the conditional probability for each value of Y, given a specific value of X. 4: summing up the product of the differences of each pair of values from their expected values, weighted by their probabilities.

1. Joint PMF: To find the joint PMF, we need to consider all possible outcomes when rolling two balanced tetrahedra. Each tetrahedron has four faces numbered 1, 2, 3, and 4. So, there are 4 * 4 = 16 possible outcomes. For each outcome, we calculate the probability by dividing 1 by the total number of outcomes, which is 16. This gives us the joint PMF for X and Y.

2. Marginal PMFs: The marginal PMFs provide the probabilities for each individual variable. To find the marginal PMF for X, we sum up the probabilities for each value of X across all values of Y. Similarly, to find the marginal PMF for Y, we sum up the probabilities for each value of Y across all values of X.

3. Conditional Mass Function: The conditional mass function of Y given X=x represents the probability distribution of Y when X has a specific value x. We calculate this by dividing the joint probability of X=x and Y=y by the marginal probability of X=x. This gives us the conditional probability for each value of Y, given a specific value of X.

4. Expected Values, Variances, and Covariance: The expected value of a random variable is calculated by summing up the product of each value of the variable and its probability. For X and Y, we calculate their respective expected values using their marginal PMFs. The variance of a random variable measures the spread of its distribution and is calculated by summing up the squared differences between each value and the expected value, weighted by their probabilities. Finally, the covariance between X and Y measures their joint variability and is calculated by summing up the product of the differences of each pair of values from their expected values, weighted by their probabilities.

By performing these calculations, we can obtain a comprehensive understanding of the probabilities and statistical measures associated with rolling two balanced tetrahedra and the variables X and Y representing the outcomes.

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the probability density function (PDF) of Z = X + Y is given by: fZ(z) = z, for 0 ≤ z ≤ 1 = 0, otherwise. This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

What is probability density function?

A probability density function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It is used to define the likelihood of a random variable taking on a specific value or falling within a certain range of values.

To determine the probability density function (PDF) of the random variable Z = X + Y, where X and Y are independent uniform random variables with range [0, 1], we can use the convolution of the PDFs of X and Y.

First, let's recall the PDF of a uniform random variable. A uniform random variable U with range [a, b] has a constant PDF given by:

fU(u) = 1 / (b - a), for a ≤ u ≤ b

= 0, otherwise

In this case, for X and Y with range [0, 1], the PDFs are:

fX(x) = 1, for 0 ≤ x ≤ 1

= 0, otherwise

fY(y) = 1, for 0 ≤ y ≤ 1

= 0, otherwise

Now, let's find the PDF fz of Z = X + Y by convolution:

fZ(z) = ∫ fX(x) * fY(z - x) dx

Since X and Y are independent, fY(z - x) = fY(z) since the range of Y is [0, 1].

fZ(z) = ∫ fX(x) * fY(z) dx

As the PDFs of X and Y are both 1 in the range [0, 1], the integral becomes:

fZ(z) = ∫ 1 * 1 dz

Since the integration bounds are not dependent on z, the integral evaluates to:

fZ(z) = ∫ 1 dz = z

Therefore, the probability density function (PDF) of Z = X + Y is given by:

fZ(z) = z, for 0 ≤ z ≤ 1

= 0, otherwise

This means that Z has a triangular distribution with a PDF that linearly increases from 0 to 1 over the range [0, 1], and then remains 0 outside that range.

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Answer:

4x-5y=-13. 4x−5y=−13 4 x - 5 y = - 13.

Step-by-step explanation:

Step 1. Solve the equation for y y . Tap for more steps.

The correct conclusion is:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

Given,

At a huge institution, a doctor is determining the typical height of the male students.

Inches are used to measure the heights of a sample of 40 male baseball team players.

The doctor computes the 95% confidence interval using this information (63.5, 74.4).

The following conclusions is valid:

"The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches."

We can guarantee that the target variable will be within the confidence interval for a given confidence level since we know the confidence interval reflects an interval.

The true mean of heights for male students at the college where the doctor measured heights is represented by the provided case's confidence level of 95% and confidence interval of (63.5, 74.4).

The doctor is therefore 95% certain that the range of the mean height of male students at the college is valid (63.5, 74.4).

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Answer:

2x^2+7x-4

Step-by-step explanation:

(2x-1)(x+4)

\(=2x^{2} + 8x-x-4\\=2x^{2} +7x-4\)

Hope this helps!

Answer:

Step-by-step explanation:

2x\(2x² + 7x - 4.\)

Answer:

The answer would be 5.

Step-by-step explanation:

If you take away 18 from 90 would be 72.

72 - 18 =54

54 - 18 =36

36 - 18 =18

18 - 18 =0

If you count that would equal 5 .

Hope this helps .

Answer:

Yes, if two random vectors are independent, then after a same transformation they are still independent. This is a consequence of the fact that the transformation of independent random variables does not affect their independence.

To understand this, suppose we have two independent random vectors X and Y, and a transformation function f(.).

If we apply the same transformation f(.) to both X and Y to get f(X) and f(Y), then the independence between X and Y will still hold in the transformed variables f(X) and f(Y).

This is because the transformation f(.) does not introduce any new relationship between the variables, it simply changes their scale or shape. As a result, if X and Y are independent, then f(X) and f(Y) will also be independent.

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To maximize the likelihood function, we take the derivative with respect to θ and set it equal to zero: d/dθ[L(θ|X1,X2,...,Xn)]=−n/θ+(X1+X2+⋯+Xn)/θ2=0.

The MLE for θ in the exponential distribution is simply the sample mean of the observed data.

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson point process. X1,X2,...,XnX1,X2,...,Xn is a random sample of size n from this distribution, which means that each XiXi is an independent and identically distributed random variable with the same exponential distribution.

The probability density function (pdf) of the exponential distribution is given by f(x:θ)=(1/θ)e−x/θ, where θ is the scale parameter. This means that the probability of observing a value x from the distribution is proportional to e−x/θ, with the constant of proportionality being 1/θ.

To estimate the value of θ based on the observed data, we can use the method of maximum likelihood estimation (MLE). The likelihood function for the sample X1,X2,...,XnX1,X2,...,Xn is given by L(θ|X1,X2,...,Xn)=∏i=1n(1/θ)e−Xi/θ=(1/θ)n e−(X1+X2+⋯+Xn)/θ.

Solving for θ, we get θ=(X1+X2+⋯+Xn)/n, which is the sample mean.

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Answer:

the measure of angle Z=(8x-2) and the measure of angle W=(13x-7)

Step-by-step explanation:

lines wz and xy are the same, as shown with the same number of dashes through the lines, and lines zy and we are parallel, meaning they will never cross over each other.

This means that angle z and angle y are the exact same and angle w and angle x are the exact same.

Answer:

y = 13x -107

Step-by-step explanation:

(10 - -3) / (9-8) =13

10= 13* 9 + b

b = 10 - 117 = -107

To construct a box plot from the given data, which represents the diameters of cans in an assembly line, we need to determine the five-number summary and plot the corresponding box and whisker plot.

The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

To construct the box plot, we start by arranging the data in ascending order: 5.1, 5.2, 5.2, 5.2, 5.3, 5.5, 5.5, 5.5, and 5.6. The minimum value is 5.1, and the maximum value is 5.6. The median is the middle value, which in this case is 5.3.

To find the first quartile (Q1) and the third quartile (Q3), we divide the data into two halves. Q1 is the median of the lower half, which consists of 5.1, 5.2, 5.2, and 5.2. Q3 is the median of the upper half, which consists of 5.5, 5.5, 5.5, and 5.6. The box plot will show the minimum value, Q1, Q2 (median), Q3, and the maximum value, giving us a visual representation of the distribution and variability of the data.

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Answer:

0.0015232292460015

I think you mean 2,626/4

Then it is  656.5

Step-by-step explanation:

What you wrote is probably not what you wanted the bottom is

Answer:

656 remainder of 2

Step-by-step explanation:

Step-by-step explanation:

Answer:

Domain All real x.

Range f(x) >= 1.

Step-by-step explanation:

The domain is all real numbers.

|x| is always positive.

At x = 0:

f(x) = |0| + cos 0

= 1  which is the minimum value.

Answer:

see down

Step-by-step explanation:

10. a one to one function means only one  input goes to the same output,

this one is not a one to one function, because there is 2 out put for each input except vertx

9514 1404 393

Answer:

  a.  (-1/2, 5)

Step-by-step explanation:

The coefficients of x have opposite signs, so the x-terms can be eliminated by adding the two equations.

  (2y -12x) +(3y +12x) = (16) +(9)

  5y = 25 . . . . . . simplify

  y = 5 . . . . . . . . .divide by 5

This matches only answer choice A.

__

Check

The other part of answer choice A is x = -1/2. We can test this to make sure it works:

  2(5) -12(-1/2) = 16

  10 + 6 = 16 . . . . . . true, the selected answer works OK

The slope of the budget constraint represents the rate at which the quantity of cake (S) is traded off for the quantity of coffee (C) while keeping the total expenditure constant.

a) The budget constraint for Alice and Betty is given by the equation:

1C + 2S = 10

where C represents the quantity of coffee and S represents the quantity of cake they can purchase. This equation represents the total amount they can spend on coffee and cake, which should not exceed their weekly allowance of $10.

b) To graph the budget constraint, we can plot the points that satisfy the equation 1C + 2S = 10. The graph will be a straight line in the C-S coordinate plane. Here are a few points that lie on the budget constraint line:

(0, 5): They can buy 5 slices of cake and no coffee.

(5, 0): They can buy 5 cups of coffee and no cake.

(2, 4): They can buy 2 cups of coffee and 4 slices of cake.

By connecting these points, we get a straight line that represents their budget constraint.

c) In this case, the slope of the budget constraint is -1/2. This means that for every additional cup of coffee they buy, they have to give up 1/2 slice of cake to stay within their budget. The negative sign indicates that the two goods are substitutes – as they consume more coffee, they have to reduce their consumption of cake.

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Answer:

1/y^2

Step-by-step explanation:

y^8/y^10 = 1/y^2 ( y^-2 )

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

\(y=b_1x+b_0\)

There is always one straight line that fits the data more accurately than any other, in the sense of minimizing the total of the squared errors, given any set of integers in pairs (apart from the case when all the x-values are the same). The least squares regression line is what it is known as. Additionally, its slope and y-intercept have formulae.

Given a collection of pairs (x,y) of numbers, there is a line \(y=b_1x+b_0\) that best fits the data in the sense of the least squares regression line, its slope is b1 and the y-intercept is b0.

\(b_1=\frac{SS_{xy}}{SS{_xx}}}\\\\and\\\\b_0=y-b_1x\\\\SS_{xx}=\sumx^2-1/n[\sum x]^2\\\\SS_{xy}=\sum{xy}-1/n(\sum x)(\sum y)\)

x' is the mean of all the x-values,  y' is the mean of all the y-values, and n is the number of pairs in the data set.

\(y=b_1x+b_0\)

specifying the least squares regression line is called the least squares regression equation.

Example,

Find the least squares regression line for the five-point data set

x = 2  2  6  8  10  

y=  0  1   2  3  3.

compute the table,

x   y     x2         xy

2  0     4           0

2  1      4            2

6   2   36       12

8   3   64        24

10  3   100    30

28  9   208    68   (sum)

\(S_{xx}=208-(1/5)(28)^2=51.2\\\\SS_{xy}=68-(1/5)(28)(9)=17.6\\\\x'=\frac{28}{5}=5.6\\\\y'=1.8\\\\b_1=17.6/51.2=0.34375\\\\b_0=y-b_1(x)=1.8-(0.34375)(5.6)= -0.125\)

The regression line is y=0.34375x-0.125

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Based on the information given, we can assume that when a coin is tossed 50 times, the difference between the number of heads and the number of tails is x. Additionally, we are told that the probability function p(x) is equal to 12.

To understand this better, we need to consider the probability of getting different values of x.

For example, if we get 25 heads and 25 tails, then x is equal to 0. If we get 30 heads and 20 tails, then x is equal to 10.

If we get 20 heads and 30 tails, then x is equal to -10.

Since we are told that p(x) is equal to 12, we can assume that the probability of getting any value of x is 12%. This means that the probability of getting x = 0, x = 10, or x = -10 is all 12%.

To find out the actual number of times we can expect to get each value of x, we need to use the binomial distribution formula.

This formula takes into account the number of trials (in this case, 50 coin tosses), the probability of success (getting heads), and the value of x.

Overall, the information given tells us that we can expect to get a difference of 10 more heads than tails or 10 more tails than heads about 12% of the time when tossing a coin 50 times.

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Answer:

yes

Step-by-step explanation:

34.95 + 15.75(4)

34.95 + 63 = 97.95

The mass of the meter stick can be determined by considering the torques acting on it. The mass of the meter stick is 1 kg.

To determine the mass of the meter stick, we need to analyze the torques acting on it. Torque is the rotational equivalent of force and depends on both the magnitude of the force and the distance from the pivot point (fulcrum). In this case, the 1 kg mass suspended at the 0 cm end creates a downward force due to gravity.

For the meter stick to be in equilibrium, the torques on both sides of the fulcrum must balance each other. Since the mass at the 0 cm end creates a clockwise torque, the meter stick must have a counterclockwise torque to balance it. The torque produced by a force is given by the equation torque = force * distance.

Since the meter stick is in equilibrium, the torques must be equal. The force due to gravity on the 1 kg mass is 9.8 N. The distance from the fulcrum to the 1 kg mass is 25 cm. Therefore, to balance the torque, the counterclockwise torque produced by the meter stick must be 9.8 N * 25 cm.

To achieve this balance, the mass of the meter stick must be such that its own weight creates an equal and opposite torque. Since the torque is directly proportional to the mass, the mass of the meter stick should be equal to 1 kg.

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Step-by-step explanation:

the slope (m) of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

so, going from (-8, 19) to (4, -2)

x changes by +12 (from -8 to 4).

y changes by -21 (from 19 to -2).

the slope (m) is therefore

-21/+12 = -7/4

and by using (4, -2) as the point, we get

-2 = -7/4 × 4 + b = -7 + b

5 = b

and the full equation is

y = (-7/4)x + 5

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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It take 10.374 days for the sample to be 15% of the initial amount

Radioactivity decay half life formula:

                                                    N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                     N = Quantity remaining

                     \(t_{1/2}\) = half life

                     t = time elapsed

                    \(N_{0}\) = initial amount

given,

        Half-life of radon-222 is 3.8 days

                        \(t_{1/2}\) = 3.8 days

        Initial amount of sample = 34 gm

                      15 % of 34 gm = 15 x 34 /100

                                 =  5.1 gm

               Quantity remaining = 5.1 gm

                           = 5.1 gm

                  Using the above formula

                                                          N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                        5.1 = 34x \(0.5^{t/3.8}\)

                       \(0.5^{t/3.8}\) = 5.1/34

                         \(0.5^{t/3.8}\) = 0.15

                     taking ln both side

                       ln( \(0.5^{t/3.8}\)  ) = ln (0.15 )

                     t/3.8  ln (0.5) = ln (0.15)

                          t/3.8  = ln (0.15) /  ln (0.5)

                                    = 2.73

                          t = 3.8 x 2.73 days

                              = 10.374 days

It take 10.374 days for the sample to be 15% of the initial amount.

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Answer:

210 days

Step-by-step explanation:

7 x 30 = 210 days

Answer:

210

Step-by-step explanation:

A Friday occurs every 7 days.

A new moon occurs (approximately) every 30 days.

We need the smallest number that is a multiple of both 7 and 30.

We need the least common multiple (LCM) of 7 and 30.

This is the same as finding the least common denominator for two fractions that have denominators 7 and 30.

First, we find the prime factorizations of the two numbers.

7 = 7

30 = 2 × 3 × 5

The LCM is the product of common and not common factors with the larger exponent.

LCM = 2 × 3 × 5 × 7 = 210

Answer: 210

P.S. This is the correct answer for this problem, but the problem is stated incorrectly since a new moon occurs approximately every 29.5 days, so in reality, the true answer is not 210 days.

Responder:

1/15

Explicación paso a paso:

Dado que :

Número bolas verdes = 3

Número de bolas rojas = 5

Número de bolas azules = 2

Dibujo sin reemplazo; probabilidad de que el primero sea azul, el segundo sea verde

Probabilidad = resultado requerido / Total de resultados posibles

Resultados posibles totales = 3 + 5 + 2 = 10

P (1er azul) = número de azules / 10

P (1er azul) = 2/10 = 1/5

Sin reemplazo :

Total restante = 10 - 1 = 9

P (segundo verde) = número de verdes / 9 = 3/9

Probabilidad del primer azul y del segundo verde:

1/5 * 3/9 = 3/45 = 1/15

The probability that the first is blue and the second is green is 1/15

Probability is the likelihood or chance that an event will occur.

If a box contains 3 green balls, 5 red balls and 2 blue balls, the total number of balls is 10balls

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Answer:

true

Step-by-step explanation: