Jumbled words in math REAL LAQUEIT

The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

What is a normal distribution?

A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

Hence, the shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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Answer:

-2asmall2 + 4a - 8

Step-by-step explanation:

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

Step-by-step explanation:

= 1/2 ÷ 2/5

= 1/2 × 5/2

= 5/4

Answer:

\( \sf 1 \frac{1}{4} \)

Step-by-step explanation:

\( \sf = \frac{1}{2} \div \frac{2}{5} \)

\( \sf = \frac{1}{2} \times \frac{5}{2} \)

\( \sf = \frac{1 \times 5}{2 \times 2} \)

\( \sf = \frac{5}{4} \)

\( \sf = 1 \frac{1}{4} \)

Answer:

169/24 or 7 1/24

Step-by-step explanation:

Answer:

this question cannot be solved

Answer:

183

Step-by-step explanation:

Sub the values into the expression

-(-3)² - (-3)(8²)

-9 - (-192)

-9 + 192

183

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Answer:

\(2x + 18 = 15x + 33 - 8x \\ 2x + 18 = 7x + 33 \\ 2x - 7x = 33 - 18 \\ - 5x = 15 \\ x = - 3\)

(a) is the correct answer.

One common mistake that many managers make when using a causal forecasting model such as linear and multiple regression is to assume that the correlation of variables proves that one variable has caused another variable. Option (a) is the correct answer.Linear regression, also known as simple regression, is a forecasting technique that analyzes the relationship between an independent variable and a dependent variable. Multiple regression forecasting includes the use of many independent variables. The focus of regression analysis is to make predictions or decisions based on the results of the regression model.The dependent variable is the variable that is being forecasted or analyzed in regression analysis. It is referred to as the predicted or outcome variable. The independent variable is the variable that is believed to be responsible for the dependent variable's variation. It is also referred to as the explanatory variable.In regression analysis, correlation does not equate to causation. Managers should understand that the correlation between two variables does not imply that one variable caused the other. There might be a third variable that is causing both variables to vary. As a result, managers should be cautious when interpreting regression results because correlation does not equate to causation. Correlation can demonstrate the relationship between two variables, but it does not indicate causation.

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Hope you could get an idea from here.

Doubt clarification - use comment section.

The equation \(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\) has been proved to be true

The equation is given as:

\(\frac pq = \frac qr\)

Cross multiply

\(pr = q^2\)

Rewrite as:

\(q^2 = pr\)

Also, we have:

\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\)

Substitute \(q^2 = pr\)

\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3\)

Expand

\(p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3\)

Simplify

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3\)

Rewrite as:

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3\)

Substitute \(pr = q^2\)

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3\)

\(p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3\)

Divide q^6 by q^3

\(p3+q3+r3=r^3 +q^3 + p^3\)

Rewrite the equation as:

\(p3+q3+r3=p^3 +q^3 + r^3\)

Hence, the equation has been proved

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 74/5 milliliters of sand accumulate in the bag from time t=0 to time t=2.

Given that:

The rate at which sand is poured is r(t)

The function r(t) is defined as;

r(t) = 15t -\(2t^2\)

The accumulation in the bag from time t=0 to time t=2 is calculated as:

 r = \(\int_0^2 ( 15t -2t^2) dt\)

Using the limits:

    =\([\dfrac{15t^2}{2} - \dfrac{2t^3}{3}]_0^2\)

 =\(\dfrac{15(2) ^2}{2} - \dfrac{2(2)^3}{3} - (0-0)\)

\(30 - \dfrac{16}{3}\)

= \(\dfrac{74}{3}\)

  Thus, \(\dfrac{74}{3}\) milliliters of sand accumulate in the bag from time t=0 to time t=2.

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the is cStep-by-step explanation:

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

Step-by-step explanation:

This models the standard form of an exponential equation:

\(y=a(b)^x\), where a is the intial value and b is the growth rate. The number in our function that holds position a is 1200. So the initial population is 1200.

The conditional probability mass function P(X=k∣X+Y=m)= P(X=k, Y=m-k) / P(X+Y=m)

To find the conditional probability mass function P(X=k∣X+Y=m) for independent Poisson random variables X and Y, follow these steps:

1. Write down the joint probability mass function of X and Y:

P(X=k, Y=n)

= P(X=k) * P(Y=n)  since X and Y are independent.
2. Express P(X=k) and P(Y=n) using the Poisson probability mass function:

P(X=k) = (e^(-λx) * λx^k) / k! and P(Y=n) = (e^(-λy) * λy^n) / n!

3. Plug these expressions into the joint probability mass function:

P(X=k, Y=n)

= [(e^(-λx) * λx^k) / k!] * [(e^(-λy) * λy^n) / n!]

4. Write down the marginal probability mass function for

X+Y: P(X+Y=m)

= Σ [P(X=k, Y=m-k)]   for k=0 to m, where the summation is over all possible values of k.

5. Calculate the conditional probability mass function P(X=k∣X+Y=m) by dividing the joint probability mass function by the marginal probability mass function:

P(X=k∣X+Y=m) = P(X=k, Y=m-k) / P(X+Y=m)

In summary, the conditional probability mass function P(X=k∣X+Y=m) for independent Poisson random variables X and Y can be found using the joint probability mass function, the Poisson probability mass function, and the marginal probability mass function.

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Answer:

33.9

Step-by-step explanation:

Lilly can read 33.9 pages in 0.75 hours

Answer:  The correct answers are: 6) x =7 and y=3  AND 7) x=1 and y=−2

Step-by-step explanation:

QUESTION 6:

Rewrite equations

y=x+4

3x+2y=27

Solve x=y+4 for x

x=y+4

Substitute y+4 for x in 3x+2y=27

3x+2y=27

3(y+4)+2y=27

Simplify both sides of the equation

5y+12=27

Add -12 to both sides

5y+12+−12=27+−12

5y=15

Divide both sides by 5

5y/5=15/5

y=3

Substitute y for 3 to solve for x:

x=3+4

x =7 and y=3

QUESTION 7:

Rewrite equations

3x+4y=−5

y=x−3

Substitute y=x−3 for x in 3x+4y=−5

3x+4(x−3)=−5

3x+4x-12=-5

Add 12 to both sides

7x=-5+12

7x=7

Divide by 7 into both sides

x=1

Substitute x for 1 to solve for y:

y=x−3

1=y+3

Subtract 3 from both sides

y=-2

x=1 and y=−2

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Answer:

Exponential

Step-by-step explanation:

The rate of change is exponential.

Answer:

the answer is 6/7.

you're welcome.

The solution is, the factorized form of  of the expression (x² + 10x + 16) is (x+2)(x+8).

Here, we have,

given that,

Factor of the expression

(x² + 10x + 16)

now, we get,

Let's start out by finding 2 factors of 16 that add up to 10. Since 16 is positive and 10 is positive, both factors will be positive.

Factors of 16: 1,2,4,4,8,16.

2+8=10

Our 2 factors are 2 and 8.

Now convert into factored form:

(x+2)(x+8)

i.e. (x² + 10x + 16)

=(x² + 8x + 2x + 16)

= (x+2)(x+8)

Hence, The solution is, the factorized form of the expression

(x² + 10x + 16) is (x+2)(x+8).

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Answer:

\(y - 3 = - 4(x + 2)\)

The strategy defined in part a is superior to go for 1 point after each touchdown for p > 0.362. Hence, the required answer is 0.362.

a. Set of States for the situation in which Temple's coach attempts a 2-point conversion after the first touchdown will be:{-2,-1,0,1,2, W, L} where L stands for loss and W stands for win.

-2 stands for down by 16 points-1 stands for down by 15 points0 stands for down by 14 points1 stands for down by 13 points2 stands for down by 12 points

W stands for a win

L stands for a loss tree Diagram for the given situation and can be shown as Tree diagram for Temple Wildcats' 2-point conversion

b. Transition Probability matrix for this decision problem in part (a) is shown below:

$$\begin{array}{|c|c|c|c|c|c|} \hline From/To & -14 & -8 & -6 & 0 & WIN & LOSE\\ \hline -2 & 0 & 0 & 0 & 1-p & 0 & 0\\ \hline -1 & 0 & 0 & 0 & 1-p & 0 & 0\\ \hline 0 & 0 & 0 & 0 & 1-p & 0 & 0\\ \hline 1 & 0 & 0 & p & 1-p & 0 & 0\\ \hline 2 & 0 & p & 1-p & 1-p & 0 & 0\\ \hline WIN & 0 & 0 & 0 & 0 & 1 & 0\\ \hline LOSE & 0 & 0 & 0 & 0 & 0 & 1\\ \hline \end{array}c.

As per the given situation, Temple needs to score two touchdowns to win the game, and coach must decide whether to attempt a 1-point or 2-point conversion after each touchdown.

If the coach goes for a 1-point conversion after each touchdown, the game is assured of going to overtime and Temple will win with a probability of 0.53.

Let us calculate the probability of winning if the coach goes for a 2-point conversion after the first touchdown.

If Temple attempts a 2-point conversion after the first touchdown, they can win if they score 2 points after the second touchdown or if they score 1 point after the second touchdown and win the game in overtime.

So, the probability of winning, in this case, can be calculated as: P(win) = P(2-point conversion is successful and 1-point conversion is successful in next touchdown) + P(2-point conversion is successful and Temple wins in overtime)P(win) = p * (1-p) + p * 0.53P(win) = p - p² + 0.53p

Now, let us calculate the probability of winning if Temple goes for a 1-point conversion after each touchdown.P(win) = 0.53

Therefore, the strategy defined in part a is superior to go for 1 point after each touchdown for p > 0.362. Hence, the required answer is 0.362.

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Answer: A = 6.5

B = 10.

Step-by-step explanation:

First, remember that when we have a triangle of height H and base B, the area of the triangle is:

Area = B*H/2.

A:

First, count the complete squares:

We have 6 complete squares.

Now the diagonal part:

The diagonal connects a section of 1 by 3 squares, and the shaded area is a right triangle

Then the shaded area will be half of 1 by 3.

this is 1.5 squares.

The total area of A is:

6 + 1.5 = 7.5 squares.

B:

This is more complicated.

At the beginning, we have 4 completed squares in the top right.

At the left, we have a 2 by 4 = 8 square region, where the shaded part is only a triangle rectangle.

Then the area of this triangle is half of 8 squares:

8/2 = 4 squares.

Last, at the bottom, we have two times a 2 by 1 = 2 square region, where the shaded part is a triangle rectangle.

Then the area of each triangle is 2/2 = 1 square.

And we have two of them, so there are 2 squares here.

Then the total area is:

A = 4 + 4 + 1 + 1 = 10 squares.

Each small square In the graph paper represents 1 square unit

Answer:

-80

Step-by-step explanation:

you pass the 25 to the right side adding and the the 1/5 multiplying by -5 to the right side

Answer:

1) No it repeating

2)No it doesn't terminate nor repeat

3) yes this terminates

4) no its repeating

Step-by-step explanation:

The frequency table that would show the data on the Record High temperatures in the state is:

Temperature Range (°F) Frequency

100 - 104                                         2

105 - 109                                  7

110 - 114                                  12

115 - 119                                  12

120 - 124                                  5

125 - 129                                  1

To create a frequency table, first identify the range of temperatures, which is from 100 to 134 degrees Fahrenheit. Then, choose intervals of 5 degrees and counted how many temperatures fell within each interval. For example, there were 3 temperatures between 100-104, 6 between 105-109, and so on.

To construct a histogram, we can use the temperature ranges on the x-axis and the frequency on the y-axis. Each bar will represent the number of states that had a record high temperature within that range.

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