A die is rolled twice.
What is the probability of rolling a 3 followed by a 2?

Answer:

Jordin weighs 96 pounds

Step-by-step explanation:

The Mean Value of a Data Set

The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:

\(\displaystyle \bar x=\frac{\sum x_i}{n}\)

Where xi is the value of each data and n is the total number of values.

We are given the average weight of n=5 marathon runners:

\(\bar x=92\)

Multiplying the formula by n and expanding the sum:

\(n\bar x=\sum x_i=x_1+x_2+x_3+x_4+x_5\)

We are given the weighs of four of the runners:

\(5*92=89+95+90+90+x_5\)

\(460=364+x_5\)

Solving for x5:

\(x_5 = 460-364=96\)

Jordin weighs 96 pounds

a) The pattern we noticed in the sequence is; A geometric sequence

b) The value of 3⁻¹ which is the fourth term is; 1/3

c) The value of 3⁻² which is the fifth term is; 1/9

The general formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

where;

a is first term

r is common ratio

We are given the sequence as;

3², 3¹, 3⁰,____

Thus;

First term a = 9

Common ratio; r = 3/9

r = 1/3

b) Thus; 3⁻¹ will be the 4th term and as such will be;

3⁰ * 1/3 = 1/3

c) Similarly, The fifth term is 3⁻² expressed as;

1/3 * 1/3 = 1/9

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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The value of m =  87 kg

The magnitude of force = 978.87 N

use Newton's second law (F = ma) to determine the mass of the man.

Then Tension force

= 192 kg.wt * 9.81 N/kg

≈ 1883.52 N

Net force = (Mass of lift + Mass of man) * Acceleration

Net force = (98 kg + m) * 1.4 m/s²

Net force = Tension force - Gravitational force

(98 kg + m) * 1.4 m/s²

= 1883.52 N - (98 kg + m) * 9.81 m/s²

Now, we can solve for m:

137.2 kg + 1.4m = 1883.52 N - 960.18 kg - 9.81m

10.61m = 923.34

m ≈ 87 kg

The mass of the man is approximately 87 kg

Force exerted by man = (87 kg * 9.81 m/s²) + (87 kg * 1.4 m/s²)

≈ 857.07 N + 121.8 N

≈ 978.87 N

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Answer: 10 + 10 + 5 + 5 + 20 + 20 + 25 + (25 - 10) = 110

Step-by-step explanation:

I think this is correct

The LU factorization of the given matrix is:

\(L = \(\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]\) and U = \(\left[\begin{array}{rrr}3 & -1 & 2 \\ 0 & -1 & 12 \\ 0 & 0 & -4\end{array}\right]\).\)

To find the LU factorization of the matrix, we aim to decompose it into the product of a lower triangular matrix L and an upper triangular matrix U.

We start by performing row operations to eliminate the coefficients below the main diagonal. First, we divide the second row by 3 and add it to the first row. Then, we multiply the third row by 3 and subtract 3 times the first row from it.

After performing these row operations, we obtain the following matrix:

\(\(\left[\begin{array}{rrr}3 & -1 & 2 \\ 0 & -1 & 12 \\ 0 & 0 & -4\end{array}\right]\)\)

The upper triangular matrix U is now obtained. The entries below the main diagonal are all zeros.

Next, we construct the lower triangular matrix L. The entries of L are determined by the row operations performed. The non-zero entries in the first column of U (excluding the pivot element) are divided by the pivot element and placed in the corresponding position in L.

The final result is:

\(L = \(\left[\begin{array}{rrr}1 & 0 & 0 \\ -1 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]\) and U = \(\left[\begin{array}{rrr}3 & -1 & 2 \\ 0 & -1 & 12 \\ 0 & 0 & -4\end{array}\right]\).\)

Therefore, the LU factorization of the given matrix is obtained.

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Find an LU factorization of the matrix n show workings

please

\(\( \left[\begin{array}{rrr}3 & -1 & 2 \\ -3 & -2 & 10 \\ 9 & -5 & 6\end{array}\right] \)\)

Answer:

c

Step-by-step explanation:

using the continously compounded formula, let a be unknown, p= 530, r be 0.05 and t be 12.

the equation would then be a=530e to the (0.05*12)th power, so that's why it's c

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

Continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The continuous compound interest formula is \(P(t)=P_0e^{rt}\).

Where, P(t)=value at time t, \(P_0\) =original principal sum, r=nominal annual interest rate and t= length of time the interest is applied

Now, \(P(12)=530\times e^{0.05\times12}\)

⇒ \(P(12)=530\times e^{0.6}\)

⇒ P(12)= 530×1.822

⇒ P(12)= $965.66

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

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The Slope-Intercept form of the equation of a line, is:

Where "m" is the slope of the line and "b" is the y-intercept.

According to the information given in the exercise, you know that The older model submarine can dive down 3 feet per minute. Then, you can identify that:

Let be "y" the location of the submarine (in feet) and "x" the number of minutes.

You can identify that the line passes through this point:

Knowing the slope of the coordinates of a point on the line, you can find "b":

Therefore, knowing "b" and "m", you get that the equation of the line in Slope-Intercept form that models this situation, is:

The value of 1 cm : 1 km is 6.66666667e-7

The ratio expression is given as:

1 cm : 15 km

Convert km to cm

So, we have

1 cm : 1 km = 1 cm : 1500000 cm

Express as quotient

1 cm : 1 km = 1 cm/1500000 cm

Evaluate the quotient

1 cm : 1 km = 6.66666667e-7

Hence, the value of 1 cm : 1 km is 6.66666667e-7

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Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

Answer:

a.4

Step-by-step explanation:

Because 10 is greater than 6 so, it turns into a positive instead of a negative. and of course 10 + 6 = 4

Answer: no it’s not

Step-by-step explanation:

it’s a square

The y(t) = e^-t + e^5t + 3t^3 is also a solution to the given differential equation.

To determine which function is also a solution to the given differential equation, we need to substitute each function into the equation and see if it satisfies the equation. When we substitute y(t) = 3t^3 into the equation, we get g(t) = 0. Now, when we substitute each of the given functions into the equation, we find that only option (c) y(t) = e^-t + e^5t + 3t^3 satisfies the equation.

Therefore, the answer is (c). This is because when we substitute y(t) = e^-t + e^5t + 3t^3 into the differential equation, we get y" – 4y’ - 5y = -16e^-t + 80e^5t, which is equal to g(t).

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If the arithmetic mean of the given measurement is 12, then then the standard deviation is most nearly option (A) 1.45

To find the population standard deviation, we can use the formula:

σ = √( Σ(x - μ)² / N )

where σ is the population standard deviation, x is each observation in the data set, μ is the population mean, and N is the number of observations.

The given data set has 9 observations, and the arithmetic mean is 12. So, we can calculate the sum of squares of deviations from the mean as:

(11-12)² + (11-12)² + (11-12)² + (11-12)² + (12-12)² + (13-12)² + (13-12)² + (14-12)²

= 4 + 4 + 4 + 4 + 0 + 1 + 1 + 4

= 22

Then, we can calculate the population standard deviation as:

σ = √( Σ(x - μ)² / N ) = √(22/9) ≈ 1.45

Therefore, the correct option is (A) 1.45

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Answer:

4

Step-by-step explanation:

The value of x is 10

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

The large triangle is divided into 2 similar triangles

The ratios of corresponding sides are equal

8/12 = x+4/2x+1

=> 8( 2x+1) = 12( x+4 )

=>  16x+8 = 12x+48

=> 16x-12x = 48-8

=> 4x = 40

=> x= 40/4 = 10

The value of x is 10

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C, D, and E are most likely to be right. Its either all of them, one of them, or two of them. A is impossible to use in the equation and if you use b, you get 45.5.

Answer:

I chose 793

you can chose anything from 750-799

Step-by-step explanation:

Those all round to 800

The expected value remains at $15, the variance remains at 0, and the standard.

The multipliers for the results remain the same.

Probability Distribution of the Portfolio Bet: There are a total of 9 sample points, and each sample point has a probability of 1/9.

To construct the probability distribution of the portfolio bet, we first need to define the sample points. Since the portfolio is composed of two independent bets on 3 numbers, let's denote the bets as Bet 1 and Bet 2, respectively.

For Bet 1, let's assume the numbers chosen are 1, 2, and 3. The sample points for Bet 1 would be the three individual numbers: {1}, {2}, and {3}.

For Bet 2, let's assume the numbers chosen are 4, 5, and 6. The sample points for Bet 2 would be: {4}, {5}, and {6}.

Now, let's combine the sample points of both bets to create the sample points for the portfolio bet:

Sample points for the portfolio bet: {1, 4}, {1, 5}, {1, 6}, {2, 4}, {2, 5}, {2, 6}, {3, 4}, {3, 5}, {3, 6}.

(a) Probability Distribution of the Portfolio Bet:

To construct the probability distribution, we need to assign probabilities to each of the sample points. Since each bet is independent, we assume that each number has an equal chance of being chosen.

There are a total of 9 sample points, and each sample point has a probability of 1/9.

The probability distribution of the portfolio bet is as follows:

{1, 4}: 1/9

{1, 5}: 1/9

{1, 6}: 1/9

{2, 4}: 1/9

{2, 5}: 1/9

{2, 6}: 1/9

{3, 4}: 1/9

{3, 5}: 1/9

{3, 6}: 1/9

(b) Expected Value, Variance, and Standard Deviation of the Portfolio Bet:

To calculate the expected value (E), variance (Var), and standard deviation (SD) of the portfolio bet, we need to assign a payoff or outcome for each sample point.

Let's assume the payoff for each winning sample point is $15 (which would include the return of the initial $5 bet).

The expected value (E) is calculated as follows:

E = Σ(P * X),

where P is the probability and X is the payoff. Summing up the products of the probabilities and payoffs for all sample points, we get:

E = (1/9 * $15) + (1/9 * $15) + ... + (1/9 * $15) (9 times) = 9/9 * $15 = $15.

The variance (Var) is calculated as:

\(Var = Σ(P * (X - E)^2).\)

For each sample point, we calculate\((X - E)^2\) and multiply it by the probability. Summing up these values, we get:

\(Var = (1/9 * ($15 - $15)^2) + (1/9 * ($15 - $15)^2)\) + ... + (\(1/9 * ($15 - $15)^2\)) (9 times) = 0.

The standard deviation (SD) is the square root of the variance, so in this case, SD = sqrt(0) = 0.

(c) Multipliers when switching from a $10 single bet to the portfolio bet:

When switching from a single $10 bet to the portfolio bet, the multipliers for the results remain the same. The expected value remains at $15, the variance remains at 0, and the standard.

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Answer:

50

Step-by-step explanation:

20/ 100 x 50

then u will get 10 as the answer

Answer:

h = 10 ft

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh

Here A = 75 and b = 15, thus

\(\frac{1}{2}\) × 15h = 75 ( multiply both sides by 2 to clear the fraction )

15h = 150 ( divide both sides by 15 )

h = 10

Answer:10/60

If need to  simply it is 1/6.

Step-by-step explanation: Mutiply 5/12 by 2/5 .

Answer:

1/2

Step-by-step explanation:

M=11

N=2

11•11=121

2•2=4

121-4=117

Answer:

Step-by-step explanation:

$587.34 x 6.2% = $36.42

$587.34 x 1.45% = $8.52

$36.42 + $8.53 + $164.45 + $76.34 + $50 + $8 + $23 + $8 = $374.73

$587.34 - $374.73 = $212.61

Michael's net pay for this pay period should be $212.63.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's calculate Michael's total deductions first:

Social Security tax = 6.2% of $587.34 = $36.40

Medicare tax = 1.45% of $587.34 = $8.52

Federal withholding tax = $164.45

State withholding tax = $76.34

Retirement insurance contribution = $50.00

Disability insurance fee = $8.00

Medical insurance fee = $23.00

Dental insurance fee = $8.00

Total deductions.

= $36.40 + $8.52 + $164.45 + $76.34 + $50.00 + $8.00 + $23.00 + $8.00

Total deductions = $374.71

Now we can calculate Michael's net pay:

Net pay = Gross pay - Total deductions

Net pay = $587.34 - $374.71

Net pay = $212.63

Therefore,

Michael's net pay for this pay period should be $212.63.

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We determine that approximately 34.23 megabytes have been downloaded out of a total file size of 226 megabytes if the download is 15.1% complete.

In this problem, we are given a file size of 226 megabytes that is being downloaded and we are asked to find the number of megabytes that have been downloaded if the download is 15.1% complete.

To solve the problem, we can use the formula for finding a percentage of a value, which is:

Percentage = (Part / Whole) x 100

Here, we want to find the part (the number of megabytes downloaded) given the percentage (15.1%) and the whole (the total file size of 226 megabytes). Rearranging the formula to solve for the part, we get:

Part = (Percentage / 100) x Whole

Substituting the values given in the problem, we get:

Part = (15.1 / 100) x 226

Simplifying the expression, we get:

Part = 0.151 x 226

Part = 34.226

Therefore, approximately 34.23 megabytes have been downloaded, which is the answer to the problem.

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The orthogonal complement S is the set of all vectors orthogonal to the subspace S in R5 whose third and fourth components are zero. To find S, we need to find vectors such that vu = 0 for all u in S using the dot product. The orthogonal complement S has dimension three and a basis for it is f1, f2, f3, where f1 = (1,-1,0,0,0) f2 = (0,0,1,0,0) f3 = (0,0,0,1,0).

Let's begin by defining the orthogonal complement S⊥, which is the set of all vectors orthogonal to the subspace S in question. The subspace S is defined as the set of all vectors in R5 whose third and fourth components are zero. Let's go through the steps to find S⊥.

Step 1: Determine the dimensions of S The dimension of the subspace S is two. This is because the subspace consists of vectors whose third and fourth components are zero. Therefore, only the first, second, fifth components are nonzero, making up a 3D subspace. Since S is a subspace of R5, the remaining two components can also take any value and thus the dimension of S is 2.

Step 2: Determine a basis for S To determine a basis for S, we can use the fact that the subspace is defined as all vectors whose third and fourth components are zero.

Therefore, a basis for S is given by {e1, e2}, where e1 = (1,0,0,0,0) and e2 = (0,1,0,0,0).

Step 3: Find the orthogonal complement S⊥ To find S⊥, we need to find all vectors orthogonal to S. This means we need to find vectors v such that v⋅u = 0 for all u in S. To do this, we can use the dot product: v⋅u = v1u1 + v2u2 + v3u3 + v4u4 + v5u5= v1u1 + v2u2 + v5u5We want this to be zero for all u in S. This implies:v1 + v2 = 0 andv5 = 0Therefore, S⊥ is given by the set of all vectors in R5 of the form (a,-a,b,c,0), where a, b, and c are arbitrary constants. The orthogonal complement S⊥ has dimension three, and a basis for it is {f1, f2, f3}, where:f1 = (1,-1,0,0,0)f2 = (0,0,1,0,0)f3 = (0,0,0,1,0)The above result gives us a complete characterization of S⊥.

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Answer:

602.88

Step-by-step explanation:

Formula for area is r²

4² is 16

16*3.14 = 50.24

50.24 × 12 = 602.88

Brainliest please?  

Answer:

To find how much peanut butter is in this jar, we use the formula for the volume of a cylinder.

(formula for vol. of cylinder)

V = π\(r^{2}\)h

Where 'π' represents pi(22/7 or 3.14), 'r' represents the radius which is being squared, and lastly 'h' stands for the height.

We are given the dimensions of:

This is all the information we need to fulfill the equation to this formula(volume of cylinder).

Plug in what you know:-

V = π\(r^{2}\)h

(For 'pi' I'll be using 3.14 instead of 22/7)

V = 3.14(4^2) · 12 ← (The symbol ' ^ ' means to the power of.)

V = 3.14(16) · 12

V = 50.24 · 12

V = 602.88, 602.88 centimetres is the volume for this jar.