Prove the following statement.
The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integers r and s so that m can be expressed in terms of r and n can be expressed in terms of s as follows.
m =
n =

Answer:

it don't make sence where is the table

Step-by-step explanation:

Answer:

59.55

Step-by-step explanation:

27.30+0.30= 27.60

27.60+31.95=59.55

Answer:

y+1=-3(x+2)

Step-by-step explanation:

point-slope form is the formula y-y1=m(x-x1), where (x1, y1) is a point and m is the slope

we are given a point (-2, -1) and a slope of -3

all we really need to do is substitute the given into the formula

remember: since the formula gives subtraction, we're going to be subtracting, even though we have negative numbers

substitute -2 as x, -1 as y and -3 as m

y--1=-3(x--2)

we can simplify this equation:

y+1=-3(x+2)

Hope this helps!

The number of hamburgers sold on Friday was 442.

Let us form the linear equation to find the number of burgers;

Let the cheeseburger be represented by x.

Since there were 67 more cheeseburgers sold than hamburgers. This means that hamburgers will be:

The number of hamburgers = x + 67.

Since the local hamburger shop sold a combined total of 817 hamburgers and cheeseburgers. This will be:

x + x + 67 = 817

2x + 67= 817

2x = 817 - 67

2x = 750

x = 750 / 2

x = 375

So, 375 cheeseburgers were sold on Friday.

Therefore, the number of hamburgers sold will be:

= 817 - 375

= 442

Thus, the number of hamburgers sold on Friday was 442.

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The value of the expression \((01111∧10101)∨01000\)is 01101.

To calculate the value of the expression (01111∧10101)∨01000, we need to evaluate each operation separately.

First, let's perform the bitwise AND operation (∧) between the numbers 01111 and 10101:

  \(01111∧ 10101--------- 00101\\\)
The result of the bitwise AND operation is 00101.

Next, let's perform the bitwise OR operation (∨) between the result of the previous operation (00101) and the number 01000:

  \(00101∨ 01000--------- 01101\)

The result of the bitwise OR operation is 01101.

Therefore, the value of the expression (\(01111∧10101)∨01000\) is 01101.

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The value of (01111 ∧ 10101) ∨ 01000 is 01101, which represents the decimal number 13.

The given expression is (01111 ∧ 10101) ∨ 01000. Here, ∧ represents the logical AND operator and ∨ represents the logical OR operator.

The value of the given expression is 01101 in binary, which is equivalent to 13 in decimal.

Explanation: Main part: The value of (01111 ∧ 10101) ∨ 01000 is 01101

Explanation: Let's break down the given expression into smaller parts and evaluate them one by one. First, we need to evaluate the expression (01111 ∧ 10101). To do this, we perform a bitwise AND operation between the binary numbers 01111 and 10101 as follows: 01111 (in binary)10101 (in binary)------00101 (in binary). Here, we get the binary number 00101 as the result. This represents the decimal number 5. Now, we need to evaluate the expression (5 ∨ 01000).

To do this, we perform a bitwise OR operation between the decimal number 5 and the binary number 01000 as follows: 5 (in decimal)01000 (in binary)------01101 (in binary)

Here, we get the binary number 01101 as the result. This represents the decimal number 13.Therefore, the value of the given expression is 01101 in binary, which is equivalent to 13 in decimal.

Conclusion: The value of (01111 ∧ 10101) ∨ 01000 is 01101, which represents the decimal number 13.

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Answer:

X=50

Step-by-step explanation:

If you algebraically plug in 50 you come to an answer of X=50

Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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Option a is correct. we are given that Jones invests only a part of his wealth into a risky asset that has a positive return of 10% with probability π and has a negative return of −4% with probability 1−π.

The risk-free rate is 1%. Jones' utility function is u=ln(w), where w is his wealth.

Let us solve the problem: Let x be the fraction of Jones’ wealth that he invests in the risky asset. Thus, (1 - x) is the fraction he invests in the risk-free asset.:

\(U = x * ln(1 + 10%) + (1 - x) * ln(1 + 1%) = x * ln(1.1) + (1 - x) * ln(1.01)\)

Let EV be the expected value of his investment. Thus, we have:
\(E(V) = x * 10% + (1 - x) * 1% = 9% * x + 1%\)

Let us assume that Jones invests enough of his wealth in the risky asset so as to make it the optimal portfolio. This means that the expected utility from the investment in the risky asset equals the expected utility from the risk-free asset. Mathematically,
\(x * ln(1.1) + (1 - x) * ln(1.01) = ln(w)\)

On solving this equation, we get x =\((ln(w) - ln(1.01)) / (ln(1.1) - ln(1.01)) = ln(w) - ln(1.01) / ln(1.1) - ln(1.01)\)
Let us assume that Jones invests at least part of his wealth in the risky asset. Thus,\(0 ≤ x ≤ 1\). This means that \(0 ≤ π ≤ 1\).

The correct option is a.\(0.2857 ≤ π ≤ 0.358\).

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The income you need to afford a $425,000 house is largely dependent on your debt-to-income ratio, credit score, and down payment. However, a general rule of thumb is to have an annual income that is at least three times the purchase price of the home, which in this case would be $1,275,000.

To more accurately determine the income needed to afford a $425,000 house, consider factors such as the interest rate on the mortgage, property taxes, homeowners insurance, and any homeowner association fees.

These additional expenses can significantly impact your monthly mortgage payment and thus your income requirements.
It's important to keep in mind that lenders have varying criteria when determining mortgage eligibility and income requirements, so it's best to speak with a mortgage professional to get a more accurate estimate based on your individual circumstances.

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a basis for the eigenspace corresponding to the eigenvalue λ = 1 is { [4, -2] }, and a basis for the eigenspace corresponding to the eigenvalue λ = 2 is { [0, 0] }.

To find a basis for the eigenspace corresponding to each listed eigenvalue of matrix A, we need to solve the system (A - λI)v = 0, where A is the given matrix, λ is the eigenvalue, I is the identity matrix, and v is a non-zero vector in the eigenspace.

Given the matrix A = [[11, 2], [1, 2]], we will find the eigenspaces corresponding to the eigenvalues λ = 1 and λ = 2.

1) For λ = 1:

We need to solve the equation (A - λI)v = 0.

Substituting λ = 1 and I as the 2x2 identity matrix, we have:

(A - I)v = 0

[[11, 2], [1, 2]] - [[1, 0], [0, 1]] = [[10, 2], [1, 1]]v = 0

To find the basis for the eigenspace corresponding to λ = 1, we need to solve the homogeneous system of equations:

10v₁ + 2v₂ = 0

v₁ + v₂ = 0

One solution to this system is v = [2, -1]. However, since we want a basis (more than one vector), we can multiply this solution by any non-zero scalar. Let's multiply by 2:

v₁ = 4, v₂ = -2

Therefore, a basis for the eigenspace corresponding to λ = 1 is { [4, -2] }.

2) For λ = 2:

We need to solve the equation (A - λI)v = 0.

Substituting λ = 2 and I as the 2x2 identity matrix, we have:

(A - I)v = 0

[[11, 2], [1, 2]] - [[2, 0], [0, 2]] = [[9, 2], [1, 0]]v = 0

To find the basis for the eigenspace corresponding to λ = 2, we need to solve the homogeneous system of equations:

9v₁ + 2v₂ = 0

v₁ = 0

From the first equation, we can see that v₁ = 0. Substituting this into the second equation, we have v₂ = 0 as well.

Therefore, a basis for the eigenspace corresponding to λ = 2 is { [0, 0] }.

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Answer:

3.75

Step-by-step explanation:

Follow PEMDAS

P = parentheses so first it will turn to 30 divided by 3 times 5

E = exponents we dont have any

M = multiplication 30 divided by 8

D = division = 3.75

Using simpson's rule, the arc length of the curve y = x sin x is 1.999227549442 approx 1.999228

Simpson's Rule states that, if we want to approximate a definite integral, we can split the interval of integration into n subintervals of equal width and apply Simpson's Rule to each subinterval, using the following formula: ∫abf(x)dx≈(b−a)6n[f(a)+4f(a+h)+2f(a+2h)+4f(a+3h)+2f(a+4h)+...+2f(b−2h)+4f(b−h)+f(b)] where h=(b−a)/n denotes the subinterval width. With n = 10, estimate the arc length of the curve y = x sin x:

Simpson's Rule says that ∫abf(x)dx≈(b−a)6n[f(a)+4f(a+h)+2f(a+2h)+4f(a+3h)+2f(a+4h)+...+2f(b−2h)+4f(b−h)+f(b)]where h=(b−a)/n is the subinterval width. In this example, we havea=0, b=π, andf(x)=|y′(x)|=|sinx+xcosx|.Thus, we have h=π/10=0.314159,f(0)=|sin0+0cos0|=0,f(π)=|sinπ+πcosπ|=π, andf(xi)=|sinxi+xicosxi|for i=1,...,9. Substituting the given values in the formula, we get ∫0π|y′(x)|dx≈(π−0)6·10[0+4·(0.314159)(0.5)+2·(0.628319)(0.5)+4·(0.942478)(0.5)+...+2·(2.79966)(0.5)+4·(3.11382)(0.5)+π] = 1.999227549442approx1.999228.

Comparing the answer with the value of the integral produced by your calculator.

The exact value of the integral produced by the calculator is 1.999227550934, which is correct to nine decimal places. The error in the approximation is less than 0.000001, which is negligible, so the answer is correct.

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If the stock sells for $58 a share the Dragon company's cost of equity will be 8.97%.

The cost of equity is the return that investors require from the stock of the company. We have to use the DDM (Dividend discount model) here,

The formula for the DDM is,

P₀ = D₁/(ke - g), current stock price is P₀, the expected dividend per share in the next period is D₁, required rate of return (cost of equity) is ke, and expected growth rate of dividends  g.

In this case, we have,

D₁ = D₀ x (1 + g)

= $2.85 x (1 + 0.036)

= $2.95 (expected dividend per share in the next period)

P₀ = $58 (current stock price)

g = 0.036 (expected growth rate of dividends)

Substituting these values into the DDM formula, we get,

$58 = $2.95 / (ke - 0.036)

Solving for ke, we get,

ke = ($2.95 / $58) + 0.036

= 0.0897 or 8.97%

Therefore, Dragon Company's cost of equity is 8.97%.

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Answer:

ITS B !!!!!!!!!!!!!

Step-by-step explanation:

The equivalent expression is -9/4 ÷ (-2/3).

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Negative 2 and one-fourth divided by negative two-thirds.

This can be written as,

-2(1/4) ÷ (-2/3)

= -9/4 ÷ (-2/3)

= -9/4 x -3/2

= 27/8 _____(A)

Now,

StartFraction 9 over 4 EndFraction divided by three-halves

This can be written as,

9/4 ÷ 3(1/2)

= 9/4 x 2/7

= 18/28 ______(1)

Negative StartFraction 9 over 4 EndFraction divided by (negative two-thirds)

This can be written as,

-9/4 ÷ (-2/3)

= -9/4 x -3/2

= 27/8 ______(2)

Negative StartFraction 9 over 4 EndFraction divided by two-thirds

This can be written as,

-9/4 ÷ 2/3

= -9/4 x 3/2

= -27/8

StartFraction 9 over 4 EndFraction divided by (negative three-halves)

This can be written as,

9/4 ÷ -3(1/2)

= 9/4 x 2/7

= 18/28

Thus,

From (A) and (2),

-9/4 ÷ (-2/3) is the equivalent expression.

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Answer:

g = \(\frac{4}{3}\)

Step-by-step explanation:

4 - \(\frac{1}{12}\) g - 2 = \(\frac{3}{2}\) g + 1 - \(\frac{5}{6}\) g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = \(\frac{-12}{-9}\) = \(\frac{12}{9}\) = \(\frac{4}{3}\)

Step-by-step explanation:

Convert the given value in cm into feet and inches.

Use the unit rates:

Convert:

or

Answer:

90:60

Step-by-step explanation:

3x30= 90

2x30= 60

Answer:

4.45

Step-by-step explanation:

1,99   1,99  3.2   4,36  4,54 4,78  4,8  4,83

                          (2 numbers remain as medium)

4,36

4,54

8,90/2=     4.45

i hope i have help you :)

Answer:

3

Step-by-step explanation:

\(5.67 \times {10}^{2} \\ = 5.67 \times 100 \\ = 567\)

Hence, the given number has 3 significant figures.

The type of error that could have occurred in this scenario is a Type II error. A Type II error occurs when the null hypothesis is not rejected, even though it is false.

In this case, the null hypothesis is that the proportion of defective bulbs in the shipment is greater than or equal to 5%. By not rejecting this null hypothesis, the company is accepting the possibility that the shipment has a high proportion of defective bulbs, when in reality it does not. This can lead to significant costs for the company, such as the cost of returning the shipment or the cost of replacing defective bulbs in the future.

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The inverse of p v q →  p ∧ q is ~p v -q →-p ∧ ~q. hence option c is correct

What is mean by Inverse?

Opposite in order, nature or effect is called an Inverse.

Given that;

The statement is;

p → q

Now,

The inverse of p → q is written as;

~p → ~q

Thus, The inverse of p → q is ~p → ~q.

What is inverse in simple words?

something of a contrary nature or quality : opposite, reverse. : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem. the inverse of "if A then B" is "if not-A then not-B"

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Answer:

Y-intercept (0,4)

X-intercept (0,2)

Step-by-step explanation:

It the point where the line crosses the y or x intercept

Answer:

im not sure but i think its a bargraph if the answer is coreect please tell

Answer:

Step-by-step explanation:

let do lcm of the three measures

LCM of 7,3,12 m = 84

therefore,84 is the longest which can be used to measure 7,3,12 m exactly

15% of 190 = 28.5

190-28.5=161.5

A: 28.5

B: 161.5

In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

Total 21 teams completed the escape room this week.

An employee records the number of minutes it takes each team to complete the escape room this week the dot plot shows the data.

To determine how many teams completed the escape room this week we use the dot plot.

From the dot plot we can see that at 41 min have one found one employee escape from room.

At 44 min have one found 3 employee escape from room.

At 45 min have one found 2 employee escape from room.

At 46 min have one found 4 employee escape from room.

At 47 min have one found 5 employee escape from room.

At 48 min have one found 3 employee escape from room.

At 49 min have one found 2 employee escape from room.

At 50 min have one found one employee escape from room.

Team completed the escape room this week = 1 + 3 + 2 + 4 + 5 + 3 + 2 + 1

Team completed the escape room this week = 21

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Answer:21 i got it correct

Step-by-step explanation:

Hello,

a) photo attached

b) When y = 1, x ≈ 0.5

Verification through calculation :

We have :

y = 4x - 1

⇔ 1 = 4x - 1

⇔ 4x = 2

⇔ x = 2/4 = 0.5

This is just !

:-)

To solve the initial value problem, we need to first find the general solution of the differential equation Dy/dx = 5x^3. Since dy/dx is a function of x,

the general solution of the differential equation is simply the general antiderivative (also called the indefinite integral) of the right hand side.

The antiderivative of x raised to a numerical power not equal to negative one is given by the formula:

∫ x^n dx = (x^(n+1))/(n+1) + C,

where C is the constant of integration. Applying this formula to our given differential equation, we get:

∫ Dy/dx dx = ∫ 5x^3 dx

Integrating both sides with respect to x, we get:

y = (5/4) x^4 + C

Now we use the given initial condition y(0) = 6 to find the specific value of C.

Substituting x=0 and y=6 in the general solution, we get:

6 = (5/4) (0)^4 + C

Simplifying, we get:

C = 6

Thus, the particular solution of the initial value problem is:

y = (5/4) x^4 + 6

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