20 POINTS JUST FOR YOU IF YOU GET IT RIGHT

HELP ME PLEASE

10 points each I WILL GIVE THE BRAINLIEST

(1) Write a paragraph proof for the following conjecture:

Given: m∠ 1 + m∠ 2 = m∠ 4

Prove: m∠3 + m∠1 + m∠2 = 180

(2)Write a paragraph, flowchart or, 2 column proof for the following conjecture:

Given: ∠1≅∠4

Prove: ∠3≅∠2

Answer: The answer is 1/4.

Step-by-step explanation:

Given :

Claudia spends $2.15 day for lunch.

Her cafeteria lunch account has a balance of 48.00 .

To Find :

The maximum number of days, d that she can eat without adding money to her lunch account.

Solution :

Number of days she can eat without adding money in her account is :

\(n = \dfrac{Remaining \ Balance }{2.15}\\\\n = \dfrac{48}{2.15}\\\\n = 22.325\)

But, number of days cannot be in decimal.

Therefore, maximum number of days she can eat without adding money to her lunch is 22 days.

Answer:

397/20

Step-by-step explanation:

i think?

if im wrong im sorry

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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The Gibbs-Duhem equation relates the activity coefficients of the individual components in a mixture. It states that the activity coefficients are not independent of each other but are related by a differential equation.

In the case of a binary mixture (chemical A and chemical B), the Gibbs-Duhem relation can be written as:

x1 * (∂x1/∂lnγ1)T,P = x2 * (∂x2/∂lnγ2)T,P

Here, x1 and x2 represent the mole fractions of chemical A and chemical B, respectively. The activity coefficients for chemical A and chemical B are denoted as γ1 and γ2, respectively.

The equation shows that the change in mole fraction of one component (x1) with respect to the change in the logarithm of its activity coefficient (lnγ1) is proportional to the change in mole fraction of the other component (x2) with respect to the change in the logarithm of its activity coefficient (lnγ2).

This relationship helps us understand how changes in the activity coefficients of the components affect each other in a binary mixture. By studying this relationship, we can gain insights into the behavior of the mixture and make predictions about its properties.

For example, let's consider a mixture of ethanol (chemical A) and water (chemical B). If the activity coefficient of ethanol (γ1) decreases, the Gibbs-Duhem equation tells us that the mole fraction of ethanol (x1) will also decrease. Similarly, if the activity coefficient of water (γ2) increases, the mole fraction of water (x2) will increase.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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4/5 is already in the simplest form but it can be written as 0.8 in decimal form

____________________________________________

To get the decimal

divided 4 by 5

which = 0.8

_______________

Hope this helps!

-Lexi

There are 462 different ways to select a planning board of 6 scientists from a group of 11 scientists.

The problem requires selecting 6 scientists from a group of 11 scientists. This is a combination problem, and the formula for combination is nCr, where n is the total number of items, and r is the number of items to be selected. The formula is given by:

nCr = n! / (r! * (n-r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

Using the given formula, the number of ways of selecting a planning board of 6 scientists can be calculated as:

11C₆ = 11! / (6! * (11-6)!)

= (11109876!) / (6! * 54321)

= (1110987) / (5432*1)

= 462

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Answer:

2.5%

Step-by-step explanation:

Given data

Profit = Euro 20,000,000

Tax paid= Euro 500,000

The percentage tax paid is

% Tax= Tax paid/Profit*100

% Tax= 500,000/20,000,000*100

% Tax=0.025*100

% Tax=2.5

Hence the percentage tax paid is 2.5%

Answer:

c=1875/15

Explanation:

The equation to find the cost of each monitor is given as:

To write a division equation that can be used to find the cost of each computer monitor, we divide each side of the equation by 15.

Using proportions, it is found that both patterns have the same number of ovals.

For Phil:

1 oval - 2 shapes

x oval - 96 shapes

Applying cross multiplication:

\(2x = 96\)

\(x = \frac{96}{2}\)

\(x = 48\)

For Stacy:

2 oval - 4 shapes

x oval - 96 shapes

Applying cross multiplication:

\(4x = 192\)

\(x = \frac{192}{4}\)

\(x = 48\)

Both patterns have the same number of ovals.

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The smallest number is x = 11/3. The smallest number in the given ratio of 1:2:3:4:5 whose mean is 11 is 11/3.

Given that the mean of 5 numbers is 11. The numbers are in the ratio 1:2:3:4:5. We need to find the smallest number. We can start solving the problem by following these steps:

Step 1: Let us assume the smallest number to be x.

Step 2: According to the question, the numbers are in the ratio 1:2:3:4:5. Hence, the other four numbers can be written as 2x, 3x, 4x, and 5x.

Step 3: The mean of these 5 numbers is given as 11.

Therefore, we can write:(x + 2x + 3x + 4x + 5x)/5 = 11.

Step 4: Simplifying the above equation, we get:15x/5 = 11x = 11/3.

Step 5: Therefore, the smallest number is x = 11/3.

The smallest number in the given ratio of 1:2:3:4:5 whose mean is 11 is 11/3.

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Based on the dimensions of the triangular flower bed, the cost of the border will be $70.

First, you need to find the total length of the triangular flower bed to find out how much thin metal border is needed.

This length is:

= 7 feet + 6 feet + 9 feet

= 22 feet

Then convert these to yards because the cost of the thin metal border wall is in yards. Every yard is about 3 feet so 3 feet is 1/3 yeards.

If you have 22 feet therefore, the number of yards is:
= 22 x 1/3

= 22 / 3

= 7.33 yards

Only whole numbers of yards can be bought so we round this up to 8 yards.

The cost of the border would be:

= Number of yards x Cost per yard

= 8 x 8.75

=  $70

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Answer:

\(m=− 32​ ≈−0.666666667\)

Step-by-step explanation:

The probability that the committee has a majority of women is approximately 0.0044.

To calculate the probability that the committee has a majority of women, we need to determine the number of ways we can select a committee with a majority of women and divide it by the total number of possible committees.

First, let's calculate the total number of possible committees. Since there are 63 senators in total (19 women + 44 men), we have 63 options for the first committee member, 62 options for the second, and so on.

Therefore, there are 63*62*61*60*59 = 65,719,040 possible committees.

Next, let's calculate the number of ways we can select a committee with a majority of women. Since there are 19 women in the NY Senate, we have 19 options for the first committee member, 18 options for the second, and so on.

Therefore, there are 19*18*17*16*15 = 28,7280 ways to select a committee with a majority of women.

Finally, let's calculate the probability by dividing the number of committees with a majority of women by the total number of possible committees:

287280/65719040 ≈ 0.0044.

In conclusion, the probability that the committee has a majority of women is approximately 0.0044.

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Answer:

2+2=4

Step-by-step explanation:

if I just want to be here

Answer:

-2

Step-by-step explanation:

(i) y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) y = ±√(-25)

The square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. There are no points on the circle with those coordinates.

(i) To express y in terms of a, b, x, and r, we can rearrange the equation of the circle as follows:

(x - a)² + (y - b)² = r²

Expanding the square terms, we get:

x² - 2ax + a² + y² - 2by + b² = r²

Rearranging the equation to isolate the y term, we have:

y² - 2by = r² - x² + 2ax - a² - b²

Completing the square by adding (b² - r²) to both sides, we obtain:

y² - 2by + (b² - r²) = -x² + 2ax - a²

Factoring the left side as a perfect square, we have:

(y - b)² = -x² + 2ax - a² + (b² - r²)

Taking the square root of both sides, we get:

y - b = ±√(-x² + 2ax - a² + (b² - r²))

Finally, isolating y, we have:

y = ±√(-x² + 2ax - a² + (b² - r²)) + b

(ii) Given a = 2, b = 3, r = 5, and x = 5, we can substitute these values into the equation we derived in part (i). Plugging in the values, we have:

y = ±√(-(5)² + 2(5)(2) - (2)² + (3)² - (5)²) + 3

Simplifying the equation:

y = ±√(-25 + 20 - 4 + 9 - 25) + 3

y = ±√(-25)

Since the square root of a negative number is not real, there are no real y-coordinates for the given values of a, b, r, and x. Therefore, there are no points on the circle with those coordinates.

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9514 1404 393

Answer:

  A, B, D

Step-by-step explanation:

The sides in order from smallest to largest are ...

  AC, BC, AB

Then the opposite angles in order from smallest to largest are ...

  B, A, C

Let's consider the choices:

A. m∠A < m∠C --- true

B. m∠B = m∠C --- true

C. m∠A < m∠B --- false

D. m∠B < m∠A < m∠C --- true

Answer:

no./0=undefined

0/no.=zero

Answer:

35

Step-by-step explanation:

a=√ c^2−b^2

a=√12^2−35^2

a=√ 144−1225

a=√  −1081

a= 35

Answer:

x= 9.8

Step-by-step explanation:

Just did it said it was correct

Answer: 9.5 and 9.500

Answer:

13.7

Step-by-step explanation:

13.7+90+70+6= 179.7 when you round it is 180

Answer:

1 meter

Step-by-step explanation:

Circumference of circle = 2 · r · π

Circumference = 2π

Let's solve

2π = 2 · r · π

2 = 2 · r

r = 1 meter

So, the radius is 1 meter

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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This is a line portrayed in point-slope form.

First, put a point at (0, -1). This is your y-intercept.

Next, go down 4 units and to the right one unit. Place a point at (1, -4). Then go down another 4 units and right once more. Place a point at (2, -8).

Now, go back to your y-intercept and go up 4 units and to the left one unit. Place a point at (-1, 3).

Finally, draw a line connecting all your points.

Answer:

16,712.38

Step-by-step explanation:

Periodic interest rate 7.2%/12 = 0.6%

First find the monthly payment

M = $14,000 * 0.006(1 +0.006)^60/(1+0.006)^60-1 = 278.54

The total payment is $278.54 * 60= $16,712.38

Jesse's total payment amount for this loan is $16,712.38

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that Jesse took out a $14,000 car loan for 5 years at a 7.2% interest rate.

Periodic interest rate = 7.2%/12

= 0.6%

First we need to find the monthly payment

M = $14,000 x 0.006(1 +0.006)^60/(1+0.006)^60-1

M = 278.54

The total payment is

$278.54 x 60= $16,712.38

Hence, Jesse's total payment amount for this loan is $16,712.38

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