30 points, please help, no links
Complete the proof.

Given: r | | s

Prove: angle 2, angle 8 are supplementary

Answer:

y = 4

Step-by-step explanation:

First, distribute 8 through the parentheses

8y - 8 - 3y = 6(2y - 6)

Then, distribute 6 through the parentheses

8y - 8 - 3y = 12y - 36

Collect like terms (8y - 3y)

5y - 8 = 12y - 36

Move the variable (12y) to the left hand side and change its sign

5y - 12y - 8 = -36

Move the constant (-8) to the right hand side and change its sign

5y - 12y = -36 + 8

Collect like terms

-7y = -36 + 8

Calculate the sum

-7y = -28

Divide both sides of the equation by -7

y = 4

Answer:

Step 1-2

Step-by-step explanation:

The person doing this question, did not distribute the 6 properly.

They distributed the 6 to the x, but not to the 4.

When done properly, it should be:

6x+24=3x-2

Answer:

step 2

Step-by-step explanation:

4 times 6=24

6(x+4)=3x-2

6x+24=3x-2

3x+24=-2

3x=-26

The slοpe οf the line that gοes thrοugh the fοllοwing pοints is 0.

Slοpe is a measure οf the steepness οf a line, calculated as the ratiο οf the change in y (vertical) cοοrdinates tο the change in x (hοrizοntal) cοοrdinates between twο pοints οn the line.

a. The line passes thrοugh the pοints (4, -6) and (4, 0). Since the x-cοοrdinates οf bοth pοints are the same, the line is a vertical line.

b. The line passes thrοugh the pοints (8, -2) and (-7, -2). Using the slοpe fοrmula, we can get the slοpe:

slοpe = (change in y)/(change in x)

slοpe = (-2-(-2))/(8-(-7))

slοpe = 0/15

slοpe = 0

Therefοre, the slοpe οf the line is 0.

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To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

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Answer:

1/12 5/12 11/12

Step-by-step explanation:

Um it was pretty obvious but...

Answer:

8

Step-by-step explanation:

Answer:

48 would be your answer. <3

Step-by-step explanation:

1/4y=12

Multiply both sides by 4.

4 * (1/4y) = (4) * (12)

y=48

Answer:

Given that a circle of radius 5 miles has an arc of length 3 miles.

The central angle of the arc can be found using the formula:\(\[\text{Central angle} = \frac{\text{Arc length}}{\text{Radius}}\]\)

Substitute the given values into the formula to get:\(\[\text{Central angle} = \frac{3}{5}\]\)

To get the answer in degrees, multiply by 180/π:\(\[\text{Central angle} = \frac{3}{5} \cdot \frac{180}{\pi}\]\)

Simplify the expression:\(\[\text{Central angle} \approx 34.38^{\circ}\]\)

Therefore, the measure of the central angle that subtends the arc of length 3 miles in a circle of radius 5 miles is approximately 34.38 degrees.

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Answer:

1. h=1.5d. 2. 30cm in 20 days

Step-by-step explanation:

2. 20×1.5

The time it takes to empty a full tank in case both the pipes are open is calculated to be 3 hours.

The time it takes to empty a full tank can be calculated by using an algebraic expression as follows;

Consider; x = time it takes to empty the full tank if both pipes are open

Then with both pipes open, the tank empties at the rate of (1/x) tank per minute

Inlet pipe fills at the rate of 1/90 tank per minute and outlet pipe empties at the rate of 1/60 tank per minute

So with both pipes open the tank empties at the rate = (1/60-1/90) tank per min

Therefore;

1/60 - 1/90 = 1/x

multiply each term by 180x

(1/60)(180x) - (1/90)(180x) = (1/x)(180x)

3x - 2x= 180

x = 180 min or 3 hr

Hence it takes 3 hours to empty the full tank.

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Mateo ate 3/8 of the pizza and it contained 510 calories in total.The entire pizza contains 1,360 calories.

Therefore, we need to find the number of calories in the whole pizza.

Let’s consider that the whole pizza contains x calories. Then, we can represent 3/8 of that pizza as:(3/8) x

Now, we can use proportionality to determine the calories in the whole pizza:

3/8 = 510/x

We can now cross-multiply and solve for x by multiplying both sides by 8x:

8x(3/8) = 510 x 8x/8x = 510*8/3x = 1,360 calories

Therefore, the entire pizza contains 1,360 calories.

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Answer:

10 = c

Step-by-step explanation:

Distribute -4 to the parentheses:

8 = 8c - 4(c + 8)

8 = 8c - 4c - 32

Add like terms:

8 = 4c - 32

Add 32 to both sides:

40 = 4c

10 = c

Answer:

Question:

8=8c-4(c+8)

Step-by-step explanation:

8=8c-4c-32

8=4c-32

8+32=4c

40=4c

Or

4c=40

c=10

The root test is inconclusive for the series Σ 1/n8n.

To determine the convergence or divergence of the series Σ 1/n8n using the root test, we need to calculate the limit as n approaches infinity of the nth root of the absolute value of the nth term. In this case, the nth term is 1/n8n.

Calculating the limit, we have lim n→∞ (n√|1/n8n|).

Simplifying the expression inside the absolute value, we get 1/n^8n = 1/n^(8n) = 1/n^(8n) = 1/(nⁿ⁸) = 1/(n⁸ⁿ).

Taking the nth root of the absolute value, we have

n√|1/n⁸ⁿ| = n√(1/(n⁸ⁿ)).

As n approaches infinity, the expression (1/(n^8n)) approaches zero because the denominator, n⁸ⁿ, grows much faster than the numerator, 1. Therefore, the nth root of the absolute value approaches 1.

Since the limit is equal to 1, the root test is inconclusive. The root test does not provide sufficient information to determine whether the series

Σ 1/n8n is convergent or divergent.

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Answer:

C 3/2

Step-by-step explanation:

Since triangle PRQ is the original and is getting bigger proportionally (can tell by side lengths) you can eliminate options A and B since you have to multiply by a number/fraction greater than one since it's getting bigger. Then pick a side corresponding to another side of the other triangle. For example, the side length of PQ is 8. Side length P'Q' is 12. You will need to consider how you get from that 8 since it's the original to the 12. To do that you will need to multiply by 1.5 to get to 12. this is what it means by dilation. Since 3/2=1.5 that would be your answer.

The first three nonzero terms of the Taylor polynomial approximation for the given initial value problem are: x(t) ≈ 1

To find the first three nonzero terms in the Taylor polynomial approximation for the given initial value problem, we can use the Taylor series expansion formula:

x(t) = x(0) + x'(0) * t + (1/2!) * x''(0) * t^2 + ...

Given the initial value problem 2x'' + 4tx = 0, and initial conditions x(0) = 1, x'(0) = 0, let's find the first three terms:

1. x(0) = 1 (Initial condition)
2. x'(0) = 0 (Initial condition)
3. To find x''(0), we can substitute the initial conditions into the initial value problem: 2x''(0) + 4*0 = 0, which simplifies to 2x''(0) = 0, and finally x''(0) = 0.

Now, substitute these values into the Taylor series expansion formula:

x(t) = 1 + 0 * t + (1/2!) * 0 * t^2 + ...

Since x'(0) and x''(0) are both 0, the first three nonzero terms of the Taylor polynomial approximation for the given initial value problem are: x(t) ≈ 1

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Answer:

12

Step-by-step explanation:

Find the distance between each maximum, which is 13-1=12

the percent change in the number of cards collected from last month to this month is:

that is equivalent to say:

the percent change in the number of cards collected from last month to this month is 60%

(a)The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident  is approximately 0.522.

(c) The probability that at least one adult is very confident is   approximately 0.478.  

What is the probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults, given the proportion of very confident individuals?

The probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults depends on the proportion of very confident individuals. By calculating the probability of all four adults being very confident (a), none of the four adults being very confident (b), and at least one of the four adults being very confident (c), we can determine the likelihood of these scenarios occurring based on the given information.

To solve this problem, we can use the concept of probability and combinations.

(a)Given that there are 150 out of 1000 U.S. adults who are very confident, the probability of selecting one adult who is very confident is:

P(very confident) = 150/1000

= 0.15

Since the sampling is done without replacement, after each selection, the sample size decreases by 1. Therefore, for the second selection, the probability becomes 149/999, for the third selection, it becomes 148/998, and for the fourth selection, it becomes 147/997.

To find the probability that all four adults are very confident, we multiply these probabilities together:

P(all four adults are very confident) = (0.15) * (149/999) * (148/998) * (147/997)

≈ 0.0056

(b) The probability of selecting one adult who is not very confident (opposite of very confident) is:

P(not very confident) = 1 - P(very confident)

= 1 - 0.15

= 0.85

Since we are selecting four adults at random without replacement, the probability of none of them being very confident can be calculated as:

P(none very confident) = P(not very confident) * P(not very confident) * P(not very confident) * P(not very confident)

= (0.85)* (0.85) * (0.85) * (0.85)

≈ 0.522

(c) The probability of at least one adult being very confident is the complement of none of them being very confident:

P(at least one very confident) = 1 - P(none very confident)

= 1 - 0.522

= 0.478

Therefore,

(a) The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident is approximately 0.522.

(c) The probability that at least one adult is very confident is approximately 0.478.  

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Answer:

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

Step-by-step explanation:

Answer:

i cat see it

Step-by-step explanation:

The solution to the simultaneous equation using elimination method is x = -4 4/11 and y = -1/11

Elimination method of solving simultaneous equation is by completing removing or eliminating a variable in order to solve for the other variable.

-4x+5y=17

4x+6y= - 16

Add both equations to eliminate x

5y + 6y = 17 + (-16)

11y = 17 - 16

11y = -1

divide both sides by 11

y = -1/11

Substitute into equation (1)

-4x+5y=17

-4x + 5(-1/11) = 17

-4x -5/11 = 17

-4x = 17 + 5/11

-4x = (187 + 5) /11

-4x = 192/11

divide both sides by -4

x = 192/11 ÷ -4

= 192/11 × -1/4

= -192/44

= - 4 16/44

x = -4 4/11

Therefore, x = -4 4/11 and y = -1/11 is the solution to the simultaneous equation -4x+5y=17; 4x+6y= - 16

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The probability that Antoine's marble will also be green would be = 3/13

To determine the probability of the given event, the formula that should be used is given below. That is;

Probability = possible outcome/sample space.

The sample space = 4+7+9+6 = 26 marbles.

The number of green marbles = 6

The probability of choosing green marbles = 6/26 = 3/13

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Answer:

1) B. the labels can he make to the tape

2) D. he can make 73 labels

Step-by-step explanation:

1) We are told that He will make labels 1.25 inches long each. We are asked the number of labels he can make.

Thus, correct answer is option B.

2) He wants to make labels 1.25 inches long out of 91.25 inches of plastic.

Thus, number of labels he can make = 91.25/1.25 = 73 labels

The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Answer:

d) f(n) = 4 . 3^(n-1)

______________

Answer:

24 feet

Step-by-step explanation:

Use the perimeter formula, P = 2l + 2w, where l is the length and w is the width.

Plug in the values, and solve:

P = 2l + 2w

P = 2(7) + 2(5)

P = 14 + 10

P = 24

So, the perimeter of the canvas is 24 feet

The function f(x) = ln(2 + sin(x))) is concave up for the range of x [0,2].

To discover the interval(s) on which f(x) = ln(2 + sin(x)) is concave up, compute the function's second derivative and check its sign.

To begin, compute the first derivative of f(x) with respect to x:

(1 / (2 + sin(x)) = f'(x)cos(x)

The second derivative of f(x) can therefore be found by taking the derivative of f'(x) with regard to x:

f''(x) = -(1/(2 + sin(x))(-sin(x)) cos2(x) + (1/(2 + sin(x))

When we simplify f''(x), we get:

f''(x) = -1/(2 + sin(x))²)sin(x)(sin(x)-2)

To discover the interval(s) where f(x) is concave up, we must first locate the interval(s) where f''(x) is positive. Because sin(x) might vary from -1 to 1, we must solve the inequality:

-(1/(2 + 1))^2(-1)(-1-2)≤f''(x)≤-(1 / (2 - 1))²(1) (1-2)

When we simplify this inequality, we get:

1/9 ≤ f''(x) ≤ -1/4

So, f is never negative at 0 ≤ x ≤ 2, so f is concave up in the range 0 ≤ x ≤ 2.

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Complete question - f(x) = ln(2 + sin(x)), 0 ≤ x ≤ 2 . Find the interval(s) on which f is concave up.

The number of times the hydrogen ion concentration of Aeen’s drink is the hydrogen ion concentration of Marien’s drink is 4 approx.

The phrase "times bigger" shows this:

If a number 'x' is 't' times bigger than 'y', then that means:

\(x = t \times y\)

It is because 'y' had to multiply itself with 't' to get in equal level of 'x'

A solution with 'x' as its pH contains \(10^{-x} mol/L\) of hydrogen ions.

For the considered case, we have:

Thus, its hydrogen ion concentration is \(10^{-2.7}\) = x (say)

Thus, its hydrogen ion concentration is \(10^{-3.3}\) = y (say)

Then, let x is t times bigger than y, then that means:

\(x = t\times y\\\\t = \dfrac{x}{y} = \dfrac{10^{-2.7}}{10^{-3.3}} = 10^{-2.7 - (-3.3)} = 10^{-0.6} \approx 4\)

It is because of the property \(a^b \times a^c = a^{b+c}\)

Thus, hydrogen ion concentration of Marien's drink is approx 4 times the hydrogen ion concentration of Aeen's drink.

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126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even

For given question,

We need to find number of three-digit numbers formed using elements from the set {1,2,3,4,5,6,7,8}  if no element may be used more than once in a number and the number must be even.

3-digit even  numbers are to be formed using the given six digits,1 ,2,3,4,6,7, and 8 without repeating the digits.

Then, units digits can be filled in 4 ways by any of the digits, 2,4, 6 or 8.

Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 7 digits.

So, the number of ways in which hundreds and tens place can be filled with the remaining 7 digits is the permutation of 7 different digits taken 2 at a time.

\(\Rightarrow ~^7P_2=\frac{7!}{(7-2)!} \\\\\Rightarrow ~^7P_2=42\)

Thus, by multiplication principle, the required number of 3-digit numbers is 3 × 42 = 126

Therefore, 126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even

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