Use the scientific calculator if needed
Sin^-1 squareroot 2/2

The probability that the remaining bill is a $2 bill is approximately 0.2857 or 28.57%.

To solve this problem, we can use conditional probability. Let's denote the events as follows:

A: The wallet initially contains a $2 bill.

B: The wallet initially contains a $20 bill.

C: The bill drawn from the wallet is a $2 bill.

We want to find the probability of Provenience is the horizontal and vertical position of an artifact within the matrix.  A occurring given that event C has occurred, P(A|C).

To begin, let's analyze the given information:

- The wallet either contains a $2 bill or a $20 bill, with equal likelihood. So, P(A) = P(B) = 0.5.

- If the wallet initially contains a $2 bill (event A), the probability of drawing a $2 bill (event C) is 2/3, since there are two $2 bills and one $20 bill in the wallet.

- If the wallet initially contains a $20 bill (event B), the probability of drawing a $2 bill (event C) is 1/2, as there is only one $2 bill left in the wallet.

Now, let's calculate the probability using Bayes' theorem:

P(A|C) = (P(C|A) * P(A)) / P(C)

P(C|A) = 2/3 (probability of drawing a $2 bill given that the wallet initially contains a $2 bill)

P(C) = P(C|A) * P(A) + P(C|B) * P(B) (total probability of drawing a $2 bill)

P(C|B) = 1/2 (probability of drawing a $2 bill given that the wallet initially contains a $20 bill)

P(C) = (2/3 * 0.5) + (1/2 * 0.5) = 1/3 + 1/4 = 7/12

P(A|C) = (2/3 * 0.5) / (7/12)

      = 4/6 / 7/12

      = (4/6) * (12/7)

      = 2/7

Therefore, the chances that the remaining bill in the wallet is a $2 bill, given that a $2 bill was drawn, is 2/7 or approximately 0.2857 (or 28.57%).

So, the probability that the remaining bill is a $2 bill is approximately 0.2857 or 28.57%.

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Answer:

(x+6)(x-6)

Step-by-step explanation:

Given: x²-36

Difference of Squares Formula: x²-a²=(x+a)(x-a)

Since 6²=36: x²-6²=(x+6)(x-6)

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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Answer:

\(8w+\frac{12}{4}\) = 8w+3

\(\frac{8w+12}{4}\) = 2w+3

Step-by-step explanation:

For \(8w+\frac{12}{4}\), you can divide 12 by 4 which is three.

For \(\frac{8w+12}{4}\), you have to divide each term. 8w is the same as 8·w. 8·w/4 is 2·w. 12/4 is 3.

The correct value of this simplified expression is 8w + 3

- Algebraic expression is a mathematical sentence that involves letters accompanied by real numbers, where it can be a variable or unknown.

- Simplification of a number is just the division of the same divisor by the numerator and denominator.

Given the expression: 8w+12/4, the only term in this expression that can be simplified is the fraction. So let's divide these two numbers by the number 2:

8w + 12 / 4

8w + 12 ÷ 2 / 4 ÷ 2

8w + 6 /2

It is still possible to simplify this expression - dividing the numerator by the denominator, so:

8w + 6 /2

8w + 6 ÷ 2

8w + 3

Therefore, the correct answer of this expression will be 8w + 3

The value of tan(A - B) by using trigonometric identities is StartFraction 12 minus 5 StartRoot 13 EndRoot Over 5 + 12 StartRoot 13 EndRoot, which is option (B)

To find the value of tan(A - B), we need to use trigonometric identities to express it in terms of the given trigonometric functions. One identity that will be useful here is the tangent difference formula, which states:

tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

First, we need to find the values of tan A and tan B. We are given that:

sin A = 5/13 and cos A < 0 (since pi/2 < A < pi, and cosine is negative in the second quadrant)

We can use the Pythagorean identity sin^2 A + cos^2 A = 1 to find the value of cos A:

cos A = -sqrt(1 - sin^2 A) = -12/13

Therefore, tan A = sin A / cos A = -5/12

We are also given that:

tan B = -sqrt(13) and cos B < 0 (since pi/2 < B < pi, and cosine is negative in the second quadrant)

We can use the Pythagorean identity tan^2 B + 1 = sec^2 B to find the value of sec B:

sec B = sqrt(tan^2 B + 1) = sqrt(14)

Therefore, cos B = 1 / sec B = sqrt(14) / 14

Now we have all the values we need to use the tangent difference formula: tan(A - B)

= (tan A - tan B) / (1 + tan A tan B)

= (-5/12 - (-sqrt(13))) / (1 + (-5/12)(-sqrt(13)))

= (12sqrt(13) - 5) / (12 + 5sqrt(13))

= (12sqrt(13) - 5) / (12 + 5sqrt(13)) * (12 - 5sqrt(13)) / (12 - 5sqrt(13)) (multiplying the numerator and denominator by the conjugate)

= (144 - 6513) / (144 - 6513)

= -5/12 + (12sqrt(13))/144

= -5/12 + sqrt(13)/12

= (sqrt(13) - 5) / 12

Therefore, the value of tan(A - B) is StartFraction 12 minus 5 StartRoot 13 EndRoot Over 5 + 12 StartRoot 13 EndRoot, which is option (B).

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Answer:

slope is = -1/2

Step-by-step explanation:

y2-y1= 2-0= 2

x2-x1= -3-1= -4

2/-4= -1/2

Answer:

(a) $52,400

(b) $44,540.

Step-by-step explanation:

(b) $52,400 - $7,860 = $44,540

tax-deferred retirement plans like

401k

are great because

$7,860 wouldve been lost to taxes.

instead it goes to retirement

the probability of drawing a green marble, putting it aside, and then drawing another green marble is 3/68

Total 17 marbles

4 - blue marbles

6 - green marbles

2 - red marbles

The rest - yellow marbles

Probability of drawing red first:

P(red) = number of red / total number = 2/17

Probability of drawing green second, without replacement:

P(green) = number of green / number left in the bag = 6/16 = 3/8

Probability of red and green in order:

P = P(red)*P(green) = 2/17*3/8 = 3/68

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Answer:

the answer would be a % because of the divisibility rule

Answer:

-24

Step-by-step explanation:

-3 multiply 8 = -24

Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.

Answer: -24

Step-by-step explanation: When you're asked to multiply

positives and negatives together, the rules are simple.

positive times a positive is a positive

positive times a negative is a negative

negative times a positive is a negative

negative times a negative is a positive

One way that I think will help you is to think

about the problem in terms of the signs.

If the signs are the same, the product will always be positive.

For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.

If the signs are different, the product is negative.

So (+6) · (-4) is -24 and (-10) · (+5) is -50.

So don't get caught up on the signs.

Do the problem first, then determine if the

signs are the same or if they are different.

Answer:

hello

g (x)= x² - 5

g (3) = 3² - 5 =  9 - 5 =  4

Step-by-step explanation:

Answer:

2 and 4 are true.

Step-by-step explanation:

1. False. Centi (100) times smaller than a meter, gram, or liter. Deci (10) times smaller than a meter, gram, or liter.

2. True. Hecto (100) times larger. Kilo (1000) times larger.

3. False. Deka (10) times larger. Kilo (1000) times larger.

4. True. Deka (10) times larger than a gram, which is a base unit.

Answer:

126 mm / 3 = 42 mm

The length of each side of this equilateral triangle is 42 mm.

Answer:

Answer bellow

Step-by-step explanation:
Pythagorean Theorem or PT= a2+b2

Yes you can Construct a right triangle C=25

If 7 = a2 and 24=b2 you can

The table B would not be an appropriate model for the function shown here.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A function is shown here.

In the graph:

When x = 2, then f(x) = 2 ≠ 0.

From the given choices:

The table B gives contradiction.

Therefore, the table D is not an appropriate model.

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Step-by-step explanation:

if you mean is 30×4 divisible by 2 then yes because it gives an even number and both are multiples of 2

if you mean 2.c I have no idea what you mean then

Answer:

how much does she get each hour

Step-by-step explanation:

Answer:

The answer is x+8.

Because you gotta factor out first and then cancel.

Answer

Picture too blurry

Step-by-step explanation:

Answer:

-----------------------

Let Anita be x now.

Her mother is 5 times older and in two years time she will be 5x + 2.

Rita is half the age of Anita and in two years time she will be (x/2) + 2.

The sum of ages after two years will be 58:

Anita is 8 years old.

Answer:

10 km/hr.

Step-by-step explanation:

Speed of the boat with the current = 20 + c   where c is the speed of the current.

Against the current the speed is 20 - c.

Distance = speed * time :

With the current:

180 = (20 + c)t..........A

Against the current:

20 = (20 - c)(8- t)......B

Solving this system of equations:

From A:

t = 180/(20 + c)

So

20 = (20 - c)(8 - 180/(20+c))

160 - 3600/(20 + c) - 8c  + 180c/(20 + c) = 20

Mltiplying throagh by (20 + c):

160(20 + c) - 3600 - 8c(20 + c) + 180c = 20(20 + c)

3200 + 160c - 3600 - 160c - 8c^2 + 180c - 400 - 20c = 0

-8c^2 + 160c  - 800 = 0

8c^2 - 160c + 800 = 0

c^2 - 20c + 100 = 0

(c - 10)*2 = 0

c = 10

So the speed of the crrent = 10 km/hr

The marginal cost of producing one more unit of the product when x = 100 is $150 per unit. To find the instantaneous rate of change (or the marginal cost) of c with respect to x when x = 100, we need to calculate the derivative of the cost function c(x) with respect to x and evaluate it at x = 100.

Let's assume that we have the cost function c(x) = 0.5x^2 + 50x + 1000, where x is the number of units produced. To find the derivative of this function, we need to use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our cost function, we get:

c'(x) = d/dx (0.5x^2 + 50x + 1000)
     = 1x^(2-1) + 50x^(1-1) + 0
     = x + 50

Now, we can evaluate this derivative at x = 100 to find the marginal cost:

c'(100) = 100 + 50
       = 150

Therefore, the marginal cost of producing one more unit of the product when x = 100 is $150 per unit. This means that if the company produces one more unit of the product, it will cost them $150 more than the cost of producing the previous unit. The significance of the marginal cost will be explained in a future chapter, but for now, it is important to understand that it is a crucial concept in economics and business decision-making.

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The level of sound at this point in the audience is approximately 96.02 decibels.

To find the level of sound at a point in the audience, we can use the given formula L = 10 log(I x 10^12), where I is the intensity of the sound in watts per square meter.

Given that the intensity of the sound at a rock concert is 0.004 watts per square meter at a distance of 76 meters from the stage, we can substitute this value into the formula:

L = 10 log(0.004 x 10^12)

First, we simplify the expression inside the logarithm:

0.004 x 10^12 = 4 x 10^9

Then we substitute this value back into the formula:

L = 10 log(4 x 10^9)

Using logarithmic properties, we can simplify further:

L = 10(log 4 + log 10^9)

Since log 10^9 equals 9, we have:

L = 10(log 4 + 9)

Calculating the logarithm and adding:

L = 10(0.602 + 9)

L = 10(9.602)

L ≈ 96.02 dB

Therefore, the level of sound at this point in the audience is approximately 96.02 decibels.

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Answer:

I think it's B.

Step-by-step explanation:

The profit made as of investor borrows $100 is $25.

Investing in foreign currencies can be a profitable venture, but it comes with a certain level of risk.

If an investor borrows $100, converts it to pesos, and invests the pesos in Mexico for one year, the profit made is $25.

This is calculated by borrowing $100 and converting it to 625 pesos at the spot rate of 6.25 pesos per dollar.

The 625 pesos are then invested in Mexico for a year at a 45% interest rate, resulting in 281.25 pesos.

The 281.25 pesos are then converted back to dollars at the forward rate of 7.25 pesos per dollar, resulting in $38.75.

The resulting profit is $38.75 - $100 = -$61.25.

Investing in foreign currencies is not without its risks.

When investing in foreign currencies, the exchange rate can change drastically over short periods of time, resulting in losses or gains.

Additionally,

The interest rate in the country of investment can also change, resulting in different levels of returns.

The profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year is $25.

The calculation is as follows:

Borrow $100 and convert to pesos:

100 x 6.25 = 625 pesos

Invest 625 pesos in Mexico for one year:

625 x 45% = 281.25 pesos

Convert 281.25 pesos back to dollars at the forward rate:

281.25 / 7.25 = $38.75

Profit = $38.75 - $100 = -$61.25

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.

To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:

1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).

2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.

3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.

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The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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