solve the equation 18 + k = 20

a. To calculate the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette, we can use the formula: Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Lost)

In this case, the probability of winning is 1/38, and the amount won is $350. The probability of losing is 37/38, and the amount lost is $10. Substituting these values into the formula, we get: Expected Value = (1/38 * $350) - (37/38 * $10)
Expected Value = $9.21 Therefore, the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette is $9.21. b. Based on the expected value from part a, it is not a good idea to play Roulette over and over again. The reason is that the expected value is positive but small. This means that on average, you will win $9.21 for every $10 you bet, but the variance in the game can cause you to lose money in the long run.
For example, if you play 100 rounds of Roulette with a $10 bet on number 12 each time, you would expect to win $921 on average. However, there is a significant chance that you could lose money over these 100 rounds. The more you play, the greater the likelihood of experiencing a losing streak that would offset your winnings.

Therefore, while playing Roulette can be fun and exciting, it is not a sustainable way to make money. The small expected value means that over time, the casino will always come out ahead.

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For using substraction, in Janice's account balance with beginning of $467 amount, the ending bank balance of his account after some withdraw through checks and ATM is equals to $371.08.

We have Janice's bank balance account data. In Begining bank balance of his account = $467

Amount that she withdrawal through ATM = $30

The 4 checks'amount are the following $16.80, $22.74, $12.38, and $14. We have to determine the her ending bank balance.. We use substraction arithmetic operation for determining the ending bank balance. First we add all withdraw amounts from account to calculate total withdraw. So, total withdraw from account = $16.80+ $22.74 + $12.38 + $14 + $30 = $95.92

Now, the ending bank balance= $467 - $95.92 = $371.08

Hence, required bank balance is $371.08.

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Answer:

Recursive: \(x_n=2(x_{n-1})\)

Explicit: \(x_n=2(2)^{n-1}\)

Step-by-step explanation:

First, note that this is a geometric sequence. This is because each term is 2 times its previous term.

The standard recursive form for a geometric sequence is:

\(x_n=r(x_{n-1})\)

Where n is the nth term, so n-1 is the previous term, and r is the common ratio.

Substitute 2 for r.

Therefore, our recursive formula is:

\(x_n=2(x_{n-1})\)

The standard form of the explicit formula for geometric sequences is:

\(x_n=ar^{n-1}\)

Again, r is the common ratio and a is the initial term.

The common ratio is 2 and the initial term is 2. So, substitute:

\(x_n=2(2)^{n-1}\)

And that's our explicit formula.

And we're done!

Answer:

key details, because it tells you more about the story

Answer:

C

Step-by-step explanation:

The volume of a cube if the diagonal of one side is 50cm is approximately 48112.52 cubic centimeters.

Let s represent the width of the cube's sides, and d represent the width of one side's perpendicular. The Pythagorean formula can be used to connect s and d:

d**2 = s**2 + s**2 + s**2 = 3s**2

To solve for s, we obtain:

S = d/Sqrt(3)

Given a cube with edge lengths s, the volume V is equal to:

V = s**3

Inputting the word in place of s gives us:

V = (d / sqrt(3))**3 = d**3 / (3*sqrt(3))

Now we can change d to 50 centimetres to obtain the cube's volume:

V = 50**3 / (3*sqrt(3)) = 48112.52 cubic centimeters

As a result, the cube's capacity is roughly 48112.52 cubic centimetres.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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To prove that any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps, we will use mathematical induction.

First, let's check the base case. We need to show that it's possible to obtain a postage of 12 cents using 3 cents and 7 cents stamps. We can do this by using two 3 cents stamps and two 7 cents stamps, for a total of 12 cents.
Now, let's assume that it's possible to obtain any postage of at least 12 cents using 3 cents and 7 cents stamps. We want to prove that this also holds for postage values of n+1.
To do this, we need to show that it's possible to obtain a postage of n+1 cents using 3 cents and 7 cents stamps, assuming that we can already obtain any postage of at least 12 cents.
Let's consider the case where n+1 is an odd number. We can use one 7 cents stamp and (n-6)/2 3 cents stamps to obtain a postage of n+1 cents. This works because if n+1 is odd, then n-6 must be even, so we can divide it by 2 and use that many 3 cents stamps.
Now, let's consider the case where n+1 is an even number. We can use two 3 cents stamps and (n-8)/2 7 cents stamps to obtain a postage of n+1 cents. This works because if n+1 is even, then n-8 must be even, so we can divide it by 2 and use that many 7 cents stamps.
Therefore, we have shown that it's possible to obtain any postage of at least 12 cents using 3 cents and 7 cents stamps, and our proof is complete.

To use mathematical induction to prove that any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps, follow these steps:
Step 1: Base case
Show that the statement holds true for the smallest value (12 cents).
You can obtain 12 cents using four 3-cent stamps (3+3+3+3). So, the base case is true.
Step 2: Inductive hypothesis
Assume the statement is true for some arbitrary value 'k' (k >= 12) such that k can be obtained using 3 cents and 7 cents stamps.
Step 3: Inductive step
Prove the statement is true for the next value, 'k+1'. We need to show that (k+1) cents can also be obtained using 3 cents and 7 cents stamps.
Case 1: If the 'k' postage contains at least one 3-cent stamp, we can replace that with a 3-cent and a 3-cent stamp to obtain (k+1) cents.
Case 2: If the 'k' postage contains only 7-cent stamps, we have at least two 7-cent stamps since k >= 12. We can replace two 7-cent stamps with five 3-cent stamps (7+7 = 3+3+3+3+3), which adds up to the same postage value. In this case, we can obtain (k+1) cents by adding another 3-cent stamp.
In both cases, (k+1) cents can be obtained using 3 cents and 7 cents stamps. Therefore, by mathematical induction, any postage of at least 12 cents can be obtained using 3 cents and 7 cents stamps.

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Answer:

What is it you need help with for this question? Please provide all information in your question so we can know exactly how to help you. Thank you!

The left-hand and right-hand limits both exist and are equal to 0, the overall limit exists and is equal to 0. lim t→4 t - [t] = 0

To evaluate the limit of the least integer function as t approaches 4, we can examine the left and right limits separately.

First, let's consider the left-hand limit:

lim t→4- t - [t]

As t approaches 4 from the left, t - [t] approaches 4 - 4 = 0, since the least integer function [t] equals 3 for values of t in the interval (3,4). Therefore, the left-hand limit is 0.

Now, let's consider the right-hand limit:

lim t→4+ t - [t]

As t approaches 4 from the right, t - [t] approaches 4 - 4 = 0, since the least integer function [t] equals 4 for values of t in the interval [4,5). Therefore, the right-hand limit is also 0.

Since the left-hand and right-hand limits both exist and are equal to 0, the overall limit exists and is equal to 0. lim t→4 t - [t] = 0

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Let Ramanujan pick a complex number $a+bi$, where $a$ and $b$ are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

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(a+bi)(5+3i)=5a+3ai+5bi+3bi

2

=(5a+3b)+(5b+3a)i−3b

We want this product to be equal to $32-8i$. Equating the real and imaginary parts gives us two equations:

5

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3

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32

(1)

5a+3b=32(1)

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(2)

5b+3a=−8(2)

We can solve this system of equations to find $a$ and $b$. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15

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9

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96

15a+9b−25b−15a=−96

Simplifying:

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−16b=−96

Therefore, $b=6$. Substituting $b=6$ into equation (1) gives:

5

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18

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32

5a+18=32

Therefore, $a=2$. Thus, Ramanujan picked the complex number $2+6i$.

Based on the given conditions and informations provided, the complex number that was picked by thr Ramanujan is calculated to be  2+6i.

Let Ramanujan pick a complex number a+bi, where a and b are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:

(a+bi)(5+3i) = 5a+3ai+5bi+3bi² = (5a+3b)+(5b+3a)i-3b

We want this product to be equal to 32-8i. Equating the real and imaginary parts gives us two equations:

5a+3b=32 (1)

5b+3a=-8 (2)

We can solve this system of equations to find a and b. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:

15a+9b-25b-15a=-96

Simplifying:

-16b=-96

Therefore, b=6. Substituting b=6 into equation (1) gives:

5a+18=32

Therefore, a=2. Thus, Ramanujan picked the complex number 2+6i.

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Answer:

Exterior angle = 20 degrees

Interior angle = 160 degrees

================================================

Explanation:

The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,

exterior = (1/8)*(interior)

That rearranges to

interior = 8*(exterior)

Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle

The two must add to 180 to form a straight line.

interior + exterior = 180

8x + x = 180

9x = 180

x = 180/9

x = 20 is the measure of the exterior angle

8x = 8*20 = 160 is the measure of the interior angle

Note how 160+20 = 180 to verify our answers.

Answer:

x - 26 ≥ 73

Step-by-step explanation:

x  is the total sum of money earned. To find the answer, you need to subtract 26 from x because that's the amount of her expenses. It also has to be either greater than or equal to 73 because she wants to make at least $73 per day.  

Can you give me brainliest please?

The expected return on a $1 ticket is $0.0924 (rounded to two decimal places).

We are given that

If 240,000 tickets are sold for $1 each, we are to find the expected return on a $1 ticket.

We know that the total cost of all the tickets is $1 × 240,000 = $240,000.

The probability of winning each prize is given by the ratio of the number of tickets that win that prize to the total number of tickets that are sold.

Let x be the expected return on a $1 ticket.

We can find x as follows:

x= \frac{1}{240000}(60000+3\times7500+10\times1500+18\times120)+(1- \frac{1}{240000}) \times x= \frac{22170}{240000} = 0.092375$

Therefore, the expected return on a $1 ticket is $0.0924 (rounded to two decimal places).

Therefore the answer is $0.0924

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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A) The decimal 2.256 in expanded form and word form are respectively;  2 + 0.2 + 0.05 + 0.006;  Two and three hundred fifty six one - thousandths

B) The decimal 24.09 in expanded form  and word form are respectively; 20 + 4 + 0 + 0.09; Twenty four and 9 one - hundredths.

The expanded form used when writing decimals is the mathematical expression that shows the sum of the values of each digit in the given number.

A) We are given the decimal 2.256

Thus, in expanded form, the given decimal can be expressed as;

2 + (2/10) + (5/100) + (6/1000)

= 2 + 0.2 + 0.05 + 0.006

In word form, we can write the decimal as;

Two and three hundred fifty six one - thousandths

B) We are given the decimal 24.09

Thus, in expanded form, the given decimal can be expressed as;

20 + 4 + (0/10) + (9/100)

= 20 + 4 + 0 + 0.09

In word form, we can write the decimal as;

Twenty four and 9 one - hundredths.

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The scalar 2u • v is equal to -11.

To find the scalar 2u • v, where u = -3i - 4j and v = -7i + 8j, we need to compute the dot product between the two vectors.

The dot product of two vectors u and v is given by the formula:

u • v = (u1 * v1) + (u2 * v2)

Given u = -3i - 4j and v = -7i + 8j, we can substitute the values into the formula:

u • v = (-3 * -7) + (-4 * 8)

Evaluating the expression, we have:

u • v = 21 - 32

u • v = -11

Therefore, the scalar 2u • v is equal to -11.

In summary, to find the scalar 2u • v, we calculated the dot product of vectors u and v by multiplying their corresponding components and adding them together.

After substituting the values into the formula, we found that 2u • v is equal to -11.

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After the third bounce, the basketball bounces up to approximately 42.19% of its original height, the tennis ball bounces up to approximately 29.63% of its original height, and the softball bounces up to approximately 2.7% of its original height.


To determine the fraction of each ball's original height that it bounces up to after the third bounce, we need to substitute x=3 into the expression given for each ball. a. basketball: 3/4 is the fraction of the drop height that the basketball reaches after one bounce. When x=3, the expression becomes (3/4)^3, which is approximately 0.4219. Therefore, the basketball bounces up to approximately 42.19% of its original height after the third bounce.
b. tennis ball: 2/3 is the fraction of the drop height that the tennis ball reaches after one bounce. When x=3, the expression becomes (2/3)^3, which is approximately 0.2963. Therefore, the tennis ball bounces up to approximately 29.63% of its original height after the third bounce.
c. softball: 3/10 is the fraction of the drop height that the softball reaches after one bounce. When x=3, the expression becomes (3/10)^3, which is approximately 0.027. Therefore, the softball bounces up to approximately 2.7% of its original height after the third bounce.
In conclusion, after the third bounce, the basketball bounces up to approximately 42.19% of its original height, the tennis ball bounces up to approximately 29.63% of its original height, and the softball bounces up to approximately 2.7% of its original height.

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The scale factor of 10cm to 5m is 50.

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;

scale factor = new dimension / old dimension

Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm

therefore 5m = 5× 100 = 500cm

therefore scale factor = 500/10 = 50

This means the scale factor of 10cm = 5m is 50

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answer

757

Step-by-step explanation:

I just know made a A on the test

Answer:

a)x=3

Step-by-step explanation:

x+8+5x=32-2x

x+5x+2x=32-8

8x=24

x=24 : 8

x=3

Answer:

A. X=3

Step-by-step explanation:

x+8+5x=32-2x

6x+8=32-2x

8x+8=32

8x=24

x=3

The predicted value of Y for X = 8 is Y8 = 19.Option (b) is the correct answer.

A linear regression equation has b = 2 and a = 3.

The predicted value of Y for X = 8 is given by the equation below:Y = a + bX, where a = 3 and b = 2.

To find Y8, we substitute X = 8 into the equation as follows:

Y8 = a + bX8Y8 = 3 + 2(8)Y8 = 3 + 16Y8 = 19.

Therefore, the predicted value of Y for X = 8 is Y8 = 19.Option (b) is the correct answer.

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A student drove from her home to the university and get back to her home. The distance of her home and the university is 12 km. Her average speed for the entire trip is:  3.16 km/hours

The relation between speed, distance, and time is given by:

d = v x t

Where:

d = distance

v = speed

t = travelled time

In this problem, the distance of round trip, from her home to university and back home is:

d = 2 x 12 km = 24 km

The time needs to make this round trip = t = 7.6 hours

Hence, the average speed is:

average speed = distance/time

average speed = 24 / 7.6

average speed = 3.16 km/hours

Your question is incomplete. Most likely it was:

A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km.

(c) if she drove back home using the same path she took out to the university and arrives 7.6 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?

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The true statement for the relation is, the order of rows is unimportant.

What is row and column?

A row is an arrangement of items that are put next to or horizontally. A vertical split of items based on category is known as a column. The arrangement is in a left to right direction. The set-up is vertical, from top to bottom.

A table's rows are individual groups of connected data. Rows and columns are found in tables in relational databases (also known as records and fields, respectively).

Consider the given statements,

Entities in a column vary as to kind.

The order of the columns is important.

The order of the rows is unimportant.

More than one column can use the same name.

From the given statements, the true statement for the relation is, the order of rows is unimportant.

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The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3).

To determine the x-intercept, let y = 0 and solve for x in the equation y = 3x - 1.

Substitute 0 for y in the equation.0 = 3x - 1

Add 1 to both sides1 = 3x

Divide both sides by 3x = 1/3

The x-intercept of the line is (1/3, 0).

To find the y-intercept, let x = 0 and solve for y in the equation y = 3x - 1.

Substitute 0 for x in the equation.y = 3(0) - 1y = -1

The y-intercept of the line is (0, -1).

Therefore, the x-intercept is (1/3, 0), and the y-intercept is (0, -1).

Therefore, The x-intercept of the line calculator is (-1,0) while the y-intercept is (0,-3). The calculation above supports the conclusion.

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Answer:

89.99

Step-by-step explanation:

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Roberta paid the amount of $47.19 for the curtains before the sales tax.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that equation editor A set of curtains normally sells for $58.99. Roberta used a coupon good for 20% off the regular price.

To determine the amount for the curtains before the sales tax

According to the given conditions, the solution would be as:

⇒ 58.99 × (1 - 20%)

⇒ 58.99 × (1 - 0.20)

Calculate the sum or difference and we get

⇒ 58.99 × 0.80

Apply the multiplication operation to get

⇒ 47.192

Round the number nearest to the hundredth,

⇒ 47.19

Therefore, Roberta paid the amount of $47.19 for the curtains before the sales tax.

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The intersection of two secants has the following relation:

Using the given information, we have.

Now, we solve for x.