A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 9 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings?

Answer:

Step-by-step explanation:

Given that The top of a 22-foot ladder rests against the top of an 18-foot wall.

The ladder, the wall and the floor together make a right angled triangle with hypotenuse as ladder.

Thus we have a right triangle with hypotenuse = 22 ft

and the side of the wall = 18

The required angle is the angle  the ladder form with the ground.

Hence we have if x is the angle

[tex]sin x =\frac{Opposite}{Hypotenuse} =\frac{18}{22}[/tex]

From this we can find the angle X

X = sin inverse of 18/22

X=54.9

Round it off to X=55 degrees

The conversion of the expression 6^2=36 into logarithmic form results in log6(36) = 2. This method involves identifying the base (6), the exponent (2), and the result (36) in the original exponential equation.

In mathematics, you can interchange between an exponential form and a logarithmic form. Your given expression is 6^2=36, which is in exponential form.

To change this into logarithmic form, identify the base (which is 6 in this case), the exponent (which is 2), and the result (which is 36). The logarithmic form of the equation would then be 'log base 6 of 36 is 2'.

So, written in the usual mathematical notation, your answer would be log6(36) = 2. Here, 'log' stands for logarithm; the number following 'log' (6 in this case) is the base, the term within parentheses (36 in this case) is the number we're taking log of, and '2' is the value of the logarithm.

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Answer:

f(x) = 15x + 25; f(6) = 115

Step-by-step explanation:

the flat rate of $25 will be the y-intercept and the slope will be $15. since u are charged $115, plug that in for f(x) and solve for x. so the right answer is

f(x) = 15x + 25; f(6) = 115

Answer with explanation:

Saving Account →A savings account is a type of bank account in which you can keep extra money possessed by you in an institution, which is most safest place,The money you get  as an interest  is proportional to amount of money deposited in that institution.

A. Passbook Account :  A Passbook Savings account is also a saving account,in which you get interest for your deposit and also get a passbook for easy record keeping.

B.Statement account : It is also a saving account,in which you get statement for your credit and debit in your account.

C. Club Account: In this type of Saving account, you deposit money for your future investment or for any future purpose by a group.You have to deposit and withdraw money within a certain time frame.

D. Automatic account: In this type of account , money is transferred to it's customers automatically in their accounts by a certain process. It is not a saving Account.

Option 4→: Automatic Account : is the type of account which is not a saving Account.

The relationship between the books and the students is an illustration of a linear function

The formula for the function is: [tex]b(s) = 560 - 3s[/tex]

From the question, we have:

[tex]b = 560[/tex] --- number of books in the morning

[tex]r = 3[/tex] ---- the number of books per students

So, the number of books as a function of number of students is:

[tex]b(s) = b - r \times s[/tex]

Substitute known values

[tex]b(s) = 560 - 3 \times s[/tex]

[tex]b(s) = 560 - 3s[/tex]

Hence, the formula for the function is:

[tex]b(s) = 560 - 3s[/tex]

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Answer: Its 329.18 just took a test.

Final answer:

Mr. Lopez can fill 21 full packages of dried fruit, each containing 3/16 of a pound, with his 4 pounds of dried fruit.

Explanation:

The question asks how many packages of dried fruit Mr. Lopez can fill if each package contains 3/16 of a pound and he has 4 pounds of dried fruit. To answer this, we need to perform a division to find out how many 3/16 are in 4 pounds.

To solve this, we divide 4 pounds by 3/16 pounds per package:

4 ÷ (3/16) = (4/1) ÷ (3/16) = (4 × 16) / 3 = 64/3 = 21 with remainder 1.

Therefore, Mr. Lopez can fill 21 full packages of dried fruit and will have a little left over which is not enough to fill an additional full package.

The exact value of the expression √180 - √125 + √5 simplifies to 2√5, by combining like terms after simplifying each square root separately.

The exact value of the expression [tex]\sqrt{180}[/tex] - [tex]\sqrt{125}[/tex] + [tex]\sqrt{5}[/tex] can be calculated by simplifying each square root separately. Firstly, the [tex]\sqrt{180}[/tex] can be simplified to 6√5, because 180 = 36 × 5, and 36 is a perfect square whose square root is 6. Similarly, the [tex]\sqrt{125}[/tex] simplifies to 5√5, since 125 = 25 × 5 and the [tex]\sqrt{25}[/tex] is 5. The [tex]\sqrt{5}[/tex] remains as it is because it cannot be simplified further.

The expression then becomes 6√5 - 5√5 + √5. Now, we combine like terms. Since all terms involve the [tex]\sqrt{5}[/tex], we can combine them as follows: (6 - 5 + 1)√5, which simplifies to 2√5. Therefore, the exact value of the expression is 2√5.

Final answer:

To estimate the difference between 615 and 342, round each number to the nearest ten or hundred and subtract. Rounding to the nearest hundred gives an estimate of 300, while rounding to the nearest ten gives an estimate of 280.

Explanation:

To estimate the difference between 615 and 342, you can round each number to the nearest ten or hundred and then subtract the rounded numbers. Here's the step-by-step process:

This gives an estimate of the difference between 615 and 342 as 300.

If you prefer to round to the nearest ten instead, you'd get:

In this case, the estimate would be 280. You can choose the level of precision you want in your estimate based on how you round the numbers.

The value of 4 in the given number is 4000.

The given number is 24,659.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

In the given number 24,659, 4 is in thousands place.

So, the value of 4 is 4000

Therefore, the value of 4 in the given number is 4000.

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To find the width of the river, use trigonometry and the tangent function. The width of the river is approximately 67.1 meters.

To find the width of the river, we can use trigonometry. The surveyor measured an angle of 35° from the baseline to the tree on the opposite bank. We know the distance along the river is 100 m. Let's denote the width of the river as 'x'.

We can use the tangent function to solve for 'x'. The tangent of the angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 'x' (the width of the river) and the adjacent side is 100 m (the distance along the river).

So, the equation becomes:

tan(35°) = x/100

To find the value of 'x', we can multiply both sides by 100:

x = 100 * tan(35°)

Using a calculator, we can find that x is approximately 67.1 m. Therefore, the width of the river is approximately 67.1 meters.

a. Set 2 has larger standard deviation.

b. Set 1 and set 2 have same standard deviation.

c. Set 2 has larger standard deviation.

a. Set 1: 4, 7, 7, 7, 10

Set 2: 4, 6, 7, 8, 10

It seems like Set 2 might have a larger standard deviation because the numbers are more spread out from the mean (which appears to be around 7).

The set 3 has larger standard deviation.

For Set 1:

Mean = (4 + 7 + 7 + 7 + 10) / 5

= 7

Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (7-7)^2 + (7-7)^2 + (7-7)^2 + (10-7)^2)}{5}[/tex]]

= 1.89

For Set 2:

Mean = (4 + 6 + 7 + 8 + 10) / 5

=7

Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (6-7)^2 + (7-7)^2 + (8-7)^2 + (10-7)^2)}{5}[/tex]]

= 2

Hence, set 2 has larger standard deviation.

b. Set 1: 100, 140, 150, 160, 200

Set 2: 10, 50, 60, 70, 110

Here, Set 1 seems to have same standard deviation as set 2.

For set 1:

Mean = (100 + 140 + 150 + 160 + 200) / 5 = 150

Standard Deviation =[tex]\sqrt{\frac{(100-150)^2 + (140-150)^2 + (150-150)^2 + (160-150)^2 + (200-150)^2)}{5}}[/tex]

= 32.24

For set 2:

Mean = (10 + 50 + 60 + 70 + 110) / 5

= 60

Standard Deviation =  [tex]\sqrt{\frac{(10-60)^2 + (50-60)^2 + (60-60)^2 + (70-60)^2 + (110-60)^2)}{5}}[/tex]

=32.24

Hence, set 1 and set 2 have same standard deviation.

c. Set 1: 10, 16, 18, 20, 22, 28

Set 2: 48, 56, 58, 60, 62, 70

Set 2 generally has larger values, suggesting that it could have a larger standard deviation because the mean is larger for set 2.

For Set 1:

Mean = (10 + 16 + 18 + 20 + 22 + 28) / 6

= 19

Standard Deviation = [tex]\sqrt{\frac{(10-19)^2 + (16-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (28-19)^2)}{6}}[/tex]

= 5.50

For Set 2:

Mean = (48 + 56 + 58 + 60 + 62 + 70) / 6

= 58.33

Standard Deviation = [tex]\sqrt{\frac{(48-58.33)^2 + (56-58.33)^2 + (58-58.33)^2 + (60-58.33)^2 + (62-58.33)^2 + (70-58.33)^2)}{6}}[/tex]

=6.641

Hence, the second set have the larger standard deviation.

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Answer:

-22

Step-by-step explanation:

This is a case of directed numbers. The numbers 23 and 2 carry negative signs like this:

- 23

- 2

Therefore, adding these negative numbers gives -23 - 2 = -25

Adding the sum to 3 gives: 3 - 25 = -22

A cell phone weighing 2 ounces translates to 0.125 pounds, since there are 16 ounces in one pound.

Cell phones can weigh as little as 2 ounces. The first step in determining how much a cell phone can weigh in pounds is to know the conversion factor between ounces and pounds. Since there are 16 ounces in one pound, you can divide the weight of the cell phone in ounces by 16 to convert it to pounds. For a cell phone that weighs 2 ounces:

Therefore, a cell phone that weighs 2 ounces is equivalent to 0.125 pounds.