How would the domain and range of the function y = one-fourth x minus 6 be determined? Explain.

The function f(x) = |x| - 5 is a piecewise function with two different cases: when x is negative and when x is positive.

This means that the function can take on different values depending on whether x is negative or positive.Case 1: x is negativeIf x is negative, then f(x) = -x - 5. To find the range of this function, we can look at the minimum value that f(x) can take on. Since -x is always nonpositive, the smallest value that f(x) can take on is when x = 0, which gives f(0) = -5.

Therefore, the range of f(x) for x negative is given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}Case 2: x is positiveIf x is positive, then f(x) = x - 5. To find the range of this function, we can look at the minimum value that f(x) can take on. Since x is always nonnegative, the smallest value that f(x) can take on is when x = 0, which gives f(0) = -5. Therefore, the range of f(x) for x positive is also given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}Overall, the range of the function f(x) = |x| - 5 is given by:r: {f(x) ∈ ℝ | f(x) ≤ -5}

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Answer:

Where are the picture and problems so I can help?

The area of the circle is approximately 1089.59 square centimeters.

To find the area of a circle with a circumference of 117 cm, we need to first determine the radius.

We can use the circumference formula:

C = 2πr

where C is the circumference (117 cm), r is the radius, and π is approximately 3.14159.

Rearranging the formula to find the radius:

r = C / (2π) = 117 / (2 x 3.14159) ≈ 18.61 cm

Now, we can calculate the area using the area formula:

A = πr² A = 3.14159 x (18.61)²≈ 1089.59 square centimeters

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There are approximately 2.97 billion droplets per acre being sprayed.

To calculate the number of droplets per acre, we need to first convert the diameter of the droplets from microns to inches (since we are using acres as our unit of area). There are 25,400 microns in one inch, so the diameter of the droplets in inches is 250/25,400 = 0.0098 inches.

Next, we need to calculate the area of one droplet. The formula for the area of a circle is A = πr², so the area of one droplet is A = π(0.0049)² = 0.0000754 square inches.

Finally, we can calculate the number of droplets per acre by dividing the total area of one acre (43,560 square feet) by the area of one droplet: 43,560 / 0.0000754 = 2.97 billion droplets per acre.

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Let x be the number of child tickets sold

Let y be the number of adult tickets sold

Amount received for the child tickets: 5.90x

Amount received for the adult tickets: 9.40y

Total sales of 1001.30:

127 tickets were sold:

Use the two equations above as a system of equations, to solve it:

1. Solve y in the second equation.

2. Use the value you get in step 1 to substitute y in the first equation:

3. Solve x:

The value of x is 55

Answer:

400.582

Step-by-step explanation:

Hope it helps!!!!!!!

Answer:

y=40 z= 5h+15

5 hours to make the same amount of money

Step-by-step explanation:

40-15=25

25/5=5

hope this helped

Answer:

Step-by-step explanation:

-1,1,3

Answer:

28 tickets were purchased

Step-by-step explanation:

If angle 1 is complementary to angle 2, then m∠1 + m∠2 = 90.

This statement is the Definition of Complementary Angles. The sum of complementary angles is 90 degrees.

Complementary angles always come in pairs while right angle is just one.

The total amount the mechanic will need in retirement savings to meet their retirement income goal is 870,000. The correct option is C.

In mathematics, an expression is a combination of numbers, symbols, and operations (such as addition, subtraction, multiplication, and division) that represents a quantity or a value.

Expressions can be very simple, such as a single number or variable, or they can be more complex, such as a combination of multiple terms with different operators.

The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x 43,500 = $34,800 per year

The mechanic plans to draw 4% the first year from their retirement savings, which means the total retirement savings needed are:

34,800 / 0.04 = $870,000

Therefore, the answer is C) 870,000.

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a) The probability of a very good poker player earning a profit (more than $0) after playing 40 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31). b) The proportion of the time a very good poker player can expect to earn at least $500 after playing 100 hands in $100/$200 Texas Hold'em can be calculated using the normal distribution and the given mean ($1) and standard deviation ($31).

To compute these probabilities, we need to make some assumptions and use probability distribution calculations based on the given information.

a) To determine the probability of a profit after playing 40 hands, we can use the concept of the normal distribution. We need to calculate the z-score using the formula: z = (x - μ) / σ, where x is the desired profit, μ is the expected profit per hand, and σ is the standard deviation. In this case, x = $0, μ = $1, and σ = $31.

Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.

b) Similarly, to find the proportion of the time a player can expect to earn at least $500 after playing 100 hands, we need to calculate the z-score for x = $500, using the same formula as in part (a). Then, we can use the standard normal distribution table or calculator to find the corresponding proportion.

c) To determine the probability of earning a profit during a 14-hour session, we need to calculate the number of hands played, which is 20 hands per hour multiplied by 14 hours. Let's denote it as N. Then, we can calculate the mean profit for the 14-hour session by multiplying the expected profit per hand ($1) by N.

The standard deviation for the session can be calculated by multiplying the standard deviation per hand ($31) by the square root of N. Finally, we can use the normal distribution and the same z-score calculation as in part (a) to find the probability.

Please note that the above calculations assume that the profits from each hand are independent and follow a normal distribution. Real poker outcomes may deviate from these assumptions.

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Answer:

200 ml

Step-by-step explanation:

Orange squash is mixed with water in the ratio 1 : 3. If you use 600 ml of water, how much squash do you need?

1 is to 3 as x is to 600

1 is 1/3 of 3 so x should be 1/3 of 600

1/3 of 600 = 200

use 200 ml squash to keep the ratio the same.

Answer:

I don't know ask your parents

Step-by-step explanation:

The value of x that makes the given lines perpendicular is -8

From the question, we are to calculate the value of x that makes the lines perpendicular to each other

Two lines are perpendicular if the slope of one line is the negative reciprocal of the other line

Now, we will determine the slope of the first line

Using the formula for the slope of a line,

Slope = (y₂ - y₁) / (x₂ - x₁)

x₁ = 1

x₂ = 7

y₁ = 2

y₂ = 6

Slope = (6 - 2) / (7 - 1)

Slope = 4 / 6

Slope = 2/3

If the lines are perpendicular, the slope of the other line must be -3/2

For the other line,

x₁ = 3

x₂ = 11

y₁ = 4

y₂ = x

Thus,

-3/2 = (x - 4) / (11 - 3)

Solve for x

-3/2 = (x - 4) / 8

2(x - 4) = -3 × 8

2x - 8 = -24

2x = -24 + 8

2x = -16

x = -16/2

x = -8

Hence, the value of x is -8

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Answer:

The slope is 1/6.

Step-by-step explanation:

The slope of the given equation is -6. Perpendicular lines have negative reciprocal slopes.

Let's denote the time it took Juan Pablo to drive from home to college as "t1" and the time it took him to drive back from college to home as "t2". We know that the average speed is equal to the total distance divided by the time taken.

The distance from home to college is the same as the distance from college to home, so we can denote it as "d".  Using the formula: Speed = Distance / Time, we can write the equations: 59.6 = d / t1     (Equation 1) 67.2 = d / t2     (Equation 2) We are also given that the total round trip took 10 hours, so we have the equation: t1 + t2 = 10     (Equation 3) To solve these equations, we can rearrange Equation 1 and Equation 2 to solve for "d" in terms of "t1" and "t2": d = 59.6 * t1     (Equation 4) d = 67.2 * t2     (Equation 5) Now, substituting Equation 4 and Equation 5 into Equation 3, we get: 59.6 * t1 + 67.2 * t2 = 10 Solving this equation will give us the values of t1 and t2. However, we need additional information to find a unique solution for t1 and t2.

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Answer:

8 tacos

Step-by-step explanation:

40 tacos    to     15 students

8 tacos       to      3 students

15/3 =5, so divide 40 by 5 to get 8

Answer:64 students

Step-by-step explanation:

using the empirical rule, we know that 34% of a normal distribunion is below the mean but above 1 standard deviation. This means that 16% of the students enter before 9:55. Take 16% of 400 and you get the amount of students in before 9:55

Answer:

mxv

Step-by-step explanation:

2.0x2.8=5.6

momentums equation is mass times velocity so 2.0kg is the mass and you multiply it by the velocity which is 2.8m/s and that is how you get your answer. your answer is number 3

Answer:

Step-by-step explanation:

Approximately 68% of the IQ scores are between 87 and 121.

The empirical rule is also known as the 68-95-99.7 rule.

It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.

Here, the IQ scores follow a bell-shaped distribution with a mean of 104 and a standard deviation of 17, i.e., N(104, 17).

To find out what percentage of IQ scores are between 87 and 121, we need to calculate the z-scores for these two values. A z-score tells us how many standard deviations an observation is from the mean. We use the formula:

z = (x - μ) / σ

where x is the observation, μ is the mean, and σ is the standard deviation.

For x = 87,

z = (87 - 104) / 17
z = -1

For x = 121,

z = (121 - 104) / 17
z = 1

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since the standard deviation here is 17, one standard deviation is 17. Therefore, 68% of the data falls within the range 104 - 17 = 87 to 104 + 17 = 121. This means that approximately 68% of the IQ scores are between 87 and 121.


So, the  answer to the question is 68% of IQ scores are between 87 and 121, according to the empirical rule.

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Answer:

MAKE HIS EVELS  FRGURE IT OUT XD

Step-by-step explanation:

Answer:

ratio of girls to boys = 14:10 or 7:5 (simplified)

ratio of boys to class = 10:24 or 5:12 (simplified)

Step-by-step explanation:

Answer:

\(ax - y + z = b \\ ax = b + y - z \\ \\ x = \frac{ b + y - z }{a} \)

I hope I helped you^_^

If A is a subset of B, it does not necessarily mean that A is a proper subset of B. The union of any set A and its complement is indeed the universal set.

1. False: If A is a subset of B, it does not necessarily mean that A is a proper subset of B. A proper subset is a subset that contains some, but not all, elements of the superset. In other words, if A is a proper subset of B, it means that there exists at least one element in B that is not in A. However, if A is simply a subset of B, it is possible for A and B to have the same elements, making them equal sets.

For example, let's consider two sets:

A = {1, 2}

B = {1, 2, 3}

In this case, A is a subset of B because every element in A (1 and 2) is also in B. However, A is not a proper subset of B since there are no elements in B that are not in A. Therefore, statement 1 is false.

2. True: The union of any set A and its complement is indeed the universal set. The complement of a set A, denoted as A', consists of all elements that are not in A but are in the universal set U. When we take the union of A and its complement, we are effectively combining all elements from A and all elements not in A.

Let's consider a set A and its complement A' within a universal set U. The union of A and A' is denoted as A ∪ A' and can be represented as U. This is because every element in the universal set U is either in A or not in A (in A').

For example, let's consider the following sets:

U = {1, 2, 3, 4, 5}

A = {1, 2}

The complement of A, A', would be {3, 4, 5}. The union of A and A' (A ∪ A') is {1, 2} ∪ {3, 4, 5}, which is equal to U: {1, 2, 3, 4, 5}. Thus, the union of any set A and its complement is indeed the universal set. Therefore, statement 2 is true.

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The probability that both pencils picked at random with replacement from a basket containing 5 purple and 9 brown pencils are purple is 9/98.

To calculate the probability of picking two purple pencils with replacement, we need to use the multiplication rule of probability. The probability of picking the first purple pencil is 5/14, and the probability of picking a second purple pencil from the basket is also 5/14 since we are replacing the first pencil. Therefore, the probability of picking two purple pencils with replacement is (5/14) × (5/14) = 25/196. However, we also need to account for the possibility of picking a brown pencil first and a purple pencil second.

The probability of picking a brown pencil first is 9/14, and the probability of picking a purple pencil second is 5/14. So, the probability of picking a brown pencil followed by a purple pencil is (9/14) × (5/14) = 45/196. Adding the probability of picking two purple pencils and the probability of picking a brown pencil followed by a purple pencil gives us the total probability of (25/196) + (45/196) = 9/98.

Therefore, the probability that both pencils picked at random with replacement from a basket containing 5 purple and 9 brown pencils are purple is 9/98.

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