Which of the following could be an example of a function with a range (-, ) and a domain [b, ) where a > 0 and b>0?

Which of the following could be an example of a function with a range (-∞, α) and a domain [b, ∞) where a > 0 and b>0?

Answers

Answer 1

Answer: Choice D

Explanation:

Choices A and B are ruled out because they are cube root functions, which have a domain and range of "all real numbers".

Choice C is ruled out because the domain is [tex][a, \infty)[/tex]

To determine this domain, we set the radicand (aka stuff under the square root) to be greater than or equal to zero.

[tex]x-a \ge 0 \ \ \text{ solves to } \ \ x \ge a[/tex]

[tex]x \ge a \ \ \text{ turns into the interval notation } \ \ [a, \infty)[/tex]

The square bracket is used to include the value 'a' as part of the interval. This is the interval from x = a to positive infinity.

The domain of choice D is [tex][b, \infty)[/tex] found using similar steps as shown above.

The range is [tex](-\infty, a][/tex] since this square root function is decreasing, due to the negative out front, which means y = a the largest output possible. I recommend graphing it out using a tool like desmos or geogebra. These tools offer a way to use parameters.

Related Questions

is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.

Answers

Answer:

Not parallel.

Step-by-step explanation:

Given:

m∠9 = 110°m∠8 = 70°

Linear Pair

Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

Angles 9 and 10 form a linear pair:

⇒ m∠9 + m∠10 = 180°

⇒ 110° + m∠10 = 180°

⇒ m∠10 = 70°

Angles 7 and 8 form a linear pair:

⇒ m∠7 + m∠8 = 180°

⇒ m∠7 + 70° = 180°

⇒ m∠7 = 110°

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:

m∠1 = m∠6 = m∠9 = m∠14 = 110°m∠2 = m∠5 = m∠10 = m∠13 = 70°m∠3 = m∠8 = m∠11 = m∠16 = 70°m∠4 = m∠7 = m∠12 = m∠15 = 110°

If line a was parallel to line b, then according to the corresponding angles postulate:

m∠1 = m∠3 = m∠6 = m∠8m∠2 = m∠4 = m∠5 = m∠7

As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.

Angle ABC is taken by a dilation with centerpoint, P and scale factor of four to angle A’B’C’ the measure of angle, BCA is 75° what is the measure of angle B’C’A’

Answers

Answer:

75°

Step-by-step explanation:

You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.

Dilation

Dilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.

m∠B'C'A' = 75°

Chandrani had a Rs 100 note she bought a geometry box for ₹ 37 . 75. Find the amount left with her

Answers

Answer:

The amount left with her si 62.25

A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

Answers

The mean and standard deviation of a random variable can be used to describe the distribution of its possible values. In this case, the mean of the random variable X represents the average number of bottles of soda that are bought from the vending machine on a given day, and the standard deviation represents the amount of variation in the number of bottles bought from one day to the next.

To find the mean and standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, you will need to use the mean and standard deviation of X and the price per bottle of soda.

The mean of Y can be calculated using the formula:

mean of Y = mean of X * price per bottle

Plugging in the given values, we get:

mean of Y = 50 * $1.50 = $75

So the mean of the random variable Y, which represents the total revenue from the vending machine on a given day, is $75.

The standard deviation of Y can be calculated using the formula:

standard deviation of Y = standard deviation of X * price per bottle

Plugging in the given values, we get:

standard deviation of Y = 15 * $1.50 = $22.50

So the standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, is $22.50.

Therefore, the mean and standard deviation of Y, the total revenue from the vending machine on a given day, are $75 and $22.50, respectively.

Question 60
Find the probabilities below using a standard 52 card deck.

Answers

By using the concept of probability, it can be calculated that-

1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]

5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur.

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

1) Number of ace card = 4

Number of '5' card = 4

P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]

= [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)

Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]

P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) Number of black coloured even numbered card = 10

Number of even numbered card = 20

Number of card of black colour = 26

P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]

= [tex]\frac{36}{52}[/tex]

5) Number of face cards of diamond = 3

P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

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a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg

Answers

The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18

Maximum and Minimum:

The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value

The least amount or value or number that may be admitted or reached or can be counted is the Minimum value

Here we have a table

Which represents the masses of various dogs

Mass (x) kg frequency

0 ≤ x < 10 2

10 ≤ x < 20 7

20 ≤ x < 30 12

30 ≤ x < 40 6

Here the mass of dogs is represented in class intervals

a) The minimum number of dogs with a mass of more than 24kg.

From the given table,

24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40

In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg

In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg

So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40

Therefore,

The minimum number of dogs with a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.

And in class 30 ≤ x < 40 the mass will be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs with a mass of than 24kg is 18

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The equation of the graph
is y = pq* where p and q are
positive constants.
Find the values of p and q.

Answers

The graph is y = 3 * 2^x where * means multiplication
It might be easier to read as y = 3(2^x)

Not sure what pq* meant in your question but p is probably 3 and q is 2

Writing Equations of lines

Write the equation of each line with the given information

through: (-3, 4) and (-5, -1)

Answers

Answer:

y = 5/2x + 11.5

Step-by-step explanation:

(-3, 4) (-5, -1)

m = -1-4/ -5+3

m = -5 / -2

m = 5/2

y = 5/2x + b

-1 = 5/2(-5) + b

-1 = -12.5 + b

b = 11.5

y = 5/2x + 11.5

Answer:

y-y1=y2-y1/x2-x1(x-x1)

y-4= (-1-4/-5+3) (x+3)

y-4= -5/-2(x+3)

y=5/2x+15/2+4

y=5/2x+15+8/2

y=5/2x+23/2

Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.

Answers

The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².

What is Area :

The space around a shape's perimeter or boundary is known as its area. To determine the areas of various forms, many mathematical formulae are available.

Area of circle = πr², where r is the radius of the circle. Area of rectangle = lb, where l = length and b = breadth.

Here we have

composed of a rectangle and two semicircles.

Dimensions of the rectangle are,

Length = 14 and breadth = 4

=>Area of the rectangle = 14 × 4 = 56 units²

If we join the two semicircles,

we will have one circle with a diameter of 4 units

=> As we know Radius of the circle = Diameter/2

=> Radius of circle = 4/2 = 2 units

=> Area of the circle = 2πr

= [tex]2 \times\frac{22}{7} \times 2[/tex] = 12.56 unit²

Area of the figure = Area of rectangle + Area of the circle

= 56 units² + 12.56 unit²

= 68.56 unit²

Therefore,

The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².

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Which ordered pair satisfies the inequality? 6x + 5y < -15

Answers

The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).

What is inequality?

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:

(2, 0):

6x + 5y > 2

6(2)+5(0)>2

12+0>2

12>0

Since the inequality holds, then the ordered pair is a solution.

(7, -8):

6x + 5y > 2

6(7)+5(-8) > 2

42-40>2

2>2

Since the inequality is not satisfied, then the ordered pair is not a solution.

(3, 2):

6x + 5y > 2

6(3)+5(2) >2

18+10>2

28>2

Since the inequality holds, then the ordered pair is a solution.

(-8, 6):

6x + 5y > 2

6(-8)+5(6) >2

-48 + 30 > 2

-18 > 2

Since the inequality is not satisfied, then the ordered pair is not a solution.

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help please very easy proportional relationship due hurry please than u!

Answers

1) h=1/5 k

(10/2 = 1/5, 20/4 = 1/5... etc)

2) k=5/4 h

(5/4 = 5/4, 10/8=5/4... etc)

3) h=5/1 k

(25/5 = 5/1, 30/6 = 5/1 ... etc)

Hope this helps!

Two basketball players are trying to have the most
points per game for the season. The current leader has
2112 points in 77 games and the second place player
has 2020 in 74 games. How many points per game did
the leading team score?

Helpppppp

Answers

The leading team has scored 0.13 points per game for the season that the second place player.

What is PPG Statistics?

The average number of points a player scores in a game of a sport, over the course of a series of games, a season, or a career, is known as points per game, or PPG, and it is an important statistic. By dividing the total points by the number of games, it is calculated. Basketball and ice hockey are two sports that frequently use PPG statistics.

First, consider the PPG of the current leader of the season from among the two basketball players.

The total number of points obtained by the current leader is equal to 2112.

The total number of games played by the current leader is equal to 77.

The points per game obtained by the current leader can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2112}{77}\\\implies PPG=27.42[/tex]

Now, consider the PPG of the second place player for the season.

The total number of points obtained by the second place player is equal to 2020.

The total number of games played by the second place player is equal to 74.

The points per game obtained by the second place player can be calculated as follows,

PPG = Total Points Obtained / Total Number of Games

[tex]\implies PPG=\frac{2020}{74}\\\implies PPG=27.29[/tex]

Subtracting the points per game of both players, we get

[tex]27.42-27.29=0.13[/tex]

Hence, the leading team has scored 0.13 points per game (PPG) for the season compared to the second place player.

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What is the inverse of f(x)=2x+9?

Answers

Answer:Find the Inverse f (x)=-2x+9Find the Inverse f (x)=-2x+9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9 f (x) = −2x + 9 f (x) = - 2 x + 9 Write f (x) = −2x+ 9 f (x) = - 2 x + 9 as an equation. y = −2x+9 y = - 2 x + 9

Step-by-step explanation:

Solve the equation for v.

0.5v + 0.03 > 2.83

v > 1.3
v < 1.3
v > 5.6
v < 5.6

Answers

Answer:

[tex] \huge{ \boxed{v > 5.6}}[/tex]

Step-by-step explanation:

[tex]0.5v + 0.03 >2.8[/tex]

In order to solve this inequality, first subtract 0.03 from both sides of the inequality to isolate 0.5v

[tex]0.5v + 0.03 - 0.03 > 2.83 - 0.03 \\ 0.5v > 2.8[/tex]

Next divide both sides by 0.5

[tex] \frac{0.5v}{0.5} > \frac{2.8}{0.5} \\ v > 5.6[/tex]

We have the final answer as

[tex] \bold{v > 5.6}[/tex]

6x + 3y = 3 3x - y = 4

Answers

Answer:

x = 1

y = -1

Step-by-step explanation:

Given equations:

6x + 3y = 3 -------------(1)

3x - y = 4 ----------------(2)

Multiply Eq. (2) by 2

2(3x - y) = 4 × 2

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

Subtract Eq. (3) from Eq. (1)

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

6x + 3y - 6x + 2y = -5

3y + 2y = -5

5y = -5

Divide 5 to both sides

y = -5/5

y = -1

Put y = -1 in Eq. (1)

6x + 3(-1) = 3

6x - 3 = 3

Add 3 to both sides

6x = 3 + 3

6x = 6

Divide 6 to both sides

x = 1

[tex]\rule[225]{225}{2}[/tex]

Prove that the roots of the equation mx² + (m − 2)x − (m + 1) = 0 are real for all values of m

Answers

Answer:

Below

Step-by-step explanation:

For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)

b^2 - 4ac >= 0 where a = m b = m-2 c = -m-1

(m-2)^2 - 4(m)(-m-1) >=0

5m^2 +4 >= 0

5 m^2 +4 <===== will always be >= 0 for any value of 'm'

so all roots will be real

Complete the ratio 4:16 = 1:?

Answers

Answer:

1:4

Step-by-step explanation:

4:16 = 1:?

4/4 = 1

16/4 = 4

= 1:4

A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71° from the horizontal.

Find the tension in the support cable. Give answer to the nearest whole number.

Answers

The tension in the support cable is 2731 N

How to find the tension in the support cable?

Given that:

A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N) and a support cable running to the ground is inclined 71° from the horizontal.

This can sketch as shown in the attached image. Considering the image:

T is the tension in the support cable

Using trigonometric ratio:

cos 71° = 889/T (adjacent/hypotenuse)

T = 889/cos 71°

T = 2731 N

Therefore, the tension in the support cable is 2731 N

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A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.

Answers

The value of x inside the triangle is 24°

How to calculate the value of x(angle)?

A straight line's total number of angles adds up to 180°. Supplementary angles are two angles whose sums equal 180 degrees. Angles are referred to as neighbouring if they have a similar vertex and side.A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight.Angles in a straight line are the total of all the angles that can be arranged in a straight line. Straight line angles add up to 180°.

The angle of the straight line = 180°

156° + x = 180°

x = 180° - 156°

x = 24°

Hence, the value of x inside the triangle is 24°.

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1.6y+y-4/15y+1 1/6y=2 1/3 pls help

Answers

The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

What is the domain of the function?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

1.6y+y-4/15y+7/6y=21/3

Move all terms to the left:

1.6y+y-4/15y+7/6y-(21/3)=0

Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R

Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R