The one-to-one functions g and h are defined as follows.

6. The value of P(7) = 1/10

7. P(less than 5) = 2/5

8. P(odd) = 1/2

9. P(less than 1) = 0

10. P(greater than 10) = 0

11. P(divisible by 2 or 3) = 3/5

Let's consider each probability separately:

P(7):

Since Dave's number is a whole number greater than 0 and less than 11, there are 10 possible numbers he could have chosen (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

Out of these 10 numbers, only one is 7.

Therefore, the probability that Dave's number is 7 is 1/10.

P(less than 5):

Out of the 10 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), there are four numbers that are less than 5 (1, 2, 3, 4).

Hence, the probability that Dave's number is less than 5 is 4/10, which simplifies to 2/5.

P(odd):

Out of the 10 possible numbers, there are five odd numbers (1, 3, 5, 7, 9). Therefore, the probability that Dave's number is odd is 5/10, which simplifies to 1/2.

P(less than 1):

Since the number must be greater than 0, it cannot be less than 1.

Thus, the probability of choosing a number less than 1 is 0.

P(greater than 10):

Since the number must be less than 11, it cannot be greater than 10.

Thus, the probability of choosing a number greater than 10 is 0.

P(divisible by 2 or 3):

Out of the 10 possible numbers, there are six numbers that are divisible by 2 or 3 (2, 3, 4, 6, 8, 9).

Therefore, the probability that Dave's number is divisible by 2 or 3 is 6/10, which simplifies to 3/5.

For similar question on probability.

https://brainly.com/question/30390037  

#SPJ8

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

For more such questions on subsequent stop

https://brainly.com/question/29636800

#SPJ8

Answer:

x = 5

Step-by-step explanation:

4x - 8 = 12

4x - 8 + 8 = 12 + 8    correct

4x = 20     correct

Now, multiply both sides by 1/4.

¼ × 4x = ¼ × 20

x = 5

Answer: X = 5

Step-by-step explanation:

4X - 8 = 12

4X = 12 + 8

4X = 20

X = 20/4

X = 5

The probability that the date on the penny will be earlier than 1990 is A. 7/15

Probability is the likelihood of an event.

Since Kevin looked at the dates on a random sample of 15 pennies taken from a small jar of pennies. He made the graph shown below to display the data. Kevin will take 1 penny from the jar at random. Based on the data in the graph, what is the probability that the date on the penny will be earlier than 1990?

To find the probability, we proceed as follows

Let P(<1990) = probability that the date on the penny will be earlier than 1990

Now, P(<1990) = n/N where

From the graph

So, substituting these into the equation, we have that

P(<1990) = n/N

P(<1990) = 7/15

So, the probability is A. 7/15

Learn more about probability here:

https://brainly.com/question/30768613

#SPJ1

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

For such more questions on coordinate

https://brainly.com/question/29660530

#SPJ8

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 17 cm and X cm, and another side labeled as 15 cm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 17 cm + X cm + 15 cm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

However, it's important to note that we need additional information to solve for X. In a triangle, any two sides must be greater than the third side. So, we need to know the relationship between the lengths of the sides to determine the possible values for X.

The linear function that describes the data in the table for this problem is given as follows:

C. P(h) = h + 11.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

From the table, we have that when h increases by 1, P(h) also increases by 1, hence the slope m is given as follows:

m = 1/1 = 1.

Hence:

P(h) = h + b.

When h = 4, P(h) = 15, hence the intercept b is given as follows:

15 = 4 + b

b = 11.

Hence the rule is:

P(h) = h + 11.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

1.) The angle that cannot be an exterior angle of a regular polygon among 36°, 50°, 30°, and 45° is 30°. The sum of the other three angles is less than 360°.

2.) The angle is -60° as its complement is one-fourth of its supplementary angle based on the given condition.

3.) A rhombus has no volume as it is a 2D shape. However, its area is 24 square cm with a diagonal measure of 4√3 cm.

1.) Among the angles 36°, 50°, 30°, and 45°, the angle that cannot be an exterior angle of a regular polygon is 30°. This is because the sum of the exterior angles of any polygon is always 360°, and the sum of the other three angles (36° + 50° + 45°) equals 131°, which is less than 360°. Therefore, 30° is the angle that cannot be an exterior angle of a regular polygon.

2.) Let's assume the measure of the angle is 'x' degrees. The complement of the angle would be (90 - x) degrees, and the supplementary angle would be (180 - x) degrees. According to the given condition, the complement is one-fourth of the supplementary angle:

90 - x = (1/4)(180 - x)

Multiplying both sides by 4 to eliminate the fraction:

360 - 4x = 180 - x

Simplifying the equation:

3x = 180 - 360

3x = -180

Dividing both sides by 3:

x = -60

Therefore, the measure of the angle is -60 degrees.

3.) A rhombus does not have a volume since it is a two-dimensional shape. Volume is a measure of space, and rhombi are flat shapes with no thickness. However, we can calculate the area of a rhombus.

The formula to calculate the area of a rhombus is given by:

Area = (diagonal 1 * diagonal 2) / 2

In this case, the diagonal measure is 4√3 cm:

Area = (4√3 * 4√3) / 2

Area = (16 * 3) / 2

Area = 48 / 2

Area = 24 square cm

Therefore, the area of the rhombus is 24 square cm.

For more question on angle visit:

https://brainly.com/question/31615777

#SPJ8

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)[tex]^{(-n)})[/tex]/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)[tex]{(-360)}[/tex])/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

For more questions on interest rates

https://brainly.com/question/31261623

#SPJ8

The equation of the line parallel to y = x - 5 that goes through the point (7, 0) is y = x - 7.

This line has the same slope as the given line and passes through the specified point.

To find the equation of a line parallel to the given line y = x - 5, we know that parallel lines have the same slope.

The slope of the given line is 1, as it has the coefficient of x.

Therefore, the parallel line we are looking for will also have a slope of 1.

We can use the point-slope form of a linear equation to find the equation of the line.

The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point on the line and m is the slope.

We are given the point (7, 0), so we can substitute x₁ = 7 and y₁ = 0 into the equation.

Also, since we want a parallel line with a slope of 1, we have m = 1. Substituting these values, we get:

y - 0 = 1(x - 7)

Simplifying, we have:

y = x - 7.

For similar question on line parallel.

https://brainly.com/question/30195834  

#SPJ8

The facts that are not needed to solve the problem are:B.

The wait to ride the roller coaster was 40 minutes.C.

It was Tuesday.D.

The roller coaster is the fastest ride at the fair. Option B, C, D

To determine the facts that are not needed to solve the problem of estimating the waiting time for a roller coaster, we can examine the information provided and identify the essential elements for solving the problem.

The problem asks how long one would expect to wait if the line was 50 meters long. The key factor for estimating the waiting time is the length of the line, so the relevant information is:

A. The line of people was 100 meters long. This information is needed because it provides the basis for estimating the waiting time.

B. The wait to ride the roller coaster was 40 minutes. This information is not necessary to solve the problem because it refers to the waiting time on a specific day, which is not directly related to the length of the line.

C. It was Tuesday. This information is not necessary to solve the problem because the day of the week does not affect the relationship between line length and waiting time.

D. The roller coaster is the fastest ride at the fair. This information is not necessary to solve the problem because the speed or type of the ride does not directly influence the waiting time based on the line length.

Option B, C , D

For more such questions on facts visit:

https://brainly.com/question/30308987

#SPJ8

In the expression 7x - 12, the terms, coefficients, and constants can be identified as follows:

Terms:

7x: This is a term consisting of the variable x multiplied by the coefficient 7.

-12: This is a term without a variable, and it is a constant term.

Coefficients:

The coefficient of the term 7x is 7.

It represents the factor by which the variable x is multiplied.

Constants:

The constant in the expression is -12.

It is a term without a variable, representing a fixed value.

or the term 7x.

For such more questions on expression

https://brainly.com/question/723406

#SPJ8

Answer:

x² + 12x + 36 = 0

(x + 6)² = 0

x = -6 is not in the domain of h(x).

In a 30-60-90 triangle, the special relationship between the side lengths is based on the ratios of the sides.

Let's denote the length of the shorter leg (opposite the 30-degree angle) as "x," the length of the longer leg (opposite the 60-degree angle) as "y," and the length of the hypotenuse as "z."

The special relationship can be described as follows:

The length of the shorter leg (opposite the 30-degree angle) is always x.

The length of the longer leg (opposite the 60-degree angle) is always √3 times the length of the shorter leg, which can be written as y = √3x.

The length of the hypotenuse is always twice the length of the shorter leg, which can be written as z = 2x.

To summarize:

Shorter leg: x

Longer leg: √3x

Hypotenuse: 2x

These ratios hold true for any 30-60-90 triangle.

For  such more questions on 30-60-90 triangle

https://brainly.com/question/31061827

#SPJ8

The coefficient of the second term, 6x⁴, is 6.

The terms of the polynomial are:

-4y⁵, 6x⁴, 9w³, -4w, -1

The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.

The coefficient is 6.

Therefore, the list of terms is:

-4y⁵, 6x⁴, 9w³, -4w, -1

Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.

The coefficients indicate the scalar value by which each term is multiplied.

The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.

Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.

There is a 6 coefficient.

As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.

Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.

The scalar value by which each phrase is multiplied is shown by the coefficients.

For similar questions on coefficient

https://brainly.com/question/1038771

#SPJ8

The relations that are functions in this problem are given as follows:

a, d, e.

A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

Hence the relations that are not functions in this problem are listed as follows:

More can be learned about relations and functions at brainly.com/question/10283950

#SPJ1

1: The probability of collecting a specific dinosaur is very unlikely.

2: The number of spins that it takes before you had at least one of each dinosaur in

Trial 1 is: 25 spins

Trial 2 is: 14 spins

Trial 3 is: 25 spins

3: The  number of spins correlates to the boxes of cereal by giving you a good representation on how many you will need to buy to collect all the dinosaurs.

5: The difference between experimental and theoretical probability is the experimental results can be different the theoretical results.

6: If someone bought eight boxes of cereal and got all eight dinosaurs I would be very surprised.

7: The probabilities change by starting at 25 then 14 then back up to 25.

8: The advantages of of using a simulation is that you do not have to waste as much money.

1: The probability of collecting a specific dinosaur is very unlikely.

2: The number of spins that it takes before you had at least one of each dinosaur in Trial 1 is: 25 spins

The number of spins that it takes before you had at least one of each dinosaur in Trial 2 is: 14 spins

The number of spins that it takes before you had at least one of each dinosaur in Trial 3 is: 25 spins

3: The  number of spins correlates to the boxes of cereal by giving you a good representation on how many you will need to buy to collect all the dinosaurs.

4: The experimental probability for each dinosaur from Trial 1 is: 25 spins

Trial 2: 14 spins

Trial 3: 25 spins

5: The difference between experimental and theoretical probability is the experimental results can be different the theoretical results.

6: If someone bought eight boxes of cereal and got all eight dinosaurs I would be very surprised because getting it is only eight boxes is highly unlikely but not impossible.

7: The probabilities change by starting at 25 then 14 then back up to 25.

8: The advantages of of using a simulation is that you do not have to waste as much money.

Read more about Probability of Selection at: https://brainly.com/question/251701

#SPJ1

The spinner and description of how it works is as shown in the attached files.

The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

For more such questions on number, click on:

https://brainly.com/question/24644930

#SPJ8

The y-intercept of the LSRL for the given data, with x = 12 representing the year "1912," is approximately 80.28.

To find the y-intercept of the Least Squares Regression Line (LSRL) for the given data, we can use linear regression to fit a line to the data points.

The LSRL equation is in the form y = mx + b, where y represents the response variable (in this case, the gold medal times), x represents the explanatory variable (in this case, the year represented by x = 12 for "1912"), m represents the slope of the line, and b represents the y-intercept.

First, let's assign the given data to the variables x and y, where x represents the year and y represents the gold medal times:

x = [12, 24, 32, 52, 60, 68, 76, 84, 92]

y = [82.2, 72.4, 66.8, 66.8, 61.2, 60.0, 55.65, 55.92, 54.64]

Next, we perform linear regression to find the equation of the LSRL. Using statistical software or calculators, we can find that the equation of the LSRL is y ≈ -0.29x + 80.28.

Since we are interested in the y-intercept, we set x = 0 and solve for y:

y-intercept = -0.29(0) + 80.28 = 80.28

Therefore, the y-intercept of the LSRL for the given data, with x = 12 representing the year "1912," is approximately 80.28. This value represents the predicted gold medal time in seconds for the women's 100-meter freestyle event in the year 1912, based on the regression line fitted to the available data.

For more such questions on intercept visit:

https://brainly.com/question/25722412

#SPJ8

The function that could have the graph shown above include the following: B. [tex]f(x)=20e^x[/tex].

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

By critically observing the graph of f(x) shown in the image attached above, we can reasonably infer and logically deduce that the initial value or y-intercept is located at (0, 20).

Therefore, the required exponential function for the graph shown above include the following:  

[tex]f(x)=20e^x[/tex].

Read more on exponential functions here: brainly.com/question/28246301

#SPJ1

The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

Learn more about domain and range at https://brainly.com/question/26098895

#SPJ1

Step-by-step explanation:

if you are not sure what a word means, use the general internet.

that is much faster than putting such a question in here and then waiting for an answer.

e.g.

a pentagon has 5 corners and 5 sides connecting these corners.

as penta is Greek for 5.

for a decagon, well, deca means 10.

so, a decagon has ... ... 10 corners and 10 sides.

the perimeter is the whole way around the object, so, it is the sum of all 10 sides.

therefore one side is

85 in / 10 = 8.5 in

The value of x is 67. 3 degrees

To determine the value of the angle labelled x, we need to know that there are six different trigonometric identities.

These identities are listed as;

From the information given, we have that;

The angle = x

The opposite side = 43

The adjacent side = 18

Using the tangent identity, we have;

tan x = 43/18

Divide the values, we have;

tan x = 2. 3888

Find the tangent inverse, we get;

x = 67. 3 degrees

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

The expression tan√3 tanø + 1 simplifies to the value of 2.

To find the value of tan√3 tanø + 1, we need to use the given information that 2sinø = 1 and 2cosø = √3.

We can start by rearranging the equations to solve for sinø and cosø individually.

From 2sinø = 1, we can divide both sides by 2 to get sinø = 1/2.

From 2cosø = √3, we can divide both sides by 2 to get cosø = √3/2.

Now, we can use these values to find the value of tanø. We know that tanø = sinø / cosø.

Substituting the values we found earlier:

tanø = (1/2) / (√3/2)

To simplify this expression, we multiply the numerator and denominator by the reciprocal of √3/2, which is 2/√3:

tanø = (1/2) * (2/√3)

tanø = 1 / √3

To further simplify, we rationalize the denominator by multiplying both the numerator and denominator by √3:

tanø = (1 * √3) / (√3 * √3)

tanø = √3 / 3

Now, we can substitute this value of tanø into the expression tan√3 tanø + 1:

tan√3 tanø + 1 = tan(√3) * (√3 / 3) + 1

Using the value of √3 as the square root of 3:

tan√3 tanø + 1 = (√3 * √3 / 3) + 1

tan√3 tanø + 1 = (3 / 3) + 1

tan√3 tanø + 1 = 1 + 1

tan√3 tanø + 1 = 2

Therefore, the value of tan√3 tanø + 1 is 2.

For more question on expression visit:

https://brainly.com/question/1859113

#SPJ8

Note the correct and the complete question is

If 2sinø=1 &2cosø= √3 then find the value of tan√3 tanø+1​ ?

Answer:

3x^2

Step-by-step explanation:

3x^2(9x)^0

Calculate 9x to the power of 0 and get 1.

3x^2 * 1

Multiply 3 and 1 to get 3.

3x^2

Alvarado can create 20 different arrangements of plants on the new display stand.

To determine the number of different arrangements of plants that Alvarado can create, we can use the concept of combinations.

When selecting 3 plants out of 6, the order of the plants doesn't matter, since all that matters is which plants are chosen. Therefore, we need to calculate the number of combinations.

The formula for calculating combinations is:

C(n, r) = n! / (r!(n - r)!)

Where:

n is the total number of items (in this case, the total number of plants)

r is the number of items chosen (in this case, the number of plants to be placed on the display stand)

! represents factorial, which is the product of all positive integers up to a given number

Using the values from the problem:

n = 6 (total number of plants)

r = 3 (number of plants to be placed on the display stand)

C(6, 3) = 6! / (3!(6 - 3)!)

C(6, 3) = 6! / (3! × 3!)

C(6, 3) = (6 × 5 × 4) / (3 × 2 × 1)

C(6, 3) = 20

Therefore, Alvarado can create 20 different arrangements of plants on the new display stand.

for such more question on different arrangements

https://brainly.com/question/25731911

#SPJ8

The minimum hours for Company B to be a better deal is 9 hours.

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the total charge for x hours.

Company A charges a $80 annual fee plus a $10/hr car share fee. Hence:

y = 10x + 80

Company B charges $125 plus $5/hr. Hence:

y = 5x + 125

For company B to be a better deal, hence:

5x + 125 < 10x + 80

-5x < -45

x > 9

The minimum hours for Company B to be a better deal is 9 hours.

Find out more on equation at: https://brainly.com/question/25638875

#SPJ1

Answer:

Step-by-step explanation:

El área de un trapecio se calcula multiplicando la suma de sus bases por la altura y dividiendo el resultado entre 2. En este caso, la base mayor es de 30 cm y la base menor es de 2/3 de la mayor, lo que equivale a 20 cm. La altura es de 0,8 m o 80 cm. Por lo tanto, el área del trapecio es ((30 + 20) * 80) / 2 = 2000 cm².

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

[tex]\sf{18x+5-3=65}[/tex]

[tex]\sf{18x+2=65}[/tex]

Subtract 2 from each side:

[tex]\sf{18x=63}[/tex]

Now, divide each side by 18:

[tex]\sf{x=\dfrac{63}{18}[/tex]

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

[tex]\sf{x=\dfrac{7}{2}}[/tex]

[tex]\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}[/tex]