Which of these is an exponential parent function?

Answer: To subtract mixed fractions with different denominators, you need to convert the mixed fractions to equivalent fractions with a common denominator. Once the fractions have a common denominator, you can simply subtract the numerators and keep the denominator the same.

Example:

the difference of 2 1/3 and 1 3/4 is 5/12.

Step-by-step explanation:

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3

Next, convert 1 3/4 to an improper fraction: 1 3/4 = 7/4

Now, both fractions have the same denominator, 3. So, you can subtract the numerators:

7/3 - 7/4 = (7 * 4 - 7 * 3) / (3 * 4) = 28/12 - 21/12 = 7/12

Finally, convert the answer back to a mixed fraction: 7/12 = 7 ÷ 12 =  5/12.

The expected value of the random variable X, denoting the number of boys in the front half of the line, is E[X] ≈ 1.5.

To find the expected value of the random variable X, which denotes the number of boys in the front half of the line, follow these steps:

1. Determine the total number of ways the kids can line up, which is 10! (10 factorial) since there are 10 kids.
2. Calculate the number of ways to choose 5 kids for the front half of the line: C(10, 5) = 10! / (5! * 5!).
3. For each possible value of X (0, 1, 2, or 3 boys in the front half), compute the probability of that value occurring:
  - P(X=0): C(7, 5) * C(3, 0) / C(10, 5) [5 girls, 0 boys]
  - P(X=1): C(7, 4) * C(3, 1) / C(10, 5) [4 girls, 1 boy]
  - P(X=2): C(7, 3) * C(3, 2) / C(10, 5) [3 girls, 2 boys]
  - P(X=3): C(7, 2) * C(3, 3) / C(10, 5) [2 girls, 3 boys]
4. Multiply each probability by its corresponding value of X and sum the products:
  - E[X] = P(X=0)*0 + P(X=1)*1 + P(X=2)*2 + P(X=3)*3

Following these, you'll find that the expected value of the random variable X, denoting the number of boys in the front half of the line, is E[X] ≈ 1.5.

To know more about probability refer here :

https://brainly.com/question/29145342#

#SPJ11

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line

m = \(\frac{-4-2}{2-(-2)}\) = \(\frac{-6}{2+2}\) = - \(\frac{6}{4}\) = - \(\frac{3}{2}\)

and using (a, b ) = (2, - 4 ) , then

y - (- 4) = - \(\frac{3}{2}\)(x - 2) , that is

y + 4 = - \(\frac{3}{2}\) (x - 2) → C

We have shown that the row sum s is an eigenvalue of the matrix A with eigenvector x = (1, 1, ..., 1)T.

To show that s is an eigenvalue of the nxn matrix A, we need to find a nonzero vector x such that Ax = sx, where s is the row sum of A. One way to find such a vector is to take the vector x = (1, 1, ..., 1)T, where T denotes transpose.

Using this choice of x, we have

Ax = (s, s, ..., s)T = sx,

which shows that s is indeed an eigenvalue of A with eigenvector x.

To see why this works, consider the kth entry of Av for any nonzero vector v in R^n. We have

(Av)_k = ∑ A_ki v_i, i=1 to n

where A_ki denotes the entry in the kth row and ith column of A. Since the row sums of A all equal s, we can write

(Av)_k = ∑ A_ki v_i = s ∑ v_i

where the sum on the right-hand side is taken over all i such that A_ki is nonzero.

If we take v = x, then we have ∑ v_i = nx, and hence

(Ax)_k = s(nx) = (ns)x_k,

which shows that x is an eigenvector of A with eigenvalue s.

For such more questions on Eigenvalue:

https://brainly.com/question/31311021

#SPJ11

Answer:

\(2(x+2)/x+1\)

Step-by-step explanation:

Answer:

2( x +2 )

x+1

Step-by-step explanation:

to add or subtract expressions expand them to make their denominators the same, multiply 1 time \(\frac{x-2}{x-2}\)

since \(\frac{x}{x-2}\) and \(\frac{x-2}{x-2}\) have the same denominators add them by adding their numerators

combine x + x -2

factor \(x^{2}\) - 4

to add or subtract expressions expand them and multiply by 1

have same denominator add them by adding their numerators

do the multiplications in 3 + ( x-2 )(x+2)

combine like terms in 3 + \(x^{2}\) + 2x - 2x -4

divide \(\frac{2x-2}{x-2}\) by \(\frac{-1 + x^{2} }{(x-2)(x+2) }\) multiplying \(\frac{2x-2}{x-2}\)

cancel out x-2 in both numerator and denominator

factor the expression that are not already factored

cancel out x-1  in both numerator and denominator

expand the expression

Answer:

Equation is Y=x/2

Step-by-step explanation:

Answer:

Angle A = Angle L

Angle D = Angle M

Angle C = Angle N

Segment AB = Segment LB

Segment CD = Segment NM

Segment DA = Segment ML

2nd part

Quadrilateral URST has moved by a translation of (x-5,y+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

<95141404393>

The length of the hypotenuse is approximately 30.8 units.

The angle at vertex X is approximately 36.9 degrees.

The angle at vertex Y is approximately 35.2 degrees.

In your problem, we have a right triangle XYZ, where the angle at vertex Y is the right angle. The length of leg YZ is given as 18 units, and the length of leg XZ is given as 25 units.

In this particular problem, we can use the sine ratio to solve for the length of leg XY. Specifically, we have:

sin(XYZ) = XY / XZ

Since we know that XYZ is a right angle (i.e., 90 degrees), we can substitute in the appropriate values to get:

sin(90) = XY / 25

Since the sine of 90 degrees is 1, we can simplify this to:

1 = XY / 25

Multiplying both sides by 25 gives us:

XY = 25

So the length of leg XY is 25 units.

To find the other angles in the triangle, we can use the inverse trigonometric functions (such as arcsine or arccosine). For example, we can use the cosine ratio to solve for the angle at vertex X:

cos(XYZ) = XZ / hypotenuse

cos(90) = 25 / hypotenuse

0 = 25 / hypotenuse

Since the cosine of 90 degrees is 0, we know that hypotenuse = 25 / 0 is undefined. However, we can use the Pythagorean theorem to find the length of the hypotenuse:

hypotenuse² = XY² + XZ²

hypotenuse² = 25² + 18²

hypotenuse² = 625 + 324

hypotenuse² = 949

Taking the square root of both sides gives us:

hypotenuse = √(949) ≈ 30.8

Now that we know the lengths of all three sides of the triangle, we can use the sine and cosine ratios to solve for the other angles. For example, to find the angle at vertex X, we can use the cosine ratio:

cos(X) = XZ / hypotenuse

cos(X) = 25 / 30.8

cos(X) ≈ 0.811

Taking the inverse cosine (or arccosine) of both sides gives us:

X ≈ 36.9 degrees

Similarly, we can use the sine ratio to find the angle at vertex Y:

sin(Y) = YZ / hypotenuse

sin(Y) = 18 / 30.8

sin(Y) ≈ 0.584

Taking the inverse sine (or arcsine) of both sides gives us:

Y ≈ 35.2 degrees

To know more about triangle here

https://brainly.com/question/8587906

#SPJ1

Answer:

t=-3.7

Step-by-step explanation:

5 (t+3)=-3.5

solving the bracket we have;

5t+15=-3.5

collect like terms

5t=-3.5-15

5t=-18.5

divide both sides by 5;

t=-3.7

The value of t in the given algebraic expression is; t = -2.3

We are given the equation;

5(t + 3) = 3.5

Using distributive property on the left hand side, we have;

5t + (5 × 3) = 3.5

5t + 15 = 3.5

Using subtractive property of equality, subtract 15 from both sides to get;

5t + 15 - 15 = 3.5 - 15

5t = -11.5

Divide both sides by 5 to get;

5t/5 = -11.5/5

t = -2.3

Read more at; https://brainly.com/question/23202310

To evaluate the integral by reversing the order of integration, we first need to draw the region of integration. From the given limits of integration, we can see that the region is a rectangle with vertices at (0,4), (0,12), (11,4), and (11,12).

Now, we can reverse the order of integration by integrating with respect to y first, and then x. The new limits of integration will be y = 4 to y = 12 and x = 0 to x = 11e^(2y/3).

So, the new integral will be:

∫(0 to 11) ∫(4 to 12) 3y e^(2x/3) dy dx

We can evaluate this integral using integration by parts. Integrating with respect to y gives us:

∫(0 to 11) [3y^2/2 e^(2x/3)] from y = 4 to y = 12

Simplifying this expression gives us:

∫(0 to 11) [36e^(2x/3) - 6e^(8x/3)]/2 dx

Now, integrating with respect to x gives us:

[27e^(2x/3) - 9e^(8x/3)] from x = 0 to x = 11

Substituting these values and simplifying gives us the final answer:

(27e^22/3 - 9e^88/3) - (27 - 9) = 27e^22/3 - 9e^88/3 - 18

To know more about integration visit:

https://brainly.com/question/31744185

#SPJ11

Answer:

aww i help u.....

Step-by-step explanation:

my answer is letter ~~B CAUSE STUDEN BIS CONDYCTION LIKR FREE AT THE SCORED

Answer:

In the triangle below the red side is a leg and should be labeled a . The pink side is a leg and should be labeled b. and the light blue side is the hypotenuse and should be labeled c.

In right triangles the angles are labeled with upper case letters and the sides are labeled with lower case letters.

Step-by-step explanation:

The proportion of customers who require an oil change and wait for nine minutes or less is 0.07.

The information provided by the question can be used to calculate the percentage of customers who wait for nine minutes or less, and the percentage of customers who wait for nine minutes or less and require an oil change. This information can be used to find out the ratio between these two percentages, which is the percentage of customers who wait for nine minutes or less and require an oil change.

The proportion of customers who require an oil change and wait for nine minutes or less can be calculated using the following formula:

Proportion of customers who require an oil change and wait for nine minutes or less = (Number of customers who require an oil change and wait for nine minutes or less) / (Total number of customers who wait for nine minutes or less)

The number of customers who wait for nine minutes or less and require an oil change is 35. The total number of customers who wait for nine minutes or less is 500. Thus, the proportion of customers who require an oil change and wait for nine minutes or less is:

Proportion of customers who require an oil change and wait for nine minutes or less = 35/500 = 0.07 or 7%.

Thus, 7% of customers who wait for nine minutes or less require an oil change.

For more such questions on Customers.

https://brainly.com/question/13506337#

#SPJ11

Complete Question:

Using classes of 0-4, 5-9, and so on, show the proportion of customers needing an oil change who wait 9 minutes or less.

The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a 1-month period:

2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3

Answer:

Not a function

Step-by-step explanation:

There are two points that correspond to the same variable

Hope this helps

Answer:

not a function

Step-by-step explanation:

There are two points that have the same x and  different y values

This would fail the vertical line test.

The equation shows that we need the graph of a line with a slope of 2 and cross the y-axis at (0, -3)

A line is defined as the shortest distance between two points. The equation  of a line in slope-intercept form is given as:

y = mx +b

where

According to the question we are to graph the equation y = 2x- 3. This means that we need the graph of a line with a slope of 2 and cross the y-axis at (0, -3)

Learn more on equation of a line here: https://brainly.com/question/18831322

#SPJ1

The truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

The statement q(x) is x² = 2x. Now, we will check the truth value of each statement in terms of q(x):

(i) q(0): \(0^2=2\times 0\)

   q(0): 0 = 0; so, the statement q(0) is true.

(ii) q(1): \(1^2=2\times 1\)

    q(1): 1 = 2; so, the statement q(1) is false.

(iii) q(-2): \((-2)^2=2\times (-2)\)

     q(-2): 4 = -4; so, the statement q(-2) is false.

(iv) q(2): \(2^2=2\times 2\)

     q(2): 4 = 4; so, the statement q(2) is true.

So, the truth values of the given statements in terms of q(x) are: q(0) is true, q(1) is false, q(-2) is false, and q(2) is true.

To learn more about truth values visit:

https://brainly.com/question/29137731

#SPJ11

Answer:

Step-by-step explanation:

Answers and explanations in attachment.  Problem 29 was cut off a bit.  I assumed the question was what percent of the total are cubs.

The complete code to create a histogram in Kotlin that allows you to inspect the frequency visually with nine or fewer lines is shown below:import kotlin.random.

Randomfun main() {val array = Array(200) { Random.nextInt(1, 101) }array.sort()var i = 1while (i < 100) {val count = array.count { it < i + 10 && it >= i }println("${i} - ${i + 9} | ${count} | " + "*".repeat(count))i += 10}}

The program above first generates an array of 200 random integers between 1 and 100 inclusive. It then sorts the array in ascending order. Next, the program loops through the ranges from 1 to 100 in steps of 10.

Within the loop, the program counts the number of elements in the array that fall within the current range and prints out the corresponding row of the histogram chart.

Finally, the program increments the loop variable by 10 to move to the next range and continues the loop.

To know more about histogram visit:

brainly.com/question/30200246

#SPJ11

Answer:

\(\sf -3xy\left(2x^2-3xy+4y^2\right)\)

Step-by-step explanation:

\(\sf -6x^3y+9x^2y^2-12xy^3\)

To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-

\(\boxed{\sf a^{b+c}=a^ba^c}\)

\(\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}\)

\(\sf -6xx^2y+9xxyy-12xyy^2\)

Rewrite,

\(\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2\)

Now, factor out the common term \(\sf -3xy\):-

__________________________

Answer:

11/12

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

The slope-intercept form of the equation of the line through the given point and parallel to the given line is y=x−14.

In the given question we have to write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

The given points are (–2, –16).

The given equation of line is y = x – 5.

Standard equation of line is y=mx+c.

After comparing to the standard equation.

Slope m(1) = 1

The line passes through (−2,−16), so the point will satisfy the equation y=mx+c. So

−16=−2*1+c

Simlifying

−16=−2+c

Add 2 on both side, we get

c = −16+2

c = −14

As we know that if line is parallel then

m(1)=m(2)

So the value of solpe m = 1

Now the equation of line

y=1*x+(−14)

y=x−14

To lear more about slope-intercept form of equation link is here

brainly.com/question/21298390

#SPJ4

The right answer is:

How do you write the slope-intercept form of the equation of the line through the given point and parallel to the given line?

Point (−2,−16), y = x – 5

Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.

We have,

In the context of geometry and visual representation, the terms "form" and "shape" have distinct meanings and characteristics.

Form generally refers to a three-dimensional object that has depth, such as a solid object or a structure with volume.

It encompasses objects that have length, width, and height, and it extends beyond a two-dimensional representation.

Form can have irregular or complex shapes and is not limited to a specific number of sides.

Shape, on the other hand, refers to the two-dimensional outline or boundary of an object.

It is limited to the external appearance or silhouette of an object without considering its depth or volume.

Shapes are typically described by their attributes, such as the number of sides (e.g., triangle, square) or specific geometric properties (e.g., circle, rectangle).

Thus,

Form refers to three-dimensional objects with depth, while shape pertains to the two-dimensional outline or boundary of an object.

Learn more about form and shape here:

https://brainly.com/question/25440372

#SPJ12

There are 60 ways of selecting 5 balls from the bag, consisting of 3 red balls and 2 blue balls.

To calculate the number of ways, we can break it down into two steps:

Selecting 3 red balls

Since there are 6 red balls in the bag, we need to calculate the number of ways to choose 3 out of the 6. This can be done using the combination formula: C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be chosen. In this case, we have C(6, 3) = 6! / (3! * (6 - 3)!), which simplifies to 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20.

Selecting 2 blue balls

Similarly, since there are 5 blue balls in the bag, we need to calculate the number of ways to choose 2 out of the 5. Using the combination formula, we have C(5, 2) = 5! / (2! * (5 - 2)!), which simplifies to 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.

To find the total number of ways, we multiply the results from Step 1 and Step 2 together: 20 * 10 = 200.

Therefore, there are 200 ways of selecting 5 balls from the bag, consisting of 3 red balls and 2 blue balls.

To know more about combinations, refer here:

https://brainly.com/question/31586670#

#SPJ11

The approximately 21.18% of the people surveyed have exactly one sibling.

To complete the table, we need to calculate the cumulative frequency, which is the sum of the frequencies up to and including the given value.

The table should look like this:

# of Siblings  Frequency Relative Frequency Cumulative Frequency

0                       33                  0.1941                    33

1                       36                  0.2118                    69

2                       35                  0.2059                   104

3                       42                  0.2471                    146

4 or more       24                  0.1412                    170

To find the percentage of people who have exactly one sibling, we need to look at the frequency for that value and divide it by the total number of people (which is the last value in the cumulative frequency column). Then we multiply by 100 to convert to a percentage.

So, the percentage of people who have exactly one sibling is:

(36 / 170) x 100%

= 21.18%

Therefore, approximately 21.18% of the people surveyed have exactly one sibling.

For such more question on approximately:

https://brainly.com/question/30115107

#SPJ4

The equation of the line passing through the point (-1,2) with slope m is y = mx + m-2. This is a general equation of the line and we can find different equations by putting different values of m.

We know that when a point and slope of the equation are given, an equation can be written as

\(\frac{y-y_{1} }{x - x_{1} } =m\)

which is known as the slope-point form

where m is the slope of the equation

y1 is the  y coordinate of the given point

x1 is the x coordinate of the given point

In the given question, y1 = 2 and x1 = -1

Substituting the value of coordinates in the slope point equation, we get

\(\frac{y-2}{x-(-1)} = m\)

\(\frac{y-2}{x+1}=m\)

y-2 = mx + m

y = mx + m-2

Hence, the equation of the line passing through the point (-1,2) with slope m is y = mx + m-2.

To learn more about the slope:

https://brainly.com/question/3605446

What is the equation of the line passing the point (-1, 2) with a slope m?

Answer:

3.14

Step-by-step explanation:

-8 - 92.5 = -100.5, and then -100.5/(-32) = 3.14

Alternatively, type in (-8 -92.5)/(-32)