Let f(x)=8x+2 and g(x)=4x2+2x.

Then
(fg)(x)=?

The slope of the line is 7/9

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ1

Answer:

D 98°

Step-by-step explanation:

180-82 = 98 or the long way

3x+5 = 180-82

3x = 93

x = 31

3(31) + 5 = 98

Answer:

m = 1/3, b = 2

Step-by-step explanation:

The equation is already written is slope-intercept form, y = m x + b.

Answer:

52%

Step-by-step explanation:

There is a total of 25 marbles in the bag. 13 of them consist of red and blue marbles.

13 / 25 = 0.52 or 52%

Answer: 3:1

Step-by-step explanation:

Given:

Rosie and dan share some sweets.

Dan gets ¼ of sweets

To find:

Write down the ratio of the number of sweets Rosie to the number of sweets Dan gets

the ratio of the number of sweets Rosie gets to the number of sweets Dan gets is → 3 : 1.

Answer:

Step-by-step explanation:

Note

I think the question means "What do you multiply -26 by to get - 468

call the number that you need x

x * -26 = - 468                        Divide both sides by - 26

-26x/-26 = - 468/ - 26           There are 2 minus signs on the right. They cancel.

x = 18

Conclusion

When you multiply 18 * -26 the answer is --468

Answer: 18

Answer:

\((a)\ g(x) = \frac{2}{3}(x+1)\)

\((b)\ h(y) = \frac{1}{3}[1 + 4y]\)

\((c)\) \(P(x>0.5) =\frac{5}{12}\)

Step-by-step explanation:

Given

\(f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.\)

Solving (a): The marginal density of X

This is calculated as:

\(g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy\)

\(g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy\)

\(g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy\)

Integrate

\(g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}\)

Substitute 1 and 0 for y

\(g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}\)

\(g(x) = \frac{2}{3}[(x+1)}\)

Solving (b): The marginal density of Y

This is calculated as:

\(h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx\)

\(h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx\)

\(h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx\)

Integrate

\(h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}\)

Substitute 1 and 0 for x

\(h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ]\)

\(h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)]\)

\(h(y) = \frac{1}{3}[1 + 4y]\)

Solving (c): The probability that the drive-through facility is busy less than one-half of the time.

This is represented as:

\(P(x>0.5)\)

The solution is as follows:

\(P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)\)

Represent as an integral

\(P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy\)

\(P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy\)

Integrate w.r.t. x

\(P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy\)

\(P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy\)

\(P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy\)

\(P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}\)

\(P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})]\)

\(P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})]\)

\(P(x>0.5) =\frac{2}{3}[(0.125 + 0.5]\)

\(P(x>0.5) =\frac{2}{3} * 0.625\)

\(P(x>0.5) =\frac{2 * 0.625}{3}\)

\(P(x>0.5) =\frac{1.25}{3}\)

Express as a fraction, properly

\(P(x>0.5) =\frac{1.25*4}{3*4}\)

\(P(x>0.5) =\frac{5}{12}\)

Answer:

In the diagram shown of circle A, tangent MB is drawn along with chords BAC and BF . Secant MFE intersects BAC at G. It is known that angle FBC = 52 and arc BE = 138 .

Step-by-step explanation:

A probability mass function (pmf) for a random variable X must satisfy the following two conditions:
1. f(x) ≥ 0 for all x
2. Σf(x) = 1

(a) f(x) = x/c
To find the constant c, we can use the second condition and sum over all possible values of x:
Σf(x) = Σ(x/c) = 1/c Σx = 1
Since we don't have a specified range for x, we cannot solve for c.

(b) f(x) = cx
Again, we can use the second condition to find the constant c:
Σf(x) = Σ(cx) = cΣx = 1
Without a specified range for x, we cannot solve for c.

(c) f(x) = c(1/4)^x
Using the second condition:
Σf(x) = Σ(c(1/4)^x) = cΣ(1/4)^x = 1
We can use the formula for an infinite geometric series to find the sum:
Σ(1/4)^x = 1/(1 - 1/4) = 4/3
So, c = 3/4

(d) f(x) = c(x + 1)^2
Using the second condition:
Σf(x) = Σ(c(x + 1)^2) = cΣ(x + 1)^2 = 1
Without a specified range for x, we cannot solve for c.

(e) f(x) = x/c
This is the same as part (a), so we cannot solve for c without a specified range for x.

(f) f(x) = c/(x+1)(x+2)
Using the hint, we can rewrite f(x) as:
f(x) = c(1/(x+1) - 1/(x+2))
Using the second condition:
Σf(x) = Σ(c(1/(x+1) - 1/(x+2))) = cΣ(1/(x+1) - 1/(x+2)) = 1
We can use the formula for a telescoping series to find the sum:
Σ(1/(x+1) - 1/(x+2)) = 1 - 1/(x+2)
As x approaches infinity, the sum approaches 1.
So, c = 1

To depict each pmf as a line graph, we would plot the values of f(x) on the y-axis and the values of x on the x-axis. However, without a specified range for x, we cannot create accurate graphs for parts (a), (b), (d), and (e). For part (c), the graph would be a decreasing exponential curve, with f(x) approaching 0 as x increases. For part (f), the graph would be a decreasing curve, with f(x) approaching 0 as x increases.

Learn more about probability mass function:

brainly.com/question/14932242

#SPJ11

Answer:

208

Step-by-step explanation:

Given that;

Given that;

y= a(1 - b)^t

Where;

wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

To obtain the constant b,

y= ae^-bt

Substituting values;

1000 = 3000 e^-b(50)

1000/3000 = e^b(50)

0.33 = e^b-(50)

ln (0.33) = ln(e^b(-50))

-1.1 = -50b

b= 1.1/50

b= 0.022

After two hours or 120 minutes;

y= 3000(1 - 0.022)^120

y= 207.8661772

y= 208

To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

For similar questions on pool

https://brainly.com/question/28063924

#SPJ11

Answer:1.5

Step-by-step explanation:

Step-by-step explanation:

is there a picture that you could put on here so i can see?

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

Read more on piecewise function here: brainly.com/question/18670055

#SPJ1

We can conclude that: B. the table is proportional because the ratios for y over x are all equivalent to 1/3.

A table that represents a proportional relationship has a constant of proportionality, k, which is the same for any pair of value in the given table where k = y/x.

Find out if k is the same for each of the pair of values given in the table:

(36.75, 12.25):

k = 12.25/36.75 = 0.33

(16.8, 5.6):

k = 5.6/16.8 = 0.33

(77.1, 25.7):

k = 25.7/77.1 = 0.33

The value of k is the same across all values, therefore, we can conclude that, B. It is proportional because the ratios for y over x are all equivalent to 1/3.

Learn more about proportional relationship on:

https://brainly.com/question/15618632

#SPJ1

the anwser :

It is B

Yes, it is proportional because the ratios for y over x are all equivalent to one third.

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

For similar question on length.

https://brainly.com/question/30582409  

#SPJ8

Step-by-step explanation:

1 week = 7 days of 24 hours each = 7×24 = 168 hours.

the first team can do 1/700 of the total work per hour.

the second team can do 1/600 if the total work per hour.

if they work together, then 1/700 + 1/600 of the total work can be done per hour.

to add these 2 fractions we need to bring them to the same denominator. and that would be 4200 (LCM of 700 and 600).

1/700 + 1/600 = 6/4200 + 7/4200 = 13/4200

so, together, they can do 13/4200 if the total job in 1 hour.

how many hours will they need together to finish the job ?

well, how often does 13 fit into 4200 (as 4200/4200 is the complete job) ?

4200 / 13 = 323.0769231... hours

so, it will still take a little bit over 323 hours to clean all the streets.

but there are only 168 hours until the film crew starts.

so, no, there is not enough time.

Explanation:

The relative frequency of an outcome is the number of times you get this outcome divided by the number of times the experiment was repeated:

To find it as a percentage we just have to multiply by 100:

Answer:

42.5%

Answer:

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events (9/10).

0.729

Answer:

134

Step-by-step explanation:

Based on equation 750=40x, the value of x is 18.75 weeks.

An equation is a mathematical statement that two or more algebraic expressions are equal or equivalent.

Equations must have the equation symbol (=) to show the equality of the mathematical expressions.

Equations are started with let statements, defining the variables.

Let the total amount of money in the account = y (in dollars)

Let the number of weeks Reuben has been adding money = x

750 = 40x

40x = 750

x = 18.75 (750/40)

Thus, based on the solution to the equation, we know that Reuben has added money into the account for 18.75 weeks.

Learn more about equations at https://brainly.com/question/17145398

#SPJ1

Compute the number of weeks Reuben has been putting money into the account.

The period of the given trigonometric graph is identified as: ²/₃π

The period of a trigonometric function is defined as the time it takes to complete one complete cycle. For y = sinx and y = cosx , you can measure the duration between consecutive maxima or minima, or other repeated points in the figure that have the same function values ​​and properties.

Now, looking at the given trigonometric graph, it is very clear that the amplitude is 1 while the period is ²/₃π

Read more about Trigonometric Graph Period at: https://brainly.com/question/24329125

#SPJ1

Answer:

19 units²

Step-by-step explanation:

First, divide the shape into two triangles, find the area of those triangles, and then add the areas together.

Big Triangle:

1/2bh

1/2 6(5)

1/2 30

15

Little Triangle

1/2bh

1/2 2(4)

1/2 8

4

Total Area:

15 + 4 = 19 units squared

The algebraic expression for the given phrase is: 17x - 8x. To simplify this expression, we can combine like terms by subtracting the coefficients of x. The simplified expression is: 9x.

In the given phrase, "The product of 8 and a number" can be represented as 8x, where x represents the number. Similarly, "The product of 17 and the number" can be represented as 17x. Since we are subtracting the product of 8x from the product of 17x, the algebraic expression becomes 17x - 8x.

To simplify the expression, we combine like terms. The coefficients of x are 17 and -8. Since we are subtracting 8x from 17x, we subtract the coefficient of 8x from the coefficient of 17x, resulting in 17x - 8x. Combining like terms gives us 9x.

In conclusion, the simplified expression for the phrase "The product of 8 and a number, which is then subtracted from the product of 17 and the number" is 9x.

for such more questions on expression

https://brainly.com/question/1859113

#SPJ8

The measure in radians for the central angle is approximately 0.7 radians.

To find the measure in radians for the central angle of a circle, we can use the formula:

θ = s / r

where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.

In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.

Plugging these values into the formula, we have:

θ = 5.6 cm / 8 cm

Simplifying the expression:

θ = 0.7

We may use the following formula to get the centre angle of a circle's measurement in radians:

= s / r

s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.

The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.

When these values are plugged into the formula, we get:

θ = 5.6 cm / 8 cm

Condensing the phrase:

θ = 0.7

For similar questions on radians

https://brainly.com/question/29058626

#SPJ11

Answer:

6  3/5

Step-by-step explanation:

finding the difference?

im guessing you might wanna ask your teacher? ummmmm....

The total surface area of the triangular prism using the net is 96 square units

From the question, we have the following parameters that can be used in our computation:

The net of a triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 3 * 7 + 6 * 7+ 2 * 1/2 * 2 * 6

Evaluate

Area = 96

Hence, the surface area is 96 square units

Read more about surface area at

brainly.com/question/26403859

#SPJ1