30 points !! Please help now math

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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Answer:

P + S / P [(r - 1) P - S] dP

Step-by-step explanation:

If r = 0.10 and S = 900 then,

P + 900 /  P [(0.10 - 1) P - 900] dP

Solving the equation we get,

P + 900 = (B - 0.9A)P - 900A

If A = -1,

B = 0.10

t = 0 and P = 10,000

ln 10000 - 1 /9 ln (0.9 * 10000 + 900) + C

C = 10.2326.

Answer:

Well I would assume it is 50 km, but I could be wrong if the question states that the 10km south is going home hope this helps <3

Answer:

Step-by-step explanation:

47,57,68

adding 1 to the next number and so on

plus 4, plus 5, plus 6 and so on

The exterior angle of the triangle is 62°.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Let us take the triangle as ABC.

Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].

We know that sum of all angles in triangle is add upto 180° Then,

=> \(m\angle A+m\angle B+m\angle C\)=180

=> 43°+3x°+180-5x+3=180°

=> -2x=180-180-43-3

=> -2x=-46

=> x=13°

Now exterior angle ,

=> 5x-3

=> 5*13-3

=> 65-3

=> 62°

Hence the exterior angle of the triangle is  62°.

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People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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This question is incomplete, the complete question is;

A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey that attended college is randomly selected what is the probability that they also lived in 2 or more states during their life? P(2 state or more | College Degree)

                                             Lived in just             Lived in 2 or               Total

                                                1 state                     more states

No High School Diploma           6                                 2                           8

High School Diploma                 14                               16                          30

College Degree                           2                               18                          20

Total                                            22                             36                           58

Options;

a) 0.111

b) 0.310

c) 0.500

d) 0.900

Answer:

The required probability is 0.9

Option d) 0.900 is the correct answer.

Step-by-step explanation:'

Given the data in the question;

Total number of people in the survey or sample size n = 58

Number of people with college degree who live in 2 or more state = 18

P(2 states or more and college degree) = Number of people with college degree who live in 2 or more state / Total number of people in the survey

P(2 states or more and college degree)  = 18 / 58

Also, Total number of people with college degree = 2 + 18 = 20

so, P( College Degree ) =  Total number of people with college degree / Total number of people in the survey

P( College Degree ) = 20 / 58

Therefore, P(2 state or more | College Degree) will be;

⇒ P(2 states or more and college degree) / P( College Degree )

⇒ ( 18 / 58 ) / ( 20 / 58 )

⇒ ( ( 18 / 58 )58 ) / 20

⇒ (( 18 × 58 ) / 58 ) / 20

⇒ 18 / 20

⇒ 0.9

Therefore, The required probability is 0.9

Option d) 0.900 is the correct answer.

Answer:

Let's use the formula:

distance = rate × time

Let's assume Latasha's rate of travel as "r". Then, Nathan's rate of travel would be "r + 8".

For Latasha:

distance = r × 9

For Nathan:

distance = (r + 8) × 9

According to the problem, the combined distance they traveled is 288 miles. So:

r × 9 + (r + 8) × 9 = 288

Simplifying the equation:

18r + 72 = 288

18r = 216

r = 12

So, Latasha's rate of travel is 12 mph, and Nathan's rate of travel is 20 mph (12 + 8).

Therefore, Latasha is traveling at 12 mph and Nathan is traveling at 20 mph.

1:2

Looking at the image, there are 2 grey squares and 1 black square. Since the question is asking how many black squares to grey squares, it would be a 1:2.

The volume of the composite figure is

The volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes

The simple shapes used here include

Volume of rectangle = length x width x depth

= 30 * 9 * 7

= 1890 cubic yd

Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth

= 1/2 (30 + 19) x 10 x 9

= 2205 cubic  yd

Total volume

= 1890 cubic yd + 2205 cubic yd

=  4095 cubic yd

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Answer:

Step-by-step explanation:

You want to factor the trinomial. What two numbers multiply to equal 1, but add to equal 2? Thats easy, its just 1.

You now have (x + 1) twice, so you can just square it like this:

\((x+1)^2>0\)

We can make that term equal to 0 to get x = -1, but remember that this isnt an equation. This is an inequality, so x > -1

In order to graph this, you should shade everything to the right of -1 because we have the greater than sign. Make the circle open because we are not including -1. It is everything greater than -1

Answer: E

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Answer:

wat graph

Step-by-step explanation:

The distance between gab's house and library will be 4km

Distance is a numerical measurement  of how far apart object or point are or it may also refer as the physical length.

From graph we can see that Gabe's house is 3 km on positive x axis in respect to the origin

Whereas library is 1 km apart from origin on negative x axis

Since we are calculating distance , we simply add both the above mentioned distances irrespective of their direction since distance is a scaler quantity.

Distance between Gab's house and library will be :

D = |3| + |-1|

D = 3+1 = 4 km option A)

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Answer:

a) 0.3012 = 30.12% probability that one of these light bulbs will last at least 24,000 hours.

b) 0.1813 = 18.13% probability that one of these light bulbs will last no longer than 4,000 hours.

c) 0.5175 = 51.75% probability that one of these light bulbs will last between 4,000 hours and 24,000 hours.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

Mean of 20,000 hours.

This means that \(m = 20000, \mu = \frac{1}{20000} = 0.00005\)

a. At least 24,000 hours.

\(P(X > 24000) = e^{-0.00005*24000} = 0.3012\)

0.3012 = 30.12% probability that one of these light bulbs will last at least 24,000 hours.

b. No longer than 4,000 hours.

\(P(X \leq 4000) = 1 - e^{-0.00005*4000} = 0.1813\)

0.1813 = 18.13% probability that one of these light bulbs will last no longer than 4,000 hours.

c. Between 4,000 hours and 24,000 hours.

Less than 4000 or more than 24000:

We found in a and b, so

0.3012 + 0.1813 = 0.4825

Between these bounds:

1 - 0.4825 = 0.5175

0.5175 = 51.75% probability that one of these light bulbs will last between 4,000 hours and 24,000 hours.

The probability of one of these light bulbs will last at least 24,000 hours, no longer 4,000 hours, and between 4,000 hours and 24,000 hours is 23.12%, 18.13%, and 51.75% respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Lucky Lumen light bulbs have an expected life that is exponentially distributed with a mean of 20,000 hours.

The exponential probability distribution, with mean m, will be

\(f(x) =\rm \mu e^{\mu x}\\\\Where \ \mu = \dfrac{1}{m}\)

Then the probability that x is lower o equal to a is given by

\(P(X\leq x) = \int_0^a f(x) \rm \ dx\)

Then we have

\(P(X\leq x) = 1 - e^{-\mu x}\\\\P(X > x ) = 1 - P(X\leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

Mean of 20,000 hours, then

\(\mu = \dfrac{1}{20,000}\\\\\mu = 0.00005\)

a. At least 24,000 hours.

\(P(X > 24,000) = e ^{-0.00005 \times 24,000} = 0.3012 \ or \ 32.12\%\)

The probability of one of these light bulbs will last at least 24,000 hours is 32.12%.

b. No longer than 4,000 hours.

\(P(X \leq 4,000) = e ^{-0.00005 \times 4,000} = 0.1813\ or \ 18.13\%\)

The probability of one of these light bulbs will last no longer than 4,000 hours is 18.13%.

c. Between 4,000 hours and 24,000 hours.

Then we have a and b, so

0.3012 + 0.1813 = 0.4825

Between these bound

1 - 0.4825 = 0.5175

The probability of one of these light bulbs will last between 4,000 hours and 24,000 hours is 51.75%.

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Answer:

Parameter estimates

The coefficient for Px (-5) suggests that there is an inverse relationship between the price of the fruit drink and the quantity demanded. In other words, as the price of the drink increases, the quantity demanded decreases.

The coefficient for M (0.001) suggests that there is a positive relationship between the median annual family income and the quantity demanded. In other words, as the median income increases, the quantity demanded also increases.

The coefficient for Py (10) suggests that there is a positive relationship between the price of the competing brand of fruit drink and the quantity demanded for this brand. In other words, as the price of the competing brand increases, the quantity demanded for this brand also increases.

Step-by-step explanation:

To calculate the monthly consumption of the fruit drink, we plug in the given values into the demand equation,

Qx = 10 - 5(2) + 0.001(20,000) + 10(2.5)

Qx = 10 - 10 + 20 + 25

Qx = 45 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family is 45 liters.

If the median annual family income increased to $30,000, then the new monthly consumption of the fruit drink per family can be calculated as follows,

Qx = 10 - 5(2) + 0.001(30,000) + 10(2.5)

Qx = 10 - 10 + 30 + 25

Qx = 55 liters per family per month.

Therefore, the monthly consumption of the fruit drink per family would increase from 45 liters to 55 liters per family per month.

To determine the demand function, we need to solve for Qx in terms of the other variables,

Qx = 10 - 5Px + 0.001M + 10Py

Qx - 10Py = 10 - 5Px + 0.001M

Qx = (10 - 5Px + 0.001M) / 10Py

Therefore, the demand function is:

Qx = (10 - 5Px + 0.001M) / 10Py

To find the inverse demand function, we need to solve for Px in terms of Qx.

Qx = 10 - 5Px + 0.001M + 10Py

5Px = 10 - Qx - 0.001M - 10Py

Px = (10 - Qx - 0.001M - 10Py) / 5

Therefore, the inverse demand function is,

Px = (10 - Qx - 0.001M - 10Py) / 5

The linear equation written in the slope-intercept form is:

y = (-3/5)*x

The correct option is C.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.

b = 0

y = a*x + 0

y = a*x

To find the value of a, we can use another point on the graph.

We can see that the linear equation passes through (5, - 3), replacing these values:

-3 = a*5

-3/5 = a

Then the linear equation is just:

y = (-3/5)*x

The correct option is C.

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Answer:

x=108'

y=25'

Step-by-step explanation:

180 = 72+x

so,

x = 180-72

  = 108'

x = 5y-17 ( but we know x is 108')

so 108 = 5y -17

108+17 = 5y

5y = 125

y = 25

Answer:

x = 108 degree

y = 25 degree

Step-by-step explanation:

You can use law of transversal to get these

Answer:

Add all the values up and then divide by 2

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

that means the radius of the left and right circles is 2 units.

and the height of the cylinder is 5 units.

the volume of a cylinder is calculated by first standing it upright on one of the circles, and then the volume is ground area times height.

the area of a circle is pi×r².

so the volume here for us is then

pi×2²×5 units = pi×4×5 = pi×20 = 62.83185307... units

and that makes A the correct answer.

1. The unknown in the 'x- mean' column are 2 and -8

2. The unknown in the '(x-mean)²' square column is

25 and 106

A frequency table is simply a “t-chart” or two-column table which outlines the various possible outcomes and the associated frequencies observed in a sample.

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

1. X - mean = 13 - 11 =2

X - mean = 3 -11 = -8

2. (X - mean)² = 5²

= 25

The total value of (x-mean)²

= 9+ 4+25+4+4+64

= 13 +25 + 8 +64

= 106

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

Given value:

\(\to f_X (x) \ \ xe^{-x} \ , \ x>0\)

For point a:

Moment generating function of X=?

Using formula:

\(\to M(t) =E(e^{tx})= \int^{\infty}_{-\infty} \ e^{tx} f(x) \ dx\)

\(M(t) = \int^{\infty}_{-\infty} \ e^{tx}xe^{-x} \ dx = \int^{\infty}_{0} \ xe^{(t-1)x} \ dx\)

integrating the values by parts:

\(u = x \\\\dv = e^{(t-1)x}\\\\dx =dx \\\\v= \frac{e^{(t-1)x}}{t-1}\\\\M(t) =[\frac{e^{(t-1)x}}{t-1}]^{-\infty}_{0} -\int^{\infty}_{0} \frac{e^{(t-1)x}}{t-1} \ dx\\\\\)  

        \(= \frac{1}{t-1} (0) - [\frac{e^{(t-1)x}}{(t-1)^2}]^{\infty}_{0}\\\\=\frac{1}{(t-1)^2}(0-1)\\\\=\frac{1}{(t-1)^2}\\\\\)

Therefore, the moment value generating by the function is \(=\frac{1}{(t-1)^2}\)

In point b:

\(E(X^n)=?\)

Using formula: \(E(X^n)= M^{n}_{X}(0)\)

form point (a):

\(\to M_{X}(t)=\frac{1}{(t-1)^2}\)

Differentiating the value with respect of t

\(M'_{X}(t)=\frac{-2}{(t-1)^3}\)

when \(t=0\)

\(M'_{X}(0)=\frac{-2}{(0-1)^3}= \frac{-2}{(-1)^3}= \frac{-2}{-1}=2\\\\M''_{X}(t)=\frac{(-2)(-3)}{(t-1)^4}\\\\M''_{X}(0)=\frac{(-2)(-3)}{(0-1)^4}= \frac{6}{(-1)^4}= \frac{6}{1}=6\\\\M''_{X}(t)=\frac{(-2)(-3)}{(t-1)^4}\\\\M''_{X}(0)=\frac{(-2)(-3)}{(0-1)^4}= \frac{6}{(-1)^4}= \frac{6}{1}=6\\\\M'''_{X}(t)=\frac{(-2)(-3)(-4)}{(t-1)^5}\\\\M''_{X}(0)=\frac{(-2)(-3)(-4)}{(0-1)^5}= \frac{24}{(-1)^5}= \frac{24}{-1}=-24\\\\\therefore \\\\M^{K}_{X} (t)=\frac{(-2)(-3)(-4).....(k+1)}{(t-1)^{k+2}}\\\\\)

\(M^{K}_{X} (0)=\frac{(-2)(-3)(-4).....(k+1)}{(-1)^{k+2}}\\\\\therefore\\\\E(X^n) = \frac{(-2)(-3)(-4).....(n+1)}{(-1)^{n+2}}\\\\\)

Answer:

Þe eye in Þe sky does not lie

Step-by-step explanation:

Answer:

3 x 1/6 = 1/2

Step-by-step explanation:

The coordinates of the midpoints of the given line segment is:

(3.5, 1.5)

The midpoint of a line segment is simply referred to as the center of that specific line segment.

Thus, the coordinates at that point will be referred to as the coordinates of the midpoint.

The coordinates of the endpoints of the line are:

(4,6) and (3,-3)

The formula to find the coordinates of the midpoint of the line is:

(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Thus, we have:

(x, y) = (4 + 3)/2, (6 - 3)/2

= (3.5, 1.5)

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Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).