An Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Required:a. What is the 1-step transition matrix? b. Suppose he is in city B, what is the probability he will be in city A after two trips? c. After many trips between the two cities, what is the probability he will be in city B?

Answers

Answer 1

Answer:

a.  1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. The probability that he will be in City A after two trips given that he is in City B  = 0.585

c. After many trips, the probability that he will be in city B = 0.3571

Step-by-step explanation:

Given that:

For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25

If he is in city B, the probability that he has to drive passengers to city A is 0.45.

The objectives are to calculate the following :

a. What is the 1-step transition matrix?

To  determine the 1 -step transition matrix

Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.

∴  The transition probability from state ∝ to state β is 0.25.

The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75

The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55

Hence; 1-step transition matrix is be expressed as:

[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]

b. Suppose he is in city B, what is the probability he will be in city A after two trips?

Consider [tex]Y_n[/tex] = ∝ or β  to represent the Uber driver is in City A or City B respectively.

∴ The probability that he will be in City A after two trips given that he is in City B

=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]

= 0.45 × 0.75 + 0.55 × 0.45

= 0.3375 + 0.2475

= 0.585

c. After many trips between the two cities, what is the probability he will be in city B?

Assuming that Ф = [ p  q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.

Then, ФP = Ф  , also  p+q = 1  , q = 1 - p  and p = 1 - q

[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]

0.75p + 0.45q = q

-0.25p + 0.45q = 0

since p = 1- q

-0.25(1 - q) + 0.45q = 0    

-0.25 + 0.25 q + 0.45q = 0

0.7q = 0.25

q = [tex]\dfrac{0.25} {0.7 }[/tex]

q =  0.3571

After many trips, the probability that he will be in city B = 0.3571


Related Questions

2. Use the diagram and given information to answer the questions and prove the statement.

a. Re-draw the diagram of the overlapping triangles so that the two triangles are separated.

b. What additional information would be necessary to prove that the two triangles, XBY and ZAY , are congruent? What congruency would be applied?

c. Prove (AZ) is congruent to (BX) using a flow chart proof. ( ):both have a line over them

Answers

[tex] \huge{ \underline{ \tt{ \purple{Solution:}}}}[/tex]

2) a)⚘ Refer to the attachment....

After separating, we will get two triangles △XYB and △ZYA where ∠Y is common to both the triangles, hence their measure is equal. This will be use in further proof.

b) We have,

∠X = ∠Z (Given, ATQ)∠Y = common to both triangles. XY = ZY

So, here

Two pairs of corresponding angles are equal along the side contained between them. So, The above triangles are congurent by ASA criterion.

✤ No more additional information Required to prove the above triangles be congurent.

△XYB ≅ △ZYA (By ASA Criterion)

c) By using flow chart proof:

[tex] \boxed{ \sf{ \angle X = \angle Z}} \searrow[/tex]

[tex] \boxed{ \sf{\small{ \angle Y = com.}}} \rightarrow \boxed{\small{ \sf{ \triangle XYB \cong \triangle ZYA}}}\rightarrow \small{\boxed{ \sf{AZ= XB}}}[/tex]

[tex] \boxed{ \sf{XY = ZY}} \nearrow[/tex]

━━━━━━━━━━━━━━━━━━━━

Step-by-step explanation:

Hey mate ut answer is in the given attachment.

hope i help u

solve for x: 5x+3+8x-4=90

Answers

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.

[tex]5x+3+8x-4=90[/tex]

Combine like terms:

[tex]13x - 1 = 90[/tex]

Add 1 to both sides:

[tex]13x = 91[/tex]

Divide both sides by 13:

[tex]x = 7[/tex]

Hope this helped!

Answer:

x = 7

Step-by-step exxplanation:

5x + 3 + 8x - 4 = 90

5x + 8x = 90 - 3 + 4

13x = 91

x = 91/13

x = 7

probe:

5*7 + 3 + 8*7 - 4 = 90

35 + 3 + 56 - 4 = 90

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.1 degrees. Low Temperature ​(◦​F) 40−44 45−49 50−54 55−59 60−64 Frequency 3 6 13 7

Answers

Answer:

[tex]Mean = 53.25[/tex]

Step-by-step explanation:

Given

Low Temperature : 40−44 || 45−49 ||  50−54 || 55−59 || 60−64

Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7

Required

Determine the mean

The first step is to determine the midpoints of the given temperatures

40 - 44:

[tex]Midpoint = \frac{40+44}{2}[/tex]

[tex]Midpoint = \frac{84}{2}[/tex]

[tex]Midpoint = 42[/tex]

45 - 49

[tex]Midpoint = \frac{45+49}{2}[/tex]

[tex]Midpoint = \frac{94}{2}[/tex]

[tex]Midpoint = 47[/tex]

50 - 54:

[tex]Midpoint = \frac{50+54}{2}[/tex]

[tex]Midpoint = \frac{104}{2}[/tex]

[tex]Midpoint = 52[/tex]

55- 59

[tex]Midpoint = \frac{55+59}{2}[/tex]

[tex]Midpoint = \frac{114}{2}[/tex]

[tex]Midpoint = 57[/tex]

60 - 64:

[tex]Midpoint = \frac{60+64}{2}[/tex]

[tex]Midpoint = \frac{124}{2}[/tex]

[tex]Midpoint = 62[/tex]

So, the new frequency table is as thus:

Low Temperature : 42 || 47 ||  52 || 57 || 62

Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7

Next, is to calculate mean by

[tex]Mean = \frac{\sum fx}{\sum x}[/tex]

[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]

[tex]Mean = \frac{1065}{20}[/tex]

[tex]Mean = 53.25[/tex]

The computed mean is greater than the actual mean

x/5=-2 . And how did you get it?

Answers

[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]

Answer:

[tex]\huge \boxed{{x=-10}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{5} =-2[/tex]

We need the x variable to be isolated on one side of the equation, so we can find the value of x.

Multiply both sides of the equation by 5.

[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]

Simplify the equation.

[tex]x=-10[/tex]

The value of x that makes the equation true is -10.

change 4 5/9 from a mixed number to an improper fraction

Answers

Step-by-step explanation:

Hello, there!!

The answer would be 41/9.

The reason for above answer is to change any mixed fraction into improper fraction we should follow a simple step:

multiply the denominator with whole number.Add the answer (after mutiplied ).

look here,

=[tex] \frac{4 \times 9 + 5}{9} [/tex]

we get 41/9.

Hope it helps...

The given fraction into the improper fraction should be [tex]\frac{41}{9}[/tex]

Given that,

The mixed number fraction is [tex]4 \frac{5}{9}[/tex]

Computation:

[tex]= 4\frac{5}{9}\\\\ = \frac{41}{9}[/tex]

Here we multiply the 9 with the 4 it gives 36 and then add 5 so that 41 arrives.

learn more about the fraction here: https://brainly.com/question/1301963?referrer=searchResults

A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing ​(Simplify your​ answer.) nothing ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answers

Complete Question

A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26

Answer:

The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]

The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  

    [tex]\sigma _{\= x} = 2.746[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 77[/tex]

     The  standard deviation is  [tex]\sigma = 14[/tex]

     The sample size is  [tex]n = 26[/tex]

     

Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  mathematically represented as

           [tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]

substituting values  

          [tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]

          [tex]\sigma _{\= x} = 2.746[/tex]

Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is  equivalent to the population mean i.e  

      [tex]\mu_{\= x } = \mu[/tex]

      [tex]\mu_{\= x } = 77[/tex]

GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!!

One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?

A. 2:3

B. 1:6:4

C. 1:16

D. 1:64

Please include ALL work! <3

Answers

Answer:

The answer is option C

Step-by-step explanation:

To find the ratio first find the diameter of the larger circle

Diameter of first circle = 6 inches

Diameter of second circle = 4 × diameter of the first circle

Which is

Diameter of second circle

= 4 × 6 = 24 inches

Area of a circle = πr²

r is the radius

Area of smaller circle

Diameter = 6 inches

Radius = 6 / 2 = 3 inches

Area = (3)² π = 9π in²

Area of larger circle

Diameter = 24 inches

Radius = 24 / 2 = 12 inches

Area = (12)²π = 144π in²

The ratio of the smaller circle to the larger circle is

[tex] \frac{9\pi}{144\pi} [/tex]

Reduce the fraction by 9π

That's

[tex] \frac{1}{16} [/tex]

We have the final answer as

1 : 16

Hope this helps you

Answer:

C. 1:16

Step-by-step explanation:

Area of a circle is:

[tex]\pi \times {r}^{2} [/tex]

Small circle Area:

radius = diameter/2

radius = 6/2 = 3

[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]

a = 28.27

Large circle 4 times larger diameter

6*4 = 24

diameter = 24

r = 24/2

r = 12

[tex]a \: = \pi {12}^{2} [/tex]

a = 452.39

area of large circle/ area of small circle

452.39/28.27 = 16.00

ratio is 1:16

The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.

Answers

Answer:

[tex]\approx \bold{6544\ in^3/sec}[/tex]

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]

(This is increasing rate so positive)

Rate of change of height of cylinder:

[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

[tex]V = \pi r^2h[/tex]

Differentiating it w.r.to 't':

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]

Let us have a look at the formula:

[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]

[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]

Applying the two formula for the above differentiation:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]

Now, putting the values:

[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]

So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]

Find the point(s) on the ellipse x = 3 cost, y = sin t, 0 less than or equal to t less than or equal to 2pi closest to the point(4/3,0) (Hint: Minimize the square of the distance as a function of t.) The point(s) on the ellipse closest to the given point is(are) . (Type ordered pairs. Use a comma to separate answers as needed.)

Answers

Answer and Step-by-step explanation:

The computation of points on the ellipse is shown below:-

Distance between any point on the ellipse

[tex](3 cos t, sin t) and (\frac{4}{3},0) is\\\\ d = \sqrt{(3 cos\ t - \frac{4}{3}^2) } + (sin\ t - 0)^2\\\\ d^2 = (3 cos\ t - \frac{4}{3})^2 + sin^2 t[/tex]

To minimize

[tex]d^2, set\ f' (t) = 0\\\\2(3cos\ t - \frac{x=4}{3} ).3(-sin\ t) + 2sin\ t\ cos\ t = 0\\\\ 8 sin\ t - 16 sin\ t\ cos\ t = 0\\\\ 8 sin\ t (1 - 2 cos\ t) = 0\\\\ sin\ t = 0, cos\ t = \frac{1}{2} \\\\ t= 0, \ 0, \pi,2\pi,\frac{\pi}{3} , \frac{5\pi}{3}[/tex]

Now we create a table by applying the critical points which are shown below:

t            [tex]d^{2} = (3\ cos t - \frac{4}{3})^{2} + sin^{2}t[/tex]

0           [tex]\frac{25}{9}[/tex]

[tex]\pi[/tex]           [tex]\frac{169}{9}[/tex]

[tex]2\pi[/tex]         [tex]\frac{25}{9}[/tex]

[tex]\frac{\pi}{3}[/tex]          [tex]\frac{7}{9}[/tex]

[tex]\frac{5\pi}{3}[/tex]         [tex]\frac{7}{9}[/tex]

When t = [tex]\frac{\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{\sqrt{3} }{2})[/tex]

When t = [tex]\frac{5\pi}{3}[/tex], x is [tex]\frac{3}{2}[/tex] and y is [tex]\frac{-\sqrt{3} }{2}[/tex]. So, the required points are [tex](\frac{3}{2},\frac{-\sqrt{3} }{2})[/tex]

A triangle has sides with lengths of 5x - 7, 3x -4 and 2x - 6. What is the perimeter of the triangle?

Answers

Answer:

Step-by-step explanation:

perimeter of triangle=sum of lengths of sides=5x-7+3x-4+2x-6=10x-17

Answer:

10x - 17

Step-by-step explanation:

To find the perimeter of a triangle, add up all three sides

( 5x-7) + ( 3x-4) + ( 2x-6)

Combine like terms

10x - 17

How many dimensions does an angle have?

Answers

Answer:

the length has dimension 1, the area has the dimension 2, the volume has dimension 3, etc. And the angle has dimension 0.

Step-by-step explanation:

A dimension has 0 angles

PLEASE HELP FAST!! The cone and the cylinder below have equal surface area. True or False??

Answers

Answer:

B. FALSE

Step-by-step explanation:

Surface area of cone = πr(r + l)

Where,

r = r

l = 3r

S.A of cone = πr(r + 3r)

= πr² + 3πr²

S.A of cone = 4πr²

Surface area of cylinder = 2πrh + 2πr² = 2πr(h + r)

Where,

r = r

h = 2r

S.A of cylinder = 2πr(2r + r)

= 4πr² + 2πr²

S.A of cylinder = 6πr²

The surface are of the cone and that of the cylinder are not the same. The answer is false.

Answer:false

Step-by-step explanation:

False

Factor this trinomial completely. -6x^2 +26x+20

Answers

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

=-2(x-5)(3x+2)


The X- and y-coordinates of point P are each to be chosen at random from the set of integers 1 through 10.
What is the probability that P will be in quadrant II ?
О
1/10
1/4
1/2

Answers

Answer:

Ok, as i understand it:

for a point P = (x, y)

The values of x and y can be randomly chosen from the set {1, 2, ..., 10}

We want to find the probability that the point P lies on the second quadrant:

First, what type of points are located in the second quadrant?

We should have a value negative for x, and positive for y.

But in our set;  {1, 2, ..., 10}, we have only positive values.

So x can not be negative, this means that the point can never be on the second quadrant.

So the probability is 0.

line m in the xy-plane above is to be reflected through the x-axis. if the slope of line m is 2/3,whats is the slope of the image of line m under the reflection.

Answers

Answer: The new slope is -(2/3)

Step-by-step explanation:

Ok, we know that our line can be written as:

y = (2/3)*x + b

where b is the y-intercept, and here does not really matter.

Ok, remember that if we have a point (x, y) and we reflect it over the x-axis, the new point will be (x, -y).

For our linear equation, the point (x, y) can be written as:

(x, y = (2/3)*x + b) = (x,  (2/3)*x + b)

Now, after the reflection, our point is:

(x, - ( (2/3)*x + b)) = (x, -(2/3)*x - b)

Then our new line is y = -(2/3)*x - b

The new slope is -(2/3)

Find the distance between the points. Give an exact answer and an approximation to three decimal places.
TI
(S.
(3.1, 0.3) and (2.7, -4.9)
Th
(Rd

Answers

Answer:

5.215 units (rounded up to three decimal places)

Step-by-step explanation:

To find the distance between points (3.1 , 0.3) and (2.7, -4.9)

We use the Pythagoras Theorem which states that for a right triangle of sides a,b and c then;

a² + b²  = c² ,  Where c is the hypotenuse.

In our case, the distance between the two points is the hypotenuse of triangle formed by change in y-axis and change in x-axis.

The distance (hypotenuse) squared = (-4.9 - 0.3)² + (2.7 - 3.1)² = 27.04 + 0.16 = 27.2

Hypotenuse (the distance between) = [tex]\sqrt{27.2}[/tex] = 5.215 units (rounded up to three decimal places)

The net of a triangular prism is shown below. What is the surface area of the prism? A. 128 cm^2 B. 152 cm^2 C. 176 cm^2 D. 304 cm^2

Answers

Answer:

B. 152 cm²

Step-by-step explanation:

To find the surface area using a net, do this:

Take apart the figure. We see that there are three rectangles and two triangles. Find the area of each ([tex]A=l*w[/tex]) and then add the values together:

The first rectangle on the left is the same as the one on the right.

[tex]5*8=40[/tex]

Two measures are 40 cm².

The middle rectangle is:

[tex]6*8=48[/tex]

48 cm²

The formula for the area of a triangle is [tex]A=\frac{1}{2}*b*h[/tex]:

[tex]A=\frac{1}{2}*6*4\\\\A=\frac{1*6*4}{2}\\\\A=\frac{24}{2}\\\\ A=12[/tex]

The area of the two triangles is 12 cm².

Now add the values:

[tex]40+40+48+12+12=152[/tex]

The area of the figure is 152 cm².

:Done

Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?

Answers

Answer:

92 inches squared

Step-by-step explanation:

T/P = 8 * 3

L/R = 3 * 2

F/B = 8 * 2

Solving for surface area!

2(24) + 2(6) + 2(16) = 92

[PLEASE HELP] Consider this function, f(x) = 2X - 6.

Match each transformation of f (x) with its descriptions..

Answers

Answer:

Find answer below

Step-by-step explanation:

f(x)=2x-6

Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}

Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}

Parity of 2x-6: Neither even nor odd

Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)

inverse of 2x-6: x/2+6/2

slope of 2x-6: m=2

Plotting : y=2x-6

Solve for y.
-1 = 8+3y
Simplify you answer as much as possible.

Answers

Answer:

-3

Step-by-step explanation:

[tex]8+3y = -1\\3y = -9\\y = -3[/tex]

Answer:

y = -3

Step-by-step explanation:

-1=3y+8

3y+8=-1

3y=-9

y=-3

Simplify the following expression. (75x - 67y) - (47x + 15y)

Answers

7x - 13y.

First you simplify all the similar variables. 75x - 47x and -67y + 15y. This gets you to 28x - 52y. Dividing both answers by 4 gives you 7x - 13y

Hi there! :)

Answer:

[tex]\huge\boxed{2(14x - 41y)}[/tex]

(75x - 67y) - (47x + 15y)

Distribute the '-' sign with the terms inside of the parenthesis:

75x - 67y - (47x - (15y))

75x - 67y - 47x - 15y

Combine like terms:

28x - 82y

Distribute out the greatest common factor:

2(14x - 41y)

can someone help me answer this??

Answers

Answer:

hkkr

need school the long said

Answer:

That would indicate 20.0 ml

id appreciate a rating thanks XP

In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ

Answers

Answer:

2.7 in²

Step-by-step explanation:

Since ∆BAC and ∆EDF are similar, therefore, the ratio of their area = square of the ratio of their corresponding side lengths.

Thus, if area of ∆EDF = x, area of ∆BAC = 6 in², EF = 2 in, BC = 3 in, therefore:

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = (1.5)^2 [/tex]

[tex] \frac{6}{x} = 2.25 [/tex]

[tex] \frac{6}{x}*x = 2.25*x [/tex]

[tex] 6 = 2.25x [/tex]

[tex] \frac{6}{2.25} = \frac{2.25x}{2.25} [/tex]

[tex] 2.67 = x [/tex]

[tex] x = 2.7 in^2 [/tex] (nearest tenth)

if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged

Answers

Answer:

35%

Step-by-step explanation:

[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]

[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]

Answer:

35%

Step-by-step explanation:

I REALLY HOPE I HELPED

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

 ✌ -ZYLYNN JADE ARDENNE

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A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician

Answers

Answer:

[tex]Probability = \frac{3}{7}[/tex]

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

[tex]Total = n(Electrician) + n(Mechanic)[/tex]

[tex]Total = 6 + 8[/tex]

[tex]Total = 14[/tex]

Next, is to determine the required probability using the following formula;

[tex]Probability = \frac{n(Electrician)}{Total}[/tex]

[tex]Probability = \frac{6}{14}[/tex]

Divide numerator and denominator by 2

[tex]Probability = \frac{3}{7}[/tex]

Hence, the probability of selecting an electrician is 3/7

In training to run a half marathon, Jenny ran 2/5 hours on Tuesday, 11/6 hours on
Thursday, and 21/15 hours on Saturday. What is the total amount of hours that Jenny
ran this week? (Simplify your answer and state it as a mixed number.)
I​

Answers

Answer:

Total hours that Jenny ran = 3.63 hours.

Step-by-step explanation:

Jenny ran on Tuesday for = 2/5 hours or 0.4 hours.

Time consumed to run on Thursday = 11/6 hours or 1.83 hours.

Time consumed to run on Saturday = 21/ 15 hours or 1.4 hours.

Here, the total hours can be calculated by just adding all the running hours. So the running hours of Tuesday, Thursday, and Saturday will be added to find the total hours.

Total hours that Jenny ran = 0.4 + 1.83 + 1.4 = 3.63 hours.

If you randomly select a letter from the phrase "Sean wants to eat at Olive Garden," what is the probability that a vowel is randomly selected

Answers

Answer:

12/27

Step-by-step explanation:

Count all letters and all vowels then divide vowels by letters

The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

What is the probability of an event in an experiment?

The probability of any event suppose A, in an experiment is given as:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

How to solve the given question?

In the question, we are given an experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden".

We are asked to find the probability that the selected letter is a vowel.

Let the event of selecting a vowel from the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden" be A.

We can calculate the probability of event A by the formula:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

The number of outcomes favorable to event A (n) = 12 (Number of vowels in the phrase)

The total number of outcomes in the experiment (S) = 27 (Number of letters in the phrase).

Now, we can find the probability of event A as:

P(A) = 12/27 = 4/9

∴ The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

Learn more about the probability of an event at

https://brainly.com/question/7965468

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Answer the question :)

Answers

Answer:

A. -11

Step-by-step explanation:

In the function, replace x with -2

R(x) = x^2 - 3x - 1 ➡ R(-2) = (-2)^2 - 3 × 2 -1 = -11

A patio 20 feet wide has a slanted roof, as shown in the figure. Find the length of the roof if there is an 8-inch overhang. Show all work and round the answer to the nearest foot. Be sure to label your answer appropriately. Then write a sentence explaining your answer in the context of the problem.

Answers

Answer:

[tex]Slanted\ Roof = 20.77\ ft[/tex]

Step-by-step explanation:

The question has missing attachment (See attachment 1 for complete figure)

Given

Width, W = 20ft

Let the taller height be represented with H and the shorter height with h

H = 10ft

h = 8ft

Overhang = 8 inch

Required

Determine the length of the slanted roof

FIrst, we have to determine the distance between the tip of the roof and the shorter height;

Represent this with

This is calculated by

[tex]D = H - h[/tex]

Substitute 10 for H and 8 for h

[tex]D = 10 - 8[/tex]

[tex]D = 2ft[/tex]

Next, is to calculate the length of the slant height before the overhang;

See Attachment 2

Distance L can be calculated using Pythagoras theorem

[tex]L^2 = 2^2 + 20^2[/tex]

[tex]L^2 = 4 + 400[/tex]

[tex]L^2 = 404[/tex]

Take Square root of both sides

[tex]\sqrt{L^2} = \sqrt{404}[/tex]

[tex]L = \sqrt{404}[/tex]

[tex]L = 20.0997512422[/tex]

[tex]L = 20.10\ ft[/tex] -------Approximated

The full length of the slanted roof is the sum of L (calculated above) and the overhang

[tex]Slanted\ Roof = L + 8\ inch[/tex]

Substitute 20.10 ft for L

[tex]Slanted\ Roof = 20.10\ ft + 8\ inch[/tex]

Convert inch to feet to get the slanted roof in feet

[tex]Slanted\ Roof = 20.1\ ft + 8/12\ ft[/tex]

[tex]Slanted\ Roof = 20.10\ ft + 0.67\ ft[/tex]

[tex]Slanted\ Roof = 20.77\ ft[/tex]

Hence, the total length of the slanted roof in feet is approximately 20.77 feet

Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a. .4 × .15 = .060 b. 0.40 + .15 = .55 c. 1 − (.40 + .15) = .45 d. 1 − (.6 × .85) = .490

Answers

Answer: a. 0.4 × 0.15 = 0.060

Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.

For P(A):

P(A') = 1 - 0.6

P(A') = 0.4

For P(B):

P(B') = 1 - 0.85

P(B') = 0.15

To determine probability of A' and B':

P(A' and B') = P(A')*P(B')

P(A' and B') = 0.4*0.15

P(A' and B') = 0.06

Probability of the complement of the event is 0.060

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