8. Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek

Answers

Answer 1

Solution :

Case I :

If Collen is late on [tex]0[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} $[/tex]

[tex]$=\frac{1}{32}[/tex]

Case II :

When Collen is late on [tex]1[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_1$[/tex]

[tex]$=\frac{1}{32} \times 5$[/tex]

[tex]$=\frac{5}{32}[/tex]

Case III :

When Collen was late on [tex]2[/tex] out of [tex]5[/tex] days.

[tex]$= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times ^5C_2$[/tex]

[tex]$=\frac{1}{32} \times 10$[/tex]

[tex]$=\frac{5}{16}[/tex]

Therefore, the [tex]\text{probability}[/tex] that Collen will arrive late to work no more than [tex]\text{twice}[/tex] during a [tex]\text{five day workweek}[/tex] is :

[tex]$=\frac{1}{32} + \frac{5}{32} + \frac{5}{16} $[/tex]

[tex]$=\frac{1}{2}$[/tex]


Related Questions

Số nghiệm của pt | 2x-3| - | 3x+2|=0 là?

Answers

Answer:

2 solutions

Step-by-step explanat

ion:|2x-3|-|3x-2|=0

<=>|2x-3|=|3x-2|

<=>2x-3=3x-2

Or 2x-3=-3x+2

<=>2x-3x=-2+3

or 2x+3x=2+3

<=>x=-1

Or x=1

simplify 1+tan^2x÷1+tan^2x​

Answers

Answer:

uihuii

Step-by-step explanation:

Are 5-x=y and x-5=y the same ?

Answers

Answer:

not really

Step-by-step explanation:

because on the first equation you subtract 5and take to y as a negative and in the second equation 5 goes as a positive at least that is what i think

Answer:

no cause

5-x=y

5 is positive , x is negative

BUT

x-5=y

5 is negative, and x is positive

y=8200(0.96)^x growth or decay find

Answers

Answer:

This would be a .04 or 4% decay.....

for every "time unit" (x in this case) you will be multiplying

the amount by .96 ... in other words if you started with one dollar

the results would be 96 cents... after two "time" steps you would have

only 92 cents (.96 *.96)

Step-by-step explanation:

For the function p defined by p(m)=2m2−4m+3, find p(13).
A. 41/9
B. 17/9
C. 5
D. 1.8

Answers

Answer:

Here we have:

p(m) = 2m^2 - 4m + 3

And we want to find p(13)

This means that we just need to replace all the m's by the  number 13 in the equation, so we get:

p(13) = 2*(m = 13)^2 - 4*(m = 13) + 3

p(13) = 2*(13)^2 - 4*13 + 3

       = 338 - 52 + 3 = 289

You can see that none of the options matches this, so maybe the equation or some other part of the question is written incorrectly, but here you have at least the general way of solving these type of problems.

What are the leading coefficient and degree of the polynomial?
-12x5–8+23x+3x

Answers

Answer:

d = 5      l = 12

Step-by-step explanation:

degree = 5

leading coefficient = 12

Find the measure of each angle indicated.
A) 25°
C) 35°
B) 45°
D) 40°

Answers

Answer:

here's the answer to your question

Answer:

D) 40

Step-by-step explanation:

To solve the question you can use the knowledge that every triangle has a total of 180 degrees. Two of the angles are known one is 50 and the other is 90. We know one is 90 because of the square around the angle. Then, you can set up an algebraic equation to solve. We know that 50+90+x=180, so solve for x for the final answer of 40.

Guys please help me with this problem

Answers

Answer:

11. 5%

Step-by-step explanation:

1 + percent increase = 1.115

Percent increase = 1.115 - 1 = 0.115 = 11.5 /100 = 11.5 %

Answer:

Step-by-step explanation:

In the exponential form of an equation, the growth or decay rate is found inside the parenthesis. The standard form of an exponential equation is

[tex]y=a(1+r)^x[/tex] if it's growth, or

[tex]y=a(1-r)^x[/tex] if it's decay.

Looking at those equations, logically a growth equation is greater than 1, while a decay equation is less than 1. Obviously, our function is a growth.

To determine the rate of growth, we look closely at (1.115) inside the parenthesis. BECAUSE that is greater than 1, we KNOW it is growth, therefore, it follows the (1 + r) pattern. Let's break up our (1.115) so it models that pattern:

(1.115) --> (1 + .115) and since these are percentages in their decimal form, it follows that 1 is 100% and .115 is 11.5%. Our growth rate is 11.5%

15) A new BMW decreases in value exponentially after it is purchased. If a new BMW is valued at $55,000 and
depreciate at a rate of 22% a year, what is the value after 4 years? After 8 years)

Answers

The values of BMW after 2, 4 and 8 years  according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.

Using the parameters given, we define an decreasing exponential function :

[tex]A = A_{0} (1 - r)^{t}[/tex]

Where,

[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount

Value after 2 years :

t = 2

A = 55000(1 - 0.22)²

A = 55000(0.78)²

A = $33,462

Value after 4 years :

t = 4

A = 55000(1 - 0.22)^4

A = 55000(0.78)^4

A = $20,358.28

Value after 8 years :

t = 4

A = 55000(1 - 0.22)^8

A = 55000(0.78)^8

A = $7,535.63

Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.

Learn more about Exponential functions :

https://brainly.com/question/14355665

Solve 4 sinx + 9 cosx=0 for 0° ​

Answers

4 sin(x) + 9 cos(x) = 0

4 sin(x) = -9 cos(x)

tan(x) = -9/4

x = arctan(-9/4) + … … … (in radians)

or

x = arctan(-9/4) + 180n ° … … … (in degrees)

where n is any integer.

I'm guessing you're solving for x over some domain, probably 0° ≤ x < 360°. In that case, you would have two solutions for n = 1 and n = 2 of

x ≈ 113.96°   and   x ≈ 293.96°

[tex]\sqrt{x^{2} +4x+4[/tex] -3=0

Answers

Answer:

Given,

[tex] \sqrt{ {x}^{2} + 4x + 4} - 3 = 0 \\ = > \sqrt{ {x}^{2} + 4x + 4} = 3 \\ = > {( \sqrt{ {x}^{2} + 4x + 4} })^{2} = {3}^{2} \\ = > {x}^{2} + 4x + 4 = 9 \\ = > {x}^{2} + 4x + 4 - 9 = 0 \\ = > {x}^{2} + 4x - 5 = 0 \\ = > {x}^{2} + 5x - x - 5 = 0 \\ = > x(x + 5) - 1(x + 5) = 0 \\ = > (x - 1)(x + 5) = 0 \\ \\ \sf \: either \: x - 1 = 0 \: \: \: \: \\ = > x = 1 \: \: \\ \\ \sf \: or \\ x + 5 = 0 \\ = > x = - 5 \\ \\ \green{ \boxed{ \bf \: \: \: \: \: x = 1 \: \: or \: - 5}}[/tex]

But if we put the value of x = 5 then it doesn’t satisfy the equation.

So,

X = 1

Answer:

The answer is [tex]x=1[/tex].

Step-by-step explanation:

To solve this problem, start by factoring the equation using the perfect square trinomial rule, which is states that the middle term is the first term multiplied by the last term, and then multiplied by 2. The formula for the perfect square trinomial rule looks like [tex]a^2+2ab+b^2[/tex], where [tex]a=x[/tex] and [tex]b=2[/tex]. The equation will look like [tex]\sqrt{(x+2)^2}-3=0[/tex].  

Next, pull out the terms from under the radical, assuming positive real numbers, which will look like [tex]x+2-3=0[/tex]. Then, simplify the equation by subtracting 3 from 2, which will look like [tex]x-1=0[/tex]. Finally, add 1 to both sides of the equation, and the answer will be [tex]x=1[/tex].


a) 61°
b) 29°
C) 40°
d) 50°

Answers

Answer:

29 degrees (~0.506 rad)

Simplify (b9)3. See picture please

Answers

Answer:

b^27

Step-by-step explanation:

Answer:

A. b^27

You multiply 9x3 and you get 27 with the base "b"

Step-by-step explanation:

Evaluate: 2-4 А. =100 В. -8 ОО С. -16 D. 1 16​

Answers

Answer:

D. 1/16

Step-by-step explanation:

Evaluate: 2^-4

А. =100

В. -8ОО

С. -16

D. 1/16

Given

2^-4

= 1 / 2⁴

= 1 / (2 * 2 * 2 * 2)

= 1 / 16

Therefore,

2^-4 = 1/16

D. 1/16

2(2x+3)=3(3x+1)
Duýdhdhdjjdjdjđm

Answers

Answer:

12

Step-by-step explanation:

.......................

Answer:

x=1/2

Step-by-step explanation:

A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.​

Answers

Answer:

A fruit seller bought 160 kg of apples at Rs. 32 per kg. He sold one fourth of them at Rs. 40 per kg and sold the rest at Rs. 31 per kg. Find his profit or loss.

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Letsanswers

How many numbers of the set {1, 2, 3, 4, . . . , 297, 298, 299, 300} are multiples of 10 but not multiples of 15?

Answers

Answer:

I get 20

Step-by-step explanation:

While there probably is some logical way to go about this I just did it in excel

screenshot below

Answer:

20

Step-by-step explanation:

10

20

40

50

70

80

100

110

130

140

160

170

190

200

220

230

250

260

280

290

Given m
n, find the value of x and y.
m
35°
x

X=
y =
PLS HELP I’m kinda really confused

Answers

Answer:

x = 145°, y = 35°

Step-by-step explanation:

Given,

m || n

So,

35° = y° [Alternate interior angles]

And,

y° + x° = 180° [Since linear pair]

=> x + 35 = 180

=> x = 180 - 35

=> x = 145°

Hence,

x = 145°, y = 35°

Answer:

x = 145

y = 35

Step-by-step explanation:

35 and y are alternate interior angles and alternate interior angles are equal when the lines are parallel

35 = y

x+y = 180 because x and y form a straight line

x+35 = 180

x = 180-35

x = 145

Factorise [tex]2t^2+5t+2[/tex]
and pls explain why 2t(t+2) becomes (2t+1) when you get to it in your working out ty

Answers

Answer:    [tex]\displaystyle\ \large \boldsymbol{ 2t^2+5t+2= {(2t+1) (t+2)}}[/tex]

Step-by-step explanation:

[tex]\displaystyle\ \large \boldsymbol{} 2t^2+5t+2=0 \\\\2t^2+\underbrace{4t+t}_{5t}+2=0 \\\\ (2t^2+4t)+(t+2)=0 \\\\ 2t(\underline{t+2})+(\underline{t+2})=0 \\\\ \boxed{(2t+1) (t+2)=0 }[/tex]

A music shop sold 25 50$ radios at a profit of 8% and 6 30$ radios at a loss of 15% how much was the profit or loss combined

Answers

Answer:

The profit or loss combined is $2.99

Step-by-step explanation:

Given;

cost price of first radio, CP = $25.50

profit percent, = 8%

The profit made is calculated as;

[tex]\frac{Profit}{CP} \times 100\% = \frac{SP-CP}{CP} \times 100\% = 8\%\\\\Profit = SP-CP = 0.08CP = 0.08\times \$25.50 = \$ 2.04[/tex]

Cost price of the second radio, CP = $6.30

loss percent = 15%

The loss incurred is calculated as;

[tex]\frac{Loss}{CP} \times 100\% = 15\%\\\\Loss = 0.15CP\\\\Loss = 0.15 \times \$6.30 = \$0.95[/tex]

The profit or loss combined = $2.04 + $0.95

                                               = $2.99

factorize
a)a²x+2ax-3x+5a²+10a-15
b)(a+b)(a-b)-a+b
c)x³-x²+x+x²y-xy+y​

Answers

Answer:

(a)x(a^2+2a-3)+5(a^2+2a-3)

chứng minh mệnh đề sau bằng phương pháp phản chứng:
" Nếu phương trình bậc hai ax2+bx+c=0 vô nghiệm thì a và c cùng dấu"

Answers

Answer:

Which language is this ?????

can you help me i got two wrong if I get one wrong I will have a falling grade

Answers

Answer:

the bottom left is wrong

Step-by-step explanation:

if u add 40+5+7/10+1/100 it'll only equal to 45.71

Answer:

40 + 5 + [tex]\frac{7}{10}[/tex] + [tex]\frac{1}{100}[/tex] = 45.71

Step-by-step explanation:

The one needs to be in the thousandths place.

Find the value of x.
A. 5
B. 31
C. 7
D. 11

Answers

Answer:

5

Step-by-step explanation:

EB is the median so it is the average of the top and bottom lengths

(38 + 6x-6) /2 = 7x-4

Combine like terms

(32+6x)/2 = 7x-4

Multiply by 2

32+6x = 14x-8

Subtract 6x from each side

32+6x-6x = 14x-6x -8

32 = 8x-8

Add 8 to each side

32+8 = 8x-8

40 = 8x

Divide by 8

40/8 = 8x/8

5 =x

PLEASE HELP ITS TIMED
If x/3=5/6,
then x= ​

Answers

Step-by-step explanation:

x/3 = 5/6

cross multiply

6x=15

x=2.5

Answer:

x=5/2

Step-by-step explanation:

state the equation, in slope-intercept form of each of the following graph

Answers

Answer:

A) y=(1/4)x-1, 4y=x-4

B) y=-2x

Does Anybody Know The Answer?

Answers

Yes. When a graph has more than one line it is a piece wise graph.

A number, y, is equal to the difference of a larger number and 3. The same number is one third of the sum of the larger
number and 9 Which equations represent the situation?
x+y 3 and - 3y -27
Oxxy-3
and-3--
Oy - 3
and-3--27
X-Y-3 and x-3y --9

Answers

Answer:

Set the larger number as x

"A number, y, is equal to the difference of a larger number and 3."

[tex]y=x-3[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y-x=-3\\x-y=3[/tex]

"The same number is one third of the sum of the larger number and 9."

[tex]y=\frac{1}{3} (x+9)[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y=\frac{1}{3} x+3\\3y=x+9\\3y-x=9\\x-3y=-9[/tex]

Write and algebraic expression:
The tens digit of a number is b and the units digit is twice as big. What is the value of the number in terms of b if the digits are reversed?

Answers

Answer:

21b

Step-by-step explanation:

A painter made the table below to show the amount of paint it takes to cover a certain amount of square feet. The amount of paint varies directly with the area of each wall.

Amount of Paint and Size of Wall
Area of wall feet squared, x
64
144
400
Amount of paint (pints), y
4
9
25

How much paint should the painter expect to use to paint a wall with an area of 256 square feet?
16 pints
32 pints
128 pints
225 pints

Answers

Answer:

16 pints

Step-by-step explanation:

it seems like there's a pattern. when you divide x by 16, you get the result of y.

64/16 = 4

144/16 = 9

400/16 = 25

so to find the answer would be x/16 = y.

sqrt ft is x, pints is y.

we're looking for how many pints of pain we should use for 256 sqrt ft. we use that same equation, but replace x with 256, and solve for y.

256/16 = 16

therefore, your answer is 16 pints.

please subscribe to #Gauthmath# subreddit if ya can ^^

Answer:

16 pints

Step-by-step explanation:

I did it on edge.

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