A die is rolled five times and a 5 or 6 is considered a success. Find the probability of
(i) at least 2 successes,
(ii) at least one but no more than 3 successes.

Problem 1

The idea here is to follow PEMDAS in reverse to undo what is happening to the variable b, so we can isolate it.

-11b + 7 = 40

-11b = 40-7

-11b = 33

b = 33/(-11)

b = -3

To check this value, plug it back into the original equation. You should get 40 on each side to help confirm the answer.

=====================================================

Problem 2

There are two ways we can solve. One method is to use the hint your teacher gave you. So we'll distribute first and then follow the same idea as problem 1

9(p-4) = -18

9p-36 = -18

9p = -18+36

9p = 18

p = 18/9

p = 2

Another method you can use is to follow these steps

9(p-4) = -18

p-4 = -18/9

p-4 = -2

p = -2+4

p = 2

Either way, we get the same result. To check the answer, replace every p with 2 in the original equation. You should get -18 on the left side after simplifying.

Step-by-step explanation:

i) [tex]\overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]

[tex]\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3[/tex]

ii) [tex]m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6[/tex]

iii) [tex](\overline{x},\:\overline{y}) = \left(\dfrac{x_A + x_B}{2},\:\dfrac{y_A + y_B}{2}\right)[/tex]

[tex]\:\:\:\:\:\:\:=(3,\:-2)[/tex]

Answer:

2 * 10^3 = 2000.

Step-by-step explanation:

3.8/1.9 * 10^5/10^2

= 2 * 10^3

[tex]\\ \sf\longmapsto 49\times 51[/tex]

[tex]\\ \sf\longmapsto (50-1)(50+1)[/tex]

[tex]\\ \sf\longmapsto (50)^2-(1)^2[/tex]

[tex]\\ \sf\longmapsto 2500-1[/tex]

[tex]\\ \sf\longmapsto 2499[/tex]

49 × 51

⇛(50 + 1) (50 - 1)

⇛(50)² - (1)²

⇛2500 - 1

⇛2499

Answer: TRUE

Step-by-step explanation: THE COMPOUD STATE MEN DETERMEND BY HE GRAPH IS THE SOLUTION AS SAID BY YOU IT IS TRUE BECAUSE THE READINGS ON THE GRAPH SHOW ITS TRUE

Answer:

1217

Step-by-step explanation:

Given

[tex]Subjects = 2353[/tex]

[tex]Improvement = 1136[/tex]

Required

The number that didn't improve --- missing from the question.

Let the unimproved be represented as x.

So, we have:

[tex]x + Improvement = Subjects[/tex]

Substitute known values

[tex]x + 1136 = 2353[/tex]

Solve for x

[tex]x =- 1136 + 2353[/tex]

[tex]x =1217[/tex]

Step-by-step explanation:

x - 5 < 2 (y - 8) • 1/4

x - 5 < (y - 8) / 2

2 (x - 5) < y - 8

2x - 10 < y - 8

2x - 10 + 8 < y

y > 2x - 2

graph 2x - 2 and shade the section above

The graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²

The inequality of the graph is given as:

x - 5 < 1/4(y - 8)²

Multiply both sides by 4

4x - 20 < (y - 8)²

Rewrite the inequality as:

(y - 8)² > 4x - 20

Hence, the graph of (y - 8)² > 4x - 20 is the same as the graph of x - 5 < 1/4(y - 8)²

See attachment for the graph

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Answer:

The correct answer is B. It will take them 7.2 hours.

Step-by-step explanation:

Given that to collect data on the signal strengths in a neighborhood, Briana must drive from house to house and take readings, and she has a graduate student, Henry, to assist her, and Briana figures it would take her 12 hours to complete the task working alone, and that it would take Henry 18 hours if he completed the task by himself, to determine how long will it take Briana and Henry to complete the task together the following calculation must be performed:

1/12 + 1/18 = X

18 / (12 x 18) + 12 / (18 x 12) = X

30/216 = X

5/36 = X

36/5 = 7.2

Therefore, they will be able to finish the task in 7.2 hours.

Answer:

Diameter = 2 × Radius

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diameter of a circle is the length of the line through the center and touching two points on its edge. In the figure above, drag the orange dots around and see that the diameter never changes. The diameter is also a chord.

Answer:

The lines are:

and

Since after multiplying by -3 the equations sum to 0, the equations are same.

Same equations produce overlapping lines, hence you can see one line only.

Divide second equation by 3

LInes are same so you can see only one line

Answer:

r^9/r^3 = r^9-3 = r^6

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]r^6[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\\frac{r^9}{r^3} \\--------------\\\\\text{Recall the quotient rule:}} \frac{a^x}{a^y}=a^{x-y}\\\\\rightarrow \frac{r^9}{r^3}\\\\\rightarrow r^{9-3}\\\\\rightarrow \boxed{r^6}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Explanation:

Normally, y = cos(x) has a period of 2pi. This means that every 2pi horizontal units, the graph repeats itself. However, we can see that the period here is pi units instead.

One way to see this is to start at (0,1). This is a local max point. Move to its neighboring local max at (pi,1). We have moved pi units along the x axis and the cycle is finished, after which point the cycle repeats itself.

Since T = pi is the period, we then can say B = 2pi/T = 2pi/pi = 2

This is then plugged into y = A*cos(B(x-C))+D where

A = 1

C = 0

D = 0

That leads us to y = cos(2x)

Since the period is often connected to time values, it might help to think of this wave's oscillations occurring twice as often compared to y = cos(x). So that might help see why we replace the x with 2x.

Answer:

y = 4x -1.5

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b where m is the slope and b is the y intercept

y = 4x -1.5

Answer:

1/3

Step-by-step explanation:

.444444444(repeating)- .111111111111(repeating)

.44444444......

-.11111111........

--------------------

.33333333........

Let x = .3333333.....

10x = 3.3333333.....

Subtract the first equation from the second

10x = 3.33333.....

-x =     .33333.....

--------------------------

9x = 3

x = 3/9

x = 1/3

---------------------------

Answer:

For octagon =1080.......

Explanation:

180(8-2)

180×6

1080°

Answer: 20/52 x 4/51 x 3/50 x 2/49 x 1/48 = .00000153908

Step-by-step explanation:

The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the number of cards in deck be = 52 cards

Total number of cards selected = 5

The number of ways of choosing 5 cards = ⁵²C₅

The cards selected are of the same suit

So , there are 4 ways to select them , Hearts , Clubs , Spades and Diamonds = ⁴C₁

And there is only one way to select the cards 6 , 7 , 8 , 9 , 10 = 1

Now , we use combination to select the cards in a deck,

So,

The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10, all of the same suit is calculated by,

P ( x ) = 1 / ⁵²C₅ x ⁴C₁ x 1

P ( x ) = 1 /  52! / ( 47! x 5! )  x  4! / 3!  x  1

P ( x ) = 1 / ( 52 x 51 x 50 x 49 x 48 ) / ( 2 x 3 x 4 x 5 ) x 4

P ( x ) = 1 / ( 2598966 ) x 4

P ( x ) = 4 / 2598966

P ( x ) = 0.00000153908

Hence , The probability of being dealt 5 cards from a standard 52 card deck, and the cards are 6,7,8,9, and 10 of the same suit is 0.00000153908

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Answer:

425 or 937

Step-by-step explanation:

First, I listed out all the possible numbers for the first digits, namely, the squares under 10.

1*1=1

2*2=4

3*3=9

Since all the digits have to be different, the first digit cannot be 1 because 1 squared is 1. So that leaves us 4 and 9 to work with, which I tried out one at a time.

Starting with 4:

2 squared is 4.

42

2 times 2 plus 1 equals 5.

425

Starting with 9:

3 squared is 9.

93

2 times 3 plus 1 equals 7.

937

So here we have two numbers that both work and meet the requirements (unless I understood the problem wrong at the part where it says "...the second digit in the 3rd digit on one more than twice the second digit")!

I hope this helped! :D

Step-by-step explanation:

combination

is answer of this question

Terms given

No of terms=8

We know

[tex]\boxed{\sf Mean=\dfrac{Sum\;of\:terms}{No\;of\:terms}}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{40+35+32+39+34+35+35+37}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=\dfrac{270}{8}[/tex]

[tex]\\ \sf\longmapsto Mean=35[/tex]

Final Answer:

35

Step-by-step explanation:

-median is the middle number in the data set-

arrange the data set from least to greatest:

40, 30, 32, 39, 34, 35, 35, 37 ⇒ 30, 32, 34, 35, 35, 37, 39, 40

we start from the lowest number and the highest  number and work your way to the middle:

30, 32, 34, 35, 35, 37, 39, 40

notice that there is no middle number:

30, 32, 34, 35, ?, 35, 37, 39, 40

so what we do is add both 35's and then divide it by 2

35 + 35 = 70 ÷ 2 = 35

median: 35

The n-th row in Pascal's triangle tells you the coefficients of terms in the expansion of (a + b)ⁿ. Starting with n = 0,

1

1 … 1

1 … 2 … 1

1 … 3 … 3 … 1

1 … 4 … 6 … 4 … 1

1 … 5 … 10 … 10 … 5 … 1

In more concrete terms, this translates to

(x - 5y)⁵ = 1 x ⁵ (-5y)⁰ + 5 x ⁴ (-5y)¹ + 10 x ³ (-5y)² + 10 x ² (-5y)³ + 5 x ¹ (-5y)⁴ + 1 x ⁰ (-5y)⁵

Simplify:

(x - 5y)⁵ = x ⁵ - 25x ⁴y + 250x ³y ² - 1250x ²y ³ + 3125xy ⁴ - 3125y ⁵

1) you find the multiplier by dividing 15÷100=0.15

2) multiply the answer by 11.95 so 0.15x11.95=1.792 so the answer is $1.792 because it is 15% of $11.95

Answer:

13.74

Step-by-step explanation:

To determine the tip, take the total amount and multiply by the tip percentage

11.95 * .15

1.7925

Round to the nearest cent

1.79

Add this to the cost of the haircut

11.95+1.79

13.74

Answer:

f(x) + f(4)

Step-by-step explanation:

TRUST ME DO THIS PROCESS

Answer:

12

Step-by-step explanation:

120 divided by 100 =1.2 x 10

Answer:

A or B depending on whether replacement takes place

Step-by-step explanation:

probability of getting a red marble=6/25

probability of getting a green marble (considering no replacement of marble drawn has taken place)=10/24

probability of randomly drawing a red marble and then a green marble=(6/25)*(10/24)=0.1=10%

probability of getting a red marble=6/25

probability of getting a green marble (considering replacement of marble drawn has taken place)=10/25

probability of randomly drawing a red marble and then a green marble=(6/25)*(10/25)=0.096=9.6%

Answer:

5√3 / 2

Step-by-step explanation:

tan 30 = ( 5 / 2 ) / y

1 / √3 = 5 / 2y

2y = 5√3

y = 5√3 / 2

You are giving the angle and opposite leg.

Using the law of sines:

Sin(angle) = opposite leg / hypotenuse

Sin(30) = 2/ hypotenuse

Hypotenuse = 2/sin(30)

Hypotenuse = 4 meters

The maximum length of the seesaw is : (C). 4 meters

Maximum length can be defined as the total distance between two point in consideration.

Maximum length can also be said to be the total sum of all the length along a distance.

In the case above, the hypotenuse side is the maximum length.

In conclusion, The maximum length of the seesaw is : 4 meters

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Step-by-step explanation:

Start Unlimited: 

$70 for one line

$60 for two lines

$45 for three lines

$35 for four lines

Play More Unlimited: 

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Do More Unlimited: 

$80 for one line

$70 for two lines

$55 for three lines

$45 for four lines

Get More Unlimited: 

$90 for one line

$80 for two lines

$65 for three lines

$55 for four lines

Answer:

4 months

As we show that ;

40 + (60x * 4)  = 280

100 + (45x * 4) = 280

but in simultaneous equations Verizon must be set equal to 240 being 80 x 3

and T mobile must be equal to 45 x 4 = 180

so that 240+ 180 = 420 to find 4

This would be a method on distribution as "60 sign up is 1/3 more than 1st equation.

Step-by-step explanation:

This is a simultaneous equation but trial and error is below to prove all is true.

step 1 make all equations same

40s + (60x)      * 3 = 180x  LCM   = 80 x 3   =  1   1/3 of 60

100s + (45x)     * 4 = 180x LCM   = 45  x 4   =  1 of 45 as verizon charges 1/3 more sign up.

100s- 40s + 180x = (180x) =  240 + 180

60s + 180x = 420

s = 60

so our equations must each end with 420

when we get 60s + 180x = 420  then

420 - 180 = 240

240/60 =  4

x = 4 months

Verizon = 1st and T mobile = 2nd

40 + (60x * 5)  = 340

100 + 45x * 5 = 325

with $15 out after 5 months so we try 6 months

40 + (60x * 6)  = 400

100 + 45x * 6 = 370

and see this is increasing in difference, so try a smaller value of months..

We try 4 months;

40 + (60x * 4)  = 280

100 + (45x * 4) = 280