Alice solves every puzzle with probability 0.6 , and Bob, with probability 0.5 . They are given 7 puzzles and each chooses 5 out of the 7 puzzles randomly and solves them independently. A puzzle is considered solved if at least one of them solves it. What is the probability that all the 7 puzzles happen to be solved by at least one of them

Answer:

The second to last choice

Step-by-step explanation:

Answer:

Area = 3x² + 7x + 3

Perimeter = 8x + 8

Step-by-step explanation:

The figure can be decomposed into two: a large rectangle and a smaller rectangle.

✍️Dimensions of the large rectangle:

Length = (x + 1) + x = x + 1 + x = (2x + 1)

Width = (x + 3)

Area = length × width

Area = (2x + 1)(x + 3)

Expand

2x(x + 3) +1(x + 3)

2x² + 6x + x + 3

Area = 2x² + 7x + 3

✍️Dimensions of the large rectangle:

Length = x

Width = x

Area = length × width

Area = x × x = x²

✍️Area of the figure = area of the large rectangle + area of the smaller rectangle

Area of the figure = (2x² + 7x + 3) + x²

Area of the figure = 2x² + x² + 7x + 3

✅Area = 3x² + 7x + 3

✍️ Perimeter of the figure = sum of the length of all sides of the figure = (x + 3) + x + x + x + (x + 1) + (x + 3) + (x + 1) + x

✅Perimeter = 8x + 8

Answer:

[tex]ln(4)+2\,\,ln(y)[/tex]

(the first option of the list)

Step-by-step explanation:

Using the properties of logarithms (first the logarithm of a product and then the logarithm of a power, we write:

[tex]ln(4\,y^2)=ln(4)+ln(y^2)=ln(4)+2\,\,ln(y)[/tex]

which agrees with the first option in the list of possible answers.

Answer:

(3/2,11/4)

Step-by-step explanation

-b/2a to find the axis of symmetry

3/2= axis of symmetry

Then plug that in to find the vertex/maximum or minimum

3/2^2-3(3/2)+5

9/4-9/2+5

You can only add fractions with like denominators multiply 9/2(2/2) and 5(4/4)

So, 9/4-18/4+20/4

9/4-18/4= -9/4+20/4= 11/4

So the maximum is

(3/2, 11/4)

Answer: Jane

Step-by-step explanation: Her pay is going up by the same amount, 12, each time.

Answer:

Matt's pay is not linear

Jane's pay is linear, and it is $12/hour

Step-by-step explanation:

Matt's Earnings:

As the time goes from 1 hour to 2 hours, the difference in hours is 1, the difference in pay is $8. From 2 hours to 3 hours, the difference in hours is again 1, but the difference in pay is $11. Since equal changes in x do not produce equal changes in y, Matt's earnings are not linear.

Jane's Earning:

As the time goes from 1 hour to 2 hours, the difference in hours is 1, the difference in pay is $12. From 2 hours to 3 hours, the difference in hours is again 1, and the difference in pay is again $12. Since equal changes in x produce equal changes in y, Jane's earnings are linear.

Jane's rate of pay is $12/hour

Answer:

f^-1 is P and f^-1(x) = 3x+4

Step-by-step explanation:

I did the work in my notebook but pretty much to find the inverse of [tex]\frac{x-4}{3\\}[/tex] you gotta do an equation and yeh its pretty simple.

The solution is , f^-1 is P and f^-1(x) = 3x+4.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

from the given figure, we get,

The line r represents f(x)=x-4/3.

so, we get,

f^-1 is P

let, y = f(x)

and, f^-1(y)=x

i.e. y = x-4/3.

3y=x-4

x=3y+4

so, f^-1(y) = 3y+4.

and f^-1(x) = 3x+4.

To learn more on Expression click:

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Answer:

25

Step-by-step explanation:

Answer:

it is 25

Step-by-step explanation:

Answer:

I am confused on this question too

Step-by-step explanation:

Answer:

I would say 14 weeks.

Step-by-step explanation:

I solved it by subtracting what she already has from the price of the bike. $164-52= 112. Then I divided that by 8 cause she saving $8 a week and you get 14. So in 14 weeks she'll have enough money to buy the bike.

Answer:

Step-by-step explanation:

1. 150 to 132 is a decrease of 12%

2. 275 to 242 is a decrease of 12%

3. 300 to 255 is a decrease of 15%

Thanks For the Brainliest!

Answer:

1. 150 - 12% = 132

2. 275 - 12% = 242

3. 300 - 15% = 255

Answer:

8 out of 11

Step-by-step explanation:

Answer:

x= -2/3 or x=-2/3y

Step-by-step explanation:

i assume this meant solve for x

start by setting the y value as 0 then isolate the x

Answer:

The 3 digit numbers are;

171, 152, 133, 114, 285, 266, 247, 228, 209, 399

Step-by-step explanation:

Let the 3 digit number be xyz

Since x is the Hundreds digit, y is the tens digit and z is the unit digit, we have;

100x, 10y and z

We are told the sum of this is equal to 19 times the sum of their digits.

Thus;

100x + 10y + z = 19(x + y + z)

100x + 10y + z = 19x + 19y + 19z

This gives;

81x - 9y - 18z = 0

Divide through by 9 to get;

9x - y - 2z = 0

x = (2z + y)/9

Now, we will need to select values of z and y between 0 to 9 in such a way that (2z + y) is divisible by 9 and in such a way that x > 0 but ≤ 10

The possible solutions are;

At z = 1, y = 7 and x = 1

At z = 2, y = 5 and x = 1

At z = 3, y = 3 and x = 1

At z = 4, y = 1 and x = 1

At z = 5, y = 8 and x = 2

At z = 6, y = 6 and x = 2

At z = 7, y = 4 and x = 2

At z = 8, y = 2 and x = 2

At z = 9, y = 0 and x = 2

At z = 9, y = 9 and x = 3

Compiling all these, the 3 digit numbers are;

171, 152, 133, 114, 285, 266, 247, 228, 209, 399

Answer:

376

Step-by-step explanation:

47 times 8 would be the number of miles that the family took in 8 trips.

Answer:15,605

Step-by-step explanation:4000(1+.065/12)^21*12

4000(1+0054)^252

Answer:

Width = [tex]7\frac{11}{16}[/tex] inches

Step-by-step explanation:

Given

[tex]End_1 = 2\frac{3}{4}[/tex]

[tex]End_2 = 10\frac{7}{16}[/tex]

Required

Determine the width of frame in between

To do this, we simply calculate the difference between both ends:

i.e.

[tex]Difference = End_2 - End_1[/tex]

This gives:

[tex]Difference = 10\frac{7}{16} - 2\frac{3}{4}[/tex]

Convert to improper number

[tex]Difference = \frac{167}{16} - \frac{11}{4}[/tex]

Take LCM

[tex]Difference = \frac{167 - 44}{16}[/tex]

[tex]Difference = \frac{123}{16}[/tex]

[tex]Difference = 7\frac{11}{16}[/tex]

Hence, the width of the frame is [tex]7\frac{11}{16}[/tex] inches

Answer: 55% or 11/20

Step-by-step explanation:

Answer:

[tex]\frac{10}{83}[/tex]  

I hope this helps!

Answer:

no

Step-by-step explanation:

Answer:

192

Step-by-step explanation:

There are 2 ways of solving for <4

The first is just to add the 2 angles not connected to <4

<4 = 51 + 51 = 102

The second is to find <2 and take that away from 180

<2 + 51 + 51 = 180

<2 = 180 - 102

<2 = 78

<4 + <2 = 180   (They are supplementary

<4 = 180 - 78

<4 = 102

Answer:

8/48

Step-by-step explanation:

the bottom they multiplied by 4 to get 48 so you do the same to the top so you get 8

Answer:

5/7

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

Answer:

Terms: 8, (-x²), x, (-4x)

Like terms: x and (-4x)

Step-by-step explanation:

A term is a single number (positive or negative), a single variable (a letter), or several variables multiplied but not added or subtracted.

Like terms are terms that have the same variables and power like x.

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[tex] \frac{x - 1}{2} - \frac{x - 2}{3} > \frac{x - 3}{4} \\ [/tex]

Multiply sides by 12

[tex]12 \times ( \frac{x - 1}{2} - \frac{x - 2}{3} ) > 12 \times ( \frac{x - 3}{4} ) \\ [/tex]

[tex](12 \times \frac{x - 1}{2} ) - (12 \times \frac{x - 2}{3} ) > 12 \times \frac{x - 3}{4} \\ [/tex]

[tex](6 \times \: (x - 1)) - (4 \times (x - 2)) > 3 \times (x - 3) \\ [/tex]

[tex]6x - 6 - (4x - 8) > 3x - 9[/tex]

[tex]6x - 6 - 4x + 8 > 3x - 9[/tex]

[tex]6x - 4x + 8 - 6 > 3x - 9[/tex]

Collect like terms

[tex](6 - 4)x + 2 > 3x - 9[/tex]

[tex]2x + 2 > 3x - 9[/tex]

[tex]3x - 9 < 2x + 2[/tex]

Add sides 9

[tex]3x - 9 + 9 > 2x + 2 + 9[/tex]

[tex]3x > 2x + 11[/tex]

Subtract sides 2x

[tex] - 2x + 3x > - 2x + 2x + 11[/tex]

[tex]x > 11[/tex]

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