An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?

If [tex]f(x)=x^2e^{-x^3}[/tex], then the area between the graph of [tex]f(x)[/tex] and the x-axis for non-negative x is given by the integral,

[tex]\displaystyle\int_0^\infty x^2e^{-x^3}\,\mathrm dx[/tex]

Let [tex]u=-x^3[/tex] and [tex]\mathrm du=-3x^2\,\mathrm dx[/tex]; then the integral is equivalent to

[tex]\displaystyle-\frac13\int_0^{-\infty}e^u\,\mathrm du=\frac13\int_{-\infty}^0e^u\,\mathrm du=\frac13\left(1-\lim_{u\to-\infty}e^u\right)=\boxed{\frac13}[/tex]

Hey there! I'm happy to help!

We want to find the volume of this  rectangular waterbed. This means the amount of space it takes up. To find the volume of a rectangular prism, you just multiply together the three side lengths.

7×5×1=35 cubic feet

Now, we need to see how many gallons fit into 35 cubic feet. We see that one gallon is equal to 0.13 cubic feet. So, we can set up a proportion to find how many gallons are needed. We will use g to represent our missing number of gallons.

[tex]\frac{gallons}{cubic feet} = \frac{1}{0.13} =\frac{g}{35}[/tex]

In a proportion, the products of the diagonal numbers are equal. This means that 35, which is 1 multiplied by 35, is equal to 0.13g, which is from multiplying 0.13 by the g.

0.13g=35

We divide both sides by 0.13/

g≈269.23

When rounded to the nearest whole gallon, we will need 269 gallons of water to fill the waterbed.

I hope that this helps! Have a wonderful day! :D

Answer:

Step-by-step explanation:

Since the waterbed is rectangular, its volume would be determined by applying the formula for determining the volume of a cuboid which is expressed as

Volume = length × width × height

Therefore,

Volume of waterbed = 7 × 5 × 1 = 35 cubic feet

1 US gallon = 0.133680556 cubic feet

Therefore, converting 35cubic feet to gallons, it becomes

35/0.133680556 = 261.81818094772 gallons

Rounding up to whole gallon, it becomes 262 gallons

Answer:

The probability is 0.04746

Step-by-step explanation:

Firstly, we calculate the z-score here

Mathematically;

z-score = x-mean/SD/√n

Where from the question;

x = 85, mean = 90 , SD = 15 and n = 25

Plugging these values into the equation, we have;

Z = (85-90)/15/√25 = -5/15/5 = -1.67

So the probability we want to calculate is ;

P(z > -1.67)

We use the standard normal distribution table for this;

P(z > -1.67) = 0.04746

Answer:

Step-by-step explanation:

area = base x height

where base = 20 ft.

        height = ?

           area = 120 ft²

plugin values into the formula

120 = 20 x height

height = 120  

               20

height = 6 ft.

Answer:

7 out of 8

Step-by-step explanation:

heads gets tossed and there's only 6 numbers to choose from on the die

Answer:    =0.375

Step-by-step explanation:

Actually we have to find the probability that both events will happened.

1st event the coin will be turned by a head P(head).

2nd event the number is greater than 2 , i.e. can be 3,4,5,6,7 or 8 P(a>2)

Both events  do not depend from each other. So the resulted probability

can be calculated multuplying probabilities P(head) and P(a>2) on each other. P(head, a>2)= P(head)*P(a>2)

P(head) =1/2=0.5 so the coin has 2 sides only one of them is head.

P(a>2)=6/8 so rolling the eight -sided doe 8 outcomes are possible and six of them 3,4,5,6,7 or 8 can give us the number that is bigger than 2.

P(a>2)=6/8=3/4=0.75

P(head, a>2)= P(head)*P(a>2)=0.5*0.75=0.375 ( rounding is not necessary, so we get exactle 3 digits after the point)

Answer:

see explanation

Step-by-step explanation:

Pythagorean Theorem

7² + 8² = x²

49 + 64 = x²

113 = x²

x = √113 or 10.63

Distance Formula

√(-4 - 4)² + (4 - -3)²

= √8² + 7²

= √113 or 10.63

Answer:

please, check the explanation.

Step-by-step explanation:

Hello, I can help you with this

using the graph of a function you can find the value of f (x), all you need to do is locate on the x axis, the value, in this case 3, and we will find f (3), locate the number (3 ) on the x-axis and see what is the value of y that the function takes at that point, that will be the value f (3)

I hope it helps , Have a nice day

Answer: look in the explanation this is the exact sample responce on ed2020 change it into your own words

Step-by-step explanation:

For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.

Answer:

y= 1/14 sin(x-3π)-5

Answer:

(5,6), (-2,8)

Step-by-step explanation:

I have a good math expertise. Don't question my skills as they are correct. woof woof waffling behavior. Thnak you hr welcne

Answer:

s = 1/t - 1/r

Step-by-step explanation:

1/r+s=1/t

Subtract 1/r from each side

1/r - 1/r+s=1/t- 1/r

s = 1/t - 1/r

Answer:

[tex]\huge{\boxed{s=t-r}}[/tex]

Step-by-step explanation:

if

[tex]\dfrac{1}{r+s}=\dfrac{1}{t}\qquad\text{cross multiply}\\\\(1)(t)=(1)(r+s)\\\\t=r+s\qquad\text{subtract}\ r\ \text{from both sides}\\\\t-r=r-r+s\\\\t-r=s\to\boxed{s=t-r}[/tex]

Answer:

3x + 2y =60

Step-by-step explanation:

x = socks

y = shoes

3x + 2y =60

Answer:

3x + 2y =60

Step-by-step explanation:

Hope this Helps you !

Answer:

A. Neither Sneha nor the credit card company owes money

Step-by-step explanation:

Answer:

576"

Step-by-step explanation:

AL=ph

AL= (4*12)12

AL= 48*12

AL=576"

Answer:

1-{0.2(m-3)+¼}=0

1{0.2m-0.6+¼}=0

1-{(0.8m-2.4+1)/4}=0

1-(0.8m-1.4)/4=0

lcm

(4-0.8m-1.4)/4=0

(2.6-0.8m)/4=0

cross multiply

2.6-0.8m=0

m=2.6/0.8

m=3.25

The solution of the expression are,

⇒ m = 3.25

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Expression is,

⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0

Now, We can simplify as;

⇒ 1 - | 0.2m - 0.6 + 1/4| = 0

⇒ 1 - |0.2m - 0.6 + 0.25| = 0

⇒ 1 - |0.2m - 0.35| = 0

⇒ 1 = 0.2m + 0.35

⇒ 1 - 0.35 = 0.2m

⇒ 0.2m = 0.65

⇒ m = 3.25

Thus, The solution of the expression are,

⇒ m = 3.25

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Answer:

Step-by-step explanation:

The table is easier to read if formatted more like a table:

Number of Weeks Avg. Number of Visits

  0 48,000

  1 24,000

  2 12,000

  3 6,000

  4 3,000

  5 1,500

__

The initial number of visits to the website was 48,000. -- the value for week 0.

The percent decrease from 4th week to 5th week was 50%. ((new/old) -1)·100% = (1500/3000 -1)·100% = -50%

The minimum number of visits on the website in the first 5 weeks since Jim began his assessment was 1,500. (the number in the 5th week)

​Answer:

14.29cm

Step-by-step explanation:

Height of the building=10cm

Angle of depression=60°

We are therefore asked to find the distance from the stone to the

the foot of the building;Therefore we use Tan ratio which is opp/adj;

Let the distance from the stone to the foot of the building be x;

10/x=Tan60°

10/x=1.7/1

We then cross multiply to get 1.7x=10

x=10/1.7

=10*10/1.7*10

=100/17

=14.29cm.

Answer:

False

Step-by-step explanation:

To find <A, we can do 5x - 80 = 3x + 20.

As we simplify, we will get 2x = 100, which is x = 50

Therefore, <A will be 50 degrees and not 45 degrees.

Also, if you need y, you can do:

3y - 7 = y + 7

2y = 14

y = 7

1 minute = 60 seconds

15 seconds /60 = 0.25 minutes.

Total time in minutes is 4.25

Divide total copies by total minutes:

153 / 4.25 = 36 copies per minute

Answer:

[tex]\boxed{\sf 36 \ copies \ per \ minute}[/tex]

Step-by-step explanation:

[tex]\sf 4 \ minutes \ 15 \ seconds = 4.25 \ minutes[/tex]

[tex]\sf The \ copy \ machine \ makes \ 153 \ copies \ in \ 4.25 \ minutes.[/tex]

[tex]\sf To \ find \ copies \ per \ minute, \ divide \ the \ number \ of[/tex]

[tex]\sf copies \ with \ the \ number \ of \ minutes.[/tex]

[tex]\displaystyle \frac{153}{4.25} =36[/tex]

[tex]\sf The \ copy \ machine \ makes \ 36 \ copies \ per \ minute.[/tex]

Answers:

sin a=12/15=4/5

step by step explanation:

AB=9, and BC=12

find c: hyp.=√12²+9²=c²

c=15

sin a=opp/hyp.=12/15=4/5 ( convert to degrees)

a=41.10

Answer:

f(0) = 0

Step-by-step explanation:

f(x) = -sqrt(x)

Let x= 0

f(0) = -sqrt(0)

f(0) = 0

Value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

" A function is defined as the relation between the given variable represents set of all input value should have one output each."

According to the question,

Given function,

[tex]f(x) = -\sqrt{x}[/tex]

Substitute the different values for 'x' for the given function we get,

[tex]x=1 , f(1) = -\sqrt{1}[/tex]

                 [tex]=-1[/tex]

[tex]x=4 , f(4) = -\sqrt{4}[/tex]

                 [tex]=-2[/tex]

[tex]x=0, f(0) = -\sqrt{0}[/tex]

                 [tex]=0[/tex]

Therefore, given relation is a function.

Hence, value of the given function [tex]f(x) = -\sqrt{x}[/tex] for [tex]f(0) = 0.[/tex]

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Answer:

3/8

Step-by-step explanation:

There are 72 students.  27 students choose football, and 18 choose tennis, which means 27 choose running.

So the probability that a student chooses running is 27/72, which reduces to 3/8.

Answer:

Gabrielle is 69 while Mikhail is 23.

Step-by-step explanation:

Let G represent Gabrielle's age and M represent Mikhail's age.

Gabrielle is three times Mikhail's age. In other words:

[tex]G=3M[/tex]

The sum of their ages is 92. In other words:

[tex]G+M=92[/tex]

This is a system of equations. Solve. Substitute in G:

[tex]G+M=92\\(3M)+M=92\\4M=92\\M=23[/tex]

Thus, Mikhail is 23. Now, find Gabrielle's age:

[tex]G=3M\\G=3(23)\\G=69[/tex]

Gabrielle is 69.

Answer:

x=5

Step-by-step explanation:

h (x) = 3

We want the x values where y =3

The values are x = -7 and x=5

Answer:

Hey there!

We can solve this by multiplying 0.3 by 546, which is about 164.

Hope this helps :)

Explanation: Set up your equation as you read through the problem.

"What" means x, "is", equals, "30%", 30/100, "of", times, "546", 546.

So our equation reads x = 30/100 · 546.

Simplifying on the right side of the equation,

we can reduce 30/100 to 3/10.

So we have x = 3/10 · 546.

Now multiply across the numerators and denominators to get 1638/10.

This reduces to 819/5 which can be written as 163.8.

Answer:

speed=3.33m/s

Step-by-step explanation:

speed= distance÷time

3.33 m/s

length = ?

Answer:

Length  : 50m

Speed   : 5 m  /  s

im sorry if im too late :'(

Answer:

C) 59.66 m

Step-by-step explanation:

C = pi d

in this case, d=19

so, when you solve, with a negative pi, you get somewhere around 59.66.

because -3.14 times 19 equals 59.69, which is closest to c.

Answer:

5/9

Step-by-step explanation:

f(x) =5•3^x

Let f = -2

f(2) =5•3^-2

     = 5 * 1/ 3^2

     = 5 * 1/9

     = 5/9

Step-by-step explanation:

F(-2) for f(x) =5•3^x

Then, replace x by - 2

F(-2)=5•3^-2 (RULE= 3^-2 = 1/3^2)

[tex] = 5. \frac{1}{ {3}^{2} } [/tex]

[tex] = 5 . \frac{1}{9} [/tex]

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

Hope this helps..have a great day!

Answer:

b.27 c. 36 (THIS ANSWER IS CORRECT....IM IN RSM ;)

Step-by-step explanation:

The bottom one is for b.

Okay now for c. Lets first think about every cube that has two faces painted. all the cubes on the edges right? So that would be 5*12=60 but that isn't the answer because the problem stated EXACTLY two faces. That means every cube on a vertices doesn't count because it has 3 faces painted. If you look back at the edges and don't count the cubes on the vertices you will see that there are 3 cubes that fit these guide lines on each edge and there are 12 edges. So your answer would be 3*12=36!

You can do it simply by seeing that the outer cubes will have their upper surfaces painted and thus 5*5 squares for each outer surface which will leave a cube with 3×3×3 dimensions. It is 3*3*3 because on every side all the outer cubes will be painted. So one layer of the cube will be decreased by one on all sides. So the length width and height will all end up as 5-2=3. Its kind of hard to explain and i suggest you draw it out if you don't understand...

The number of 1×1×1 cubes that are completely unpainted is 27 and the number of 1×1×1 cubes have exactly two faces painted. is 36.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

b. BY looking that the outer cubes will have their upper surfaces painted and thus 5 x 5 squares for each outer surface which will leave a cube with 3×3×3 dimensions.

It is 3 x 3 x 3 because on every side all the outer cubes will be painted. So one layer of the cube will be decreased by one on all sides. The length width and height will all end up as 5-2=3.

c. Let's first think about every cube that has two faces painted. So that would be 5x 12=60 but that isn't the answer because the problem stated exactly two faces.

That means every cube on vertices doesn't count because it has 3 faces painted. If you look back at the edges and don't count the cubes on the vertices you will see that there are 3 cubes that fit these guidelines on each edge and there are 12 edges.

The number is calculated as:-

N = 3x 12=36

Hence, the number of 1×1×1 cubes that are completely unpainted is 27 and the number of 1×1×1 cubes has exactly two faces painted. is 36.

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Answer:

a1 = 4

a2= -2

a3 = -8

a4= -14

a5= -20

Step-by-step explanation:

a12= a1 + 11d

-62 = 4 + 11d

-62-4 = 11d

-66= 11d

d = [tex]\frac{-66}{11}\\[/tex]

  = -6

a1 = 4

a2 = 4 - 6 = -2

a3 = 4 - (6×2) = -8

a4 = 4 - (6×3) = -14

a5 = 4 - (6×4) = -20