The sample space, S. of a coin being tossed three times is shown below, where H and T denote the
coin landing on heads and tails respectively.
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Let X = the number of times the coin comes up heads. What is the probability distribution for the
number of heads occurring in three coin tosses?
0
1
3
1
4
5
8
X
p (X)
X
p(x)
2
1
4
3
1
3
1
4
2
1
3
1
4
1
4
6
2
3
7
2
3
2
3
1
3
0
1
2
3
4
5
6
7
8
X
0
1
2
3
X 1
(x) 1
1
2
3
2
3
1
3
2
13
1
3
1
3
0
P(X)
1
8
3
8
3
8
8

Answer:

Yes. Factored form.

Step-by-step explanation:

Answer:

yes, and it's in intercept form

Step-by-step explanation:

Hi there!

We are given the function f(x)=-2(x-4)(x+3)

A quadratic function is a function that has a degree of 2 (the highest exponent in the function is to the 2nd power)

There are 3 forms to write a quadratic function:

standard form, which is f(x)=ax²+bx+c, where a, b, and c are free coefficients (numbers)

vertex form, which is f(x)=a(x-h)²+k, where a is a free coefficient and (h,k) is the vertex

intercept form, which is f(x)=a(x-[tex]x_{1}[/tex])(x-[tex]x_{2}[/tex]), where a is a free coefficient and [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are the x intercepts

You may notice that  f(x)=-2(x-4)(x+3)  is actually in intercept form; a is -2 and  [tex]x_{1}[/tex] and [tex]x_{2}[/tex] are 4 and -3 respectively (remember: the formula for intercept form has  -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex], but the x intercepts are  [tex]x_{1}[/tex] and [tex]x_{2}[/tex]. Therefore, the x intercepts should be the opposites of  -[tex]x_{1}[/tex] and -[tex]x_{2}[/tex]).

If the formula is in intercept form, it should be quadratic.

However, if you want to be sure it's quadratic, you can expand the function.

f(x)=-2(x-4)(x+3)  

first, multiply the binomials together using FOIL

(x-4)(x+3)

x²-x-12

now multiply x²-x-12 by -2

-2(x²-x-12)

do the distributive property

-2x²+2x+24

It's a quadratic function! The value of the highest exponent is 2 :)

Hope this helps!

Answer:

The correct answer is:

(a) 44.6 lb

(b) 0.371

Step-by-step explanation:

Given values are:

Mean,

[tex]\mu=36.6[/tex]

Standard deviation,

[tex]\sigma=11.9[/tex]

(a)

The z distance third quartile will be:

⇒ [tex]P(Z<0.674)=0.75[/tex]

                       [tex]z =0.674[/tex]

By using the z-score formula, we get

⇒ [tex]x=z\times \sigma+ \mu[/tex]

       [tex]=0.674\times 11.9+36.6[/tex]

       [tex]=44.62[/tex]

(b)

⇒ [tex]P(27.5<x<39.5) = P[{\frac{(27.5-36.6)}{11.9} <\frac{(x-\mu)}{\sigma} <\frac{(39.5-36.6)}{11.9} }][/tex]

                                  [tex]=P(-0.76<z<0.24)[/tex]

                                  [tex]=P(z<0.24)-P(z<-0.76)[/tex]

By using the z table, we get

                                  [tex]=0.5948-0.2236[/tex]

                                  [tex]=0.371[/tex]

Answer:

4270

Step-by-step explanation:

Answer:

Step-by-step explanation:

y/5                  That's your quotient

y/5 + 2            That's the quotient with 2 added on.

y/5 + 2 = 4      And that's your answer.

Always break the statements into the smallest possible steps that you can. Notice that I broke it down to 3 parts that are not quite equal in length.

Answer:

3x +3

Step-by-step explanation:

3x + 1 + 2units(on the x axis)= 3x +3

Answer:

x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z

Step-by-step explanation:

Solve for x:

a^(20 - 2 x) = a^12

Take reciprocals of both sides:

a^(2 x - 20) = 1/a^12

Take the logarithm base a of both sides:

2 x - 20 = log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z

Add 20 to both sides:

2 x = 20 + log(1/a^12)/log(a) + (2 i π n)/log(a) for n element Z

Divide both sides by 2:

Answer: x = 10 + log(1/a^12)/(2 log(a)) + (i π n)/log(a) for n element Z

Answer:

[tex] \displaystyle 1)48.2 \: \: \text{sec}[/tex]

[tex] \rm \displaystyle 2)3021.6 \: m[/tex]

Step-by-step explanation:

so when flash down occurs the rocket will be in the ground in other words the elevation(height) from ground level will be 0 therefore,

to figure out the time of flash down we can set h(t) to 0 by doing so we obtain:

[tex] \displaystyle - 4.9 {t}^{2} + 229t + 346 = 0[/tex]

to solve the equation can consider the quadratic formula given by

[tex] \displaystyle x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 ac} }{2a} [/tex]

so let our a,b and c be -4.9,229 and 346 Thus substitute:

[tex] \rm\displaystyle t = \frac{ - (229) \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

remove parentheses:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ {229}^{2} - 4.( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify square:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 4( - 4.9)(346)} }{2.( - 4.9)} [/tex]

simplify multiplication:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 52441- 6781.6} }{ - 9.8} [/tex]

simplify Substraction:

[tex] \rm\displaystyle t = \frac{ - 229 \pm \sqrt{ 45659.4} }{ - 9.8} [/tex]

by simplifying we acquire:

[tex] \displaystyle t = 48.2 \: \: \: \text{and} \quad - 1.5[/tex]

since time can't be negative

[tex] \displaystyle t = 48.2 [/tex]

hence,

at 48.2 seconds splashdown occurs

to figure out the maximum height we have to figure out the maximum Time first in that case the following formula can be considered

[tex] \displaystyle x _{ \text{max}} = \frac{ - b}{2a} [/tex]

let a and b be -4.9 and 229 respectively thus substitute:

[tex] \displaystyle t _{ \text{max}} = \frac{ - 229}{2( - 4.9)} [/tex]

simplify which yields:

[tex] \displaystyle t _{ \text{max}} = 23.4[/tex]

now plug in the maximum t to the function:

[tex] \rm \displaystyle h(23.4)- 4.9 {(23.4)}^{2} + 229(23.4)+ 346 [/tex]

simplify:

[tex] \rm \displaystyle h(23.4) = 3021.6[/tex]

hence,

about 3021.6 meters high above sea-level the rocket gets at its peak?

Answer:

I believe the question was written twice on accident

y=7x-38

Step-by-step explanation:

y-4=7(x-6)

y-4=7x-42

y=7x-38

Step-by-step explanation:

I'm sorry I can't answer that but I know something so you can answer that. search Chrome quickmath all your problems, equations and more can be solved

Answer:

c = 3/2x + −3/2

Step-by-step explanation:

Let's solve for c

-3x+2c=-3

Step 1: Add 3x to both sides.

2c −3x + 3x = −3 + 3x

2c = 3x −3

Step 2: Divide both sides by 2.

2c = 3x−3

2        2

c = 3/2x + −3/2

Answer:

c = 3/2x + −3/2

Answer:

18

Step-by-step explanation:

2/6

4/12

6/18

Answer:

x = 18

Step-by-step explanation:

We can write ratios

2      2+4

---- = -----

6       x

Using cross products

2x = 6(2+4)

2x = 6(6)

2x = 36

Divide by 2

2x/2 = 36/2

x = 18

Answer:

c) 11/2

Step-by-step explanation:

(-4, 7) and (-6, -4)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-4 - 7) / (-6 - (-4))

Simplify the parentheses.

= (-11) / (-6 + 4)

= (-11) / (-2)

Simplify the fraction.

-11/-2

= 11/2

This is your slope.

Hope this helps!

Answer:

4.196.754

Step-by-step explanation:

god bless stay safe po

Step-by-step explanation:

quadratic formula

-b+-√b^2

2a

-2+-√2^2-4×1×-16

2×1

-2+-√68

2

either

x= 3.125

or

x= -5.125

Answer:

1394 feets

Step-by-step explanation:

The solution triangle is attached below :

The horizontal distabce from the base is denoted as d :

Using trigonometry, we can obtain d, thus ;

Tan θ = opposite / Adjacent

Tan 51 = d / 1129

d = tan 51 * 1129

d = 1394.1988 feets

d = 1394 feets

Answer:

more

Step-by-step explanation:

The answer is (5x+3)(-5x+3)

Answer:

the answer is h=0.5m+2 I think

Answer:

option A

Step-by-step explanation:

X- axis

A . the x-axis

Step-by-step explanation:

The lines never meet

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

Explanation:

The diameter is 24 inches, so the radius is half that at r = d/2 = 24/2 = 12 inches.

We'll use this along with the approximation pi = 3.14 to get the area

A = pi*r^2

A = 3.14*12^2

A = 452.16 square inches

Your teacher should have used "square inches" instead of "inches" as the unit.

We can abbreviate the "square inches" into "sq in" or "in^2".

This value is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to find a more accurate value.

The exact area is 144pi

Answer:

D. 452.16 sq inches

Step-by-step explanation:

d = 24 ==> r = 24/2= 12 inches

the area = π×r²

= 3.14 × 12²

= 3.14 × 144

= 452.16 sq inches

9514 1404 393

Answer:

  8

Step-by-step explanation:

The notation n=1 .. 8 means that n takes on all integer values from 1 to 8. Each value of n gives one term that is added to the series.

  The number of terms is 8.

Answer: y= -1

Step-by-step explanation:

2+y=1  

y=1-2

y=-1

Answer:

Sure i can help you

Step-by-step explanation:

Answer:

Sure! What’s the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

Find (g - f)(x):

Correct choice is A

Answer:

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

Step-by-step explanation:

Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.

So, r = √(R² - z²)

r = √(4² - z²)

r = √(16 - z²)

Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4

Our volume integral in cylindrical coordinates is thus

V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π

Answer:

[tex]\displaystyle V = \int\limits^{2 \pi}_{0} \int\limits^{2\sqrt{3}}_{0} \int\limits^{\sqrt{16 - r^2}}_2 {r} \, dz \, dr \, d\theta[/tex]

General Formulas and Concepts:

Multivariable Calculus

Cylindrical Coordinate Conversions:

Volume Formula [Cylindrical Coordinates]:
[tex]\displaystyle V = \iiint_T \, dV \rightarrow V = \iiint_T {r} \, dz \, dr \, d\theta[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

Solid sphere w/ radius 4 centered at (0, 0, 0) → x² + y² + z² = 4²

Plane z = 2

Step 2: Find Volume Pt. 1

Find bounds of z.

∴ 0 ≤ r ≤ 2√3

Step 2: Find Volume Pt. 2

∴ 0 ≤ θ ≤ 2π

Step 3: Find Volume Pt. 3

∴ 2 ≤ z ≤ √(16 - r²)

Step 4: Find Volume Pt. 4

∴ the volume of the region is found with the integral above.

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Learn more about multivariable calculus: https://brainly.com/question/17203772

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Topic: Multivariable Calculus

Unit: Triple Integral Applications

Answer:

exponential form = 2.1^2

evaluation = 4.41

Step-by-step explanation:

it is times-ing 2.1 two times, therefore its 2.1^2

2.1 times 2.1 = 4.41

Answer:

Hello There!!

Step-by-step explanation:

The answer is 3,9,15,21.

hope this helps,have a great day!!

~Pinky~

Answer:

the common difference is 6. So, the missing two terms are 9 and 15 using

3 + (n-1)(6)