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Answer:

The answer is 63/256

Step-by-step explanation:

edge 2020

The probability of getting exactly 5 “heads” in 10 coin flips is; 63/256

The formula for Binomial Probability is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

Probability of getting a head = 0.5

Thus;

P(X = 5) = 10C5 * 0.5⁵ * (1 - 0.5)⁽¹⁰ ⁻ ⁵⁾

P(X = 5) = 0.2461 = 63/256

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The limit of Un as n approaches infinity is equal to 1/2(1+√5), confirming the given statement.

To prove that the limit of Un as n approaches infinity is equal to 1/2(1+√5), we can use the concept of limits and apply algebraic manipulation.

First, let's assume that the limit of Un as n approaches infinity is L. Mathematically, we can write:

lim (n→∞) Un = L

Since the given recurrence relation states that Un+1 = √(Un + 1)₁, we can substitute n+1 for n in the recurrence relation:

lim (n→∞) Un+1 = √(lim (n→∞) Un + 1)₁

Since the limit of Un as n approaches infinity is L, we can rewrite the equation as:

L = √(L + 1)₁

To solve for L, we can square both sides:

L^2 = L + 1

Rearranging the equation, we have:

L^2 - L - 1 = 0

This is a quadratic equation. By solving it using the quadratic formula, we find two possible values for L:

L = [1 ± √(1 + 4)] / 2

Simplifying the expression, we get:

L = [1 ± √5] / 2

The positive value, L = (1 + √5) / 2, corresponds to the golden ratio, which is approximately 1.618. The negative value can be ignored as the limit of Un cannot be negative.

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Answer:

1500

Step-by-step explanation:

1200/4=300

1200+300=1500

Answer:

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

Step-by-step explanation:

Equations

Let's call

x = number of snowballs the other boys throw.

4x = number of snowballs Buddy throws.

We know Buddy throws 1200 snowballs, thus

4x = 1200

Divide by 4:

x = 1200/4

x = 300

This means the boys throw 300 snowballs while Buddy throws 1200 snowballs

Answer: 192

Step-by-step explanation:

192

Answer:

6(32)

6x32

192

explanation:

Answer:

w1 = (-1/11, 1/11, -3/11)

w2 = (12/11, 21/11, 3/11)

Step-by-step explanation:

Direction ratio of w1 = Direction ratio of L (because parallel) = K+(1, -1, 3)

Let <a,b,c> be direction ratio of w2.

Then, <a,b,c>. <1,-1,3> = 0

a-b+3c = 0

v = w1 + w2

(1, 2, 0) = k(1, -1, 3) + (a, b, c)

a + k = 1

b - K = 2

c - 3k = 0

Solving 4 equations, a = 12/11, b= 21/11, c = 3/11, k=-1/11

So, w1 = -1/11(1, -1 ,3) = (-1/11, 1/11, -3/11)

w2 = (12/11, 21/11, 3/11)

Answer:

420 miles after lunch

Step-by-step explanation:

Day 1 is 630 miles travelled - total amount of travelling.

After lunch is twice the amount of m.

Twice means 2.

So,

2xm + m (they'd have travelled) = 630 total miles

(2xm = 2m & 1m is the same as m)

2m + 1m = 630

3m = 630

÷3

m = 210 miles

Initial miles travelled before lunch was 210.

After lunch is double that amount.

Thus, 210 x 2 = 420 miles

Check:

210 + 420 = 630 miles.

Hope this helps!

Answer:

Skill Tests

With a partner, complete the Skill Tests for the six areas of skill-related fitness and record both your scores and your partner’s scores below. Answer the reflection questions.

My Scores:

Agility – Agility Square Test:

Speed – Stay on Your Toes Test:

Reaction Time – Ready, Set, Go Test:

Balance – Stork Stance Test:

Coordination – Off the Wall Test:

Power – Standing Long Jump Test:

Partner Scores:

Agility – Agility Square Test:

Speed – Stay on Your Toes Test:

Reaction Time – Ready, Set, Go Test:

Balance – Stork Stance Test:

Coordination – Off the Wall Test:

Power – Standing Long Jump Test:

Compare your scores to your partner’s scores. Explain the reason for any differences.

How can improving your balance and coordination affect your performance in sports or recreational activities?

What activity was the most difficult for you to perform? Why?

Describe an activity that could help improve your striking and your reaction time skills.

Select a physical activity or sport that you have never done but would like to try one day. Identify at least one element of skill-related fitness that is important to being successful in this activity.

What power-increasing activities do you need to perform regularly to improve your performance?

Answer:

Yeah, theorem triangle

Step-by-step explanation:

Answer:

\(2(3) {}^{x} \)

Step-by-step explanation:

\(y = ab {}^{x} \)

We know that when x=1, y=6

\(6 = a {b}^{1} \)

x=2, y=18

\(18 = a {b}^{2} \)

Notice that if we divide

\( \frac{ {ab}^{2} }{ab} = b\)

So if we divide 18 and 6, that will give us our common ratio.

\( \frac{18}{6} = 3\)

So our common ratio is 3.

So know we have

\(a(3) {}^{x} \)

Plug in one of the points to find a.

\(6 = a(3)\)

\(a = 2\)

So the equation. we have

\(2 \times ({3}^{x} )\)

The shortest is blue so the 4 1/2 is blue

The 6 and 6 1/2 are pink

Pink = 6 + 6 1/2 = 12 1/2 ft

Pink - blue

12 1/2 - 4 1/2 = 8

8 ft

Immediately, by definition of cotangent, we find

tan(α) = 1/cot(α) = 1/(-√3)

⇒   tan(α) = -√3

Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.

Recall the Pythagorean identity,

cos²(α) + sin²(α) = 1

Multiplying both sides by 1/sin²(α) recovers another form of the identity,

cot²(α) + 1 = csc²(α)

Solving for csc(α) above yields

csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4

⇒   csc(α) = 2

⇒   sin(α) = 1/2

Solve for cos(α) using the first form of the Pythagorean identity:

cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)

⇒   cos(α) = -√3/2

⇒   sec(α) = -2/√3

Answer: \(3\sqrt{21}\)

Step-by-step explanation:

\((xy)^{2}+(xz)^2=(yz)^2\\so, (6)^{2}+(xz)^2=15^2 \\(xz)^2=225-36\\xy=3\sqrt{21}\)

Answer:

h(2)+g(2) = -3

Step-by-step explanation:

\(h(2) +g(2)\\ \\h(t) = 3-5, g(t) = 2t -5\)

        Replace the variable  (t)  with (

2)  in the expression.

h (2) = 3 - 5

        Replace the variable  (t)  with (

2)  in the expression.

g(2) = 2(2) -5

        Replace the function designators in h(2) +g(2) with the actual functions.

h(t) = 3 - 5 +2 (2) ← plug h(2) into 2(t)

         Remove parentheses.

3 - 5 + 2(2)

         Multiply 2 by 2

3 - 5 + 4 - 5

         Subtract  5  from  3

.

-2 + 4 - 5

          Add -2 and 4

2 - 5

          Subtract 5 from 2

-3

The mean and the median of the following gasoline prices that are listed above would be =3.29 and 4.85 respectively.

The formula that is used to calculate the mean of a data set is given as follows;

mean = sum of data set/number of data set

= 3.14+3.21+3.28+3.53/4

= 13.16/4 = 3.29

The median = 3.21+3.28/2 = 4.85

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Answer:

c. and d.

Step-by-step explanation:

c when tenth

d when hundreth

Answer: D

Step-by-step explanation: D because it is closest to 400 out of the other 3 choices.

Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

For the 3 circles, in increasing order of the radius, we have:

For a circle of radius R, the arc defined by an angle θ (in degrees) is given by:

L = (θ/360°)*2pi*R

Where pi = 3.14

In this case, we have 3 circles of different radius, and θ = 60°, then we have:

circle 1:

radius = 1 unit, then:

L₁ = (60°/180°)*2*3.14*1 = 2.09

circle 2:

radius = 2 units, then:

L₂ = (60°/180°)*2*3.14*2 = 4.18

circle 3:

radius = 3 units, then:

L₃ = (60°/180°)*2*3.14*3 = 6.28

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Answer:

a) \(P_y = \frac{4}{y} * \frac{1}{3}^y * \frac{2}{3}^{4-y}\)

b) 0.033

Step-by-step explanation:

Let Y represents the number of judges preferring a formula.

There are total four judges and each judge can select either A or B

n = 4, p = 1/3

a) The probability function is

\(P_y = \frac{4}{y} * \frac{1}{3}^y * \frac{2}{3}^{4-y}\)

b)

Substituting the value of y -3 in above equation, we get -

\(P_3 = \frac{4}{3} * \frac{1}{3}^3 * \frac{2}{3}^{4-3}\\= \frac{4}{3} * 0.037 * 0.67\\= 0.033\)

The image of the parabolic lens crosses the x axis at the points

(-8, 0) and (4, 0)

To find the points where the graph of the function crosses the x axis we need to find the values of x that make f(x) equal to zero

hence we have that

f(x) = 1/4 (x + 8) (x - 4)

0  = 1/4 (x + 8) (x - 4)

x + 8 = 0

x = -8

OR

x - 4 = 0

x = 4

hence we can say that the image of the parabolic lens crosses the x axis at the points (-8, 0) and (4, 0)

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Answer:

8 seconds

Step-by-step explanation:

-2t^2+9t+56=0

-2t^2+16t-7t+56=0

-2t(t-8)-7(t-8)=0

(-2t-7)(t-8)=0

-2t-7=0 or t-8=0

t-8=0

t=8

Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.

Answer:

3

Step-by-step explanation:

um tell me more about the question

Answer:

Solution given:

1 kg =1000g

1g=1000mg

now

1kg=1000g=1000×1000mg=1000000mg

Answer:

a = 0

Step-by-step explanation:

4(a-2) = 2(a-4) + 2a

4a - 8 = 2a - 8 + 2a

4a - 2a - 2a = -8 + 8

    0             =    0

This has infinitely many solutions.

Step-by-step explanation:

Any number you put for a would work to make them equal. Feel free to try it.

Multiply the original DE by xy:

xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)

Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes

x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0

This final equation is easily recognized as separable:

dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides

The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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