Find the measure of the unknown angle.

Solution :

The probability of winning when you choose n is =  [tex]$^nC_2\left(\frac{1}{2}\right)^n$[/tex]

[tex]$n\left(\frac{n-1}{2}\right)\times \left(\frac{1}{2}\right)^n = n(n-1)\left(\frac{1}{2}\right)^{n+1}$[/tex]

Apply log on both the sides,

[tex]$f(n) = \log\left((n)(n-1)\left(\frac{1}{2}\right)^{n-1}\right) = \log n +\log (n-1)+(n+1) \ \log\left(\frac{1}{2}\right)$[/tex]

Differentiation, f(x) is [tex]$f'=\frac{1}{x}+\frac{1}{(x-1)}+\log\left(\frac{1}{2}\right)$[/tex]

Let us find x for which f' is positive and x for which f' is negative.

[tex]$\frac{1}{x}+\frac{1}{(x-1)} > 0.693$[/tex]       , since [tex]$\log(1/2) = 0.693147$[/tex]

For x ≤ 3, f' > 0 for [tex]$\frac{1}{x}+\frac{1}{x-1}+\log\left(\frac{1}{2}\right)>0$[/tex]

[tex]$\frac{1}{x}+\frac{1}{x-1}-0.6931470$[/tex]

That means f(x) is increasing function for n ≤ 3

[tex]$\frac{1}{x}+\frac{1}{x-1}< 0.693147 $[/tex] for x > 4

f' < 0 for n ≥ 4, that means f(n) is decreasing function for n ≥ 4.

Probability of winning when you chose n = 3 is [tex]$3(3-1)\left(\frac{1}{2}\right)^{3+1}=0.375$[/tex]

Probability of winning when you chose n = 4 is [tex]$4(4-1)\left(\frac{1}{2}\right)^{4+1}=0.375$[/tex]

Therefore, we should chose either 3 or 4 to maximize chances of winning.

The probability of winning with an optimal choice is n = 0.375

Answer:

the probability is a fraction or a percentage, some times even a decimal

Step-by-step explanation:

hi, this looks complicated, however, let's deal with it.

using sine rule,

we have,

a/sin A= c/sin C

4.83/sin 46= 5.5/sin C

cross multiply

4.83sin C=5.5sin 46

sin C= (5.5sin46)/4.83

sin C= 0.8191

C=sin inverse of 0.8191

C=54.99 approximately 55

since we have C, we can now find B to get b or rather AC

A+B+C=180. (sum of angles in a triangle)

46°+ B + 54.99°=180°

B+ 100.99°=180°

B°=180°-100.99°

B=79°

since we have B, we can find b or rather AC

using cosine rule,

b²=c²+a²-2 x c x a x cos B

b²= 5.5² + 4.83² - 2 x 5.5 x 4.83 x cos 79°

b²=30.25+23.33-53.13cos79

b²=53.58-10.14

b²=43.44

b=6.59 approximately 6.6

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We can find the slope by using two points

( -1,0) and (0,1)

m = (y2-y1)/(x2-x1)

   = (1-0)/(0- -1)

    = ( 1-0)/(0+1)

    1/1

Answer:

The solid - I'll call it R - is best described in spherical coordinates:

[tex]R = \left\{(\rho,\theta,\varphi) \mid \sqrt{a}\le\rho\le\sqrt{b}, 0\le\theta\le2\pi, 0\le\varphi\le\dfrac\pi4\right\}[/tex]

Then the volume of R is

[tex]\displaystyle\iiint_R\mathrm dV = \int_0^{\frac\pi4}\int_0^{2\pi}\int_{\sqrt a}^{\sqrt b}\rho^2\sin(\varphi)\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi \\\\\\ \displaystyle = \boxed{\frac{2\pi}3\left(b^{\frac32}-a^{\frac32}\right)\left(1-\dfrac1{\sqrt2}\right)}[/tex]

Answer:

a1 = 1, a2 = 2Step-by-step explanation:

3800 mm

Hope it helps you...

Thank you!!

Answer:

price club is .28 cents per ounce and Shop mart is .26 cents per ounce.

Step-by-step explanation:

To find the unit price per ounce, you divide the cost by the weight ($3.43/12 ounces) which equals .28 cents per ounce. The non-estimated answer is .28666 but since you never round up for money it eill be .28. For shop mart, you convert pounds to ouncea. 1 pound equals 16 ounces. with this in mind, 2 pounds will be 32 ounces since its double the amount. Divide $8.35 by 32 and you get .26 cents per ounce.

Answer:

23 years

Step-by-step explanation:

Step 1: Calculate the rate constant (k) for the radioactive decay

A radioactive substance with initial concentration [A]₀ decays to 97% of its initial amount, that is, [A] = 0.97 [A]₀, after t = 1 year. Considering first-order kinetics, we can calculate the rate constant using the following expression.

ln [A]/[A]₀  = - k.t

k = ln [A]/[A]₀ / -t

k = ln 0.97 [A]₀/[A]₀ / -1 year

k = 0.03 year⁻¹

Step 2: Calculate the half-life of the substance

We will use the following expression.

[tex]t_{1/2}[/tex] = ln2/ k = ln 2 / 0.03 year⁻¹ = 23 years

Answer:

1 miles= 1.609km

so, 25x1.609 = 40.225km

Answer:

6381.4 cm²

Step-by-step explanation:

Applying,

A = n/2(a×h)................ Equation 1

Where A = Area of the regular polygon, n = number of sides of the polygon, a = length of one side of the polygon, h = length of the apothem

But,

a = 2htan∅.............. Equation 2

Where ∅ = angle substands at the center by the regular polygon.

∅ = 360/n.................... Equation 3

Substitute equation 3 into equation 2

a = 2htan(360/n)........... Equation 4

Substitute equation 4 into equation 1

A = n/2[2htan(360/n)×h).............. Equation 5

From the question,

Given: n = 6 side, h = 24.78 cm

Substitute these values into equation 5

A = 6/2[24.78×24.78×2×tan(360/6)]

A = 3[24.78×(24.78×2×tan60°)]

A = 6381.4 cm²

Answer:

69.1 cm

Step-by-step explanation:

Circumference of a circle

c = 2πr

Half of that would be a semi-circle

c = πr

c = π * 22

c = 69.115038379

Rounded

69.1 cm

Answer:

77 boxes

Step-by-step explanation:

Take the total number of boxes and divide by the number of girls

1000 boxes / 13 girls

76.92307692

Round up

77 boxes

Check

77*13 = 1001 boxes

Answer:

77 boxes

Step-by-step explanation

Hello there! Let's solve this problem together:

First, we will review our numbers.

13 girls have to sell 1,000 boxes.

Now, we will do the math.

We will solve this problem by dividing.

We will keep multiply by one until we reach 1000 or more.

They have to each sell at least 77 boxes.

Full question attached(original question isn't clear)

Answer:

0.075

Explanation:

Probability is calculated by dividing number of favorable outcomes by total number of outcomes

Now given number of junior Nutrition major and then freshman non-Nutrition major are 8 and 11 respectively

Probability of choosing junior Nutrition major and then freshman non-Nutrition major at random= 8/total of nutrition major × 11/total of non-nutrition major

=8/30×11/39

=4/15×11/39= 44/585 =0.075

Answer:

19.2m

Step-by-step explanation:

"Slice" the rectangle into two right triangles (slice along the diagonal). Now you can use the Pythagorean theorem to calculate the length of the diagonal:

[tex]a^{2} +b^{2} =c^{2} \\12^{2}+15^{2} =c^{2} \\144+225=c^{2} \\\sqrt{369} =\sqrt{c^{2} }\\19.2m =c[/tex]

Answer:

i) 18 = 7 + 11

ii) 26 = 7 + 19

iii) 30 = 7 + 23

Step-by-step explanation:

Answer:

36.8 i think

Step-by-step explanation:

Answer:

61.92

Step-by-step explanation:

Answer:

Step-by-step explanation:

x+15+x+115+90=380 degree(sum of interior angles of four angles is 360 degree)

2x+220=360

2x=360-220

x=140/2

x=70 degree

Answer:

Step-by-step explanation:

Answer:

2x+1

Step-by-step explanation:

f(g(x))= (2x)+1

(2)x+1

Answer:

x-intercepts= (-3,0) , (1,0) and y-intercepts= (0,-3)

For the graph part it would be graphed and shaped like a U.

Step-by-step explanation:

Hope this helps :)

Answer:

x=49 or B)49

Step-by-step explanation:

its is a linear pair so that means it is equal to 180 degrees

you equation will be

x-18+149=180 simplify

x+131=180 subtract 131 from both sides

x=49

Answer:

the work done in propelling the satellite is 919.2 mile-tons

Step-by-step explanation:

Given the data in the question;

we know that, the weight of a body varies inversely as the square of its distance from center of of earth;

⇒ F(x) = c / x²

given that F(x) = four-metric-ton = 4 × 1.102 = 4.408 tons

radius of earth = 4000 miles

we substitute

⇒ 4.408 = c / ( 4000 )²

c = 4.408 × ( 4000 )² = 70528000

so increment of work will be;

ΔW = ( 70528000 / x² ) Δx

Now work done in propelling to a height of 220 miles above Earth;

W = ₄₀₀₀∫⁴²²⁰  ( 70528000 / x² ) dx

W = 70528000[ - 1/x ]⁴²²⁰₄₀₀₀

W = 70528000[ - 1/4220 + 1/4000 ]

W = 70528000[ 1.3033175 × 10⁻⁵ ]

W = 919.2 mile-tons

Therefore, the work done in propelling the satellite is 919.2 mile-tons

As shown in the picture, I sent two pictures.