Brian flips a fair coin 3 times. What is the probability of getting 3 heads?

The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.

The given expression is \((\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}\).

We need to evaluate the given expression.

Laws of exponents:

Now, \((\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}=((\frac{1}{3})^{7-6})^{2}\)   (Because \(\frac{a^{m} }{a^{n} } =a^{m-n}\))

\(=(\frac{1}{3})^{2}\)

=1/9

The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.

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The speed of the runner at a time of 2 hours is approximately 11 kilometers per hour.

In this question we find a smooth curve for runner's distance, in kilometers, in time, in hours, and the speed at t = 2 hours can be estimated by constructing a line tangent to the curve. The speed (v), in kilometers per hour, can be estimated by secant line formula:

v ≈ [x(3 h) - x(1 h)] / (3 h - 1 h)

Where:

If we know that x(1 h) = 22 km and x(3 h) = 44 km, then the velocity of the runner is:

v ≈ (44 km - 22 km) / (3 h - 1 h)

v ≈ 22 km / 2 h

v ≈ 11 km / h

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Answer:

16.8 cubic centimeters

Step-by-step explanation:

3 cm * 4 cm * 1.4 cm = the volume of the prism

3 * 4 = 12

12 * 1.4

1 + 0.4 = 1.4

12 * 1 = 12

12 * 0.4 = 4.8

12 + 4.8 = 16.8

the volume of the prism is 16.8 cubic centimeters

Answer:

\(100x^2-4\pi x^2\)

Also can be said as:

\(4x^2(25-\pi )\)

Step-by-step explanation:

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

\(x=B-P\)

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is \(B=L*W\), where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

\(B=10x*10x\)

Which can be simplified to:

\(B=100x^2\)

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is \(P=\pi r^2\), where r is the radius.

Plugging in the radius of 2x, we get:

\(P=\pi (2x)^2\)

By solving this out, we end up with:

\(P=4\pi x^2\)

From the scenario, we have the equation:
\(x=B-P\)

And from steps 1 and 2, we have the values:

\(B=100x^2\) and \(P=4\pi x^2\)

Now we just plug those values in to get:

\(x=100x^2-4\pi x^2\)

And finally, the amount of the backyard remaining is:

\(100x^2-4\pi x^2\)

This answer may be simplified to:

\(4x^2(25-\pi )\)

Answer:16

Step-by-step explanation:

Answer: the answer is 0

Why 0?:

Step 1: Simplify both sides of the equation

-x * x= -x²

-x * -3= 3x all  together it is ( -x²+3x+12)

for the other side:

-x * x= -x²

6 * x= 6x and x * 2= 2x and 6 * 2= 12

then subtract 6x-4x= 2x so final would be = −x²+4x+12

Step 2: Add x² to both sides.

−x²+3x+12+x²=−x²+4x+12+x² then we are left with 3x+12=4x+12

Step 3: Subtract 4x from both sides.

3x+12−4x=4x+12−4x  --> −x+12=12

Step 4: Subtract 12 from both sides.

−x+12−12=12−12

−x=0

Step 5: Divide both sides by -1 or -x

x=0

Answer:

The volume of the cone is 75.36 cm³

Step-by-step explanation:

The rule of the volume of a cone is V = \(\frac{1}{3}\) π r² h, where

In the given figure

∵ The length of the radius of the cone is 3 cm

∴ r = 3 cm

∵ The length of the height of the cone is 8 cm

∴ h = 8 cm

→ Substitute the values of r and h in the rule of the volume above

∵ π ≅ 3.14

∵ V = \(\frac{1}{3}\) (3.14)(3)²(8)

∴ V = 75.36 cm³

∴ The volume of the cone is 75.36 cm³

The expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

The situation can be modeled by a system of equations, in which the variables are given as follows:

Frankie has sixty-five more football cards than his friend John, hence the expression that represents the number of football cards that Frankie has is given as follows:

F = J + 65.

As the term sixty-five more means that the number 65 is added to the amount of cards that John has, which is symbolized by J, to obtain the amount F, which is the number of football cards that Frankie has.

The problem asks for the expression of the number of cards that Frankie has.

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Answer:

Step-by-step explanation:

To find the slope of a line when only given two points on that line, divide the difference in the y points by the difference in the x points.

slope = (-5 - 7)/(-3 - 2) = -12/-5 = 12/5

slope = (7 - -5)/(2 - -3) = 12/

Answer:

4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.

Step-by-step explanation:

According to the question,

So, In 8 hours each student can deliver:

35 × 8 = 280 newspapers

50 × 8 = 400 magazines

To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.

\( \therefore\)

For Newspapers:

875/280 = 3.125

So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.

For magazines:

1200/400 = 3

3 students are needed to deliver magazines.

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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After 10 years, there is a difference of approximately $165.15 in interest earned between Lenny's two investments.

Lenny earned $1,200 during the summer and decided to deposit half in two different accounts. The first account has a 2% interest rate compounded monthly, while the second account has a 4% interest rate compounded continuously. To determine the difference in interest earned in these two investments after 10 years, we must first calculate the final balance for each account and then find the difference.

For the first account, he deposited $600. With a 2% annual interest rate compounded monthly, the formula to calculate the final balance is:

A1 = P(1 + r/n)^(nt)

where A1 is the final balance, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

A1 = 600(1 + 0.02/12)^(12*10)
A1 ≈ $732.81

For the second account, he also deposited $600. With a 4% annual interest rate compounded continuously, the formula is:

A2 = Pe^(rt)

where A2 is the final balance, P is the initial deposit, e is the base of the natural logarithm, r is the annual interest rate, and t is the number of years.

A2 = 600 * e^(0.04*10)
A2 ≈ $897.96

Now, we can find the difference in interest earned:

Difference = (A2 - P) - (A1 - P)
Difference = ($897.96 - $600) - ($732.81 - $600)
Difference ≈ $165.15

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1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that, in △BCD

BD = 24 m

DC = 10 m

BC = 26 m

△BCD is a right angle triangle.

The trigonometry ratio of sine is ratio of height to hypothenuse.

With respect to C, the height of △BCD is 24m and hypothenuse is 26m.

sin C = height/hypothenuse

sin C = 24/26

C = 67.38°

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Answer:

1862.25

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

If you multiply .15 times 80, you get 12. therefore the tip was 12 dollars

Answer:

7/50 = x/75

x = 10.5

therefore he would run 10.5 miles in 75 minutes

Answer:

In 75 minutes, she runs (7/50) x 75 = 10.5.

She runs 10.5 miles in 75 minutes.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Since C is the midpoint of BD, BC must be equal to CD. Therefore, we can set the equation:

x+4=3x-10

Solve:

14=2x

x=7

Then we find AC, which is:

2x-5+x+4 = 3x-1

We can plug x in to get:

3*(7)-1=20

Answer:

16 for each video game

Step-by-step explanation:

The unit rate is 16x

the ratio is 16:1

The slope is y=16x

Answer:

The ratio:  $65:4

The unit rate: 16.25:1

Step-by-step explanation:

The ratio is money to video games.

The unit rate is how much money each video games cost.

Therefore, the nth term of the sequence is 2^(n-1).

To find the nth term of a sequence, we need to identify the pattern or rule that governs the relationship between the terms.

Looking at the given sequence, we can observe that each term is obtained by multiplying the previous term by 2.

Starting with the first term:

2 * 2 = 4

4 * 2 = 8

8 * 2 = 16

We can see that each term is double the value of the previous term.

Therefore, the rule for this sequence is that each term is obtained by multiplying the previous term by 2.

To find the nth term, we can express it as a formula:

aₙ = aₙ₋₁ * 2

where aₙ represents the nth term and aₙ₋₁ represents the (n-1)th term.

For this sequence, the first term is a₁ = 2.

Using the formula, we can find the nth term:

aₙ = a₁ * 2^(n-1)

Substituting the given first term, we have:

aₙ = 2 * 2^(n-1)

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Answer:

D. 12 units

Step-by-step explanation:

For a point to be translated x units to the left, we must subtract x from the original point, so the x coordinate for M' is -4 as 4 - 8 = -4

For a point to be translated x units down, we must subtract x from the original point, so the y coordinate for M' is -3 as 6 - 9 = -3

Thus, the coordinates for M' is (-4, -3)

The formula for distance, d, between two points is

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\), where (x1, y1) is one point and (x2, y2) is another point.

If we allow M (4, 6) to be our x1 and y1 point and M' (-4, -3) to be our x2 and y2 point, we can find the distance between the two points:

\(d=\sqrt{(4-(-4))^2+(6-(-3))^2}\\ d=\sqrt{(4+4)^2+(6+3)^2}\\ d=\sqrt{(8)^2+(9)^2}\\ d=\sqrt{64+81}\\ d=\sqrt{145}\\ d=12.04159458\)

Answer:

D. 1/4

Step-by-step explanation:

The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.

1/2 x 1/2 = 1/4

Answer: Here we will learn how to find the probability of tossing two coins.

Let us take the experiment of tossing two coins simultaneously:

When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 22 = 4

The above explanation will help us to solve the problems on finding the probability of tossing two coins.

Step-by-step explanation:

THE ANSWER MUST BE AT LEAST 1/4 OR 1/8

IF THAT IS WRONG LET ME KNOW!

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36 square units make up the larger circle's surface area.

We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.

We know that the area of a circle is given by the formula A = πr^2.

We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the area of the larger circle is 36 square units

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Answer:

If you were to use the sine formula you would have to use the cosine formula to get one of the opposite sides and then use the sine formula.

For the area why not use 1/2 * 20 to get the base.

Then the height would be 24 * sin 63 = 21.38

That would give an area of 213.8