what is the value of n?

To find P(Q and R), we can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P(R) = 0.24P(Q and R) = P(Q) × P(R) = 0.37 × 0.24 = 0.0888.

Therefore, the probability of both Q and R occurring together is 0.0888. Long Answer:Independent events:In probability theory, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. Two events A and B are independent if the probability of A and B occurring together is equal to the product of the probabilities of A and B occurring separately. Mathematically,P(A and B) = P(A) × P(B) Suppose Q and R are independent events. Find P(Q and R).

We can use the formula: P(Q and R) = P(Q) × P(R) Since the events Q and R are independent, we can multiply the probabilities of each event to find the probability of both events occurring together. P(Q) = 0.37P

(R) = 0.24

P(Q and R) = P(Q) × P(R)

= 0.37 × 0.24

= 0.0888

Therefore, the probability of both Q and R occurring together is 0.0888. Hence, P(Q and R) = 0.0888. In probability theory, independent events are the events that are not dependent on each other. It means the probability of one event occurring does not affect the probability of the other event occurring.

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Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both

Step-by-step explanation:

problem a                                                    problem b

(6²-4)/2                        or                              6²-4/2

     |                                                                      |

\(6^2=36\\\)                                                            \(6^2=36\)

36-4=32                                                         36-4/2

32/2=16                                                          36-2=34

   16                                                                    34

Bond A: Maturity = 19 years, Yield = 14%, Price = $255.10

Bond B: Maturity = 5 years, Yield = 12%, Price = $608.00

Bond C: Maturity = 9 years, Yield = 8.61%, Price = $380.00

To calculate the price, maturity, and yield for each bond, we need to use the formula for present value of a zero-coupon bond:

Price = Face Value / \((1 + Yield/2)^{(2Maturity) }\)

For Bond A, with a face value of $1,000, a yield of 14% (or 0.14 in decimal form), and a maturity of 19 years, the calculation is:

Price = 1000 /\((1 + 0.14/2)^{ 38}\)= $255.10

For Bond B, we are given the price as $608.00, a yield of 12% (or 0.12 in decimal form), and we need to find the maturity. Rearranging the formula, we can solve for maturity:

Maturity = ln(Face Value / Price) / (2 × ln(1 + Yield/2))

Maturity = ln(1000/608) / (2 × ln(1 + 0.12/2)) = 5 years

For Bond C, we are given the price as $380.00, a maturity of 9 years, and we need to find the yield. Again, rearranging the formula, we can solve for yield:

Yield = 2 × ((Face Value / Price)^(1 / (2Maturity)) - 1)

Yield = 2 × ((1000/380)^(1 / (29)) - 1) = 8.61%

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Answer:

8) 92.31

9) 9

10) 60%

11)  70

12)  8%

13) By using the formula given. multiplying by 100 and dividing or dividing and then multipling.

The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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If I earned $2 more than Andrew at the end of the day, then the value of t  is \(1\frac{2}{3}\)

Number of hours that I used to work = 1 hour

My hourly pay =  $3t - 3

My total pay at the end of the day = Number of hours x hourly pay

My total pay at the end of the day = 1 (3t - 3)

My total pay at the end of the day = $ 3t - 3

Number of hours that Andrew used to work = 3t -5 hour

Andrew's hourly pay =  $2

Andrew's total pay at the end of the day = Number of hours x hourly pay

Andrew's total pay at the end of the day = 2 (3t - 5)

Andrew's total pay at the end of the day = $ 6t - 10

At the end of the day, I earned $2 more than Andrew

My total pay = Andrew's total pay + 2

3t - 3   =  6t - 10  +  2

6t  -  3t  =  -3 +10 - 2

3t  =  5

t  =  5/3

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

If I earned $2 more than Andrew at the end of the day, then the value of t  is \(1\frac{2}{3}\)

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Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Given:

The graph of a polynomial.

To find:

The polynomial function for the given graph.

Solution:

If the graph of function intersect the x-axis at x=c, then (x-c) is a factor of that function f(x).

From the given graph it is clear that the graph of the polynomial function intersect the x-axis at x=-1, x=2, x=3.

So, (x+1), (x-2) and (x-3) are the factors of required polynomial.

At x=2 and x=3, it look like a linear function. So, the multiplicity of (x-2) and (x-3) are 1.

At x=-1, it look like a cubic function. So, the multiplicity of (x+1) is 3.

The required polynomial is

\(f(x)=a(x+1)^3(x-2)(x-3)\)          ...(i)

The function passes through the point (1,10). Putting x=1 and f(x)=10, we get

\(10=a(1+1)^3(1-2)(1-3)\)

\(10=a(2)^3(-1)(-2)\)

\(10=16a\)

\(\dfrac{10}{16}=a\)

\(0.625=a\)

Putting a=0.625 in (i), we get

\(f(x)=0.625(x+1)^3(x-2)(x-3)\)

\(f(x)=0.625(x+1)(x+1)(x+1)(x-2)(x-3)\)

Therefore, the required polynomial function is \(f(x)=0.625(x+1)^3(x-2)(x-3)\)  or it can be written as\(f(x)=0.625(x+1)(x+1)(x+1)(x-2)(x-3)\).

Answer:

√3

Step-by-step explanation:

From the given parameters

Assuming the adjacent side is x

Adjacent = x

Hypotenuse = 2√√

Angle of elevation = 60degrees

Using the SOH CAH TOA identity;

Cos theta = Adj/Hyp

Cos 60 = x/2√3

x = 2√3 cos 60

x = 2√3 * 1/2

x = √3

Hence the value of x is √3

Answer:

got it right on khan. 4/3

Step-by-step explanation:

Answer: x = − \(\frac{y}{2}\) - 1

Steps for solving linear equation.

y = − 2x − 2

Swap sides so that all variable terms are on the left-hand side.

−2x − 2 = y

Add 2 to both sides.

−2x = y + 2

Divide both sides by −2.

\(\frac{-2x}{-2}\) = \(\frac{y + 2}{-2}\)

Dividing by −2 undoes the multiplication by −2.

x = \(\frac{y+2}{-2}\)

Divide y + 2 by −2.

x = -\(\frac{y}{2}\) - 1

Graph:

The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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Answer:

I think its c but im not sure

Step-by-step explanation:

Let x be the other leg or the base and the first leg is y or the perpendicular. ATQ,

One leg of a right triangle is twice as long as the other leg,

y = 2x

Hypotenuse, H = 5 cm

For a right angled triangle, using Pythagoras theorem,

\(H^2=B^2+P^2\)

Putting all the values,

\(5^2=x^2+(2x)^2\\\\25=x^2+4x^2\\\\25=5x^2\\\\x^2=5\\\\x=\sqrt{5}\ cm\)

Other leg,

\(y=2x\\\\=2\sqrt{5} \ cm\)

Hence, the measure of the shorter leg is \(\sqrt{5} \ cm\)

Answer:

\(a.\ D=\dfrac{1}{5}t\)

b. 20 seconds

Step-by-step explanation:

Let \(D\) be the distance in miles and

\(t\) be the time in seconds and

\(s\) be the speed in miles/sec

Formula for Distance is given as:

\(Distance = Speed \times Time\\OR\\D=st\)

Given that:

Distance = 2 miles and

Time = 10 seconds

Putting the values in formula:

\(2=s\times 10\\\Rightarrow s =\dfrac{1}{5} \ miles/sec\)

Answer a:

Putting the value of \(s\) back in the formula to find the direct variation equation for the relationship between time and distance:

\(D=\dfrac{1}{5}t\)

Answer b:

Using the above formula and putting \(D=4\ miles\):

\(4=\dfrac{1}{5}t\\\Rightarrow t =\bold{20\ seconds}\)

Answer:

66 miles per hour

Step-by-step explanation:

528/8 = 66 miles per hour

Answer:

66 miles/hour.

Step-by-step explanation:

Its average speed is 528/8

= 66 miles/hour.

Answer:

Point 1 to the left with a closed circle <-----*

Point 8 to the right with an open circle o------>

Step-by-step explanation:

Got the answer correct

536.2  cubic inches  is the volume of a cube with surface area of 396.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given,

\(A=6V^{\frac{2}{3}}\)

A is surface Area ‘A’, in square units, of a cube

V is  volume of cube in cubic units.

We need to find the volume, in cubic inches, of a cube with surface area of 396.

A=396

We need to find V

\(V^{\frac{2}{3} } =A/6\)

=396/6

=66

\(V=66^{\frac{3}{2} }\)

V=536.2  cubic inches

Hence, 536.2  cubic inches  is the volume of a cube with surface area of 396.

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Answer:

y=-2x

Step-by-step explanation:

slope is -2 and the y intercept is 0 so if you plug these answers into slope intercept form (y=mx+b) then it comes to y=-2x

Answer: 13

Step-by-step explanation:

Take 7 to the other side and divide 91 by 7, the answer will be 13.

We can use an integrating factor to transform the equation into a form that allows us to solve for x. By solving the resulting differential equation, we can find the solution x(t) that satisfies the given initial condition.

The given initial value problem is a first-order linear ordinary differential equation. To solve it, we first rewrite the equation in standard form:

(t−2)dx/dt +3x = 2/t

Next, we identify the integrating factor, which is the exponential of the integral of the coefficient of x. In this case, the coefficient is 3, so the integrating factor is e^(∫3 dt) = e^(3t). Multiplying both sides of the equation by the integrating factor, we get:

e^(3t)(t−2)dx/dt + 3e^(3t)x = 2e^(3t)/t

The left side of the equation can be simplified using the product rule for differentiation, which gives us:

d/dt(e^(3t)x(t−2)) = 2e^(3t)/t

Integrating both sides with respect to t, we have:

e^(3t)x(t−2) = 2∫e^(3t)/t dt + C

The integral on the right side is a non-elementary function, so it cannot be expressed in terms of elementary functions. However, we can approximate the integral using numerical methods.

Finally, solving for x(t), we get:

x(t−2) = (2/t)∫e^(3t)/t dt + Ce^(-3t)

x(t) = (2/t)∫e^(3t)/t dt + Ce^(-3t) + 2

Using the initial condition x(4) = 1, we can determine the value of the constant C.

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z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

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The magnitude of the vector QP is √73.

To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.

Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:

x-component of QP = x-coordinate of Q - x-coordinate of P

                 = (-4) - 4

                 = -8

y-component of QP = y-coordinate of Q - y-coordinate of P

                 = 4 - 1

                 = 3

Therefore, the component form of the vector QP is (-8, 3).

To find the magnitude of the vector QP, we can use the formula:

Magnitude of a vector = √(\(x^2 + y^2\))

Substituting the x-component and y-component of QP into the formula, we get:

Magnitude of QP = √((\(-8)^2 + 3^2\))

              = √(64 + 9)

              = √73

Therefore, the magnitude of the vector QP is √73.

In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.

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The answer is 72. 3•4•6=72 That is the volume of the figure.

Answer:

\(0.05cm {}^{3} \)

Step-by-step explanation:

\(density \: is \: the \: mass \: per \: unit \: volume \: of \: an \: object \: \\ density = \frac{m}{v} \\ density = \frac{0.8}{16} = 0.05cm {}^{3} \)

Answer:

69 inches

Step-by-step explanation:

The first four parts were each 16 inches, and the remaining fifth part was 5 inches long, so the total length of the ribbon before Kayleen cut it was (16*4)+5 = 64+5 = 69 inches (nice)

Answer:

A. 3 hours

Step-by-step explanation:

40 mph x 3 hours = 120 miles in 3 hours

55 mph x 3 hours = 165 miles in 3 hours

120 miles (in 3 hours) + 165 miles (in 3 hours) = 285 miles

Answer:

8 cubic meters

Step-by-step explanation:

Formula for the volume of a rectangular pyramid:

\(V=\frac{lwh}{3}\)

Take note

\(l=\) base length

\(w=\) base width

\(h=\) pyramid height

We are given \(l\), \(w\), and \(h\).

Lets solve for \(V\)

\(l=3\)

\(w=2\)

\(h=4\)

Now plug in our numbers into the formula:

\(V=\frac{3*2*4}{3}\)

Evaluate the numerator

\(3*2*4=24\)

Then we have

\(V=\frac{24}{3}\)

Simplify and we get:

\(V=8\)

Hello!

[(4πr³)/3]/2

r = 7,5yd

[4 *3,14*7,5³/3]/2

=> 883, 125yds ³

The value of sin(2θ) = 120/169.

We can use the double angle formula for sine to find sin(2θ):

sin(2θ) = 2sin(θ)cos(θ)

We know that sin(θ) = -12/13 and θ is in quadrant III, which means that both sine and cosine are negative.

We can use the Pythagorean identity to find the value of cosine:

\(cos^2(\theta ) = 1 - sin^2(\theta)\)

\(cos^2(\theta) = 1 - (-12/13)^2\)

\(cos^2(\theta) = 1 - 144/169\)

\(cos^2(\theta ) = 25/169\)

cos(θ) = -5/13

Now we can substitute these values into the double angle formula for sine:

sin(2θ) = 2sin(θ)cos(θ)

sin(2θ) = 2(-12/13)(-5/13)

sin(2θ) = 120/169

Therefore, sin(2θ) = 120/169.

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To find sin(2θ), we can use the double angle formula for sine: sin(2θ) = 2sin(θ)cos(θ). Since we know that sin(θ) = -12/13 and θ is in quadrant III, we can use the Pythagorean theorem to find the value of cos(θ). Therefore, sin(2θ) = 120/169.

Let's draw a right triangle in quadrant III where the opposite side is -12 and the hypotenuse is 13:

```
     |\
     | \
     |  \
   12|   \ 13
     |    \
     |     \
     |______\
        -  
```

Using the Pythagorean theorem, we can solve for the adjacent side:

cos(θ) = adjacent/hypotenuse = (-√(13^2 - 12^2))/13 = -5/13

Now we can plug in the values of sin(θ) and cos(θ) into the double angle formula:

sin(2θ) = 2sin(θ)cos(θ) = 2(-12/13)(-5/13) = 120/169

Therefore, sin(2θ) = 120/169.

Given that sin(θ) = -12/13 and θ is in Quadrant III, we need to find sin(2θ).

We can use the double angle formula for sine, which is:
sin(2θ) = 2sin(θ)cos(θ)

We are given sin(θ) = -12/13. To find cos(θ), we can use the Pythagorean identity:
sin²(θ) + cos²(θ) = 1

Substitute sin(θ) value:
(-12/13)² + cos²(θ) = 1
144/169 + cos²(θ) = 1

Now, we need to solve for cos²(θ):
cos²(θ) = 1 - 144/169
cos²(θ) = 25/169

Since θ is in Quadrant III, cos(θ) is negative. So,
cos(θ) = -√(25/169)
cos(θ) = -5/13

Now we can find sin(2θ) using the double angle formula:
sin(2θ) = 2sin(θ)cos(θ)
sin(2θ) = 2(-12/13)(-5/13)

Multiply the terms:
sin(2θ) = (24/169)(5)
sin(2θ) = 120/169

Therefore, sin(2θ) = 120/169.

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