Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. What is the probability that Sky scored at least two goals? Express your answer as a common fraction.

Answer:

Option D

Sine and cosine are same for complementary angles.

Answer:

Explained below.

Step-by-step explanation:

The data provided is as follows:

S = {31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7. 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3}

Compute the mean and standard deviation as follows:

\(\mu=\frac{1}{n}\sum X=\frac{1}{24}\times [31.5+36.0+37.8+...+49.3]=38.88\\\\\sigma=\sqrt{\frac{1}{n-1}\sum (X-\mu)^{2}}=\sqrt{\frac{1}{24-1}\times 299.639584}=3.61\)

(a)

Compute the​ z-score corresponding to the individual who obtained 32.3 miles per gallon as follows:

\(z=\frac{X-\mu}{\sigma}\)

  \(=\frac{32.3-38.88}{3.61}\\\\=-1.823\)

Thus, the z-score corresponding to the individual who obtained 32.3 miles per gallon is -1.823.

(b)

The data set arranged in ascending order is:

S = {31.5 , 34.2 , 34.7 , 35.6 , 36 .0, 36.2 , 37.3 , 37.6 , 37.8 , 38.1 , 38.2 , 38.4 , 38.5 , 38.7 , 39.5 , 39.6 , 40.1 , 40.6 , 41.4 , 41.7 , 42.2 , 42.5 , 43.4 , 49.3}

The set consists of 24 values.

The first and third quartile are:

\(Q_{1}=[\frac{n+1}{4}]^{th}\ obs.=[\frac{24+1}{4}]^{th}\ obs.=12.5^{th}\ obs.=\frac{36.2+ 37.3}{2}=36.75\\\\Q_{3}=[\frac{3(n+1)}{4}]^{th}\ obs.=[\frac{3(24+1)}{4}]^{th}\ obs.=18.75^{th}\ obs.=\frac{40.6+41.4}{2}=41\)

Thus, the value of Q₁ is 36.75 and Q₃ = 41.

(c)

Compute the inter-quartile​ range as follows:

\(IQR=Q_{3}-Q_{1}=41-36.75=4.25\)

The inter-quartile range is 4.25.

The inter-quartile range is the amount of data that is contained within the middle 50% of a set of observations, when arranged in order. It is the distance between the first and third quartile.

(d)

Compute the values of lower and upper fences as follows:

\(\text{Lower fence}=Q_{1}-1.5\times IQR=36.75-(1.5\times 4.25)=30.375\approx 30.38\\\\\text{Upper fence}=Q_{3}+1.5\times IQR=41+(1.5\times 4.25)=47.375\approx 47.38\)

Any values that are less than the lower fence or more than the upper fence are considered as outlier.

Consider the arranged data set.

Only one value is more than the upper fence, 47.38, i.e. 49.3.

So, yes there is one outlier, i.e. 49.3.

Answer:

17p

Step-by-step explanation:

9p+8p=17p

Answer:

It's an equilateral triangle.

My justification..... it looks like it

Answer:

B. What is the average amount of points Jenny Ortiz scores in a game?

Step-by-step explanation:

Answer:

6x^2 + 23x -18

Step-by-step explanation:

The solution as a trinomial of the given algebraic factor (3x-2)(2x+9) will be 6x² - 23x - 18.

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given algebraic factor,

(3x-2)(2x+9)

⇒ 3x(2x) + 3x(9) - 2(2x) - 2(9)

⇒ 6x² + 27x - 4x - 18

⇒ 6x² - 23x - 18

Hence "The solution as a trinomial of the given algebraic factor (3x-2)(2x+9) will be 6x² - 23x - 18".

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Answer:

       \(\huge\boxed{\sf 10x^2-13x-3}\)

Step-by-step explanation:

\(=(2x-3)(5x+1)\\\\=2x(5x+1)-3(5x+1)\\\\Distribute\\\\= 10x^2+2x-15x-3\\\\= 10x^2-13x-3\\\\\rule[225]{225}{2}\)

The largest possible volume of the inscribed right circular cylinder is 810π \(cm^3\).

To find the largest possible volume of a right circular cylinder inscribed in a cone with height 10 cm and base radius 9 cm, follow these steps:

1. Set up the problem: Let h be the height of the cylinder and r be the radius of its base. The cylinder is inscribed in the cone, so their heights and radii are proportional. Therefore, we have the relationship:

  h/10 = r/9

2. Solve for h: Multiply both sides of the equation by 10 to isolate h:

  h = 10r/9

3. Write the volume formula for a cylinder: V = π\(r^2\)h

4. Substitute h from step 2 into the volume formula:

  V = π\(r^2\)(10r/9)

5. Differentiate the volume formula with respect to r to find the critical points:

  dV/dr = d(10π\(r^3\)/9)/dr = 10πr^2

6. Set the derivative equal to zero and solve for r:

  10π\(r^2\) = 0
  r = 0 (This is not a valid solution since the radius must be greater than zero)

7. Since there's no valid critical point, the maximum volume occurs at the endpoints of the interval. In this case, the radius can be between 0 and 9, so we'll test r = 9:

  h = 10(9)/9 = 10

8. Calculate the volume with r = 9 and h = 10:

  V = π(\(9^2\))(10) = 810π \(cm^3\)

The largest possible volume of the inscribed right circular cylinder is 810π\(cm^3\).

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The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

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Answer:

6p - 2q

Step-by-step explanation:

(2p + 6q) + (4p - 8q)

= 2p + 4p + 6q - 8q

= 6p - 2q

Using the substitution method, we will see that the solution is (2, 3).

Here we have the following system of equations:

y = -2x + 7

y = 5x - 7

To solve it we can use the substitution method, y is isolated in both equations, so we can substitute y on the second equation by the right side of the first equation:

-2x+ 7 = 5x - 7

Now we can solve this for x.

-2x + 7 = 5x - 7

7 + 7 = 5x + 2x

14 = 7x

14/7 = x

2 = x

Now we can evaluate any of the two lines in x = 2 to get the y-value.

y = 5*2 - 7

y = 10 - 7

y = 3

The solution to the system is (2, 3).

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No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.

Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.

To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.

However, both of these jugs are larger than 3 gallons.

This means that it is impossible to measure 3 gallons of water using these jugs.

To measure 4 gallons of water, we can follow these steps:

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 2 gallons of water in jug A.

Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.

Thus, we can measure 4 gallons of water using these jugs.

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y = 155000 (1+.08)⁹ ⇒ 309,845.72

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

it is increasing by 3 so by using +3 we get

4+7+10+13+16+19+22+25+28+31+34+37+40+43

the sum of all of these numbers would be 329

Answer:

3 1/3

Step-by-step explanation:

5/2 divided by 3/4 = 3 1/3

The function of Car A is an exponential function.

The function that describes the value is g(x) = \(18,000(0.94^{x})\).

The value of f(x) in 9 years is $10,313.91.

The function of Car B is a linear function.

The function that describes the value is  g(x) = 18,500 -750x.

The value of f(x) in 9 years is $11,750.

The value of the car declines with the passage of time. Thus, the value of the car depreciates with the passage of time.

A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value.  

The general form of a linear function is f(x) = a + bx

Where:

Rate of change = value of the car B in year 2 - value of the car B in year 1

17,000 - 17,750 = - 750

g(x) = 18,500 -750x

Value of g(x) when x is 9:

g(x) = 18,500 -750(9)

g(x) = 18,500 - 6,750

g(x) = $11,750

An exponential function can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential function is f(x) = \(e^{x}\)

Where:

• x = the variable

• e = constant

Constant = (Value of the car in year 2 / value of the car in year 1) - 1

Constant = (16,346.60 / 17,390) - 1 = -0.06 = -6%

g(x) = \(18,000(0.94^{x})\)

Value of the car in 9 years =  \(18,000(0.94^{9})\) = $10,313.91

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The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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✍️

The answer is ✊✌️I forgot the answer but hanks for the points

Answer:

One tip I can give is to always line up your decimals when adding or subtracting.

Step-by-step explanation:

If you don't then you will get it wrong.

A) if Hank shoots inside the three-point line we can say that he has to shoot 246 in to make the ball into the hoop.

B) then the direct, in a straight line to the center of the basket is : x = √2*246inches ^2

Answer:

x = √2*246inches ^2

Step-by-step explanation:

yw

The inverse function of f(x) = ex has a vertical asymptote at x=0.

The function f(x) = ex is a one-to-one function, which means it has an inverse function. To find the inverse function of f(x), we switch the roles of x and y and solve for y.

Starting with x = ey, we take the natural logarithm of both sides to get:

ln(x) = y

Therefore, the inverse function of f(x) = ex is g(x) = ln(x).

Now, to determine if g(x) has a horizontal or vertical asymptote at x=0, we need to consider the limit of g(x) as x approaches 0 from both sides.

As x approaches 0 from the positive side, ln(x) approaches negative infinity. As x approaches 0 from the negative side, ln(x) is undefined. Therefore, g(x) does not have a horizontal asymptote at x=0.

On the other hand, the graph of g(x) has a vertical asymptote at x=0, since the natural logarithm function approaches negative infinity as x approaches 0 from the positive side. So, the answer is that the inverse function of f(x) = ex has a vertical asymptote at x=0.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}\)

Answer:

30

Step-by-step explanation:

3(2)^3+6=30

Answer:

Step-by-step explanation

dont listen to this person. you tell as many people who are close to you and that you trust tell them! they can help you through it and make sure you're okay! you can go to an adult yes that is a good choice... but its not always about attention. thats what people dont understand is that depression and sucidal thoughts take over you're life when you have them. people will say its for attention when you know its not. when you have anxiety, deppresion, sucidal thoughts, etc. its not a button you can press and be like yep im all better I just wont have these thoughts anymore. its not like that! at all. it takes time and effort just remember you are worth living and you are going to be okay!! talk to someone who is close then if you ever have tendencies then tell an adult or a friend that you're close with and tell them you need help. because you were put on this floating rock for a reason and dont you ever forget it! and dont let anyone tell you how to live you're life! d what brings you joy even if no one else is doing it do it! that thing you have always wanted to do but were too scared too just do it! you only live once so let it be an extraordinary life! make yourself proud of what you have done in life because too many people die with regrets so dont be that person!! have a great day if anyone ever needs anyone I will be here my in.sta is kitty_the_dinosaur_rawr I know weird name but just dm if you need help I will be there okay? have a great day!!

Answer:

uh. have a nice day.

Step-by-step explanation:

Answer:

(4-1)

I think not for sure

Step-by-step explanation:

Answer:

3.5 grams

Step-by-step explanation:

just divide the number of peanuts by the number of raisins, 14/4=3.5, 21/6=3.5, 35/10=3.5

Answer:

3.5 for all

Step-by-step explanation:

divide the grams of peanuts by the grams of raisins

Answer:

this question is missing needed information