Write the expression that represents the total length of this segment

Therefore , the solution of the given problem of probability comes out to be the likelihood that the band will win precisely two out of every four contests is 3/8, or roughly 0.375.

The primary goal of a procedure's criteria-based methods is to determine the probability that a statement is true or that a specific occurrence will occur. Any number range from zero to one, where 0 is frequently used for indicating the potential something could happen and 1 is typically used to indicate a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability illustration.

Here,

=> P(exactly 2 superior ratings) is equal to (the number of ways to get 2 superior ratings) * (the probability of getting a superior rating) * (the probability of not obtaining a superior rating)(4-2)

The binomial coefficient indicates the number of possible methods to win 2 out of 4 competitions with superior ratings:

=> (number of options to select 2 from 4)/  2 =  4, or 6

The likelihood of receiving a higher ranking is 1/100. (since they are equally likely to receive or not receive a superior rating).

With this knowledge, we can now determine the likelihood that:

=> P(exactly 2 superior ratings) = 6 * (1/2)² * (1/2)^(4-2)

=> 6 * (1/4) * (1/4) = 6/16 = 3/8

Thus, the likelihood that the band will win precisely two out of every four contests is 3/8, or roughly 0.375 (rounded to the nearest percent, this probability is expressed as a percentage).

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The missing number in the given table is 180 minutes.

To find the value of x in the equation 2/120 = 3/x, we can use cross multiplication.

First, we multiply both sides of the equation by 120

(2/120) * 120 = (3/x) * 120

To simplify, we have:

2 = 3 * (120/x)

2/3 = (120/x)

To solve for x, we can multiply both sides of the equation by x:

(x) * (2/3) = (120/x) * (x)

2x/3 = 120

To isolate x, we can multiply both sides of the equation by 3/2:

(2x/3) * (3/2) = 120 * (3/2)

x = 180

Therefore, the value of x in the equation 2/120 = 3/x is x = 180.

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Answer:

The value of x is 19.

Step-by-step explanation:

Given:

m∠1 = (4x + 9)°

m∠2 = (x - 14)°

Since m∠1 and m∠2 are complementary angles, we have:

m∠1 + m∠2 = 90°

Substituting the given expressions for m∠1 and m∠2:

(4x + 9)° + (x - 14)° = 90°

Combining like terms:

4x + 9 + x - 14 = 90

Combining the x terms and the constant terms:

5x - 5 = 90

Adding 5 to both sides:

5x = 90 + 5

Simplifying:

5x = 95

Dividing both sides by 5:

x = 95 / 5

Simplifying further:

x = 19

Given the indicinal expression;

According to law of indices, when the base of the values are the same and they are dividing each other, we will subtract the power as shown;

Simplifying the question now;

The quotient as repeated multiplication will be;

The quotient expresses as a power is;

Proof that cos²(x) + sin²(x) = 1 using the unit circle shows that this equation represents a circle with radius 1

The equation of the unit circle is given by:

x² + y² = 1

where x and y are the coordinates of any point on the circle. Let us assume that the point P on the circle makes an angle of x with the positive x-axis. Then, the coordinates of P are given by:

x = cos(x)

y = sin(x)

Substituting these values in the equation of the circlet:

cos²(x) + sin²(x) = 1

Therefore, we have shown that sin²(x) + cos²(x) = 1 using the unit circle.

Graphically, this equation represents a circle with radius 1 centered at the origin, and any point (cos(x), sin(x)) on the circle will satisfy this equation.

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Answer:

Step-by-step explanation:bmmmv m

The interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

To determine whether the average rate of change is positive, f(max) - f(min) must be greater than zero.

Given the function; f(x) = x³ - 9x

We determine f(max) - f(min)

At interval [ -2, 1 ]

(x³ - 9x) - ( x³ - 9x )

( (1)³ - 9(1) ) - ((-2)³ - 9(-2))= -8 - 10 = -18 NOT POSITIVE

At interval [ -2, 3 ]

(x³ - 9x) - ( x³ - 9x )

( (3)³ - 9(3) ) - ((-3)³ - 9(-3))= 0 - 0 = 0 NOT POSITIVE

At interval [ -1, 2 ]

(x³ - 9x) - ( x³ - 9x )

( (2)³ - 9(2) ) - ((-1)³ - 9(-1))= -10 - 8 = -18 NOT POSITIVE

At interval [ -4, -1 ]

(x³ - 9x) - ( x³ - 9x )

( (-1)³ - 9(-1) ) - ((-4)³ - 9(-4))= 8 - (-28) = 36 POSITIVE

Therefore, the interval that function f(x)=x³-9x has a positive average rate of change is [ -4, -1 ].

Option D) is the correct answer.

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Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The directional derivative of f at the given point in the direction indicated by the angle θ is expressed as \(\nabla f(x, y)*u\) where u is the unit vector in the direction θ.

Lets first calculate \(\nabla f(x, y)\ at\ (0, 1)\)

\(\nabla = \frac{\delta}{\delta x} i + \frac{\delta}{\delta y} j \\\nabla f(x, y) = \frac{\delta (y cos(xy))}{\delta x} i + \frac{\delta(y cos(xy))}{\delta y} j\\\nabla f(x, y)= -y^{2} sinxy\ i + (cosxy -xysinxy) j\\\)

\(\nabla f(x, y)\ at\ (0, 1)\\= -1^{2}sin0 \ i +(cos 0 - 0sin0) \j\\= 0i+j\\\\\)

The unit vector u in the direction of θ  is expressed as \(cos\theta \ i + sin\theta \ j\)

unit vector u  at θ = π/6 is cos π/6i + sin π/6 j

u= √3/2 i +1/2 j

Taking the dot product i.e \(\nabla f(x, y)*u\)

= (0i+j)*(√3/2 i +1/2 j)

= 1/2

The directional derivative of f is 1/2

Answer:

89

Step-by-step explanation:

Answer: 89 metres squared

Step-by-step explanation:

large area = 13 x 8 = 104

small area = 5 x 3 = 15

104 - 15 = 89

a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.

b) It takes approximately 13.93 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of approximately 136.04 m/s.

d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.

When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.

First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:

h(t) = h0 + vt + 0.5at²

where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.

Using the given values, we can plug in the numbers and simplify:

h(t) = 950 + 0t + 0.5(9.8)t²

h(t) = 950 + 4.9t²

To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:

0 = 950 + 4.9t^2

t^2 = 193.88

t ≈ 13.93 seconds

To find the velocity at which the stone strikes the ground, we can use the formula:

v = v₀ + at

where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:

v = 0 + 9.8(13.93)

v ≈ 136.04 m/s

Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:

h(t) = 950 - 6t + 0.5(9.8)t²

0 = 950 - 6t + 4.9t²

t² - 1.22t - 193.88 = 0

t ≈ 16.75 seconds

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Answer:

?

Step-by-step explanation:

Answer:

10 Inches

Hope it helps, have a fantastic day.

Step-by-step explanation:

The Circumference of a circle can be displayed by this formula:

\(C = 2\pi r\)

\(C\) is the circumference, and \(r\) is the radius.

So just plug in 31 for \(C\), and simplify:

\(31 = 2\pi r\)

Because the question is asking for the diameter, we only need to divide both sides by pi, as \(2r\) is the same thing as diameter.

\(9.87 = 2r\) (rounded to the nearest hundredth)

We can even rewrite \(2r\) as \(d\), which stands for diameter, to make things a little simpler.

\(9.87 = d\)

Now we just take 9.87, and round it to the nearest whole number, and we get 10. So your answer is 10 Inches.

Hope it helps, have a fantastic day.

Answer:

(V + W) * 5 = 175     boat traveling downstream

(V - W) * 7 = 189       boat traveling upstream

V + W = 35

V - W = 27

2 V = 62    

V = 31 = speed of boat

2 W = 8

W = 4    speed of water

Upstream  7 * (31 - 4) = 189

Downstream 5 * (31 + 4) = 175

There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.

To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.

Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):

Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.

Therefore, the probability that a randomly selected student scored A or B

in Biostatistics is:

Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.

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The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

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Answer:

6) F

7) B

Step-by-step explanation:

6)

\(\boxed{perimeter \: of \: rectangle = 2(length + breadth)}\)

60= 2[½(n -6) +2n +5]

Expand:

60= 2(½)(n -6) +2(2n) +2(5)

60= n -6 +4n +10

Simplify:

60= 5n +4

Minus 4 on both sides:

5n= 60 -4

5n= 56

Divide both sides by 5:

n= 56 ÷5

n= 11.2

Thus, option F is correct.

7)

\(\boxed{area \: of \: rectangle = length \: \times breadth}\)

13q +2= 9(q +6)

Expand:

13q +2= 9q +54

Bring q terms to one side, constant to the other:

13q -9q= 54 -2

Simplify:

4q= 52

Divide both sides by 4:

q= 52 ÷4

q= 13

Thus, option B is correct.

The table that represents a linear equation is the first one, and the line can be:

y = -4x - 1

A general linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Now, notice that if we evaluate the line in x + 1, we will get:

y = a*(x + 1) + b

y = a*x + a + b

So, for an increase of one unit on the variable x, we have a constant increase in the y value.

Now, if you look at the first table, you can see that for each increase of 1 unit on the value of x, the value of y decreases by 4.

So that is the table that can represent a linear function.

And the line is:

y = -4x - 1

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

The regression equation is given as:

y = 0.005x + 3.111

Next, we calculate the predicted values (y) at the corresponding x values.

So, we have:

y = 0.005 * 4 + 3.111 = 3.131

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 5 + 3.111 = 3.136

y = 0.005 * 3 + 3.111 = 3.126

y = 0.005 * 8 + 3.111 = 3.151

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 10 + 3.111 = 3.161

y = 0.005 * 15 + 3.111 = 3.186

y = 0.005 * 6 + 3.111 = 3.141

y = 0.005 * 6 + 3.111 = 3.141

The residuals are then calculated using:

Residual = Actual value - Predicted value

So, we have:

y = 3.46 - 3.131 = 0.329

y = 2.78 - 3.126 = -0.346

y = 3.2 - 3.136 = 0.064

y = 2.8 - 3.126 = -0.326

y = 3.2 - 3.151 = 0.049

y = 2.9 - 3.186 = -0.286

y = 3 - 3.161 = --0.161

y = 3.4 - 3.186 = 0.214

y = 3.57 - 3.141 = 0.429

y = 3.2 - 3.141 = 0.059

Hence, the residuals of the linear regression equation are 0.329, -0.346, 0.064, -0.326,  0.049, -0.286,  -0.161, 0.214, 0.429 and 0.059

See attachment for the residual plot.

The residual plot shows that the linear model from the regression calculator is a good model because the points are not on a straight line

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Answer:

because 2 and 3 are all prime factors

Step-by-step explanation:

Three- month simple moving average (sma) forecast for the average gas prices are $3.08

$3.16 , $3.29 and predict the average retail gasoline price for june 2020 is $3.54.

A simple moving average (SMA) is defined as an arithmetic moving average calculated by adding recent prices and then dividing that figure by the number of time periods in the calculation average. The formula for SMA is:

SMA = (A₁ + A₂ + ------+ Aₙ )/n

where, Aₙ = the price of object at nth period

n = the number of total periods

We have, a average gas prices for different months. Calculate the three-month moving average, add together the first three sets of data, for this example it would be Dec, January, and February. This gives a total of $9.25 , then calculate the average of this total, by dividing this figure by 3 we get 3-month simple moving average. We have to predict the 3-month simple moving average for June 2020. As we seen in above table we calculate the 3-month simple moving average for different months.

The 3-month simple moving average for June 2020 is ( $3.29 + $3.51 + $3.82 )/3 = $3.54

So, required value is $3.54..

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Complete question:

use the gas prices data below to calculate a 3-month simple moving average (sma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. round your answer to two decimal places, if necessary.

Year - month Averge gas price

19-Dec $3.07

20-Jan $3.10

20-Feb $3.08

20-Mar $3.29

20-Apr $3.51

20-May $3.82

20-Jun

Answer: $11.25

Step-by-step explanation:

Answer:

$11.25

Step-by-step explanation:

I assume that x = the 5 videos streamed

5*1.25=6.25

6.25+5 =11.25

y=$11.25

Answer:

y = 2x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 2 and y- intercept c = 1 , then

y = 2x + 1 ← equation of line

Answer:

√27

3√3

Step-by-step explanation:

The expression is equal to the square root of 3 cubed, so:

*The bottom of the power fraction is the root, and the top of the power is the power for the base.

√3³

√27

Answer:

Step-by-step explanation:

3^3/2 =

Change the fraction into a radical form

\(\sqrt{3^3} = \sqrt{27}\)

the solution is d

The probability that at least 2 of the colors will be the same, the following is the best simulation is Option D Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

Given, Sienna buys a mystery pack of sparkly modeling clay. The pack has 5 colors, and there are 7 possible colors that are all equally likely. We have to find the probability that at least 2 of the colors will be the same. There are 5 colors in the pack of clay, and 7 colors are possible in total.

So, the probability of picking any color at random is

P(picking a color) = 5/7 = 0.7143Let P(X = 2) be the probability that exactly 2 of the colors are the same.

Then, the probability that at least 2 of the colors are the same can be calculated by using the formula:

P(X ≥ 2) = 1 - P(X < 2).

The simulation method that can be used to find the probability of at least 2 of the colors will be the same in the mystery pack is option D.

Put 5 pieces of paper in a bag, each labeled with a different color. For each trial, randomly select and replace a paper 7 times. Run 50 trials and find the fraction of times that at least two of the same color appear.

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Answer:

h(-3) = 51

Step-by-step explanation:

h(x) = 4(x^2) - 5x                                       h(-3)

h(-3) = 4(-3²) - 5(-3)

h(-3) = 4(9) + 15

h(-3) = 36 + 15

h(-3) = 51

The sound level of a motorcycle if its intensity is 10⁹ times Io will be 90 decibles.

The sound level of a motorcycle will be calculated thus:

L = 10 log(10⁹Io/Io)

= 10 log(10⁹)

= 90 dB

The sound level of a vacuum cleaner if its intensity, is 10⁷ times I will be

L = 10log(10⁷Io/Io)

= 10log(10⁷)

= 70 dB

The number of times that the sound of motorcycle is more intense than vaccum cleaner will be:

= Intensity of sound of motorcycle ÷ Intensity of sound of vaccum cleaner = 10⁹/10⁷ = 10

= 100 times

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