Trigonometric identities: Performance task

Answer:

QUESTION:

How many 3 digit numerical passwords are there if a digit can be repeated?

ANSWER:

The first digit of the password can be any of the ten digits - 10 possibilities.

A digit cannot be repeated, so the second digit can be any digit except the one you chose for the first digit - 9 possibilities.

The third digit can be any digit except the digits you chose for the first and second digit - 8 possibilities.

Using the rule of product:

10 X 9 X 8 = 720

There are 720 passwords.

Step-by-step explanation:

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Answer:

1000?

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

\(\frac{-8--13}{-16--17} =\frac{5}{1}= 5\)

Answer:

Step-by-step explanation:

(b). ( x , 0 )

Zero where the graph crosses the X-axis: 1

Zero where the graph touches, but does not cross the X-axis: ( - 1 )

(c). ( 0, y )

- ( 0 + 1 )²( 0 - 1 ) = 1

Answer:

126.0000

Step-by-step explanation:

Answer:

Used: 1/4x +5

Left: 3/4x -5

Step-by-step explanation:

Monday: 1/4 of the x matched

1/4x are used

Tuesday: uses 5 more

1/4x +5 are used

Total used 1/4x +5

To find what is left, take what was started with x, and subtract what was used

Left: x - (1/4x+5)

        x - 1/4x -5

         3/4x -5

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Therefore, the probability that Sayan can go on the trip without having to replace the hard drive during the trip is approximately 0.868.

Since the number of hours that a computer hard drive can run before it conks off is exponentially distributed with an average value of 5 years, we can use the following exponential probability density function:

f(x) = (1/μ) * exp(-x/μ)

where x is the number of hours, μ is the mean (or average) number of hours, and exp() is the exponential function.

In this case, μ = 5 years * 12 months/year = 60 months. We want to find the probability that the hard drive will not fail during an 8 month trip, given that it has already been in use for 3 years (or 36 months).

Let X be the number of months the hard drive lasts. Then, X is exponentially distributed with mean μ = 60 months. We want to find P(X > 8 + 36 | X > 36).

Using the memoryless property of the exponential distribution, we have:

P(X > 8 + 36 | X > 36) = P(X > 8)

= exp(-8/60)

≈ 0.868

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Answer:

2560

Step-by-step explanation:

10%/100% = 256/x

100/10=10

256x10 = 2560

Answer:

2 1/2

Step-by-step explanation:

When multiplying fractions, you multiply the numerators together and the denominators together.

4 • 5/8

Multiply 4 and 5.

20/8

You can simplify this by dividing both parts by 4

5/2

5/2 is also 2.5

2.5 written as a mixed number is 2 1/2.

This is your answer.

Hope this helps!

Answer:

17

Step-by-step explanation:

From inspection of the given bar chart, the number of boys in each section is:

To find the average number of boys per section in class 8, sum the number of boys in each section and divide the result by 4.

\(\boxed{\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}\)

\(\implies \sf Average=\dfrac{16+20+16+16}{4}=\dfrac{68}{4}=17\)

Therefore, there is an average of 17 boys per section in class 8 of Jagruti High School.

Answer:

17

Step-by-step explanation:

To find the average of something, we divide the total by the amount of sections/groups.

So we need to find the total number of boys and divide by the number of sections (4).

We can find the number of boys in each section by reading it off the chart:

8A: 16 boys

8B: 20 boys

8C: 16 boys

8D: 16 boys

So the total number of boys in class 8 is the sum of each section: 16+20+16+16=68

Divide this total by the number of sections (4) to get the average:

68/4=17

So the average number of boys per section in class 8 is 17.

For a batch of 2000 flashlights, the probability of no defective flashlights is 0.85227, the probability of one defective flashlight is 0.14683 and the probability of more than two defective ones is 0.0009

(a) X is a binomial random variable with parameters n = 2000 and p = 0.0015.

(b) The expected value of X is E[X] = np = 2000*0.0015 = 3 and the standard deviation of X is σX = √(npq) = √(2000*0.0015*0.9985) = 2.9989.

(c) The probability that there are no defective flashlights is P(X=0) = (2000C0)(0.0015^0)(0.9985^2000) = 0.85227. The probability that there is one defective flashlight is P(X=1) = (2000C1)(0.0015^1)(0.9985^1999) = 0.14683. The probability that there are more than two defective flashlights is P(X > 2) = 1 - P(X=0) - P(X=1) = 0.0009.

(a) Use R to plot the pmf of X:

x <- c(96,97,98,99,100,101,102,103,104)

p <- c(0.15,0.12,0.14,0.17,0.06,0.05,0.04,0.02,0.25)

plot(x,p,type="h",xlab="x",ylab="p(x)")

(b) The probabilities of P(X < 100) and P(98 < X < 102) are P(X < 100) = 0.48 and P(98 < X < 102) = 0.26.

(c) The pmf of the random variable Y = [X – 100) is given by y 0 1 2 p(y) 0.48 0.26 0.26 The expected value of Y is E[Y] = 0.

For a batch of 2000 flashlights, the probability of no defective flashlights is 0.85227, the probability of one defective flashlight is 0.14683 and the probability of more than two defective ones is 0.0009. The pmf of the random variable Y = [X – 100) is given by y 0 1 2 p(y) 0.48 0.26 0.26 and the expected value of Y is E[Y] = 0.

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Answer:

g(x) = (x - 7)² + 5

Step-by-step explanation:

Since it is going 7 to the right, we have to subtract by 7 in the equation like this: (x - 7)²

Think of it like x becoming positive 7 to cancel out the negative 7

We also add 5 to the whole equation

Answer:

Its B.

Step-by-step explanation:

The  transformations that is possible in a linear function is: g(x) = (x - 2)².

What in the equation causes these movements?

if the function of the g (x) is known to be the original function, then one can say that:

g(x) = (x - 2)²

=> g(x) = x²

This is one that is shifted by 2 unit to the right because in the above, one need to substitute x for x - 2.

Hence , it functional graph can be said to be a parabola with a vertices that is known to be opening at (2,0)

Therefore, based on the above, the example of the transformations that is possible in a linear function is: g(x) = (x - 2)².

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Answer:

i think its option b but im not sure

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

The rejection region in a one-tailed hypothesis test with a significance level of 0.05 is the upper 5% of the distribution. The correct answer is option A.

Thus, the rejection region in a one-tailed hypothesis test with a significance level of 0.05 is the upper 5% of the distribution.

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An outlier is a mathematical value in a set of data which is quite distinguishing from the other values.

Its more like outliers are values uncommonly far from the middle. Mostly, outliers have a significant impact on mean, but not on the median, or mode.

Hence making the outliers are crucial in their influence on the mean.

we can say that the outlier is a data point that lies outside the entire pattern in a distribution.

They are mostly shown as dots and its known that the whiskers are required to change. Whiskers stretch out to the farthest point in the data set that isn't an outlier.

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Answer:

Ruby is sphere

Shriya's is incorrect

Abhishek's is correct

Step-by-step explanation:

Ruby's definition matches a sphere because it is 3D and Shriya's is wrong.

The sample size that should be used in this study is approximately 93.

To determine the sample size for the study, we can use the formula:

n = (Z * σ / E)^2,

where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the maximum allowable error or margin of error.

In this case, the researchers want the average time to fix a rivet to be off by at most 3.5 seconds, which can be considered as the margin of error (E).

Given that the confidence level is 95%, the corresponding z-score (Z) is 1.96. The population variance (σ^2) is known to be 55 seconds^2.

Plugging these values into the formula, we can calculate the sample size:

n = (1.96 * sqrt(55) / 3.5)^2,

where sqrt denotes the square root.

Evaluating the expression:

n ≈ 92.607.

Sine the sample size should be a whole number, we can round up the value to obtain the final sample size.

Therefore, the recommended sample size for the study is approximately 93.

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Answer:

Your friend made 35 bird houses.

Step-by-step explanation:

If the ratio from your houses to your friends houses is 4:5, that means that for every 9 houses built, your friend did 5. So, every 18 houses built, your friend did 10. For every 27, your friend did 15, and for 36, your friend did 20, and for every 45, your friend did 25, and for every 54, your friend did 30, and for every 63, your friend did 35.

Answer:

87.59 or 87 or 88

Step-by-step explanation:

437950/5000 = 87.59

Answer:

{x,y} = {25/9,23/9}

Step-by-step explanation:

// Solve equation [2] for the variable  x  

 [2]    x = -4y + 13

// Plug this in for variable  x  in equation [1]

  [1]    5•(-4y+13) + 2y = 19

  [1]     - 18y = -46

// Solve equation [1] for the variable  y  

  [1]    18y = 46  

  [1]    y = 23/9  

// By now we know this much :

   x = -4y+13

   y = 23/9

// Use the  y  value to solve for  x

Answer:

Anything in the form x = pi+k*pi, for any integer k

These are not removable discontinuities.

============================================================

Explanation:

Recall that tan(x) = sin(x)/cos(x).

The discontinuities occur whenever cos(x) is equal to zero.

Solving cos(x) = 0 will yield the locations when we have discontinuities.

This all applies to tan(x), but we want to work with tan(x/2) instead.

Simply replace x with x/2 and solve for x like so

cos(x/2) = 0

x/2 = arccos(0)

x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k

x = pi + 4pi*k   or    x = -pi + 4pi*k

Where k is any integer.

If we make a table of some example k values, then we'll find that we could get the following outputs:

and so on. These are the odd multiples of pi.

So we can effectively condense those x equations into the single equation x = pi+k*pi

That equation is the same as x = (k+1)pi

The graph is below. It shows we have jump discontinuities. These are not removable discontinuities (since we're not removing a single point).

The value of the missing length is c = √181

From the question, we have the following parameters that can be used in our computation:

Legs = 9 and 10

Hypotenuse = c

The missing length of the triangle can be calculated using the Pythagorean Theorem represented as a​² + b² = c²​

So, we have the following equation

c² = 9² + 10²

Evaluate the sum of squares

c² = 181

Take the square root of both sides

c = √181

Hence, the missing length is c = √181

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Answer:

3 1/2

Step-by-step explanation:

The notation for the given compositions of transformations is R180∘\(R_x\)=2.

The composition of a reflection across the line x=2, followed by a rotation of 180 degrees about the origin, can be represented using function notation as follows:

                                        R180∘\(R_x\)=2

Where:

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