How many elements does each of these sets have where a and b are distinct elements?
a.p({a,b,{a,b}})
b.p({∅,a,{a},{{a}}})?

Answer:

118.

Step-by-step explanation:

To find Jane's score on the national achievement test with a given mean of 100 and standard deviation of 15, we calculate it using her z-score of 1.20 to get her score of 118.

The question asks: A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test.

To find Jane score on the test, we use the formula for calculating scores from z-scores: Score = Mean + (Z-score × Standard Deviation).

Given that the mean is 100 and the standard deviation is 15, and Jane's z-score is 1.20, we can calculate her score as follows:

Therefore, Jane's score on the national achievement test was 118.

For two given functions f(x) and g(x), the composite function

(g ° f)(x) is: g(f(x))

Here we will find that the correct option is the last one:

(g°f)(x) = x²-2

To get this, we know that:

g(x) = x + 1

f(x) = x² - 3

Then:

(g°f)(x) = g(f(x))

So here we just need to evaluate g(x) in f(x):

g(f(x)) = f(x) + 1 = ( x² - 3) + 1 = x² - 3 + 1 = x² - 2

Then the correct option is 3:

(g°f)(x) = x²-2

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Answer:

A

Step-by-step explanation:

The  trigonometric function which represents the graph is:

         c)   [tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]

From the graph we may observe that when x=π/2 we have the value of the function  f(x)= 3

Hence, we will check in which this point hold true:

a)

      [tex]f(x)=-3\sin (x-\dfrac{\pi}{2})[/tex]

Now, when x=π/2 we have:

   [tex]f(x)=-3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\sin (0)\\\\\\f(x)=0\neq 3[/tex]

Hence, option: a is incorrect.

b)

[tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]

Now, when x=π/2 we have:

   [tex]f(x)=-3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=-3\cos (0)\\\\\\f(x)=-3\neq 3[/tex]

Hence, option: b is incorrect.

d)

[tex]f(x)=3\sin (x-\dfrac{\pi}{2})[/tex]

Now, when x=π/2 we have:

   [tex]f(x)=3\sin (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\sin (0)\\\\\\f(x)=0\neq 3[/tex]

Hence, option: d is incorrect.

c)

   [tex]f(x)=-3\cos (x-\dfrac{\pi}{2})[/tex]

Now, when x=π/2 we have:

   [tex]f(x)=3\cos (\dfrac{\pi}{2}-\dfrac{\pi}{2})\\\\\\f(x)=3\cos (0)\\\\\\f(x)=3[/tex]

Similarly we will see that the value of this function matches all the points that on the graph.

        Hence, option: c is correct.

The largest of the three integers is 127.

It is required to find  the largest of the three integers.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

Given that:

Let's assume, that first number is "x", than second number will be "x + 1" and third one is "x + 2".

  x + (x + 1) + (x + 2) = 378

   x + x + 1 + x + 2 = 378  

3x + 3 = 378   

3(x + 1)  =  378    

Divide  by  3  

 x + 1  =  126    

 x = 125

The first number is 125, second number is 126 and third number is 127.

So, the largest of the three integers is 127.

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The temperature changes by 49.2F from day to night. You calculate this by subtracting the night temperature from the day temperature and remembering to treat subtraction of a negative as addition.

The subject of your question is the calculation of temperature change, which is a simple subtraction problem in mathematics. Given a temperature of 36.6F during the day and a temperature of -12.6F at night, you can find the temperature change by subtracting the night temperature from the day temperature.

So, it will be 36.6F - (-12.6F) equals 49.2F. It's important to note here that subtracting a negative number is the same as adding a positive number which is why we add 12.6F instead of subtracting it.

This means, the temperature changes by 49.2F from day to night.

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Answer:  The correct option is (D) [tex]9x^2-12y^2-11x.[/tex]

Step-by-step explanation:  We are given to find the following sum of the polynomials :

[tex]S=(8x^2-9y^2-4x)+(x^2-3y^2-7x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the required sum, we need to add the coefficients of the same unknown variables with equal powers.

The sum of the polynomials in (i) is as follows :

[tex]S\\\\=(8x^2-9y^2-4x)+(x^2-3y^2-7x)\\\\=8x^2-9y^2-4x+x^2-3y^2-7x\\\\=(8+1)x^2-(9+3)y^2-(4+7)x\\\\=9x^2-12y^2-11x.[/tex]

Thus, the required sum of the polynomials is [tex]9x^2-12y^2-11x.[/tex]

Option (D) is CORRECT.

The mean of the integers -16, -27, 21, -19, 14, -3 is found by adding together all the numbers to get -30, and then dividing by the total number of values, which in this case is 6. This results in a mean of -5.

The solution to this problem falls under the branch of Mathematics known as Statistics, which is the study of collecting, analyzing, interpreting, presenting, and organizing data. The term mean is frequently used in statistics, and it refers to the average of a set of numbers. In this case, you are required to find the mean of the set of integers -16, -27, 21, -19, 14, -3.

To compute the mean, you need to follow a simple two-step process: Add together all the numbers in the set, and then divide the total by the number of items in the set. For the numbers given in your case (-16, -27, 21, -19, 14, -3), you add these together which gives you a total of -30. There are 6 numbers in the set, so the mean would be -30 divided by 6, which equals -5.

Therefore, the mean of the integers -16, -27, 21, -19, 14, -3 is -5.

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Final answer:

Betelgeuse will be either just above the horizon or at virtually the same position on the eastern horizon at 7:15 pm the next day, as stars like Betelgeuse rise in the east and set in the west, completing a rotation around the celestial sphere in about 24 hours.

Explanation:

The question pertains to the observation of the star Betelgeuse and its position relative to the horizon at a specific time from one day to the next. Since most stars rise in the east and set in the west, completing one full rotation around the celestial sphere in approximately 24 hours, we can infer that Betelgeuse will follow a similar path. However, due to Earth's rotation, any given star will appear to rise and set four minutes earlier each night, due to the Earth’s orbit around the Sun completing an extra degree each day. This might suggest that Betelgeuse would be slightly above the horizon at 7:15 pm the following night. Yet, the student should be aware that this four-minute difference can be negligible, and for practical observing purposes, Betelgeuse will be seen rising at virtually the same time, hence nearly at the same position on the horizon.

So you know that he earns $15 per hour so we can write that as 15h, h = # of hours worked

We also know he has to earn AT LEAST  $200, so putting all this together we form the inequality(=< means less than or equal to):     15h =< 200

so now we have to solve for h (number of hours worked):

15h =< 200

(divide both sides by 15)

h =< 13 1/3

So, the painter must work a minimum of 13 and 1/3 hours to earn at least $200.

Hope this helps!  :)

Answer:  11

Step-by-step explanation:

We are given that ∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .

We know that vertical angles are congruent, then their measures must be equal.

i.e. if ∠E and ∠F are vertical angles.

⇒ m∠E=m∠F

[tex]\Rightarrow\ 5x+10=7x-12[/tex]   [Substitute the measures of ∠E and ∠F]

Subtract 5x from both sides , we get

[tex]10=2x-12[/tex]

Add 12 on both sides , we get

[tex]22=2x[/tex]

Divide both sides by 2 , we get

[tex]11=x[/tex] or x=11

Hence, the value of x= 11

The domain of a function is the set of all possible input values that can be inserted into the function. The domain can be numerical or non-numerical, depending on what the function describes.

In mathematics, finding the domain of a function involves identifying all possible values that can be inserted into the function. A function's domain can be a set of numerical values or a set of non-numerical values.

For example, if we have a function based on majors at a university, the domain could take form as X = {English, Mathematics, ...}, i.e., a list of all the majors offered at the university, plus undeclared, which are all possible inputs into the function.

Similarly, if we have a random variable X = hair color, then the domain of X would include all possible hair colors.

If the function is based on numerical variables, such as a Quadratic Function, the domain would be the set of all real numbers. For instance, the domain of Y = {0, 1, 2, ...} consists of the integers from zero up to a certain limit. Generally, the domain of a function is the set of all possible input values that will produce a value in the function.

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Answer:

12 years old

Step-by-step explanation:

m = Michael

a = Margaret

m = 3a

m+6 = 2(a+6)

m+6 = 2a+12

Two equations, two unknowns, so we can use substitution.

3a+6 = 2a+12

a+6 = 12

a = 6

Plug it back in.

m = 3(6)

m = 18

When Michael was 18, Margaret was 6. So when she was born (basically when she was 0) Michael was 18-6 = 12.

Answer:

Michael was 12 years old when Margaret was born.

Step-by-step explanation:

Let Michael be x and Margaret be y.

x=3y

x+6 (years) = 2(6+y) --> x+6=12+2y --> x=6+2y

Now that we have x, substitute x=3y:

6+2y=3y --> y=6

Now we have y, substitute again with x=3(6) --> x=18

So, Michael, x, is 18 years old. Margaret, y, is 6 years old. But, to find how old Michael was when Margaret was born, do 18 (Michael's age)-6 (Margaret's age) to get 12. So, Michael was 12 years old when Margaret was born. Hope that helped, sorry if I missed something... :D

Answer:

12 square feet

Step-by-step explanation:

Final answer:

To find three solutions to the equation y = 3x + 4, you can choose different values for x and calculate the corresponding values of y. Three solutions are (0, 4), (1, 7), and (-1, 1).

Explanation:

The equation y = 3x + 4 represents a linear equation in slope-intercept form, where the coefficient of x is the slope and the constant term is the y-intercept. To find three solutions to this equation, we can choose different values for x and calculate the corresponding values of y.