Can someone help me I have to verify the trig identities.

a. distribution of X is  (257,45)

b. Probability that a randomly hit fly ball travels less than 284 feet is 0.2257

c. The 70th percentile for the distribution of distance of fly balls is 290 feet.

What do you mean by normal distribution?

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.

It is given that we have a normal distribution with mean of 257 feet and standard deviation of 45 feet.

X be the distance in feet for a fly ball.

a. As mean of the normal distribution is 257 and standard deviation is 45 feet

Therefore, distribution of X is (257,45)

b. Probability that a randomly hit fly ball travels less than 284 feet,

P(X < 284) =

The z-score can be calculated as

z = (x - μ)/σ = (284-257)/45 = 27/45 = 0.6

So, the equivalent z-score form can be given as:

P(X < 284) = P(Z < 0.6) = 0.2257

c. The 70th percentile of the distribution of fly balls is given by a raw score such that:

P(X < x)=70%⇒ x = ?

Using formula , z = (x - μ)/σ  ⇒ x = zσ + μ

P(Z < z) = 0.7000

Now, we can use the cumulative standard normal distribution table:

z = 0.7000 + 0.04  = 0.74

Finally, the required random variable can be computed as:

x = zσ + μ  = 0.74 × 45 + 257 = 33.3 + 257 = 290.3

That means P(X < 290.3) feet =70%

Therefore, the 70th percentile of the distribution of fly balls is approximately 290 feet

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.

Answer:

1) x = 3,

2) s = 11,

3) z = 14,

4) y = 2,

5) q = 6,

6) n = 10,

7) r = 7,

8) m = 0,

9) p = 1,

10) a = 9.

Step-by-step explanation:

1) Subtract 9 from both sides to isolate x, the result is 3.

2) Add one to both sides to isolate s, the result is 11.

3) Add 11 to both sides to isolate z, the result is 14.

4) Subtract 5 from both sides to isolate y, the result is 2.

5) Subtract 2 from both sides to isolate q, the result is 6.

6) Add 4 to both sides to isolate n, the result is 10.

7) Add 2 to both sides to isolate r, the result is 7.

8) Subtract 6 from both sides to isolate m, the result is 0.

9) Subtract 7 from both sides to isolate p, the result is 1.

10) Subtract 4 from both sides to isolate a, the result is 9.

Answer:

..............................

Answer:

The slope is [tex]\frac{-3}{5}[/tex]

Step-by-step explanation:

You know the slope is negative if you start on the left side and move right along the line.  You are moving down hill.  Down hill is a negative slope.

Pythagoras was a philosopher and a teacher. Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides: a2+b2=c2.

An angle with a measure of exactly 90 degrees (or /2) is referred to as a right angle. The proper angles are frequently demonstrated in everyday life. For instance, the edges of the cardboard or the corner of a book.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

A point is surrounded by four right angles. According to our definition of a degree, a "complete turn" around a point is 360°, making each right angle one-fourth of that, or 90°.

One mountain it should be 30 Kilometers and other mountain should be 40 kilometers

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The standard form equation for a line passing through the point (6, -1) and parallel to the line denoted by 8x + 3y = 15 is 8x + 3y = 45.

The standard form equation

ax + by = c

Here a, b, and c are constants and therefore use the slope-intercept form.

y = mx + c .... (1)

where m is the slope, b = y-intercept

8x + 3y = 15

3y = -8x + 15

y = -8 / 3 x + 5

Slope (m) = - 8 / 3

It passes through a line that has points (6, -1)

Let's find b by putting the value of m = - 8/3, x = 6, and y = -1 in equation (1).

-1 = - 8 / 3 (6) + c

-1 = -48 / 3 + c

-1  = -16 + c

c = -1 + 16

c = 15

Therefore,

y = - 8 / 3 x + 15

8 / 3 x  + y = 15

=> 8x + 3y = 45

8x + 3y = 45 is the standard form of the line that passes through (6,-1) and is parallel to the line represented by 8x + 3y= 15.

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The slope intercept form of equation of second graph is

d = 2.5t + 1

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]  

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

The equation describing the graph of the position of the first object with respect to time is d=2.5t+2.2.

Now, we need to find the equation of line parallel to d = 2.5t + 2.2 and passing through t = 0, d = 1

Slope of line d = 2.5t + 2.2 is 2.5

Slope of line parallel to d = 2.5t + 2.2 is 2.5

The line passes through t = 0, d = 1

Equation of second graph =

d - 1  = 2.5(t - 0)

d = 2.5t + 1

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Answer:

-1.25 or -5/4

Step-by-step explanation:

I think it would be this because I remember that the slope formula is y2-y1/x2-x1 so using that you get 8-3/9-13 which simplifies to -5/4 which then turns into -1.25 when fully simplified. I think this is right.

Answer:

First term: 3

Common difference: -1

Step-by-step explanation:

3rd term: 1

6th term: x

10th term: 3x

Formula for the nth term using the common difference d and the first term a1:

an = a1 + (n - 1)d

Third term: a3 = a1 + (3 - 1)d = a1 + 2d = 1

6th term: a6 = a1 + (6 - 1)d = a1 + 5d = x

10th term: a10 = a1 + (10 - 1)d = a1 + 9d = 3x

a1 + 2d = 1       Eq. 1

a1 + 5d = x      Eq. 2

a1 + 9d = 3x    Eq. 3

Eq. 2 - Eq. 1

3d = x - 1

Eq. 3 - Eq. 2

4d = 2x

x = 2d

3d = x - 1

Substitute 2d for x.

3d = 2d - 1

d = -1

a1 + 2d = 1

a1 + 2(-1) = 1

a1 = 3

Check:

Here are the first 10 terms:

3, 2, 1, 0, -1, -2, -3, -4, -5, -6

The third term is 1. Correct

The tenth term (-6) is 3 times the 6th term (-2). Correct

Answer:

First term: 3

Common difference: -1

The graph of a relation that is a function is the last option that is in the attachment below.

A graph that represents a relation that is a function is a graph whose x-values each have exactly one corresponding y-value. That is to say, no two y-values correspond to one x-value in the graph of a relation that represents a function.

All of the graphs represents relations that have different y-values that correspond to an x-value except the graph at the bottom far right, whose diagram is attached below.

The graph attached below has exactly one y-value that corresponds to each x-value on the graph. Therefore, the relation is a function.

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The value of 2cos² (-22.5°)-1 is 1/√2.

In trigonometry, double angle identities or double angle trig identities are a set of trigonometric identities for angles of form 2θ. There are three double angle identities for each of sine, cosine and tangent ratios.

Given that, 2cos² (-22.5°)-1

2cos²x -1 = cos2x

2cos² (-22.5°)-1 = cos2(-22.5°)

cos(-45°)

∵ cos(-x) = cosx

∴ cos(-45°) = cos(45°)

cos(45°) = 1/√2

Hence, The value of 2cos² (-22.5°)-1 is 1/√2.

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Answer:

[tex]\frac{14}{9}[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

Effective annual interest rate is an investment’s annual rate

of interest when compounding occurs more than a year.

The effective interest rate is calculated as if compounded

annually. The effective rate is calculated in following way…..

r = effective annual rate

i = nominal rate

n = number of periods

= (1+i/n)^n -1

For example, a nominal interest rate 6% compounded

monthly is equivalent to an effective interest rate of 6.17%

So, option A is the correct answer.

Answer: I think its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

2.5 x 7 = 17.5

10^-10 x 10^-6 = 10^(-10-6) = 10^-16

17.5 x 10^-16

1.75 x 10^-16 x 10

1.75 x 10^(-16+1)

1.75 x 10^-15

The required function after shifting its origin will be g(x) = |x + 5| - 4

So, the answer is option C.

To move the origin's coordinates to (h, k):

Get the new equation by changing x and y in the given equation to (x-h) and (y-k), respectively.

Given functions f(x) = |x| or y = |x| in this case

Shift now five units to the left. x is changed to x - (-5) = x + 5.

Shift four units down, and y becomes y -(-4) = y + 4.

After shifting, the equation is now

y - k = |x - h|

y = |x -h| + k

y = |x - (-5)| +(-4) (-4)

g(x) = |x+5|-4

As a result, the necessary function will be g(x) = |x + 5| - 4 after changing its origin.

Option C is the correct response.

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1) The way we transform the simultaneous equation in system A to system B is;

1 * Equation [A1] → Equation [B1]

2 * Equation [A1] + Equation [B1] → Equation [B2]

2) The way we transform the simultaneous equation in system Bto system C is;

1 * Equation [B1] → Equation [C1]

-1/11 * Equation [B2] → Equation [C2]

We are given the system of simultaneous equations as;

System A;

-7x + 2y = 5   ----A1

3x - 4y = 23  ------A2

System B;

-7x + 2y = 5   -----B1

-11x = 33  ------B2

System C;

-7x + 2y = 5   ----A1

x = -3  ------A2

1) To find out the operation that transforms system A into system B, we need to analyze both equations and by careful observation, we see that;

When we multiply A1 by 2 and add to A2, the result will give us B2.

Let us check;

A1 * 2 = 2(-7x + 2y) = 2(5)

-14x + 4y = 10

Add to A2 to get;

-11x = 33

2)  To find out the operation that transforms system B into system C, we need to analyze both equations and by careful observation, we see that;

When we multiply B2 by -1/11 and the result will give us C2.

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The equations that Nakeishia can use to determine the number of commercials and the number of movies on which Nakeisha’s songs were played include:

30m + 110(m + 2) = 760

Let the movies be represented by m

Since Nakeisha’s songs were played on 2 more commercials than movies, this will be m + 2.

Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. This will be:

30m + 110(m + 2) = 760

This represents the equation.

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a - 2b + c = -6 (1)

a = -5c - 12 (2)

-a + 6b + 4c = 3 (3)

Putting (2) into (1) & (3) gives

(-5c -12) - 2b + c = -6 (5)

-(-5c - 12) + 6b +4c =3 (6)

Neatening it up gives

-2b - 4c = 6 (7)

6b + 9c = -9 (8)

Using simulataenous equations, we want to cancel out either b or c. b in this case is easier. Multiplying (7) makes that possible

(7) * 3

gives

-6b - 12c = 18 (9)

Adding (8) & (9) gives

-3c = 9

c = -3

Now we know c we can use that to calculate b in one of the previous equations.

Using (7)

-2b -4(-3) = 6

-2b = -6

b = 3

Now, b & c are known, we can use these in any equation with a to get the final unknown.

Using (1)

a - 2(3) + (-3) = -6

a = 3

Plugging a,b&c back into each (1) (2) & (3) to check you get the right answer is also a good sanity check that you've not made any mistakes in your previous working!

The total impedance is 9+8i ohm.

From the question, we have

Z1= 2+9i

Z2=  7-i

we know,

total impedance in series,

Ztotal = Z1+Z2

            = 2+9i+7-i

            = 9+8i

The total impedance is 9+8i ohm.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer:

(3x-4y) (2x+1)

Answer:

  52 miles per hour

Step-by-step explanation:

You want to know Kenneth's average speed if he drove 174.2 miles in 3 7/20 hours.

Speed is the ratio of distance to time:

  speed = distance/time

  speed = (174.2 mi)/(3 7/20 h) = 52 mi/h

Kenneth's average speed was 52 miles per hour.

The side length of 6 units for the intermediate large square and 4 units for the smallest square, give the area of the shaded region as 32 square unites.

The area of a shape or figure is the two dimensional space occupied by the boundary line of the shape.

Please find attached a possible drawing of the figure in the question created with MS Word

From the drawing, we have;

Side length of the ;large square containing the other squares = 6 + 4 = 10

Area of the largest square, A₁ = 10 × 10 = 100

Side length of the second largest square = 6

Area of the second largest square, A₂ = 6 × 6 = 36

Side length of the two small squares = 4

Area of the two small squares, A₃ = 4 × 4 = 16

Therefore;

Area of the shaded region = A₁ - A₂ - 2·A₃

Which gives;

Area of the shaded region = 100 - 36 - 2×16 = 32

The area of the shaded region is 32

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Answer:

[tex]a_{n}[/tex] = 8 + (n-1)6

Step-by-step explanation:

Answer:

i think 47 minutes

Step-by-step explanation:

hope this helps :)

Answer: 47 minutes

Step-by-step explanation:

There are 60 minutes in an hour, so: 60-46=14

If you add 14 minutes to the original time, then it will be 6:00pm, so that leaves the 33 minutes

Add: 14+33=47

Answer:

The slope of the line is 1/2.

3)

x= 16

4)

x= 51

please ask any questions in the comments below if needed

Answer: 3. 16=X  4. X=51

Step-by-step explanation:

Okay so for number 3, both angles are the same because of the parallel lines, so you can have the angles be equal to each other. Then just do the math. Giving you 16 as the answer

For 4 the angles added up together equal 180 because of the parallel lines. So you have to make them add up and then equal to 180, at the ending the answer is 51.

The function decreasing in the interval will be (-∞, 0) and the function increasing in the interval will be (0, ∞). The function is never increasing is false.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The function decreasing in the interval will be (-∞, 0) and the function increasing in the interval will be (0, ∞).

The function is never increasing is false.

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It will take 84 hours to fill the pool.

Work is the amount of energy transferred to an object by an external force when it is moved over a certain distance.

Given that, an inlet pipe can fill a pool in 12 hours, while and outlet pipe can empty a pool in 14 hours.

Work done by inlet pipe in 1 hour = 1/12

Work done by outlet pipe in 1 hour = 1/14

Let the pool be filled in x hours, so in hour it will fill = 1/x

1/12-1/14 = 1/x

x = 84

Hence, It will take 84 hours to fill the pool.

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