Can anyone please help ASAP, will give thanks and all that fun stuff

To prove this Pythagorean Identity, we have to know that:

cot = 1 / tan

and we also know that:

tan = sin / cos

Therefore,

cot = 1 / tan = cos / sin

So we can write the given equation in the form of:

1 + (cos^2 θ / sin^2 θ) = csc^2 θ

Expanding the left hand side of the equation:

(sin^2 θ / sin^2 θ) + (cos^2 θ / sin^2 θ) = csc^2 θ

(sin^2 θ + cos^2 θ) / sin^2 θ = csc^2 θ

We know that given a unit circle, sin^2 θ + cos^2 θ = 1. So:

1 / sin^2 θ = csc^2 θ

The equation above is already true basing on the trigonometric identities. Therefore:

csc^2 θ = csc^2 θ

Answer:

The vertex J' is at (-8,1).

Step-by-step explanation:

If is given that the triangle JKL reflected once to map onto triangle J'K'L'.

The vertices of the triangle JKL are J(8,1), K(5,7) and L(3,4). The vertex L'(-3,4).

[tex]L(3,4)\rightarrow L'(-3,4)[/tex]

It is in the form of

[tex](x,y)\rightarrow (-x,y)[/tex]

Since the y-coordinate remains same and the sign of x coordinate is changed. It shows the reflection across the y axis.

The vertices of image are,

[tex]K(5,7)\rightarrow K'(-5,7)[/tex]

[tex]J(8,1)\rightarrow J'(-8,1)[/tex]

Therefore the vertex J' is at (-8,1).

There are 4,356,000 different passwords are possible.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A phone banking password consists of 2 letters followed by 4 digits.

And, The letters B, I, S, and O are not used, and the last digit cannot be 0.

Hence, We can formulate;

Number of different passwords are possible are,

⇒ 22 × 22 × 10× 10 × 10 × 9.

⇒ 4,356,000

Thus, There are 4,356,000 different passwords are possible.

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The answer is 222

All you do is multiply 500 by 0.15, which gives you 75. Then subtract that from 500 to give you 425. Now multiply this 425 by 0.15 then subtract the product form 425. Continue this process until it is done 5 times. Your answer on the fifth time will be your answer.

The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.

The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.

Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.

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The explicit formula for this geometric sequence is: a_n = 3 (-2)^{n-1}. he common ratio is negative, so the domain is all odd positive integers.

Explicit formula:

The explicit formula for a geometric sequence is of the form: a_n = a_1 r^{n-1}

In this case, the first term is 3 and the common ratio is −2. Therefore, the explicit formula for this geometric sequence is:

a_n = 3 (-2)^{n-1}

Restrictions to the domain:

The domain of a geometric sequence is all positive integers, unless the common ratio is negative. In this case, the common ratio is negative, so the domain is all odd positive integers.

Example:

Using the explicit formula, we can find the fourth term of the sequence as follows:

a_4 = 3 (-2)^{4-1} = 3 (-2)^3 = -24

We can also verify that the domain of the sequence is all odd positive integers by checking the first few terms:

n | a_n

1 | 3

2 | -6

3 | 12

4 | -24

5 | 48

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Answer:

-8

Step-by-step explanation:

Given : [tex]y=-200-12(x)[/tex]

To Find:What is the y-value when x equals -16?

Solution:

We are given that You're studying different function tools and begin working with this function:

[tex]y=-200-12(x)[/tex]

Now we are supposed to find the value of y when x is -16

So, substitute x = -16 in the equation

[tex]y=-200-12(-16)[/tex]

[tex]y=-200+192[/tex]

[tex]y=-8[/tex]

So, Value of y is -8

Hence the y-value when x equals -16 is -8

Answer:

Answer: 20°

Step-by-step explanation:

In given table of exponential function,

The interval between neighboring  x-values is of 1 unit.

The ratio is  4  between neighboring y-values

Observing given table.

To find  interval between neighboring  x-values . We have to take difference between consecutive x - values.

[tex]1-0=2-1=3-2=4-3=5-4=1[/tex]

Since, in every consecutive x- values , difference of 1 is present.

So, The interval between neighboring  x-values is of 1 unit.

To find ratio between neighboring y-values , we have to take ratio of consecutive y - values.

     [tex]\frac{4}{1}=\frac{16}{4}=\frac{64}{16}=\frac{256}{64}=4[/tex]

Thus, The ratio is  4  between neighboring y-values

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One bottle has a height of 12 centimeters or 12 cm. Let us call this h1, so h1 = 12 cm

While the other bottle has a height of 15 centimeters or 15 cm. Let us call this h2, so h2 = 15 cm

The difference in height can be calculated by subtracting the smaller number from the bigger number, therefore:

difference in height = h2 – h1

difference in height = 15 cm – 12 cm

difference in height = 3 cm

We know that in 1 meter there is:

1 meter = 100 centimeters = 1000 millimeters

Therefore,

difference in height = 3 cm (1000 millimeters / 100 centimeters)

difference in height = 30 mm

Answer:

difference in height = 30 mm

Final answer:

Approximately $17.86 is spent on gas each day.

Explanation:

To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.

First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.

Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86

Therefore, approximately $17.86 is spent on gas each day.

The solution would be like this for this specific problem:

H0: p = p0, or 
H0: p ≥ p0, or 
H0: p ≤ p0 

find the test statistic z = (pHat - p0) / sqrt(p0 * (1-p0) / n) 

where pHat = X / n 

The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis. 
H1: p ≠ p0; p-value is the area in the tails greater than |z| 
H1: p < p0; p-value is the area to the left of z 
H1: p > p0; p-value is the area to the right of z 

Hypothesis equation:

H0: p ≥ 0.67 vs. H1: p < 0.67 

The test statistic is: 
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 ) 
z = -1.538681 

The p-value = P( Z < z ) 
= P( Z < -1.538681 ) 
= 0.0619

When a point in quadrant 2 is rotated 180 degrees counterclockwise, it will land in quadrant 4.

A point lies in quadrant 2. If it is rotated 180 degrees counterclockwise, which quadrant will the point come to rest?