If tan y = 3 over y and cos x = y over z what is the value of sin x??
A. sin x = 3/z
B. sin x = 3y
C. sin x = z/3
D. sin x = 3z

Answer:

answer is b

Step-by-step explanation:

To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645

Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):

x = z s + u

x = 1.645 (15) + 100

x = 24.675 + 100

x = 124.675

Therefore the minimum iq score for the top 5% of the population is around 124.675

The minimum IQ score for the top 5% of the population, with a normal distribution mean of 100 and a standard deviation of 15, is approximately 124.7. This is found by using the z-score that corresponds to the 95th percentile, which is 1.645, and applying it to the formula for a score in a normal distribution.

To determine the minimum IQ score for the top 5% of the population, given that human IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution. Typically, the top 5% of values on a normal distribution lie above a certain z-score threshold. This z-score corresponds to the point on the distribution where the cumulative area to the left is 95% (100% - 5%), since we are looking for the score above which the top 5% of scores fall.

To find this z-score, we look up the value in a standard normal distribution table or use a statistical software or calculator. The z-score that corresponds to the 95th percentile is typically around 1.645. To find the actual IQ score, we can then apply the following formula:

IQ Score = Mean + (Z-score * Standard Deviation)

Plugging the values in:

IQ Score = 100 + (1.645 * 15)

IQ Score = 100 + 24.675

IQ Score = 124.675

Therefore, the minimum IQ score for the top 5% of the population is approximately 124.7 (since IQ scores are usually reported to the nearest whole number).

To solve sec x/2 = cos x/2, we use the identity sec(θ) = 1/cos(θ). After rearranging, we identify the solution as x = 0 and x = 2π, fitting the interval [0, 2π).

To solve the equation sec x/2 = cos x/2 for the interval [0, 2π), we first need to understand the relationship between secant and cosine functions. Recall that sec(θ) is the reciprocal of cos(θ), thus sec(θ) = 1/cos(θ). Given the equation sec x/2 = cos x/2, we can substitute sec x/2 with 1/cos x/2 to get 1/cos x/2 = cos x/2.

Next, to solve for x, we multiply both sides by cos x/2 to get rid of the fraction: 1 = cos^2(x/2). We know that the square of the cosine function can also be related to the identity cos^2(x) = (1 + cos(2x))/2. Applying this identity, we have 1 = (1 + cos x)/2. Solving for cos x, we get cos x = 1, which occurs at x = 0, 2π in the interval [0, 2π). Therefore, the solution to the equation is x = 0 and x = 2π.

The equation sec x/2 = cos x/2 is solved by finding angles where the cosine of half the angle is either 1 or -1. This leads to solutions x = 0 and x = 2pi within the interval [0, 2pi).

To solve the equation sec x/2 = cos x/2 for the interval [0, 2pi), we can make use of trigonometric identities to simplify and solve for x. The secant function is the reciprocal of the cosine function, so sec(x/2) = 1/cos(x/2). This leads to the equation 1/cos(x/2) = cos(x/2). Solving for cos(x/2), we get cos^2(x/2) = 1, which implies that cos(x/2) = ±1. Therefore, we're looking for angles where the cosine of half the angle is either 1 or -1. This corresponds to angles of 0, pi, and 2pi for cos(x/2) = 1, and pi for cos(x/2) = -1, remembering that we are considering x/2 and need to multiply these results by 2 to solve for x. Accordingly, the solution to the equation within the given interval is x = 0, 2pi, and 4pi (which is equivalent to 0 within one full rotation of the circle), but since we're restricting x to be within [0, 2pi), the accepted solutions are x = 0 and x = 2pi.

Final answer:

The length of the diagonal between points K(0,3) and L(4,1) in a parallelogram is calculated using the distance formula, which is 2√5 units.

Explanation:

To find the length of the diagonal between the points K(0,3) and L(4,1), we can use the distance formula, which is derived from the Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) in a coordinate plane is calculated by the formula:

d = √((x2 - x1)² + (y2 - y1)²)

For points K(0,3) and L(4,1), this becomes:

d = √((4 - 0)² + (1 - 3)²)

d = √(16 + 4)

d = √20

d = 2√5

The diagonal's length is 2√5 units.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the Intersecting Chords Theorem which states "when two chords intersect each other inside a circle, the products of their segments are equal".

Applying this theorem, we have

[tex]AE \times EB = CE \times ED[/tex]

Where [tex]AB=AE+EB[/tex] and [tex]CD=CE+ED[/tex], also [tex]AB \cong CD[/tex], which means

[tex]AE+EB=CE+ED[/tex]

However, if both chords are equal, then their arcs are also equal, that's the easiest way to deduct it, that is

[tex]arc(AB) \cong arc(CD)[/tex]

Because an arc is defined by its chord basically, and in this case they are congruent.

Answer:

Step-by-step explanation:

Givens:

Basically, the number of computer sold has to subtracted from the inventory, because those are articles that are going out, after being sold, they won't exist in the inventory anymore.

So, this difference between the existence in the inventory and the number of computer sold is best modelled by the second option, because the number of article sold has to subtracted from the inventory, not in the opposite way as the option A states.

If 220 computers is the existence in the inventory, that's the initial condition, which won't variate, because the number of articles in the inventory is represented by y. Also, if they sell 3 computers per day, the expression would be 3x.

Now, after we sell we take out the articles sold from the inventory, then, the function would be:

y = 220 - 3x

Therefore, option B is the answer.

Answer:

Option B is correct.

The approximate area of regular octagon is, 101 square ft.

Step-by-step explanation:

Given: A regular octagon has a radius of 6 ft and a side length of 4.6 ft.

To find the area of a regular octagon(A) of side length a is given by :

[tex]A=2\cdot(1+\sqrt{2})a^2[/tex]

Given the length of side, a= 4.6 ft

Substitute the value of a=4.6 ft in the given formula of area:

[tex]A=2\cdot(1+\sqrt{2})\cdot(4.6)^2[/tex] or

[tex]A=(2+2\sqrt{2})\cdot (21.16)[/tex] or

[tex]A=(2+2.828)\cdot(21.16)[/tex]

Simplify:

[tex]A=4.828\cdot 21.16 =102.16048[/tex] square ft.

therefore, the approximate area of regular octagon is, 101 square ft

The rate of change in words per minute will be [tex]35[/tex] words per minute.

Rate of change is a rate that tells how one quantity changes in relation to another quantity.

i.e. Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]

We have,

At [tex]4:04[/tex] pm typed [tex]275[/tex] words,

By [tex]4:18[/tex] pm you have [tex]765[/tex] words.

So,

Change in type [tex]= 4:18\ PM -4:04\ PM=14[/tex]

So,

Rate of change [tex]=\frac{Change\ in\ words}{Change\ in\ time}[/tex]

                            [tex]=\frac{765-275}{14}[/tex]

                            [tex]=\frac{490}{14}[/tex]

Rate of change [tex]=35[/tex] words per minute

So, the rate of change is  [tex]35[/tex] words per minute which is given in option [tex](D)[/tex].

Hence, we can say that the rate of change in words per minute will be [tex]35[/tex] words per minute.

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Answer:

AB overbar congruent to CD overbar

Explanation:

The question is asking whether Line segment AB is CONGRUENT to line segment CD.

The meaning of congruent is having the same shape and size.

Congruent ≅

Element ∈

Equal =

Similar ~

In conclusion, you could say:

AB ≅ CD

I cannot type the lines over the top AB and CD but they are there.

(I know this question is probably old, and i am also tying this so I remember as well, but the other answer didn't have a bit bigger explanation so if anyone comes across this i hope this helped. :)

If two or more objects are the same copy in length and shape then that will be said to be congruent thus AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent thus options (B) and (C) is correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

All line segments are in the same shape and have degrees as one in the equation therefore only one criterion which is length is needed to prove congruency.

So, congruent lines are lines whose lengths are the same.

The sign of congruency is ≅ so AB ≅ CD.

Hence " AB overbar is congruent to CD overbar and AB overbar is equal to CD overbar are the equivalent to AB ≅ CD".

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The volume of parallelepiped with 8 vertices is 75 units.

A parallelepiped's volume is determined by multiplying its surface area by its height.

The area of the parallelogram base is the cross product's magnitude, ∥a×b∥ , according to its geometric specification, and the vector a×b direction is perpendicular to the base.

Given:

let the 8 vertices are (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6).

so, Volume = det [tex]|\left[\begin{array}{ccc}0&3&2\\5&0&0\\1&0&5\end{array}\right] |[/tex]

                    = |0( 0- 0) - 3(25- 0) + 2(0 - 0)|

                    = |0 - 75 + 0|

                    = |- 75|

                    = 75 units

Hence, the volume of parallelepiped with 8 vertices is 75 units.

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Answer:

Step-by-step explanation:

the answer is a

Answer:

[tex]\sqrt{113}[/tex] is an irrational number.

Step-by-step explanation:

We are asked to find whether square root of 113 is rational or irrational.

We know that a number is rational number when it can be written as a fraction.

Upon finding the value of [tex]\sqrt{113}[/tex], we will get:

[tex]\sqrt{113}=10.6301458127346[/tex]

We can see that [tex]\sqrt{113}[/tex] has neither non-terminating nor a repeating decimal, therefore, it cannot be written as a fraction and it is an irrational number.

As the sample size increases, the distribution of the sample mean tends to become more normal regardless of the population distribution due to the Central Limit Theorem. The mean of the sampling distribution approaches the population mean, and the standard error decreases, resulting in more reliable statistical analyses.

Effects of Increasing Sample Size on the Distribution of the Sample Mean

As the sample size n increases, the distribution of the sample mean tends to become more normal, even if the population distribution is not normal. This is a result of the Central Limit Theorem, which states that the sampling distribution of the mean approaches a normal distribution as n, the sample size, increases. According to the law of large numbers, the mean of the sample means will get closer to the population mean as sample size grows.

When the population is skewed right and we take a simple random sample, the original distribution being non-normal requires a larger sample size to make the sample mean distribution resemble a normal distribution. Generally, sample sizes equal to or greater than 30 are considered sufficient for the sampling distribution to be normal; however, if the original population distribution is further from a normal curve, a larger sample size may be needed to achieve normality.

The practical implication of this is that as sample size increases, the variability (as measured by the standard error) of the sample mean decreases, and this results in a sampling distribution that is more tightly clustered around the true population mean. Therefore, statistical analyses and predictions become more reliable with larger samples.

Look at the picture.

Answer: A. (3.5, -4)

p=(5.25-5.00)/5.00

p=0.25/5.00

p=0.05

p = 5% increase

To find the perpendicular line's equation, first find the negative reciprocal of the original line's slope. Next, use the point-slope form with the given point. Lastly, rearrange the equation into standard form, resulting in x + 4y = 22.

To find the equation of a line that is perpendicular to another line and passes through a given point, you need to perform a series of steps. The first line's equation is given as 4x - y = 2. Firstly, solve for y to put it in slope-intercept form, y = mx + b. Here, the equation becomes y = 4x - 2, so the slope (m) is 4. The slope of the perpendicular line will be the negative reciprocal of this, which is -1/4.

The next step is to use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is the point through which the line passes. For the point (2,5), the equation of the line is y - 5 = -1/4(x - 2). Multiplying both sides by 4 to clear the fraction gives 4y - 20 = -x + 2.

Finally, rearrange the equation to get it into standard form, Ax + By = C, giving us x + 4y = 22. This is the standard form of the equation we were seeking.