sin(5x)sin(3x)
Express the given product as a sum or difference containing only sines or cosines.

Answer:

The average absolute deviation (or mean absolute deviation (MAD)) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be the mean, median, mode, or the result of any other measure of central tendency or any random data point related to the given data set. The absolute values of the difference, between the data points and their central tendency, are totaled and divided by the number of data points.

Measures of dispersion

Edit

Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.

Mean absolute deviation around a central point

Edit

For arbitrary differences (not around a central point), see Mean absolute difference.

The mean absolute deviation of a set {x1, x2, ..., xn} is

{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.} \frac{1}{n}\sum_{i=1}^n |x_i-m(X)|.

The choice of measure of central tendency, {\displaystyle m(X)} m(X), has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:

Mean Absolute Deviation (MAD) is a measure of the average distance between each data point and the mean of the dataset. It is calculated by finding the absolute value of the difference between each data point and the mean, and then averaging those differences. MAD is a robust statistic, less sensitive to outliers compared to standard deviation.

Mean Absolute Deviation (MAD) is a statistical measure used to quantify the average deviation of data points from the mean or average of the dataset. To calculate MAD, you follow these steps:

The mean is the sum of all data divided by the number of data points, while the median is the middle value of an ordered dataset. MAD is more robust than standard deviation as it is not affected as much by extreme values. For example, if we have a dataset of exam scores, the standard deviation tells us how scores are spread out from the mean, which could be influenced by extremely high or low scores. On the other hand, MAD gives us a measure of spread that is more resilient to outliers in the data.

Relative Average Deviation (RAD) is similar to MAD, but it expresses the deviation as a percentage of the mean and hence provides a relative measure of spread.

Answer:

The process below should work.

Step-by-step explanation:

Let's pretend we have these two points we are trying to find an exponential equation for:  (-2,6) and (2,1).

Exponential equations are of the form [tex]y=a \cdot b^x[/tex] where we must find [tex]a[/tex] and [tex]b[/tex].

So you enter both points into that equation giving you:

[tex]6=a \cdot b^{-2}[/tex]

[tex]1=a \cdot b^{2}[/tex]

I'm going to divide equation 1 by 2 because if I do the a's will cancel and I could solve or b.

[tex]\frac{6}{1}=\frac{a \cdot b^{-2}}{a \cdot b^2}[/tex]

[tex]6=\frac{b^{-2}}{b^2}[/tex]

By law of exponent, I can rewrite the right hand side:

[tex]6=b^{-2-2}[/tex]

[tex]6=b^{-4}[/tex]

Now do ^(-1/4) on both sides to solve for b:

[tex]6^\frac{-1}{4}=b[/tex]

Now we use one of the equations along with our value for b to find a:

[tex]1=a \cdot b^2[/tex] with [tex]b=6^{\frac{-1}{4}}[/tex]

[tex]1=a \cdot (6^{\frac{-1}{4}})^2[/tex]

Simplify using law of exponents:

[tex]1=a \cdot 6^{-\frac{1}{2}}[/tex]

Multiply both sides by 6^(1/2) to solve for a:

[tex]6^{\frac{1}{2}}=a[/tex]

[tex]y=a \cdot b^x[/tex] with [tex]a=6^{\frac{1}{2}} \text{ and } b=6^{\frac{-1}{4}}[/tex] is:

[tex]y=6^\frac{1}{2} \cdot (6^{\frac{-1}{4})^x[/tex]

We can simplify a smidgen:

[tex]y=6^\frac{1}{2} \cdot (6)^\frac{-x}{4}[/tex]

Answer:

12 hours

Step-by-step explanation:

If you divide 168 by 8, you get 21 which is the rate that Austin receives for every hour of work. Then divide 252 by 21 to find how many hours he worked and you get the answer, 12.

Answer: option b

on edg guys:))

Step-by-step explanation:

y ^2/3

Answer:

25,095238095 = 25 2⁄21

Step-by-step explanation:

Just multiply each denominator and numerator straight across and convert to a mixed number, decimal, or whatever you want.

I am joyous to assist you anytime.

Answer:

6.

Step-by-step explanation:

14x=84

x=84÷14

x=6

Hope this helps!

Answer:

x=6

Step-by-step explanation:

14x = 84

Divide each side by 14

14x/14 = 84/14

x =6

Answer:

Slope: [tex]\frac{3}{5}[/tex]

Y-intercept: -3

Equation: [tex]y=\frac{3}{5} x-3[/tex]

Graph is attached.

Step-by-step explanation:

To find your slope using two points, use the slope formula.

[tex]\frac{y2-y1}{x2-x1} \\[/tex]

Your y1 is -6, your y2 is 3.

Your x1 is -5, your x2 is 10.

[tex]\frac{3-(-6)}{10-(-5)} \\\\\frac{9}{15} \\\\\frac{3}{5} \\[/tex]

Now that you have your slope, use it and one of your points in point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-3=\frac{3}{5} (x-10)\\y-3=\frac{3}{5} x-6\\y=\frac{3}{5} x-3[/tex]

Answer:

A. In the graph,

Go 5 units left side from the origin in the x-axis then from that point go downward 6 unit, we will get (-5, -6),

Now, go 10 unit right from the origin in the x-axis then from that point go upward 3 unit, we will get (10, 3),

B. The slope of the line passes through (-5, -6) and (10, 3),

[tex]m=\frac{3-(-6)}{10-(-5)}=\frac{3+6}{10+5}=\frac{9}{15}=\frac{3}{5}[/tex]

C. Since, the equation of a line passes through [tex](x_1, y_1)[/tex] with slope m is,

[tex]y-y_1=m(x-x_1)[/tex]

Thus, the equation of the line is,

[tex]y+6=\frac{3}{5}(x+5)----(1)[/tex]

For y-intercept,

x = 0,

[tex]y+6 = \frac{3}{5}(0+5)\implies y = 3-6=-3[/tex]

That is, y-intercept is -3.

D. From equation (1),

[tex]5y + 30 = 3x + 15[/tex]

[tex]\implies 3x - 5y = 15[/tex]

Which is the required linear function.

Answer:

Yes. These outcomes are mutually exclusive; they cannot occur simultaneously in one spin of the wheel.

Step-by-step explanation:

It's the answer trust

Answer:

[tex]8.33\%[/tex]

Step-by-step explanation:

we know that

The total removed by milling is equal to (3.00"-2.75")=0.25"

In this problem 3.00" represent the 100%

so

using proportion

Find out how much percentage represent the total removed by milling

[tex]\frac{3.00}{100}=\frac{0.25}{x}\\\\x=100*0.25/3.00\\\\x=8.33\%[/tex]

Final answer:

To find the percentage of the block removed by milling, subtract the final size from the original size, divide by the original size, and multiply by 100. A 0.25" reduction from a 3.00" block represents an 8.33% decrease.

Explanation:

The question asks us to calculate the percentage of material removed from a block through the milling process. To find the percentage reduction, we start by determining the difference in size before and after the milling, which is 3.00" - 2.75" = 0.25". The next step is to divide the amount removed by the original size and then multiply by 100 to get the percentage. The calculation is as follows:

Find the difference: 3.00" - 2.75" = 0.25" (amount removed)

Calculate the percentage: (0.25" / 3.00") × 100 = 8.33%

Therefore, 8.33% of the original block is removed by milling.

Answer:

[tex]\large\boxed{(f-g)(x)=4^x+x+5}[/tex]

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=4^x+3x,\ g(x)=2x-5\\\\(f-g)(x)=(4^x+3x)-(2x-5)=4^x+3x-2x+5=4^x+x+5[/tex]

Answer:

Infinitely Many

Step-by-step explanation:

Equations:

y = 5 - 2x

4x + 2y = 10

There are multiple ways to solve this, but I'm going to use substitution.

Since y = 5 - 2x, I will input this y value into the second equation.

4x + 2(5 - 2x) = 10

From here, it's simple algebra.

4x + 10 - 4x = 10

     - 10         - 10

4x - 4x = 0

0x = 0

Because we essentially have the solution 0 = 0, this means that the system has an infinite amount of solutions.

Why?

Well, they're the same line. (Put both into slope intercept form.)

y = 5 - 2x OR y = -2x + 5

4x + 2y = 10

2y = -4x +10

=                     y = -2x + 5

Answer:

INFINITE  SOLUTIONS.

Step-by-step explanation:

y = 5 - 2x

4x + 2y = 10

From the first equation:

2x + y = 5         Multiply this equation by -2:

-4x - 2y = -10

Adding the above to the second equation:

0 = 0   So the 2 equations are identical and  there are Infinite  SOLUTIONS>

Answer:

4names: z3, zt, zstu, zuts

Answer: [tex]15.5\ mm^2[/tex]

Step-by-step explanation:

You can calculate the area of a kite with the following formula:

[tex]A=\frac{d_1d_2 }{2}[/tex]

Where [tex]d_1[/tex] is the length of a diagonal and [tex]d_2[/tex] is the length of the other diagonal.

In this case, you can identify that:

[tex]d_1=6.2\ mm\\d_2=5\ mm[/tex]

Therefore, the final step is to substitute the values into the formula.

Then, the area is:

 [tex]A=\frac{(6.2\ mm)(5\ mm)}{2}\\\\A=15.5\ mm^2[/tex]

Answer:

Step-by-step explanation:

[tex]\text{The formula of a distance between x and y on a number line:}\\\\d=|b-a|=|a-b|\\\\\text{We have}\ a=\dfrac{5}{2}\ \text{and}\ b=4\dfrac{7}{8}.\ \text{The distance:}\\\\d=\left|\dfrac{5}{2}-4\dfrac{7}{8}\right|=\left|4\dfrac{7}{8}-\dfrac{5}{2}\right|}[/tex]

Answer:

none of the above

Step-by-step explanation:

Answer:

When proving identities, the answer is in the explanation.

Step-by-step explanation:

[tex]\frac{\cos(y)}{1-\sin(y)}[/tex]

I have two terms in this denominator here.

I also know that [tex]1-\sin^2(\theta)=\cos^2(theta)[/tex] by Pythagorean Identity.  

So I don't know how comfortable you are with multiplying this denominator's conjugate on top and bottom here but that is exactly what I would do here.  There will be other problems will you have to do this.

[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]

Big note here: When multiplying conjugates all you have to do is multiply fist and last.  You do not need to do the whole foil.  That is when you are multiplying something like [tex](a-b)(a+b)[/tex], the result is just [tex]a^2-b^2[/tex].

Let's do that here with our problem in the denominator.

[tex]\frac{\cos(y)}{1-\sin(y)} \cdot \frac{1+\sin(y)}{1+\sin(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{(1-\sin(y))(1+\sin(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{1^2-\sin^2(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{1-\sin^2(y)}[/tex]

[tex]\frac{\cos(y)(1+\sin(y))}{cos^2(y)}[/tex]

In that last step, I apply the Pythagorean Identity I mentioned way above.

Now You have a factor of cos(y) on top and bottom, so you can cancel them out.  What we are really saying is that cos(y)/cos(y)=1.

[tex]\frac{1+\sin(y)}{cos(y)}[/tex]

This is the desired result.

We are done.

So, the inequality in slope-intercept form is [tex]\( y \geq 2x - 15 \).[/tex]

To write the given inequality in slope-intercept form [tex](y = mx + b)[/tex], let's first isolate the y term:

[tex]-6x + 3y \geq -45[/tex]

Add 6x to both sides:

[tex]3y \geq 6x - 45[/tex]

Now, divide both sides by 3:

[tex]y \geq 2x - 15[/tex]

[tex]\[\begin{align*}\frac{3y}{3} & \geq \frac{6x}{3} - \frac{45}{3} \\y & \geq 2x - 15\end{align*}\][/tex]

Answer:

B., D., E.

Step-by-step explanation:

[tex] \sqrt{9} \cdot \sqrt{100} = [/tex]

[tex] = \sqrt{9 \cdot 100} [/tex]      This is choice B.

[tex] = \sqrt{900} [/tex]          This is choice E.

[tex] = 30 [/tex]              This is choice D.

Answer:

d

Step-by-step explanation:

Definitely choose the point-slope form y - k = m(x - h) (Answer d)

Final answer:

To write the equation of a line when you have the slope and a single point on the line, the D) point-slope form is the most suitable formula to use.

Explanation:

When you know the slope of a line and a point on the line, the best form to use is the point-slope form. The point-slope formula is expressed as y - y1 = m(x - x1), where m is the slope and (x1, y1) is the known point. This formula allows you to plug in the slope and the coordinates of the point directly to form the equation of the line.

The slope-intercept form y = mx + b is used when you know the slope and the y-intercept, while the point-slope form is specifically designed to formulate an equation given a point and the slope of the line. A horizontal line, which has a slope of zero, nor a vertical line, which has an undefined slope, would not apply to this particular situation.

For this case we have that[tex]\frac {1} {4}[/tex]of the songs are jazz.

The total songs are 100.

So:

[tex]\frac {1} {4} = 0.25\\\frac {3} {4} = 0.75[/tex]

This tells us that 25% of the songs are jazz and 75% of the songs are pop.

[tex]\frac {1} {4} + \frac {3} {4} = \frac {4} {4} = 1[/tex]

So, the correct option is option D.

Answer:

Option D

Answer:

You should choose an account with a 7% annual interest rate which is compounded quarterly

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

part 1)

we have  

[tex]t=15\ years\\ P=\$14,000\\ r=0.07\\n=4[/tex]  

substitute in the formula above  

[tex]A=14,000(1+\frac{0.07}{4})^{4*15}[/tex]

[tex]A=14,000(1.0175)^{60}[/tex]  

[tex]A=\$39,645.43[/tex]  

part 2)

we have  

[tex]t=15\ years\\ P=\$14,000\\ r=0.068\\n=12[/tex]  

substitute in the formula above  

[tex]A=14,000(1+\frac{0.068}{12})^{12*15}[/tex]

[tex]A=14,000(1.0057)^{180}[/tex]  

[tex]A=\$38,713.11[/tex]  

Answer:

The correct option is D

Step-by-step explanation:

To find the solution of this problem firstly we will find the probability that some one is in the brass section and play trombone.

We will multiply the probability that a member is in the brass section which is 0.50 with the probability that a member plays trombone, given that he or she is in the brass section which is 0.36

= 0.50 * 0.36

=0.18

Therefore the probability that a randomly selected band member is in the brass section and plays trumpet is 0.18

Thus the correct option is D....

Answer:

D

Step-by-step explanation:

Answer:

sin^-1 (1/2) = 30°

Step-by-step explanation:

* Lets explain how to find the trigonometry functions from the unit circle

- The unit circle is the circle whose radius is 1 unit

- It intersects the four axes at:

# Positive part of x-axis at (1 , 0) and negative part at (-1 , 0)

# Positive part of y-axis at (0 , 1) and negative part at (0 , -1)

- The terminal of any angle intersect it at point (x , y) where x² + y² = 1

- If The angle between the terminal side and the x-axis is Ф , then

# The adjacent side of Ф = x

# The opposite side of the angle Ф = y

- In the problem the terminal side lies in the first quadrant

∴ all the trigonometry functions are positive

∵ sin Ф = opposite/hypotenuse

∵ The opposite = 1/2 and the hypotenuse is the terminal side = 1

∴ sin Ф = 1/2 ÷ 1 = 1/2

- To find Ф use the inverse function sin^-1 Ф

∵ sin Ф = 1/2

∴ Ф = sin^-1 (1/2)

∴ Ф = 30°

* sin^-1 (1/2) = 30°

Answer:

8 is the only one that will work

Step-by-step explanation:

(f o g)(x)=f(g(x)).

So this means the x will first be plug into g.

So let's check your choices.

g(6)=1/(6-6)=1/0 so 6 is not in the domain of g which means it isn't in the domain of (f o g).

g(8)=1/(8-6)=1/2  so this is a number so 8 is in the domain of g,

Let's check if 1/2 is in the domain of f.

f(1/2)=sqrt(6*1/2)=sqrt(3) so this is a number so since 1/2 is in the domain of f then 8 is in the domain of (f o g).

g(4)=1/(4-6)=1/(-2)=-1/2 so 4 is in the domain of g,

f(-1/2)=sqrt(6*-1/2)=sqrt(-3) so this is a problem because you can't square root negative numbers so -1/2 isn't in the domain of f, and therefore 4 isn't in the domain of (f o g).

g(2)=1/(2-6)=1/-4=-1/4 so 2 is in the domain of g.

f(-1/4)=sqrt(6*-1/4)=sqrt(-3/2) so again this is a problem because we can't square root negative numbers so -1/4 isn't in the domain of f, and therefore 2 isn't in the domain of (f o g).

Answer:

6 and x

Step-by-step explanation:

h(-4)

=|-4-2|

=|-6|

=6

.

h(-x+2)

=|-x+2-2|

=|-x|

=x

Answer:

c

Step-by-step explanation:

Answer:

[tex]M=-\frac{d^2F}{kn}[/tex]

Please look at what I assumed your equation was:  [tex]F=-\frac{kMn}{d^2}[/tex].

Step-by-step explanation:

I'm going to pretend that says:

[tex]F=-\frac{kMn}{d^2}[/tex].

Please correct me if I'm wrong.

We want to solve for M.

The very first thing I'm going to do is multiply both sides by [tex]d^2[/tex].

[tex]d^2F=-kMn[/tex]

Now I'm going to divide both sides by -kn:

[tex]\frac{d^2F}{-kn}=\frac{-kMn}{-kn}[/tex]

Simplifying:

[tex]\frac{d^2F}{-kn}=M[/tex]

Sometimes people don't like the negative on bottom; just move it to the center:

[tex]-\frac{d^2F}{kn}=M[/tex]

[tex]M=-\frac{d^2F}{kn}[/tex]

Answer:

0.1056

Step-by-step explanation:

Given from the question;

Mean=125cm

Standard deviation =12cm

You should find the z* value from  mean and standard deviation

The formula to apply is;

z=(wingspan in question - mean)÷standard deviation

[tex]z=\frac{140-125}{12} =\frac{15}{12} =1.25[/tex]

Using the Z score table read the value of proportion that corresponds to 1.25

From the table, the proportion is 0.1056

Answer:$96.75

Step-by-step explanation:

Answer: $64.5

Step-by-step explanation:

First let’s do 40% of 150 (40%=4/10): 4/10*150=60

The price of the bike is $60

7.5%=7.5/100, however we cannot have a decimal in a fraction so we multiply by 2/2 and get 15/200.

Next let’s multiply 60 by 15/200: 6*15/200=4.5

Then we add 60 which is the price of the bike, with 4.5, which is the tax to get the total of $64.5

Answer:

See below.

Step-by-stepexplanation:

The slope = rise/run

= (7- -5)/(-3-1)

=  12/-4

= -3

In point slope form:

y - y1 = -3(x - x1)

y - (-5) = -3(x - 1)

y + 5 = -3(x - 1) <--------- Point slope form.

y + 5 = -3x + 3

y = -3x - 2. <----------Slope-intercept form.

Answer:

y = -3x - 2

Step-by-step explanation:

If a line passes through (1.-5) and (-3, 7), the appropriate equation for the line in point-slope form is, y = -3x - 2.