Consider the following data set with a mean of 12: 9,11,12,16 using the standard deviation formula calculate the standard deviation for this data set

The unit circle is best suited for dealing with angles and trigonometric functions of multiple angles, right triangles are best for finding the lengths of the sides of triangles with a right angle, and trigonometric identities are best for simplifying or manipulating trigonometric expressions.

Each tool has its own strengths and weaknesses and is better suited for certain types of problems.

Unit Circle is a powerful tool used to relate angles to trigonometric functions. It is particularly useful when dealing with angles in radians, as it allows for easy conversion between radians and degrees. The unit circle is also useful when dealing with trigonometric functions of multiple angles, such as sine and cosine of the sum or difference of two angles.

A good example will be if we want to find the exact value of sin(π/6), we can use the unit circle to visualize the angle π/6, which corresponds to 30 degrees. The unit circle tells us that at this angle, sin(π/6) = 1/2.

Right triangles are useful when we have a right angle in the triangle, as they allow us to use the Pythagorean theorem and trigonometric ratios to find the lengths of the sides of the triangle. Right triangles are particularly useful when we know one angle and one side length, as we can use trigonometric ratios such as sine, cosine, and tangent to find the lengths of the other sides.

If we have a right triangle with an angle of 30 degrees and a hypotenuse of 2, we can use the sine ratio to find the length of the opposite side. sin(30) = opposite/hypotenuse, so opposite = sin(30) * 2 = 1.

Trigonometric identities are useful when we want to simplify or manipulate trigonometric expressions. These identities are derived from the definitions of the trigonometric functions and can be used to simplify complex expressions or prove trigonometric identities.

For example, we can use the identity:

sin²(x) + cos²(x) = 1

to simplify the expression

sin²(x) - cos²(x).

We can rewrite this expression as:

sin²(x) - cos²(x) = sin²(x) + (-1)*cos²(x)

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Answer:

Answer:

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Step-by-step explanation:

Given

[tex]Pennies = 22[/tex]

[tex]Dimes = 27[/tex]

[tex]Nickels = 9[/tex]

[tex]Quarters = 30[/tex]

Required

[tex]P(Penny\ and\ Dime)[/tex]

This is calculated as:

[tex]P(Penny\ and\ Dime) = P(Penny) * P(Dime)[/tex]

Since it is a selection without replacement, the computation is:

[tex]P(Penny\ and\ Dime) = \frac{Penny}{Total} * \frac{Dime}{Total-1}[/tex]

So, we have:

[tex]P(Penny\ and\ Dime) = \frac{22}{22+27+9+30} * \frac{Dime}{22+27+9+30-1}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{22}{88} * \frac{27}{87}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{1}{4} * \frac{9}{29}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Step-by-step explanation:

For the first one, you have the -2 step right, but now we're at

f(x) -2 = x³

We have to take the cube root of each side to solve for x, which looks like

∛(f(x)-2) = x or (f(x)-2)^(1/3) = x. This makes our inverse function ∛(x-2) Putting a 3 to the side multiplies the value by 3, and doesn't cube root it.

For your next incorrect answer, you simply need to plug the inverse function that I just gave in.

For the one after that, the question is asking to plug in f(x). We know that our inverse is ∛(x-2) , and the question is asking to plug f(x) in for x here. Thus, in the box, simply put down x³+2

For the last incorrect answer, we need to find the cube root of something, and by plugging in f(x) into the previous one, we are left with ∛(x³+2-2). Therefore, in the box, simply put down x³ as that is what's left

Answer:

c+12<16

c=16-12

c=4

answer is this

Step-by-step explanation:

simplify

8 add (12 subtract 5)

Step-by-step explanation:

13) Second angle (side shared)

14) Second side (one side shared)

15) Second side (angles where they meet are equal)

16) Second angle (one angle equal cause of a rule)

17) Third side

18) Second side

Answer:

(a) Amplitude = 4

(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period

(c)

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

Step-by-step explanation:

Given

[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]

Rewrite the function as:

[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]

Solving (a): The amplitude

A cosine function is represented as:

[tex]f(x) = A\cos[B(x - C)] + D[/tex]

Where:

[tex]|A| \to Amplitude[/tex]

So, in this equation (by comparison):

[tex]|A| = |-4|[/tex]

[tex]|A| = 4[/tex]

The amplitude is 4

Solving (b): The period (T)

This is calculated as:

[tex]T = \frac{2\pi}{B}[/tex]

By comparison:

[tex]B =3[/tex]

So:

[tex]T = \frac{2\pi}{3}[/tex]

Solving (c): The shift

The phase shift is C

The vertical shift is D

By comparison:

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

The amount of time needed to complete a job by 5 workers is

40 minutes.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

The amount of time needed to complete a job, t, varies inversely with the number of workers.

Number of workers = W

Time to complete 1 work  = T

This means,

T = 1 / W

W = 1 / T

10 workers can complete a job in 20 minutes.

This can be written as:

10 W = 1 / 20

Divide 10 on both sides.

1 W = 1 / 200

This means,

1 worker can complete a job in 200 minutes.

Now,

1 W = 1/ 200

Multiply 5 on both sides.

5 W = 5/200

5 W = 1 / 40

This means 5 workers will take 40 minutes to complete the work.

Thus,

The amount of time needed to complete a job by 5 workers is

40 minutes.

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Answer:

x < 3

Step-by-step explanation:

Given

4x - 7 < 5 ( add 7 to both sides )

4x < 12 ( divide both sides by 4 )

x < 3

Answer:

$325.50, mentioned methods below.

Step-by-step explanation:

55% means it increases by 55%.  an increase of 50% is basically taking half of the original amount .  So a 50% increase of 4 would be 4 + .5*4 = 4+2 = 6

So for 210 that's 210 + .55*210 = 325.50

You could also factor to make it a little simpler.

210 + .55*210 = 325.50

210(1 + .55) = 325.50

210*1.55 = 325.50

.55 = 55/100 = 11/20

Answer:

hope it's helpful for you

Hi, I'm so sorry I can't answer that. but I have something you can answer that. Search in browser or anything searcher that you have "Quickmath" or "Cymath" all your equations,problems can solved

Step-by-step explanation:

i hope it helps

Answer: 1.345714286

Step-by-step explanation:

This is the full answer, if you want to round it up. Then your welcome to do so.

-125

BEDMAS, like its counterpart BODMAS, is used as an acronym which gives the order of precedence of certain mathematical operations. It stands for:

B - Brackets

E - Exponentials

D - Division

M - Multiplication

A - Addition

S - Subtraction

This specifies the order in which arithmetic operations take place. That is brackets expressions should be solved first, followed by exponentials, then division and so on.

Using BEDMAS, let's solve 9+10-8(9)x2

Follow these steps;

i. Solve the bracket first.

9+10-72x2

ii. Next solve the multiplication

9+10-144

iii. Then solve the addition

19-144

iv. Now, the subtraction

-125

Therefore;

9+10-8(9)x2 = -125 using bedmas

Answer:

294 in

Step-by-step explanation:

set a ratio w/l

11/14

set it equal to 231/x

x = length

[tex]\frac{11}{14}[/tex] = [tex]\frac{231}{x}[/tex]

cross multiply

11x = 3234

divide by 11

x = 294

Answer:

I think the answer is the sequence is arithmetic because the term have a common difference

The correct option is The sequence is not arithmetic because the terms do not have a common difference.

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k called the common difference.

Given is graph, we need to conclude the true about the graph,

Finding the common difference,

4-1 = 3    

9-4 = 5

16-9 = 7

25-16 = 9

Clearly from the set of values that are given in the graph we could observe that the function that is formed using these set of values is:

y=f(n)=n² where n=1,2,3,4,5,.....

That mean, the following sequence is not an arithmetic sequence as the common difference is different.

Hence, the correct option is The sequence is not arithmetic because the terms do not have a common difference.

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Answer:

(x-3) * (x-2

Step-by-step explanation:

Answer:

Tips or taxes add money to a bill. This is the same as a markup. Markdowns are the same as discounts.Step-by-step explanation:

Answer:

Treatment variable = Teaching methods

Confounding variable = Teacher's teaching prowess

Step-by-step explanation:

The treatment variable here is that variable which is applied on the student in other to ovtujba measure of the dependent or response variable, the response variable here is the test score, while the treatment variable is the independent variable, which are the teaching methods.

The confounding variable is that variable which is capable of causing a spurious association in our measurement and also has an effect on the test score. However, this variable isn't taken into account during our experiment. One possible confounding variable could be the Teacher's individual teaching prowess regardless of the teaching method. This could cause the student to get a better grasp of what is being taught by one teacher than the other.

Answer:Treatment variable = Teaching methods

Confounding variable = Teacher's teaching prowess

Step-by-step explanation:

Answer:

option : b, c

Step-by-step explanation:

1 meter = 100 centimeters

45 meters = 4500 centimeters

1000 meter = 1 kilometer

 [tex]45 \ meters = \ \frac{45}{1000} = 0.045 \ kilometers[/tex]

1 meter = 1000 millimeters

45 meters = 45, 000 millimeters

Answer:

x = 1.7

Step-by-step explanation:

Answer:

[tex]4 ^{-3}[/tex]

or

[tex]\frac{1}{4^3}[/tex]

or

[tex]\frac{1}{64}[/tex]

Step-by-step explanation:

four to the negative power of 3 is =  4⁻³

Step-by-step explanation:

The answer is A (the first one). 4 to the negative 3rd power is 4^-3

Answer:

its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.

Step-by-step explanation:

Answer:

[tex]{ \boxed{ \bf{formular : } \: \tt{perimeter = 2(length + width)}}} \\ perimeter = 2((4x + 14) + (2x - 9)) \\ perimeter = 2(6x + 5) \\ perimeter = 12x + 10 \\ \\ { \tt{expression : 12x + 10}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

sorry, I can help with this question but the question is cut off on the right, reply to me with the full question and id be happy to help :)

Answer:

Step-by-step explanation:

Answer:

16π/9

Step-by-step explanation:

the area of sector= ¼×π.r²

= ¼× π× (8/3)²

= ¼×64/9×π

= 16π/9

Answer:

Answer:

16π/9

Step-by-step explanation:

the area of sector= ¼×π.r²

= ¼× π× (8/3)²

= ¼×64/9×π

= 16π/9

Step-by-step explanation:

Answer:

1. The correct option is:

B. H0: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.

Ha: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

2. The test statistic is -0.97.

3. The correct option is E. We fail to reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

Step-by-step explanation:

Note: This question is not complete and it contains some inconsistency errors in thee data. The correct complete question is therefore provided before answering the question. See the attached pdf for the correct complete question.

The explanation of the answer is now provided as follows:

1. State the null and alternative hypotheses.

Since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is:

B. H0: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.

Ha: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

2. What is the test statistic?

Note: See the attached excel file for the calculation of total of (f1 * x), total of (f2 * x), total of (f1 * x^2) and total of (f2 * x^2).

From the attached excel file, we have:

N2 = Total of f2 = Sample size of Hospital = 150

M1 = Mean of Private-Practice = Total of (f1 * x) / N1 = 38.40

M2 = Mean of Hospital = Total of (f2 * x) / N2 = 43.60

S1^2 = Variance of Private-Practice = Total of (f1 * x^2) / N1 = 1,541.00

S2^2 = Variance of Hospital = Total of (f2 * x^2) / N2 = 1,975.67

Therefore, we have:

t = (M1 - M2) / ((S1^2 / N1) + (S2^2 / N2))^0.5 = (38.40 - 43.60) / ((1,541 / 100) + (1,975.67 / 150))^0.5 = -0.97

Therefore, the test statistic is -0.97.

3. What can you conclude at the 5% significance level?

At 5% significance level, the test statistic from the Z distribution table known as t-tab is 1.96.

Since our calculated test statistic is -0.9727 is less than 1.96, this implies that we fail to reject the null hypothesis (H0).

Again, since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is E. We fail to reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.