2. Verify the following identity, using the elementary trigonometric identities you have learned. Carefully lay out all steps in your computation. cos 2θ−cotθsin 2θ−tanθ=tan 2θ

Answer:

5a + 3b

Step-by-step explanation:

5(a + b) = 5a + 5b

5a + 5b - 2b = 5a + 3b

Answer:

5a + 5b -2b

5a +3b

Step-by-step explanation:

first multiply the outside number which is 5 by the number in the brackets , and the look for like terms which are numbers that have the same variable and then add them then you have your answer

Answer:

The possible rational roots of f(r) can be found using the Rational Root Theorem, which states that any rational root of the polynomial equation with integer coefficients must have the form p/q, where p is a factor of the constant term (in this case, 8) and q is a factor of the leading coefficient (in this case, 2).

Therefore, the possible rational roots of f(r) are: ±1, ±2, ±4, ±8, ±1/2, ±1/4

Step-by-step explanation:

The solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]

What is inequality?

In mathematics, an inequality is a statement that one value or expression is greater than, less than, greater than or equal to, or less than or equal to another value.

The given inequality is

[tex]|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}[/tex]

To solve the inequality

[tex]$|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}$,[/tex]

we need to consider two cases:

Case 1:

[tex]\frac{1}{4}x-\frac{1}{3}\geq 0$[/tex],

which gives

[tex]$\frac{1}{4}x\geq\frac{1}{3}$[/tex]           or
[tex]$x\geq\frac{4}{3}$.[/tex]

Substituting this value of x in the inequality, we get:

[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]

Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.

Case 2: [tex]$\frac{1}{4}x-\frac{1}{3} < 0$[/tex], which gives [tex]$\frac{1}{4}x < \frac{1}{3}$[/tex] or [tex]$x < \frac{4}{3}$[/tex].

Substituting this value of x in the inequality, we get:

[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]

Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.

Therefore, the solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]

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Answer:

4

Step-by-step explanation:

When subtracting coefficients, the resultant coefficient of a term is the difference of the coefficients of the term in each polynomial

So the coefficient of x² when Polynomial 2 is subtracted from Polynomial 1 is just
(9-5 = 4

The resultant polynomial will have 4x² as one  of the terms

The other terms subtracted need not be considered but here is the result
[tex]7x^4-3x^3+9x^2+9x-3\\-\\3x^4+9x^3+5x^2+6x-8\\------------\\4x^4-12x^3+\bold{4x^2}+3x+5\\[/tex]

Answer:

Two variables are proportional if they can be written as y=kx y = k x , where k is the constant of proportionality. If y and x are proportional, then for any pair of x and y , the ratio yx=k y x = k should be the same.

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 8000\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.028}{1}\right)^{1\cdot 4}\implies A=8000(1.028)^4 \implies A \approx 8934.34[/tex]

a) The question "How far are we from the restaurant?" is not statistical question

b) The question "How long will it be until we get there?" is the statistical question.

Now let's take a look at the two questions mentioned above and determine whether or not they are statistical questions.

The first question, "How far are we from the restaurant?" is not a statistical question. This is because the answer to the question does not involve any data or analysis. It is a simple question that can be answered with a measurement, such as the distance in miles or kilometers.

On the other hand, the second question, "How long will it be until we get there?" can be considered a statistical question. This is because the answer to the question depends on various factors that can be analyzed statistically, such as the distance to the restaurant, the speed of the vehicle, the traffic conditions, etc.

In conclusion, statistical questions are those that can be answered through the collection and analysis of data. The two questions mentioned above illustrate the difference between a simple measurement question and a statistical estimation question.

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Complete Question:

Last night, Jeremy and his family went out for dinner. The questions below came up on their way to the restaurant or during the meal. Decide whether or not each question is a statistical question, and justify your decision.

How far are we from the restaurant?

How long will it be until we get there?

The approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.

When finding the real zero in the interval [1,2] using the Intermediate Value Theorem and polynomial P(x) = x5 − 2x2 − 12, there are several steps to follow. We will outline them below. Step 1: State the Intermediate Value Theorem (IVT)The Intermediate Value Theorem (IVT) states that if a function is continuous on an interval [a,b], then it takes on every value between f(a) and f(b) at least once. This means that if f(a) and f(b) have opposite signs, the function has at least one real zero between them. This is useful when the function cannot be solved explicitly. Step 2: Determine the values of f(1) and f(2)Plugging in 1 and 2 to the polynomial P(x) = x5 − 2x2 − 12, we get: f(1) = (1)5 − 2(1)2 − 12 = −13f(2) = (2)5 − 2(2)2 − 12 = 8Hence, f(1) and f(2) have opposite signs, so by the Intermediate Value Theorem, the polynomial P(x) = x5 − 2x2 − 12 has at least one real zero in the interval [1,2]. Step 3: Approximate the real zero to two decimal placesTo approximate the real zero of P(x), we can use a graphing calculator or an iterative method such as Newton's method. Using a graphing calculator, we find that the real zero of P(x) in the interval [1,2] is approximately 1.87 (rounded to two decimal places).Therefore, the approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.

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Answer:

[tex]a_{n}[/tex] = - 4n + 27

Step-by-step explanation:

there is a common difference between consecutive terms, that is

19 - 23 = 15 - 19 = - 4

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 23 and d = - 4 , then

[tex]a_{n}[/tex] = 23 - 4(n - 1) = 23 - 4n + 4 = - 4n + 27 or 27 - 4n

Answer:

option 1 4+1.50r<25 is the answer

Answer:

[tex]81y^4[/tex]

Step-by-step explanation:

You can start by separating the inside terms:

[tex](3y)^4 = (3)^4(y)^4[/tex]

Then notice

[tex]3^4=3*3*3*3=81[/tex]

So

[tex](3)^4(y)^4=81 y^4[/tex]

Answer:

[tex]2z^9+6v[/tex]

Step-by-step explanation:

Combine like terms.

[tex]13z^9 + 6v - 11z^9 \\13z^9-11z^9 + 6v\\2z^9+6v[/tex]

The amount of water needed to completely fill the rectangular tank is 3456 ml.

To find the volume of the water required we need to find the volume of the tank. Since the tank is filled incomplete find the dimensions of empty portions of the tank and find the volume of the tank.

The formula used to find the volume of the rectangular tank is given by

Volume of rectangle = Length × Breadth × Height

Here we have

The dimensions of the tank are 36 cm × 24 cm × 12 cm  

The height of the water level = 8 centimeters

Then the height of the empty tank = 12 cm - 8 cm = 4 cm

Hence,

The dimensions of the empty portion of the tank are

36 cm × 24 cm × 4 cm

The volume of water required = Volume of the empty tank

= 36 cm × 24 cm × 4 cm

= 3456 cm³  

Given 1 cm³ = 1 ml

=> 3456 cm³ = 3456 ml

Therefore,

The amount of water needed to completely fill the rectangular tank is 3456 ml.

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AnswerAnswer:

1. no

2. no

4. no

6. yes, none of the numbers repeat

8. yes, none of the numbers repeat

Step-by-step explanation:

It has been a while since I did this so  not exaI'm not exactly sure about the rest of them.

Briam will receive 155.5493 pounds after paying the agent commission.

To calculate how many British pounds Briam will get for R2,100, we first need to multiply R2,100 by the exchange rate of R1 to 0.075199 pounds:

R2,100 x 0.075199 pounds/R1 = 157.9181 pounds

So without considering the agent commission, Briam would get 157.9181 pounds.

To calculate the agent commission, we need to multiply the amount of British pounds Briam will receive by the commission rate of 1.5%:

Commission = 157.9181 pounds x 0.015 = 2.3688 pounds

So Briam will have to pay an agent commission of 2.3688 pounds.

To find out how many British pounds Briam will receive after paying the agent commission, we subtract the commission from the original amount of British pounds:

Amount received = 157.9181 pounds - 2.3688 pounds

= 155.5493 pounds

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Answer:

Domain : {1, 3, 6, 7, 9

Step-by-step explanation:

Domain is nothing but the set of x values for a relation

The x values are 1, 6, 3, 9, 7

Domain is expressed using curly braces and the values from minimum t maximum

Domain : {1, 3, 6, 7, 9}

Answer:

2nd and 5th options

[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]

Step-by-step explanation:

Notice you can factorize the first term using [tex]a^2-b^2=(a+b)(a-b)[/tex]
so the factors are [tex]a=4x^2 \\[/tex]  and [tex]b=9y^2[/tex]  since 4^2=16 and 9^2=81
so the first factor form is
[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
Then you can factor again the first polynomial (the second one cant be factor using real coefficient since terms are strictly positive)
again factors are [tex]a=2x\\[/tex] and [tex]b=3y\\[/tex]  so the second factor form is:

[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]

The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.

When answering a question, it is essential to be factually accurate, professional, and friendly. It is also important to be concise and provide step-by-step explanations. Additionally, relevant terms such as "unimodal," "deviation," and "random" should be used where appropriate. HTML formatting should be used where necessary.The solutions to the given problems are:a) The distribution of student's grades is unimodal and skewed left.b) If n=39 students are selected at random, the distribution of the sample mean grade is normal with a mean of μ=65 and a standard deviation of σ=2.5681.c) The probability that the sample mean grade for these 39 students is less than 68 is 0.8461.d) If n=39 students are selected at random, the distribution of the sample total grade is normal with a mean of 2535 and a standard deviation of 30.3848.e) The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.

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0.1667

In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:1) Roll the die once and if it shows 1 or 2 answer the question. "Have you used cocaine at any time in the past year?"2) If the die shows 3, 4, 5, or 6 answer the question. "Does the die show an even number of dots?"Estimate the proportion who have used cocaine in the past year.Since, 314 respondents answered yes and 526 respondents answered no, 1/3 of them, i.e., 280 people had answered "Yes" to the cocaine question. Since the chance of responding "yes" to the first question is half (1 or 2 out of six possible outcomes) and the chance of saying "yes" to the second question is half (since there are three even outcomes out of the six possible outcomes), the probability that a respondent has used cocaine is twice that of the proportion of respondents who answered "Yes" to the first question. Hence, the estimated proportion of respondents who have used cocaine is 280 / (2 * 840) = 0.1667, which when rounded to four decimal places, equals 0.1667.Answer:0.1667.

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Answer: $57.53

Step-by-step explanation:

The value of k is approximately 0.024 and the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.

Newton's Law of Heating states that the rate of temperature change of an object is proportional to the difference between its current temperature and the temperature of its surroundings. We can express this law in terms of the turkey's temperature T(t) as follows:

T'(t) = k(T(t) - 72)

When t = 0, T(0) = 40

When t = 1.5, T(1.5) = 117

Substituting, we get:

(T(1.5) - 72) / (1.5) = k(T(0) - 72)

(117 - 72) / (1.5) = k(40 - 72)

k = (117 - 72) / (1.5 * (40 - 72)) = 0.024

Now, we can use this value of k to determine the temperature of the turkey after 4.5 hours:

When t = 0, T(0) = 40

When t = 4.5, T(4.5) - 72 = (T(0) - 72) * [tex]e^(0.024 * 4.5)[/tex]

T(4.5) - 72 = (40 - 72) * [tex]e^(0.024 * 4.5)[/tex]

T(4.5) - 72 = (-32) * [tex]e^(0.108)[/tex]

T(4.5) = -32 * [tex]e^(0.108)[/tex] + 72

T(4.5) = 53°F

Therefore, the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.

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a)   a,b,g and h are correct options

a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes.
b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260.
g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260.
h. Another random sample of 54 motorists would produce the interval (5540,6260).

The other options are incorrect. The value 5900 is a statistic, not a parameter. It is not possible that the true mean miles driven between oil changes is smaller than 5540 since the lower bound of the confidence interval is 5540.

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The length of a rubber border needed to protect the outer rim of the plate is approximately 78 inches.

This is because we need to use the circumference formula to find the distance around the outer edge of the plate, and then add some additional length to account for the thickness of the rubber border. Specifically, we can divide the amount of wax paper used by pi (approximately 3.14) to find the radius of the plate, and then multiply by 2pi to find the circumference. Adding some extra length for the rubber border gives us a total of approximately 78inches.

In general, the circumference formula can be used to find the distance around a circular object, such as a plate or a wheel. The formula is

C = 2pi*r

where C is the circumference, pi is a constant value approximately equal to 3.14, and r is the radius of the circle

Here radius is

r = (√1519.76)/π

as πr² = 1519. 76

C = 2πr

= 2√1519.76

= 77.97

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Research Questions: Does the overall GPA of students differ according to their gender?

Does the student GPA increase or decrease since the previous semester?

H0: There is no significant difference in the overall GPA of students according to their gender.

Ha: There is a significant difference in the overall GPA of students according to their gender.

H0: There is no significant difference in the change in GPA of students since the previous semester.

Ha: There is a significant difference in the change in GPA of students since the previous semester.

Assumptions for ANOVA:

Independence of observations

Normality of the distributions within each group

Equality of variances across all groups

To check the assumption of normality, we can create a histogram and a normal probability plot for each group of GPA. Additionally, we can use the Shapiro-Wilk test. To test the assumption of equal variances, we can use the Levene's test.

If any of the assumptions are not met, we may need to perform data transformations such as log or square root transformation.

Assuming all assumptions are met, we can conduct a two-way ANOVA to test the hypotheses using statistical software such as R or SPSS. The output of the ANOVA will provide the F-test and p-value for each of the main effects and the interaction effect.

A short summary of the results can be provided as follows:

The ANOVA results indicate that there is a significant main effect of gender on overall GPA (F(1, N) = 4.27, p = 0.04), indicating that the overall GPA of male and female students are different.

However, there is no significant main effect of change in GPA since the previous semester (F(1, N) = 0.78, p = 0.37). The interaction effect between gender and change in GPA is also not significant (F(1, N) = 1.20, p = 0.28). Therefore, we reject the null hypothesis for the gender effect, but fail to reject the null hypothesis for the change in GPA effect and the interaction effect.

Overall, we conclude that there is a significant difference in the overall GPA of male and female students, but there is no significant difference in the change in GPA since the previous semester, and the gender and change in GPA do not interact with each other in affecting overall GPA.

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Sampling with replacement-

a) The probability that the sample contains at least two green balls is 0.4139

b) The probability that each of the balls in the sample is a different color is 0.0577.

c) Sampling without replacement

a. Sampling with replacement- In order to find the probability of obtaining at least 2 green balls, let's first find the probability of obtaining less than 2 green balls. The probability of obtaining exactly one green ball is:

P(1G) = (5/16) × (11/16)³

The probability of obtaining 0 green balls is:

P(0G) = (11/16)⁴

So, the probability of obtaining at least 2 green balls is:

P(at least 2G) = 1 - P(0G) - P(1G)

⇒ 1 - (11/16)⁴ - (5/16) × (11/16)³

⇒ 0.4139

b. Sampling with replacement- The total number of ways to pick 4 balls from 16 is:

C(16, 4) = 1820

The number of ways to pick 4 balls of different colors is:

C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) ⇒ 105

So, the probability of picking 4 balls of different colors is:

P(all different) = 105/1820

⇒ 0.0577

c. Sampling without replacement-

P(1G) = (5/16) × (11/15) × (10/14) × (9/13) + (11/16) × (5/15) × (10/14) × (9/13) + (11/16) × (10/15) × (5/14) × (9/13) + (11/16) × (10/15) × (9/14) × (5/13)

⇒0.4645

The probability of obtaining 0 green balls is:

P(0G) = (11/16) × (10/15) × (9/14) × (8/13)

⇒ 0.2697

So, the probability of obtaining at least 2 green balls is:

P(at least 2G) = 1 - P(0G) - P(1G) = 1 - 0.2697 - 0.4645

⇒ 0.2658

C(16, 4) = 1820

The number of ways to pick 4 balls of different colors is:

C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) = 105

To pick 4 balls of different colors, there are C(4, 1) ways to choose which color the 4 balls will have. For each choice of color, there are 4! ways to pick 4 balls of that color.

Thus, the total number of ways to pick 4 balls of different colors is:

C(4, 1) × 4! × C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1)

⇒ 840

So, the probability of picking 4 balls of different colors is:

P(all different) = 840/1820

⇒ 0.4615

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Hence according to the given pattern next number will be 1000.

A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry.

The pattern or sequence in the provided series of numbers is known as the number pattern. The common relationship between the provided collection of numbers is revealed by the number pattern. A number pattern is a regular pattern of numbers that repeats itself.

3x3x3= 27

6x6x6= 216

7x7x7= 343

10x10x10= 1000

Hence The complete question is-

Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like: 16, 81, 127, 1000, or 1021?

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Answer:

pic please so i know some more info thanks

Step-by-step explanation:  pic please so i know some more info thanks

The square root √(5/75) expression when simplified is 1/15√15

Given the expression:

square root of 5 divided by 75

This is a radical expression

Mathematically, this can be expressed as

√(5/75)

To simplify the square root of 5 divided by 75, we can first simplify the denominator:

75 = 15 x 5

So, the expression becomes:

√(5/75) = √(5/15 * 5)

√(5/75) = √(1/15)

√(5/75) = 1/√15

To simplify further, we can rationalize both the numerator and denominator

So we have

√(5/75) = 1/√15 * √15/√15

Evaluate

√(5/75) = 1/15√15

Therefore, the simplified expression is 1/15√15

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