Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions are of theta only. (sec theta - csc theta )(cos theta + sin theta)

Answers

Answer 1

Answer:

[tex]\tan \theta-\cot \theta[/tex]

Step-by-step explanation:

[tex](\sec \theta - \csc \theta)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta}-\dfrac{1}{\sin \theta} \right)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta} \cdot \cos \theta \right) + \left( \dfrac{1}{\cos \theta} \cdot \sin \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \cos \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \sin \theta \right)= \\\\\\1+\dfrac{\sin \theta}{\cos \theta}-\dfrac{\cos \theta}{\sin \theta} -1= \\\\\\\tan \theta-\cot \theta[/tex]

Hope this helps!


Related Questions

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 66 types of drinks to choose from, 55 types of sandwiches, and 44 types of chips. How many different value meal packages are possible?

Answers

Answer:

159,720

Step-by-step explanation:

Calculation of how many different value meal packages are possible at Ron's Subs :

The meal package at Ron's Subs are:

Drink 66

Sandwich 55

Bag of chips 44

Since we are looking for the how many different value meal packages are possible that means we have to multiply all the three value meal package with each other.

Hence,

Drink 66 ×Sandwich 55 ×Bag of chips 44

=159,720

Therefore 159,720 is the number of different value meal packages that are possible at Ron's Subs

40 points!! What does this graph represent

Answers

Answer:

[tex]f(x)=0.2\,(x-2)^2+1[/tex]

Option "B" as per the list of possible answers

Step-by-step explanation:

Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you  [tex]f(2) = 1[/tex]. You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.

Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square [tex](x-2)^2[/tex] which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:

[tex]f(x)=0.2\,(x-2)^2+1[/tex]

which you can check briefly by evaluating a couple of easy points  (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.

A government agency has 6000 employees. As an alternative to the traditional five-day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The accompanying segmented bar chart is based on the data collected. Which of the following statements is true about work week preferences and age category? A. Preferences appear to be independent of age. B. The distribution of preferences is the same across different age groups. C. A greater percentage of employees who prefer flex hors are in the over 45 age category compared to those who prefer 4-day work week. D. A greater percentage of employees who prefer a 4-day work week are in the over 45 age category compared to those who prefer flax hours.

Answers

Complete Question

The complete question is  shown on the first uploaded image

Answer:

Option D is the correct answer

Step-by-step explanation:

   Now looking at the bar chart we see that a greater number of employee over the age of 45 preferred the 4-day work week compared to the number of employee between 30- 45 who preferred to have a flexible work hour and employee below 30  who' s preference are the same for both type of work hours

Provide an appropriate response. A 28-year-old man pays $94 for a one-year life insurance policy with coverage of $120,000. If the probability that he will live through the year is 0.9991, what is the expected value for the insurance policy

Answers

Answer:

$ 14.08

Step-by-step explanation:

We have that the policy costs $ 94 and with life insurance with coverage of $ 120,000, to calculate the expected value, we must subtract the value of that life insurance multiplied with the probability of dying (complement of the probability of living) and the policy value multiplied by the probability of staying alive) like this:

120000 * (1 - 0.9991) - 94 * 0.9991 = 14.0846

Which means that the expected value of the policy is $ 14.08

The function V(r) = four-thirds pi r cubed can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?

Answers

Answer:

V(r) is the volume of basketball when the radius is r.

Answer:

B. the volume of the basketball when the radius is r

Step-by-step explanation:

What three-digit number with units digit 2 and hundreds digit 4 is divisible by 9?

Answers

Answer:

Dear user,

Answer to your query is provided below

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.

Step-by-step explanation:

Here , It is given that the number is three digit in which units digit is 2 and hundreds digit is 4.

As per rule, the sum of its digits should've divisible by 9. So, Let the unknown digit be X .

Therefore, 2+X+4 =9

This implies, X = 9-2-4 = 3

So, the three digit number will be 432.

Verify - 432/9 = 48

Hence proved

A man driving a car leaves a point A drives up to 32.5 km in a direction of 070. A cyclist leaves the same point in a direction 130 travelling. After some few hours both drivers are 80 km apart. Use this information to answer 3 questions. (1). What is the distance covered by the cyclist at this time in 2 d.p. (2). Find the bearing of Cyclist from the Car. correct to 1 d.p. (3). Find the shortest distance between the car and the line of path of the cyclist, in 2 d.p.

Answers

Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

y= -x + 1/2+1
- 3x+y=6

Answers

Impossible as there is two I know numbers, even if you are trying to figure out either x or y

if teta is an angle in right angle triangle if tan teta = 3/4 then find sin teta? ​

Answers

Answer:

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

Step-by-step explanation:

The adjacent sides are 3 and 4. Thus the hypotenuse is: (by Pythagoras Theorem)

$=\sqrt{3^2+4^2}$

$=\sqrt{25}$

$=5$

Now by definition of $\sin$, we get:

$\sin \theta= \frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$

Everyday, Jason has a 14-mile round-trip drive to work. He then has to drive his truck on a 296-mile delivery route 5 days a week. How many miles does he drive each day?

Answers

Answer:

73.2 miles i am not so sure

Step-by-step explanation:

What is the solution to the equation below? Round your answer to two
decimal places.
In x = 0.2
A. x= 1.22
B. X= 1.58
C. x = -1.61
D. X = -0.70

Answers

Answer:

X=1.22

Step-by-step explanation:

I just got the question wrong and it gave me the right answer

jason went shopping.
he bought a watch and a pair of trainers for a total price of £53.55
this price includes a 15% loyalty discount.
before the discount the trainers were priced at £38.
work out the price before the discount.

Answers

Answer:

The total price before discount was £63.

The price of the watch before discount was £25.

Step-by-step explanation:

Let the total original price before discount be x.

The total of £53.55 included a 15% discount. That means he paid only 85% of the original total price before the discount.

85% of x = £53.55

0.85x = 53.55

x = 63

The total before discount was £63.

£63 - £38 = £25

The total price before discount was £63.

The price of the watch before discount was £25.

To help consumers assess the risks they are​ taking, the Food and Drug Administration​ (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 25.325.3 milligrams and standard deviation of 2.72.7 milligrams for a sample of n equals 9n=9 cigarettes. Construct a 9090​% confidence interval for the mean nicotine content of this brand of cigarette.

Answers

Answer:

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 9 - 1 = 8

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8595

The margin of error is:

M = T*s = 1.8595*2.7 = 5

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 25.3 - 5 = 20.3 milligrams

The upper end of the interval is the sample mean added to M. So it is 25.3 + 5 = 30.3 milligrams.

The 90​% confidence interval for the mean nicotine content of this brand of cigarette is between 20.3 milligrams and 30.3 milligrams.

Which of the following graphs represents the equation y=3x+2?

Answers

Answer:graph C is the answer because if you put the both values from the graph it satisfies the equation

Answer:

Graph C

Step-by-step explanation:

The given equation is in the form y=mx+b

This is slope-intercept form.

This is where m represents the slope, and b represents the y-intercept.

Therefore, the slope is 3 and the y-intercept is 2.

Let's first name all the equations with a y-intercept of 2.

That would be B and C.

Now, let's find the equation with a slope of 3.

Let's find the slope for B.

The formula for slope is: y1-y2/x1-x2

A point is: (x coordinate, y coordinate)

In the formula,

y1 is the y coordinate of the first point

y2 is the y coordinate of the second point

x1 is the x coordinate of the first point

x2 is the x coordinate of the second point

This said, we can plug our points in.

6-2/2-0

4/2

2

The slope for Graph B is 2, so it is incorrect.

Let's find the slope for Graph C.

2-(-1)/0-(-1)

2+1/0+1

3/1

3

The slope for Graph C  is 3, and it has a y-intercept of 2, so Graph C is the correct choice.

For the function, f(x) = -3x + 5.
If f(x) = -1, what is the value of x?

Answers

Answer:

x=2

Step-by-step explanation:

f(x) = -3x + 5.

f(x) =-1

-1 = -3x+5

Subtract 5 from each side

-1 -5 = -3x+5-5

-6 = -3x

Divide each side by -3

-6/-3 = -3x/-3

2 =x

Pls help I really need help

Answers

Answer:

7. [tex]x \leq 5[/tex]

8. [tex]x\geq 4[/tex]

9. x < 5

10. x < -7

11.  x < 45

12. [tex]x\geq -10[/tex]

13. x < -7

14. x < 45

15. [tex]x\leq 50[/tex]

16. [tex]w\geq 16[/tex]

18. q > 4

Step-by-step explanation:

Some of the stock in a winery has been found to be infected by Brettanomyces. You independently sample 80 barrels from the winery, and find that 28 of them are infected. Carry out a hypothesis test to evaluate the claim that half of the wine barrels are infected. What is closest to the p-value that you obtain

Answers

Answer:

Step-by-step explanation:

If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5

We would set up the hypothesis test.

For the null hypothesis,

p = 0.5

For the alternative hypothesis,

p < 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 28

n = number of samples = 80

P = 28/80 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68

From the normal distribution table, the area below the test z score in the left tail 0.0037

Therefore,

p value = 0.0037

Assuming a significance level of 0.05, therefore,

Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.

Which property is illustrated by the expression 5(4+2)=20+10

Answers

Answer:

  distributive property

Step-by-step explanation:

The distributive property tells you ...

  a(b+c) = ab +ac

  5(4+2) = 5·4 +5·2 = 20 +10

[tex]\text{It would most likely be the distributive property}\\\\\text{In the equation:}\\\\5(4+2)=20+10\\\\\text{You would see that you can distribute the 5 into the variables inside }\\\text{the parenthesis}\\\\\text{In which it is set up in that particular way in order to do so}[/tex]

3] The population of a
village is 4800. There are
1200 men, 1620 women
480 boys and the rest are
girls.
(a) How many girls are
in the village?
(b) Calculate the
percentage of men in
the village.​

Answers

Answer:

A) 1500 girls

B) 25% are men

Step-by-step explanation:

I hope this helps

According to the Mortgage Bankers Association, 21% of U.S. mortgages were delinquent last year. A delinquent mortgage is one that has missed at least one payment but has not yet gone to foreclosure. A random sample of seven mortgages was selected. What is the standard deviation of this distribution

Answers

Answer:

The standard deviation for the number of delinquent mortgages in the sample is 1.08.

Step-by-step explanation:

For each mortgage, there are only two possible outcomes. Either it is delinquent, or it is not. The probability of a mortgage being delinquent is independent of other mortgages. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

21% of U.S. mortgages were delinquent last year.

This means that [tex]p = 0.21[/tex]

A random sample of seven mortgages was selected.

This means that [tex]n = 7[/tex]

What is the standard deviation of this distribution

[tex]\sqrt{V(X)} = \sqrt{7*0.21*0.79} = 1.08[/tex]

The standard deviation for the number of delinquent mortgages in the sample is 1.08.

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.

Answers

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.

A division of a multinational retail company prepared a presentation to give at the home office in Paris, France. The presentation includes a scatterplot that shows the relationship between square footage and annual sales in retail outlets owned by the chain. The units in the plot show the size in thousands of square feet and the response in thousands of dollars. A fitted line in the plot is y = 47 + 650x.
(a) Interpret the slope and intercept in the fitted line.
(b) To present the model in Europe, the plot must be shown with sales denominated in euros rather than dollars 1use the exchange rate
$1 = €0.822 and size given in square meters rather than square feet (1 square foot = 0.093 square meter). Find the slope and intercept in these new units.
(c) Would the r2 summary attached to the regression model change along with the slope and intercept when the data are changed into euros and meters?
(d) Would se change with the new scales?

Answers

Answer:

(A) Interpretation is below

(B) The slope in the new units is now 60.45

The intercept in the new units is 38.634

(C) yes

(D) yes

Step-by-step explanation:

(A) The intercept here is 47. This means that the minimum response or payment is 47 (thousand dollars).

The slope is 650. This means that the change in Y due to a change in X is 650. In other words, if there is a change of 1(thousand square feet), there will be a resulting increase of 650(thousand dollars). It will result in an increase instead of decrease because the slope is positive or bearing a + sign.

(B) The new units are EUROS and SQUARE METRES.

$1 = €0.822

1s.f. = 0.093s.m.

The new fitted line would be:

0.822Y = 47(0.822) + (0.093)(650)X

0.822Y = 38.634 + 60.45X

The slope in the new units is 60.45 and the intercept on the y-axis is 38.634.

Each have four possible answers left parenthesis a,b,c,d right parenthesis​, one of which is correct. Assume that you guess the answers to three such questions.
a. Use the multiplication rule to find ​P(CWC​), where C denotes a correct answer and W denotes a wrong answer.
b. Beginning with CWC​, make a complete list of the different possible arrangements of two correct answers and one wrong answer​, then find the probability for each entry in the list.​P(CWC​)minussee above ​P(WCC​)equals? 0.046875 ​P(CCW​)equals? 0.046875 ​(Type exact​ answers.)
c. Based on the preceding​ results, what is the probability of getting exactly two correct answers when three guesses are​made?

Answers

Answer:

a. P(CWC)=0.046875

b.  P(WCC)=0.046875

    P(CCW)=0.046875

c. P=0.140625

Step-by-step explanation:

By the rule of multiplication there are 64 forms to answer three questions. This is calculated as:

    4 _          *            4               *             4            = 64

1st question      2nd question     3rd question

Because there are 4 options for every question. At the same way, from that 64 options, 3 are CWC and it is calculated as:

    1 _          *            3               *             1            = 3

1st question      2nd question     3rd question

Because there is just one answer that is correct for the first question, there are 3 answers wrong for the second question and there are 1 answer correct for the third question.

So, the probability P(CWC) is equal to:

[tex]P(CWC)=\frac{3}{64}=0.046875[/tex]

Then, the complete list of the different possible arrangements of two correct answers and one wrong answer are: CWC, WCC and CCW

Therefore, the probabilities P(WCC) and P(CCW) are calculated as:

[tex]P(WCC)=\frac{3*1*1}{64}=\frac{3}{4}= 0.046875[/tex]

[tex]P(CCW)=\frac{1*1*3}{64}=\frac{3}{4}= 0.046875[/tex]

Finally, the probability of getting exactly two correct answers is the sum of the probabilities calculated before.

[tex]P=P(CWC)+P(WCC)+P(CCW)\\P=0.046875+0.046875+0.046875\\P=0.140625[/tex]

Find the probability. Enter your answer as a simplified fraction.



Picking a purple marble from a jar with 14 green and 14 purple marbles.

Answers

Answer:

1/2

Step-by-step explanation:

14 green and 14 purple marbles = 28 marbles

P( purple) = purple/ total

                 = 14/28

                  =1/2

What is the symbol for pi?

Answers

Answer:

π

Step-by-step explanation:

[tex]\displaystyle \pi[/tex]

Last years freshman class at big state university totaled $5330 students. Of those, $1258 received a merit scholarship to help offset tuition cost their freshman year. The amount a student received was N($3464, 489). If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?

Answers

Answer:

2.17% of students who received a merit scholarship did not receive enough to cover full tuition

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 3464, \sigma = 489[/tex]

If the cost of full tuition was $4450 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition?

This is 1 subtracted by the pvalue of Z when X = 4450. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{4450 - 3464}{489}[/tex]

[tex]Z = 2.02[/tex]

[tex]Z = 2.02[/tex] has a pvalue of 0.9783.

1 - 0.9783 = 0.0217

2.17% of students who received a merit scholarship did not receive enough to cover full tuition

Barry has $30.00 to spend on soft drinks
for a party. A case of soft drinks costs
$4.65. Which inequality can be used to find how many cases (c) of soft drinks
Barry can purchase?

Answers

Answer:

30 ≥ 4.65x

Step-by-step explanation:

He cannot purchase more than $30, so the amount that he buys must always be less than 30.

Write the expressions "Four times the difference of a number and 1 is equal to six times the sum of the number and three. Find the number

Answers

Answer:

4(x - 1) = 6(x + 3)

x = -11

Step-by-step explanation:

x represents “the number” so we would substitute this with a variable.

(I hope this helps! Have a great day AND STAN BTS)

I need help pls someone:(

Answers

Answer:

7/30

Step-by-step explanation:

Michael has a weekly food budget of $62. If he plans to budget the same amount for each of the 7 days of the week, what is the maximum amount he can spend on food each day?

Answers

Answer:

62/7

Step-by-step explanation:

The budget illustrates ratios and proportions.

The maximum amount to spend on food each day is $8

The given parameters are:

[tex]\mathbf{Budget = \$62}[/tex]

[tex]\mathbf{Days = 7}[/tex]

So, the daily budget is:

[tex]\mathbf{Daily = \frac{Budget}{Days}}[/tex]

So, we have:

[tex]\mathbf{Daily = \frac{\$62}{7}}[/tex]

[tex]\mathbf{Daily = \$8.85714285714}[/tex]

Remove decimal parts (do not approximate)

[tex]\mathbf{Daily = \$8}[/tex]

Hence, the maximum to spend each day is $8

Read more about ratios and proportions at:

https://brainly.com/question/13114933

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