For the following exercises, find the function if sint=x+1x​. cost 44. sect cott 46. cos(sin−1(x+1x​)) 47. tan−1(2x+1​x​) For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression. 16. cscxtanx+cotx​;cosx 17. 1+tanxsecx+cscx​;sinx 18. 1+sinxcosx​+tanx;cosx 19. sinxcosx1​−cotx;cotx For the following exercises, verify the identity. 29. cosx−cos3x=cosxsin2x 30. cosx(tanx−sec(−x))=sinx−1 31. cos2x1+sin2x​=cos2x1​+cos2xsin2x​=1+2tan2x 32. (sinx+cosx)2=1+2sinxcosx 33. cos2x−tan2x=2−sin2x−sec2x For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression. 40. 1−tan2θcos2θ−sin2θ​=sin2θ 41. 3sin2θ+4cos2θ=3+cos2θ 42. cotθ+cosθsecθ+tanθ​=sec2θ

Answer:

  7.8 km

Step-by-step explanation:

You want the distance between two points when the travel time is 15 minutes at an average speed of 31 km/h.

The relation between time, speed, and distance is ...

  distance = speed × time

Here, the time is the difference between 14:50 and 14:35, which is 50-35 = 15 minutes. In terms of hours, that is 15/60 = 1/4 hours.

The speed is given as 31 km/h, so the distance is ...

  (31 km/h)×(1/4 h) = 31/4 km = 7.75 km ≈ 7.8 km

The distance between the two bus stops is about 7.8 km.

Answer:7.75 km so approximately 7.8 km

Step-by-step explanation:

i am not sure but i think the answer is 7.8 km

14:50 - 14:35= 15 minutes

because in every hour the bus travel 31 km/h so,

31 km/h divided by 60

multiply  the answer by 15 = 7.75 km

Answer:

x = 3

y = -2

Step-by-step explanation:

-x + 12y = -27

-5x + 3y = -21

Time the first equation by -5

5x - 60y = 135

-5x + 3y = -21

-57y = 114

y = -2

Now put in -2 for y and solve for x

-5x + 3(-2) = -21

-5x -6 = -21

-5x = -15

 x = 3

Let's check

-5(3) + 3(-2) = -21

-15 - 6 = -21

-21 = -21

So, x = 3 and y = -2 is the correct answer.

Answer:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Step-by-step explanation:

To evaluate the function at different values of x, we need to use the appropriate formula depending on whether x is less than 0 or greater than or equal to 0.

For x less than 0:

f(x) = -6 (since the function is defined as f(x) = -6 for x < 0)

For x greater than or equal to 0:

f(x) = sqrt(7x^2 + 9)

Therefore:

f(-6) = -6 (since -6 is less than 0)

f(0) = sqrt(7(0)^2 + 9) = sqrt(9) = 3 (since 0 is greater than or equal to 0)

f(6) = sqrt(7(6)^2 + 9) = sqrt(253) (since 6 is greater than or equal to 0)

Answer:

The area of a triangle is given by the formula A = 1/2 * base * height, where "base" is the length of the triangle's base and "height" is the length of the perpendicular line segment from the base to the opposite vertex.

If the base of a triangle is doubled, the height remains constant, and the area of the triangle will also double. This is because the area of a triangle is directly proportional to its base length.

In the case of the given triangle, if the base is doubled from 3 centimeters to 6 centimeters, the area of the triangle will become:

A = 1/2 * 6 cm * 6 cm = 18 cm²

Therefore, the area of the triangle will increase from 9 cm² to 18 cm² if the base is doubled while the height remains constant at 6 cm.

Step-by-step explanation:

The value of x, y, z are 14√2, 4√7, 2√21

Trigonometric Ratios are the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Tan (45) = 14√2/x

1 = 14√2/x

x =14 √2

the third side(hypotenuse) = √14√2)²+14√2)²

= √56+56

= √112

= 4√7

sin(30) = y/4√7

1/2 = y/4√7

2y = 4√7

y = 2√7

cos 30 = z/4√7

√3/2 = z/4√7

2z = 4√21

z = 2√21

therefore the value of x , y , z are 14√2, 4√7, 2√21

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The smallest number of peanuts that could be in the bag is 4320.

Let's use the Chinese Remainder Theorem to solve this problem.

Let:

x be the number of peanuts in the bag.

Then we know that x ≡ 2 (mod 8), x ≡ 2 (mod 9), and x ≡ 2 (mod 10).

Using the Chinese Remainder Theorem, we can find a solution for x as follows:

Let

M = 8 * 9 * 10 = 720, and let M1, M2, and M3 be the remainders when M is divided by 8, 9, and 10 respectively.

That is, M1 = 720 mod 8 = 0, M2 = 720 mod 9 = 0, and M3 = 720 mod 10 = 0.

Let b1 = 1, b2 = 1, and b3 = 1.

Then we need to find integers a1, a2, and a3 such that a1 * M1 * b1 + a2 * M2 * b2 + a3 * M3 * b3 = 1.

One solution is a1 = 5, a2 = -4, and a3 = 1,

so we have 5 * 720 * 1 + (-4) * 720 * 1 + 1 * 720 * 1 = 7201

= M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2.

This means that x = M1 * b1 * 2 + M2 * b2 * 2 + M3 * b3 * 2 is a solution to the system of congruences.

Since M1 = 0, we have x ≡ 0 (mod 8).

Since M2 = 0, we have x ≡ 0 (mod 9).

Since M3 = 0, we have x ≡ 0 (mod 10).

Therefore, the smallest positive integer solution for x is x = 720 * 1 * 2 + 720 * 1 * 2 + 720 * 1 * 2 = 4320.

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Answer: - 3 1/4

Step-by-step explanation:

- 3 3/4 + 1/2

Get a common denominator

-3 3/4 + 2/4

-3 1/4

No, Jack does not have enough rope. First, we need to convert all units to the same measurement.

Since there are 36 inches in a yard, Jack has 7 x 36 = 252 inches of rope. Additionally, 4 feet is equal to 4 x 12 = 48 inches of rope.

To determine if Jack has enough rope, we need to add the 84 inches needed for the packages and the 48 inches needed for the other project, which gives a total of 132 inches.

Since 132 inches is greater than Jack's total of 252 inches, he does not have enough rope.

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Answer:

[-4, +∞)

Step-by-step explanation:

[-4, +∞)

Answer:

110x

Step-by-step explanation:

its 110x

The sink's volume in cubic inches is 8182.8 cubic inches according to the radius of hemisphere.

The volume of hemisphere is calculated by the formula -

Volume = 2/3πr³, where r represents radius of the hemisphere.

Before beginning the calculation, convert radius from mixed fraction to fraction.

Radius = (15×4)+3/4

Performing multiplication and addition

Radius = 63/4 inches

Volume =

[tex] \frac{2}{3} \times \pi \times {( \frac{63}{4}) }^{3} [/tex]

Performing multiplication and taking cube

Volume = 8182.77 inches³

Rounding to nearest tenth

Volume = 8182.8 cubic inches

Hence, the volume of hemisphere is 8182.8 cubic inches.

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The complete question is -

Jeremiah measure the volume of a sink basin by modeling it as a hemisphere. Jeremiah measures its radius to be

15 3/4 inches. Find the sink's volume in cubic inches. Round your answer to the nearest tenth if necessary

Step-by-step explanation:

To simplify the expression 16+(-3)-3/7j-6/7j+4, we first need to combine like terms. The real numbers (16, -3, and 4) can be added together, and the imaginary numbers (-3/7j and -6/7j) can also be added together. So we have:

16 + (-3) + 4 + (-3/7j) + (-6/7j)

Simplifying the real numbers:

= 16 - 3 + 4

= 17

Simplifying the imaginary numbers:

= (-3/7j) + (-6/7j)

= (-9/7j)

Putting it all together, we get:

16 + (-3) - 3/7j - 6/7j + 4 = 17 - 9/7j

So the simplified expression is 17 - 9/7j.

Answer:

0.119

Step-by-step explanation:

No. of sides a die has= 6 sides

No. of times it is rolled= 7 times

Total pairs= 6 x 7

                = 42 pairs

No. of 5 threes= 5 x 1

                        = 5

Probability of getting 5 threes= Favorable outcomes/Total outcome

                                                 = [tex]\frac{5}{42}[/tex]

                                                 = 0.119 chance

∴ probability of getting 5 threes is 0.119

Answer:

Part A:

The expression that represents the area of the rectangle is:

Area = length × width

Area = (7x - 1)(2x + 3)

Area = 14x^2 + 19x - 3

To calculate the area, we multiplied the length (7x - 1) by the width (2x + 3).

To write the expression in standard form, we rearrange the terms in descending order of degree:

Area = -3 + 19x + 14x^2

Part B:

The expression in standard form is:

-6x^4 + 4x^2 + 3y + 4

Degree: 4

Terms: 4

Part C:

Adding, subtracting, and multiplying two polynomials always results in another polynomial. Therefore, the term that makes the statement true is A) Always.

Step-by-step explanation:

The increase in price for both appliances is the same, which is ₹400

Let's first find the increase in price for the toaster:

Increase in price = New price - Old price

Increase in price = ₹800 - ₹400

Increase in price = ₹400

Now, let's find the increase in price for the microwave:

Increase in price = New price - Old price

Increase in price = ₹10400 - ₹10000

Increase in price = ₹400

As we can see, the increase in price for both appliances is the same, which is ₹400.

The increase in price for both appliances is ₹400. This is found by subtracting the old price from the new price for each appliance. For the toaster, the increase is ₹800 - ₹400 = ₹400. For the microwave, the increase is ₹10400 - ₹10000 = ₹400. Since both appliances had the same increase in price, we can conclude that the percentage increase is different for each appliance. In this case, the percentage increase for the toaster is 100% [(₹800 - ₹400)/₹400 x 100%], while the percentage increase for the microwave is only 4% [(₹10400 - ₹10000)/₹10000 x 100%].

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The given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees.

The given statement implies that the international company has a total number of employees working in various countries. Out of these, 22.9% of the employees are working in a particular country, which amounts to 19700 employees in that country.

To find out the total number of employees working in all countries, we can use the following formula:

Total number of employees = Number of employees in the given country / Percentage of employees in the given country

Substituting the values given in the problem, we get:

Total number of employees = 19700 / 0.229

Total number of employees = 85939.3

Therefore, the international company has approximately 85939 employees working in various countries.

It's important to note that this calculation assumes that the proportion of employees working in the given country is representative of the proportion of employees working in other countries. However, if the proportion of employees working in other countries is significantly different, then the actual number of employees in the company could be different from the calculated value.

In conclusion, the given information tells us that a particular country has 22.9% of the employees of an international company, and this amounts to 19700 employees. We can use this information to approximate the total number of employees working in all countries.

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complete question :

An international company had 19700 employes in one country that is 22. 9 percent of there employies. Find the total number of employes in the company ?

If the square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3, the value of x that satisfies the equation is x = 13.75.

Let's start by using the formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

In this case, we have:

(x + 1)^2 = x^2 + 2x + 1 (square of the binomial x+1)

(x - 3)^2 = x^2 - 6x + 9 (square of the binomial x-3)

We're told that the square of the binomial x+1 is 120 greater than the square of the binomial x-3. In other words:

(x + 1)^2 = (x - 3)^2 + 120

Substituting the expressions we found above, we get:

x^2 + 2x + 1 = x^2 - 6x + 9 + 120

Simplifying, we get:

8x = 110

Therefore, the solution is:

x = 13.75

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Complete question is:

The square of the binomial x+1 one hundred and 20 greater than the square of the binomial x-3. what is value of x?

Answer:

Step-by-step explanation:

The domain of a function refers to the set of all possible input values. We can easily find the domain of the given function h(t) using the following rules:

Since the denominator cannot be zero, we must exclude the value t = -3 from the domain. This means that the domain is {t | t ≠ -3}.

Furthermore, the expression inside the square root cannot be negative since the square root of a negative number is undefined. Thus, we have t^2 - 16 ≥ 0, which implies t ≤ -4 or t ≥ 4.

Therefore, the domain of the function h(t) is given by {t | t ≠ -3, t ≤ -4 or t ≥ 4}. This can also be written in set-builder notation as {t : t ≤ -4 or t ≥ 4, t ≠ -3}.

Hence, the correct option is {\color{Red}\boxed{(-\infty,-4] \cup[4, \infty) \text { or }{x \mid x \leq-4 \text { or } x \geq 4}}}

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The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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Answer:

142.5 ft^2

Step-by-step explanation:

You need to calculate each figure separately

area of the first rectangle = 5 x 4 = 20

area of the second rectangle = (5+6)x(4) = 44

area of 1/4 circle =  1/4π(10^2) = (1/4) x 3.14 x 100 = 78.5

area of figure: 78.5 + 20 + 44 = 142.5

Answer:

To find the area of this figure, we need to first determine its shape. The lengths given do not form a clear shape, so we need more information to determine the shape.

Assuming that the shape is a trapezoid with the bases of 6ft and 10ft, and a height of 5ft, we can use the formula for the area of a trapezoid:

Area = (b1 + b2) / 2 * h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

Plugging in the values, we get:

Area = (6ft + 10ft) / 2 * 5ft

Area = 8ft * 5ft

Area = 40 sq ft

Area ≈ 3.73 sq m (rounded to two decimal places)

Therefore, the area of this figure is approximately 3.73 square meters.

(If it wasn't in decimals, it would be 40 square feet.)

Hopefully this helped! I'm sorry if it's wrong. If you need more help, ask me! :]

I got ya.

I wrote the answers in the boxes.

The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.

Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.

Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.

This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.

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The lower limit with 3 decimal places at 90% confidence is 29.266.

To determine the lower limit with 3 decimal places at 90% confidence given a sample of 10 widgets with a mean of 32.500 and standard deviation of 6.050, one would use the following steps:Step 1: Calculate the standard errorThe formula for standard error is: `standard deviation / square root of sample size`.So, `standard error = 6.050 / sqrt(10) = 1.916` (rounded to 3 decimal places).Step 2: Find the t-value for 90% confidence with degrees of freedom (df) = n - 1From a t-table or calculator, with df = 10 - 1 = 9 and 90% confidence, we find that the t-value is 1.833.Step 3: Calculate the lower limitThe formula for the lower limit of a confidence interval is: `sample mean - (t-value * standard error)`.So, `lower limit = 32.500 - (1.833 * 1.916) = 29.266` (rounded to 3 decimal places).Therefore, the lower limit with 3 decimal places at 90% confidence is 29.266.

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The midpoint of the line segment with the endpoints is (-2, 5).

option B.

To find the coordinates of the midpoint of a line segment with endpoints K(-9, 3) and H(5, 7), we can use the midpoint formula:

Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

Where;

Plugging in the coordinates of K and H, we get:

Midpoint = [(-9 + 5)/2, (3 + 7)/2]

= [-2, 5]

Therefore, the midpoint of the line segment with endpoints K(-9, 3) and H(5, 7) is (-2, 5).

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Answer: o find an equation that is parallel to the given line, we need to use the fact that parallel lines have the same slope.

The given line has a slope of 1/2, so any parallel line must also have a slope of 1/2.

Now we can use the point-slope form of a line to find the equation of the parallel line that passes through (-6, 5):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Plugging in m = 1/2 and (x1, y1) = (-6, 5), we get:

y - 5 = 1/2(x - (-6))

Simplifying:

y - 5 = 1/2(x + 6)

y - 5 = 1/2x + 3

y = 1/2x + 8

So the equation of the parallel line that passes through (-6, 5) is y = 1/2x + 8.

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The 95% confidence interval for the population proportion who favor an amendment for organized prayer in public schools does not provide convincing evidence that more than two-thirds.

Because the value 2/3 = 0.667 (and values less than 2/3) are in this interval, it is plausible that 2/3 or less of the population favor such an amendment. Thus, there is not convincing evidence that more than 2/3 of U.S.The 95% confidence interval for the population proportion who favor such an amendment is (0.63, 0.69). This means that if the same poll was conducted over and over again, 95% of the time the results would fall within this interval. Since the interval includes values less than 2/3, it is possible that 2/3 or less of the population favor such an amendment. Therefore, there is not convincing evidence that more than two-thirds of  important to note that the confidence interval does not provide conclusive evidence either way, only an indication of the likely proportions in the population.

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An algebraic expression like (3+5) x (4-1) is a combination of numbers and at least one operation.

Answer: Volume = 23816.41

Answer:[tex]847\pi[/tex]

Step-by-step explanation:

[tex]v=\pi r^{2} h\\v=\pi 11^{2} 7\\v=847\pi[/tex]