The root test is conclusive for the following series:
1 / 1 n⁹ n 1
Select one:
True
O False

a. the point (-24, 7), the exact values of the six trigonometric functions are

sin θ = 7/25

cos θ = -24/25

tan θ = -7/24

b. the point (-3, -6), the exact values of the six trigonometric functions are:

sin θ = -2/√5

cos θ = -1/√5

tan θ = 2

To find the exact values of the six trigonometric functions of an angle θ, we can use the given coordinates of a point on the terminal side of the angle in standard position.

(a) For the point (-24, 7):

To determine the trigonometric functions, we first need to find the values of the adjacent side, opposite side, and hypotenuse of the right triangle formed by the given coordinates.

The adjacent side is the x-coordinate: adjacent = -24

The opposite side is the y-coordinate: opposite = 7

Using the Pythagorean theorem, we can calculate the hypotenuse:

hypotenuse = √((-24)^2 + 7^2) = √(576 + 49) = √625 = 25

Now we can find the trigonometric functions:

sin θ = opposite / hypotenuse = 7 / 25

cos θ = adjacent / hypotenuse = -24 / 25

tan θ = opposite / adjacent = 7 / -24 (or -7/24)

Since we have only found the values for sine, cosine, and tangent, we leave the values for cosecant, secant, and cotangent blank as they are the reciprocals of the corresponding trigonometric functions.

Therefore, for the point (-24, 7), the exact values of the six trigonometric functions are:

sin θ = 7/25

cos θ = -24/25

tan θ = -7/24

(b) For the point (-3, -6):

Using the same method as above, we can find the values of the trigonometric functions for this point.

adjacent = -3

opposite = -6

hypotenuse = √((-3)^2 + (-6)^2) = √(9 + 36) = √45 = 3√5

sin θ = opposite / hypotenuse = -6 / (3√5) = -2/√5

cos θ = adjacent / hypotenuse = -3 / (3√5) = -1/√5

tan θ = opposite / adjacent = -6 / -3 = 2

Again, we leave the values for cosecant, secant, and cotangent blank as they are the reciprocals of the corresponding trigonometric functions.

Therefore, for the point (-3, -6), the exact values of the six trigonometric functions are:

sin θ = -2/√5

cos θ = -1/√5

tan θ = 2

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Answer:

x = 100

Step-by-step explanation:

This problem can be solved if you ignore line DC.

We know that angle FED + angle DEB = angle FEB = 100

Now, if you ignore line DC, you realize that FEB and AEG are vertical angles(opposite angles of 2 intersecting lines). This means that FEB is actually congruent to AEG.

So therefore:

x = AEG = FEB = 100

Answer:

the answer is 24/5

.....

Answer: 14000

Step-by-step explanation:

From the question, the first thing is to first calculate the simple interest (S.I). This will be:

S.I = (principal × rate × time)/100

where principal = 10,000

rate = 4%

time = 10 years

Simple interest = (10,000 × 4 × 10)/100

= 400000/100

= 4000

The total value after 10 years will be th addition of the amount invested and the interest. This will be:

= 10,000 + 4000

= 14000

Let n1 = 80, X1 = 20, n2 = 100, and X2 = 10P_1 and P_2 values are 0.25 and 0.10

Given n1 = 80, X1 = 20, n2 = 100, and X2 = 10P_1 and P_2 values are required

We know that:P_1 = X_1/n_1P_1 = 20/80P_1 = 0.25P_2 = X_2/n_2P_2 = 10/100P_2 = 0.10

Hence, the values of P_1 and P_2 are 0.25 and 0.10 respectively.

Let n1 = 80, X1 = 20, n2 = 100, and X2 = 10P_1 and P_2 values are required

We know that:P_1 = X_1/n_1P_1 = 20/80P_1 = 0.25P_2 = X_2/n_2P_2 = 10/100P_2 = 0.10

Hence, the values of P_1 and P_2 are 0.25 and 0.10 respectively.

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For k = - 3 and n = - 2, the expression evaluates to - 6.

We have the following expression -

- \(k^{2}\) - (9k - 7n) + 5n

We have to evaluate the above expression for k = - 3 and n = - 2.

The expression ax + b for x = - 2 can be evaluated as follows -

Substituting the value of x = - 2, we get :  - 2a + b

We can similarly solve the expression given to us -

- \(k^{2}\) - (9k - 7n) + 5n

Substitute k = - 3 and n = - 2 in the equation, we get -

\(-(-3)^{2} - (9\times -3 \;\;-\;\;7\times -2) + 5\times -2\)

- 9 - (- 27 + 14) - 10

- 9 + 27 - 14 - 10

18 - 14 - 10

18 - 24

- 6

Hence, for k = - 3 and n = - 2, the expression evaluates to  - 6.

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Answer: if you need me to combine, its x6+y3. if not, say please

Step-by-step explanation:

If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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The length of the curve is given by the integral of the square root of the sum of the squares of the derivatives of each component of r(t), integrated over the given interval, length is 6 units.

In this case, we have

r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, and we need to find the length of the curve from t = 0 to t = π/4.

Using the arc length formula, we have the integrand as the square root of (-6sin(6t))^2 + (6cos(6t))^2 + (-6sin(t) / cos(t))^2.

Simplifying the integrand, we get √(36sin²(6t) + 36cos²(6t) + 36sin²(t) / cos²(t)).

Further simplifying, we have √(36 + 36sin²(t) / cos²(t)).

By applying trigonometric identities, we can rewrite the integrand as √(36cos²(t) + 36sin²(t) / cos²(t)).

Simplifying further, we obtain √(36 + 36tan²(t)).

Now,

∫√(36 + 36u²) du / (1 + u²).

Now, we can simplify the integrand:

√(36 + 36u²) / (1 + u²).

Next, we can factor out 36 from the square root:

√36(1 + u²) / (1 + u²).

Simplifying further, we get:

√36 = 6, so the integral becomes:

6∫(1 + u²) / (1 + u²) du.

Notice that the expression (1 + u²) / (1 + u²) simplifies to 1, so the integral reduces to:

6∫du.

Integrating du gives us u + C, where C is the constant of integration.

Therefore, the indefinite integral of √(36 + 36tan²(t)) dt is 6(tan(t)) + C.

To evaluate the definite integral over the interval from 0 to π/4, we substitute the upper and lower limits:

[6(tan(π/4)) - 6(tan(0))] = [6(1) - 6(0)] = 6.

Hence, the length of the curve defined by the given vector function over the interval from 0 to π/4 is 6.

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Answer:

5) -2

6) 1

7) -4/3

8) I'm not sure for this one

9) 8

10) 9/5 i think

1)   A

2)   D or A

3)   C

4)   A

Step-by-step explanation:

Slope intercept form: y = mx + b, and m is the slope, and b is the y-intercept

In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given, Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,

Since,

In 2 mins Mark's model train can go = 1/3 laps

Thus,

In 1 min Mark's model train can go = 1/3/2 laps

In 1 min Mark's model train can go = 1/6 laps

In 9 mins Mark's model train can go = 9/6 laps

In 9 mins Mark's model train can go = 1.5 laps

Therefore,  In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.

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The function f(x) = mx + b is a linear function, and the values of m and b are -1/3 and 7/3, respectively

The function is given as:

f(x) = mx + b

The solutions are (1,2) and (-20,9)

The above points mean that:

1 * m + b = 2

-20 * m + b = 9

This gives

m + b = 2

-20m + b = 9

Subtract both equations

m + 20m = 2 - 9

Evaluate the difference and sum

21m = -7

Divide both sides by 21

m = -1/3

Substitute m = -1/3 in m + b = 2

-1/3 + b = 2

Add 1/3 to both sides

b = 2 + 1/3

Evaluate

b = 7/3

Hence, the values of m and b are -1/3 and 7/3, respectively

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A technique called simple random sampling involves choosing a random group of individuals from a predetermined population.

A selection of participants from a population is chosen at random by the researcher using simple random sampling, a sort of probability sampling.

Every person in the population has the same chance of being chosen.

Then, data are gathered from as much of this randomly selected subgroup as possible.

A straightforward random sample, where each participant has an equal chance of being selected, selects a small, random portion of the entire population to represent the entire data set.

Using techniques like lotteries or random draws, researchers can generate a straightforward random sample.

Therefore, a technique called simple random sampling involves choosing a random group of individuals from a predetermined population.

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The scatter plot of the data in the table is:

And there we can see that the data is similar to a line. We can say that the two values are associated by a linear correlation.

15(x+3) = 2x(12)

15x+45 = 24x

45 = 9x

x = 5

Answer: Rex weighs more.

Step-by-step explanation:

You have to change both of the numbers into the same form. I did decimal form.

Rex - 11 7/18 = 11.389 (rounded to the hundredths)

Roman - 11.329

Rex is bigger.

Hope this helps!

Answer:

  69.6 ft

Step-by-step explanation:

The arc length can be found as a fraction of the circumference. That fraction is the ratio of the central angle measure to the measure for the whole circle.

__

Central angle of remaining arc:

  360° -150° = 210°

Fraction of full circumference:

  210°/360° = 7/12

The circumference of the circle is ...

  C = 2πr = 2π(19 ft) = 38π ft.

Then the length of the remaining arc is ...

  (7/12)(38π) ft ≈ 69.6 ft

Answer:

NKKNKND FG

Step-by-step explanation:

Answer:

1257.14 m or 1.26 km

Step-by-step explanation: hope this helps :)

Answer:

\( - 0.8b + 4.1c + 3.2b - 0.1c = 4c + 2.4b\)

The polar coordinates of the point (3³, -) are (r, θ) = (√730, 0).

To find the polar coordinates of a point given its Cartesian coordinates (x, y), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y/x)

The Cartesian coordinates (x, y) = (3³, -), we can calculate the polar coordinates as follows:

r = √((3³)² + (-)²)

  = √(27² + 1)

  = √(729 + 1)

  = √730

θ = arctan((-)/3³)

     = arctan(-/27)

     = arctan(-0)

Since the value of θ is zero, it means the point lies on the positive x-axis.

Therefore, the polar coordinates of the point (3³, -) are (r, θ) = (√730, 0).

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Answer:

110 have a good one

Step-by-step explanation:

22x5 is 110

The sum of the series is 1792/27 + 17.

To use the formula for the sum of a geometric series, we need to write the series in the form:

a + ar + ar^2 + ar^3 + ...

where a is the first term and r is the common ratio.

In this case, we can see that the first term is 112, and the common ratio is -11/16 (since each term is obtained by multiplying the previous term by -11/16).

So, we have:

112 + (11/16) * 112 + (11/16)^2 * 112 + (11/16)^3 * 112 + ...

The sum of this geometric series can be calculated using the formula:

S = a / (1 - r)

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, we have:

S = 112 / (1 - (-11/16))

= 112 / (27/16)

= 1792/27

So the sum of the series is 1792/27 + 17.

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The equation of a line perpendicular to p(t) = 3t + 4 and passing through the point (3, 1) is: P(t) = -1/3 + 1

Given:

p(t) = 3t + 4

point (3,1)

To find this out, we must use the slope perpendicular to 3

perpendicular slopes are the slope's reciprocal's negative, which in this case it is -1/3

to find the line with the points (3,1), we simply use the equation y = -1/3x + b and then plug them in

1 = -1/3(3) + b

1 = -1 + b

b = 2

the y intercept is 2 and so we can write the equation like this:

P(t) = -1/3t + 2

Hence we get the required equation of a line.

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Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

Answer:

C

Step-by-step explanation:

I'm bot sure if it is correct

The trend projection for time period 18 is 197.6. The correct option is B

A mathematical equation used to represent the trend or pattern seen in a time series of data is called a linear trend expression, sometimes referred to as a linear trend model.

To find the trend projection for time period 18 using the given linear trend expression, we substitute t = 18 into the equation:

Yt = 129.2 + 3.8t

Y18 = 129.2 + 3.8 * 18

Y18 = 129.2 + 68.4

Y18 = 197.6

Therefore, the trend projection for time period 18 is 197.6.

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Answer:

B. (4, -2)

Step-by-step explanation:

Please see attachment.

Hope this helps!

If not, I am sorry.