Determine the value of secθ given that the terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y)

Answers

Answer 1

Cosθ = x, where x = 16÷19. secθ = 1/(16÷19), secθ = 19÷16

How we can find value of secθ where terminal side of angle θ intersects?

We know that the point (16÷19, y) lies on the unit circle in the first quadrant, which means that:

x×2 + y×2 = 1 where x= 16÷19

Solving for y, we get:

y×2 = 1 - (16÷19)×2y×2 = 1 - 256÷361y×2 = 105÷361y = ±√(105÷361)

Since the point lies in the first quadrant, y must be positive, so:

y = √(105÷361)

We can now use the definition of secant to find secθ:

secθ = 1÷cosθ

The first step involves finding the value of y using the Pythagorean theorem since the point (16÷19, y) lies on the unit circle. In the second step, we use the definition of secant which is the reciprocal of cosine.

Since the point lies in the first quadrant, both x and y are positive, and we can use x = 16÷19 as the adjacent side of the angle θ, and find its cosine. Finally, we use the reciprocal of cosine to find the value of secθ, which turns out to be 19÷16.

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Related Questions

The revenue per month earned by the Couture clothing chain at time t is R(t) = N(t)S(t), where N(t) is the number of stores and S(t) is the average revenue per store per month. Couture releases a statement to their investors saying that currently they have 50 stores with a total revenue of $7,500,000 and expect to increase the number of stores by about 2 stores per month and increase total revenue by about $250,000 per month. What does this statement imply about the current rate of change of the average revenue per store per month?

Answers

The statement implies that the current rate of change of the average revenue per store per month is -$250,000, which means that the average revenue per store is decreasing by $250,000 per month

We can start by differentiating the given expression for revenue with respect to time t:

dR/dt = d(N(t)S(t))/dt

= N(t)dS/dt + S(t)dN/dt

The statement tells us that dN/dt = 2 (the number of stores is increasing by 2 per month) and dR/dt = $250,000 (the total revenue is increasing by $250,000 per month). We also know that at the current time t, N(t) = 50 and R(t) = $7,500,000.

Substituting these values into the above expression, we get:

$250,000 = 50 dS/dt + $7,500,000 × 2

Simplify this equation, we can solve for dS/dt:

dS/dt = ($250,000 - $15,000,000) / 50

= -$250,000

So the current rate of change of the average revenue per store per month is -$250,000, which means that the average revenue per store is decreasing by $250,000 per month. This could be due to various factors such as increased competition, changes in consumer preferences, or changes in pricing strategies.

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Sebastian is swimming with Ariel and Flounder. They start at 30 feet below sea level. Then, they rise 15 feet, dive 5 feet, and rise another 13 feet. Where are they at in the water?

Answers

Answer: 13 feet

Step-by-step explanation:

Answer:

they're at 7 feet below sea level

Step-by-step explanation:

it starts at -30 sea level then goes to -15 sea level and they dive again to end up at -20 sea level but they rise 13 so they end up at -7

The list shows the thickness of ice on the roads after a storm. On the line plot each x represents 1 measurement which line plot matches the data

Answers

Answer:

Step-by-step explanation:

Ice sheets have one particularly special property. They allow us to go back in time and to sample accumulation, air temperature and air chemistry from another time[1]. Ice core records allow us to generate continuous reconstructions of past climate, going back at least 800,000 years[2].

Ice coring has been around since the 1950s. Ice cores have been drilled in ice sheets worldwide, but notably in Greenland[3] and Antarctica[4, 5]. High rates of snow accumulation provide excellent time resolution, and bubbles in the ice core preserve actual samples of the world’s ancient atmosphere[6].

Simplify. (Step by step)

Simplify. (Step by step)

Answers

Answer:

Step-by-step explanation:

The answer is:

\(3x^2\sqrt{5x^2w^7\)

See work below for more detail.

Simplify. (Step by step)

Two concentric circles are of radii 10 cm and 8 cm, then the length of the chord of the larger circle which touches the smaller circle is​

Answers

Answer:

12 cm

Step-by-step explanation:

Let O be the centre of the circle of radii 10 cm and 8 cm.

In given figure,

AP = PB and OP⊥AB

Applying Pythagoras theorem in ∆OPA, we get

↠ OA² = OP² + AP²

↠ (10)² = (8)² + AP²

↠ 100 = 64 + AP²

↠ 100 - 64 = AP²

↠ 36 = AP²

↠ √36 = AP

6 = AP

Now,

↠ AB = 2AP

↠ AB = 2(6)

↠ AB = 12 cm

Hence,

The length of the chord of the larger circle 12 cm
Two concentric circles are of radii 10 cm and 8 cm, then the length of the chord of the larger circle

engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min

Answers

The largest head diameter that can accommodate the clientele is 8.5743

Mean, u = 6.4

Standard deviation = 0.9

We must utilize the inverse of the common normal table to obtain our values.

the smallest head width possible.

P(Z < z) = 1.4%

P(Z < z) = 0.014

P(Z < -2.0749) = 0.014

z = -2.0749

Using the z-score calculation,

(x - μ) ÷ σ = \(Z_{0.019}\)

Let x be the heads' breath.

Making x the focus of the equation,

x = z × σ + μ

We already have:

z = -2.0749

u = 6.5

s.d = 1

Replacing numbers,

x = (-2.0749 × 1) + 6.5

x = 4.4251

The clientele requires a minimum head breadth of 4.4251.

The largest head width that can be accommodated.

P(Z > z) = 1.4%

1 - P(Z < z) = 0.014

P(Z < z) = 1 - 0.014 = 0.981

P(Z < 2.0749) = 0.981

Using the z-score calculation,

(x - μ) ÷ σ = \(Z_{0.019}\)

Let x be the heads' breath.

Making x the focus of the equation,

x = z × σ + μ

z = 2.0749

u = 6.5

s.d = 1

Substituting figures,

x = (2.0749 × 1) + 6.5

x = 4.4251

x = 8.5743

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a product shipment contains 6 computer chips, of which two (2) are defective. if an inspector selects 4 chips at random for an order, without replacement, how many ways are there of picking both defective chips in this order (of 4 chips)?

Answers

Answer:

We know that  there are 6 ways of picking both defective chips in this order of 4 chips.

We want to find the number of ways of selecting both defective chips out of 2 from a total of 6 chips, when selecting 4 chips without replacement.

The number of ways of selecting 2 defective chips out of 2 is 1 (there is only one way to select 2 out of 2).

The number of ways of selecting 2 non-defective chips out of 4 is given by the combination formula:

C(4,2) = 4!/(2!2!) = 6

Therefore, the number of ways of selecting both defective chips and 2 non-defective chips out of 4, without replacement, is:

1 * 6 = 6

So there are 6 ways of picking both defective chips in this order of 4 chips.

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Given l∥m∥n, find the value of x.

Given lmn, find the value of x.

Answers

Answer:

x = 61

Step-by-step explanation:

\(x + 119 = 180\)

\(x = 180 - 119\)

\(x = 61\)

Answer:

x = 61

Step-by-step explanation:

Find the y- intercept of the rational function.

Answer choices:

A.) (0,-2)
B.) (-2,0)
C.) (0,6)
D.) (6,0)

Find the y- intercept of the rational function.Answer choices:A.) (0,-2)B.) (-2,0)C.) (0,6)D.) (6,0)

Answers

Answer:

A. (0,-2)

Step-by-step explanation:

Meaning of a rational number is a number that can be expressed as the quotient or fraction

p/q of two integers, a numerator p and a non-zero denominator q.

Answer:

(A). (0,-2)

Step-by-step explanation:

y-intercept means the points in which the funtion crosses the y-axis. According to the graph you can see that at (0,-2) it crosses the axis and therefore (0,-2) is the answer.

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12. Water is being pumped into a pool at a constant rate of 8.25 gallons per minute. If the pool contained 1250
gallons of water initially, write a function for the number of gallons of water, g(t),in the pool after t minutes
of pumping water into the pool.

Answers

Answer:

\(g(t)=8.25t+1250\)

Step-by-step explanation:

You can input any value for t, and that would give you the amount of water pumped in. Then, the +1250 represents the initial 1250 gallons that are in the pool.

which of the equations below has a slope of 1/4

Answers

Answer:

uh you didnt put the picture please put the picture i really want to help you:)

Step-by-step explanation:

Answer:

bra

Step-by-step explanation:

Write 0.00548 in scientific notation.

Answers

Answer: 5.48 × 10^-3.

Step-by-step explanation:

A firm experiences_______ if inputs are doubled and output more than doubles. diminishing marginal rate of technical substitution diminishing marginal product decreasing returns to scale increasing returns to scale

Answers

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Determine the value of x.
Options:
A) x = 11.2
B) x = 56
C) x = 12.4
D) x = 10

Determine the value of x.Options:A) x = 11.2B) x = 56C) x = 12.4D) x = 10

Answers

Answer:

as lengths of tangents of a circle from an external point are equal so

5x+6 = 56

5x = 50

x = 50/5

D) x = 10

i need help plszsz
plszsz

i need help plszsz plszsz

Answers

Answer:

C

Step-by-step explanation:

Sandy has 16 roses, 4 daisies, and 20 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?

Answers

Answer:

4 flowers

Step-by-step explanation:

Sandy has 16 roses, 4 daisies, and 20 tulips.

We find the factors of 4, 16 and 20

The factors of 4 are: 1, 2, 4

The factors of 16 are: 1, 2, 4, 8, 16

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4.

Therefore, the greatest number of flowers that could be in a bouquet is 4 flowers

A friend of ours takes the bus five days per week to her job. The five waiting times until she can board the bus are a random sample from a uniform distribution on the interval from 0 to 10 min. Determine the pdf and then the expected value of the largest of the five waiting times.

Answers

The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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use the graph to complete the following statements if necessary round to the nearest whole number

Answers

Your answer should and must be 5

does somebody know how to do this??​

does somebody know how to do this??

Answers

Answer:

95

Step-by-step explanation:

65+66+90+95=316

316/4=79

Identify the percent in 12 is 50% of 24

Answers

Answer:

50 percent of 24 is 12. 3.

Step-by-step explanation:

50 percent *24

= (50/100)*24

= (50*24)/100

= 1200/100 = 12

Now we have: 50 percent of 24 = 12

Question: What is 50 percent of 24?

We need to determine 50% of 24 now and the procedure explaining it as such

Step 1: In the given case Output Value is 24.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 24 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

24 = 100% (1).

x = 50% (2).

(24%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/24% = 50/100

Step 7: Simplifying the above obtained equation further will tell what is 50% of 24

x = 12%

Therefore, 50% of 24 is 12

Consider the following regression model: Y₁ =B₁ + B₂X₂1+ B3X31 + B₂X41 +14₁ Using the model above show that the maximum likelihood estimator for the variance, var (uiX21-X31-B4X4), is biased (be sure to comment of the nature of the bias).

Answers

The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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839 / 41
hurry I need it now

Answers

Answer:

20.4634146

Step-by-step explanation:

Rounded it be 20.46 or 20.5

Answer:

20.46

Step-by-step explanation:

just divide :)

have a nice day

15. What is the markdown rate of a jacket originally priced at $185 and is now on sale for $83.25?
135(63

Answers

Answer: the Markdown rate is 153.55

Step-by-step explanation:

185-34

then that subtract 0.45

Which is Overall

153.55

Select all names that apply to the number. 0

Answers

There is multiple names it has, like for example “Zero” and in British English it is “nought” which is often used as an archaic word for nothing, I hope this help’s.

a coin with an unknown probability of heads, m, is flipped 25 times resulting in 15 heads and 10 tails. what is the expected probability that the next flip is a head given the results of the previous 25 coin flips?

Answers

The expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

The expected probability of a head coming up next given the results of the 25 coin flips is 15/25 = 0.6.

This is due to the fact that 15 of the 25 flips were heads, so the probability of the next head is 15 out of the 25 total flips which is equal to 0.6 or 60%.

However, since the probability of heads (m) is unknown, the expected probability of a head coming up next is still unknown.

Therefore, the expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

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if the lenghts of the diagonals of a rhombus are 10 cm and 8 cm then its area is​

Answers

Answer:

40cm square

Step-by-step explanation:

10x8cm=80 cm/2=40cm square

Answer:80cm

Step-by-step explanation:Area=\(\frac{dxd}{2}\)

10cm x 8cm=80cm

suppose that this decade begins on 1 january 2020 which is wednesday and the next decade begins on 1 january 2030. how many Wednesday are there in this decade?​

Answers

Answer:

521

365 *10 = 3650

365/7 = 521.4

Step-by-step explanation:

What is the y - intercept?

A. 0
B. 1
C. 2
D. 7​

What is the y - intercept?A. 0B. 1C. 2D. 7

Answers

Answer:

(0,7)

explanation:

if you draw out the graph you would see the graph touches the y axis at 7

Solve for x if 2(5x + 2)2 = 48.

Solve for x if 2(5x + 2)2 = 48.

Answers

Answer:

Answer 3.

Step-by-step explanation:

took the quiz on edge

Answer:

c

Step-by-step explanation:

$200, P= $1000, r = 4 years

I need it as a fraction then turned into a decimal

Answers

Hey are you American

Step-by-step explanation:

I'm filipino

Answer:

The formula for simple interest is:

I = P * r * t

Where:

I = Interest

P = Principal amount

r = Rate of interest per year

t = Time period

Given:

P = $1000

r = 4 years

t = $200

Substituting the values in the formula, we get:

I = $1000 * 0.04 * 4

I = $160

To express this as a fraction of $200, we can write:

$160/$1000

This fraction can be simplified by dividing both numerator and denominator by 20:

$8/$50

This fraction can be further simplified by dividing both numerator and denominator by 2:

$4/$25

This fraction, when expressed as a decimal, is:

0.16

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