Use trigonometric identities to simplify each expression.

1/cot^2 (x) - 1/cos^2(x)

s = area = 11.76

p = perimeter = 16.8

r=2*11.76/16.8=23.52/16.8=1.4

r=1.4

a= 90 degrees

b=36.87 degrees

c=53.13 degrees

triangle is in a circle

Circumradius: R = 3.5

Answer:

dictionary data structures can keep track of what words mean or how to spell the words

Step-by-step explanation:

Answer:

Dictionary data structures can keep track of what words mean or how to spell the words, they can keep track of how much water you drink per day, hours spent on studying per week, and dates for upcoming assessments and tests.  

Step-by-step explanation:

9514 1404 393

Answer:

  g(x) = x^2/25

Step-by-step explanation:

For a horizontal stretch by a factor of k, x is replaced by x/k.

  g(x) = f(x/5) = (x/5)^2 = x^2/25

The new function is ...

  g(x) = x^2/25

Question 4: Laura applies for the position of ambulance medic. To give her a job simulation (behavioral interview) screening test, the interviewer...

This question involves providing a job simulation or behavioral interview, which allows the interviewer to observe how the candidate performs in a simulated work situation. This type of question assesses the candidate's skills, abilities, and behavior in a real or simulated work scenario, providing a more accurate evaluation of their capabilities for the job.

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Tthe population of the colony after 2 hours is 64a

From the question, we have the following parameters that can be used in our computation:

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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The total area of the region is: (area for x in `[-1, 1]`) + (area for x in `[1, 2]`) = (-8/3) + (1/3) = -7/3.

The region is bounded by the curve `y = 4 - x²` and the lines `y = x² - 2x` from `x = -1` to `x = 2`.

We need to find the area of this region. So, we can use definite integration to find the area bounded by two curves.

Definite integration involves finding the area of a curve between two values of x.

The formula is shown below: ∫a^b(f(x)dx)

To find the area between two curves, we need to integrate the difference of the two curves between the limits of integration.

The formula is shown below: Area between two curves = ∫a^b(g(x) − f(x))dxwhere `g(x)` is the upper curve and `f(x)` is the lower curve.

We can plot the graph for `y = 4 - x²` and `y = x² - 2x` to see what the region looks like:

Graph of y = 4 - x² and y = x² - 2x We can see from the graph that the two curves intersect at `x = -1` and `x = 2`.

The curve `y = x² - 2x` is above `y = 4 - x²` in the region `[-1, 1]` and below in the region `[1, 2]`.

So, we need to split the area into two parts and integrate each separately.

We can do this as follows: For `x` in `[-1, 1]`, the upper curve is `y = x² - 2x` and the lower curve is `y = 4 - x²`.

So, the area of this part is:

∫-1^1[(x² - 2x) - (4 - x²)]dx = ∫-1^1(2x² - 2x - 4)dx = [-(2/3)x³ + x² - 4x]_-1^1 = (-2/3 + 2 - 4) - (2/3 - 1 + 4) = -8/3For `x` in `[1, 2]`, the upper curve is `y = 4 - x²` and the lower curve is `y = x² - 2x`.

So, the area of this part is: ∫1^2[(4 - x²) - (x² - 2x)]dx = ∫1^2(2x - x²)dx = [x² - (1/3)x³]_1^2 = (4 - (8/3)) - (1 - (1/3)) = 1/3.

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Answer:

An equation of a line is written in the form y=mx+b. ”m” is the slope and “b” is the y-intercept.

Slope: 4

y-intercept: -7 or (0,-7)

:)

Answer:

slope = 4

y-intercept = 7

Answer:

\(\boxed{\text{2. 4.7 units}}\)

Step-by-step explanation:

Assume your triangle has the dimensions shown below.

Before we can use the Law of Sines, we must find ∠C.

1. Calculate ∠C

\(\begin{array}{rcl}A + B + C & = & 180^{\circ}\\66^{\circ} + 76^{\circ} + C & = & 180^{\circ}\\142^{\circ} + C & = & 180^{\circ}\\C & = & 38\, ^{\circ}\\\end{array}\)

2. Calculate b

Use the Law of Sines

\(\begin{array}{rcl}\dfrac{b}{\sin B } & = & \dfrac{c}{\sin C}\\\\\dfrac{b}{\sin 76^{\circ}} & = & \dfrac{3}{\sin 38^{\circ}}\\\\\dfrac{b}{0.9703} & = & \dfrac{3}{0.6157}\\\\ & = & 4.873\\b & = & 0.9703\times 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}\)

Answer: 4.

Step-by-step explanation:

(5−3)^2

which is 2 times 2

so you get 4.

Answer:

\(slop = \frac{y2 - y1}{x2 - x1} = \frac{ - 4 - 1}{ - 4 - 0} = \frac{ - 5}{ - 4} = 1.25\)

Answer:

285

Step-by-step explanation:

585 - 300 = 285

Answer:

x^2 +3x

Step-by-step explanation:

The outer rectangle has an area of

A = l*w = (4x)*(x+2) = 4x^2 +8x

The inner rectangle has an area of

A = (3x+5)*x = 3x^2 +5x

Subtract the inner rectangle from the outer rectangle

Shaded area = 4x^2 +8x - ( 3x^2 +5x)

Distribute the minus sign

                       =4x^2 +8x -  3x^2 -5x

Combine like terms

                       = x^2 +3x

Answer:

x = 9

Step-by-step explanation:

So We Already know that y =6

Hence, Let's set up the equation..

2x+18 =36

2x=36-18

x=18/2

x=9

If You don't get it then.

( 9 x 2 ) + ( 3 x 6 ) = 36

18 + 18 = 36

Step-by-step explanation:

If the equation is multiplying the two variables, then:

2x * 3(6) = 36

2x * 18 = 36

2/18x = 2

x = 4/18 (or 2/9)

If the equation is adding the two variables, then:

2x + 3(6) = 36

2x + 18 = 36

2x = 18

x = 9

If the equation is subtracting the two variables, then:

2x - 3(6) = 36

2x - 18 = 36

2x = 54

x = 27

The statement "When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events" is true.

When two events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event. In such cases, the joint probability of both events can be found by multiplying their individual probabilities. Mathematically, this can be expressed as P(A ∩ B) = P(A) * P(B). This rule holds true for independent events and is a fundamental concept in probability theory.

Now, let's examine the other statements:

1. The probability of the union of two events can exceed one:

This statement is false. The probability of an event is always between 0 and 1, inclusive. When you consider the union of two events, the probability of their combined occurrence cannot exceed 1. It is possible for the sum of the individual probabilities of the two events to exceed 1, but the probability of their union will never be greater than 1.

2. When events A and B are mutually exclusive, then P(A ∩ B) = P(A) + P(B):

This statement is false. Mutually exclusive events are events that cannot occur at the same time. If events A and B are mutually exclusive, their intersection (A ∩ B) will be an empty set, and therefore, the probability of their intersection is 0 (P(A ∩ B) = 0). The correct statement for mutually exclusive events is P(A ∪ B) = P(A) + P(B), where P(A ∪ B) represents the probability of the union of events A and B.

3. The union of events A and B consists of all outcomes in the sample space that are contained in both event A and B:

This statement is false. The union of events A and B, denoted as A ∪ B, consists of all outcomes that belong to either event A or event B or both. In other words, it includes all outcomes that are in A, in B, or in both A and B. The intersection of events A and B (A ∩ B) represents the outcomes that are contained in both A and B.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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Answer:

Explanation:

3x · 4 = 7x - (x + 17)

Simplify both sides of the equation

3x (4) = 7x − (x + 17)

3x (4) = 7x + −1 (x + 17) (Distribute the Negative Sign)

3x (4) = 7x + −1x + (−1) (17)

3x (4) = 7x + −x + −17

12x = 7x + −x + −17

12x = (7x + −x) + (−17) (Combine Like Terms)

12x = 6x + −17

12x = 6x − 17

Subtract 6x from both sides

12x − 6x = 6x − 17 − 6x

6x = −17

Divide both sides by 6

6x / 6 = −17 / 6

Simplify

x = ⁻¹⁷⁄₆

Turn the fraction into a decimal

-17 ÷ 6 = -2.83333333333

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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Answer:

Future population = 720800

Step-by-step explanation:

Below is the calculation of population after 15 years.

Given the present population = 340000

Growth in population = 5.25%

Use below formula to find the values:

Future population = Present population ( 1 + r)^n

Future population = 340000 ( 1 + 5.25%)^15

Future population = 340000 (2.15)

Future population = 720800

Answer:

9.(A) y + 7 < −7 OR y + 7 > 7

12.(C) 10A=44+300

Step-by-step explanation:

prob(even or Less than 5)= prob(even) + prob(<5)= 5/10 + 4/10 = 9/10 =4/5

9514 1404 393

Answer:

  22%

Step-by-step explanation:

If Denver gets 2/19 of the food, then Engle and Fido share the remaining 17/19 of the food.

If Engle and Fido share their food in the ratio of 6:2, then Fido's share is 2/(6+2) = 2/8 = 1/4 of the portion they have.

Fido's share of all the food is then (1/4)(17/19) = 17/76.

As a percentage of the whole, that is ...

  17/76 × 100% ≈ 22%

The statement that "when dealing with fixed effects, a de-meaned model approach is superior to the lsdv approach because the de-meaned model gives us more accurate coefficient estimates" is true.

Fixed effects are a type of regression technique used to understand the effect of a single variable across different groups (such as across countries, across states, across individuals, etc.) by comparing the variance of the variable within each group to the variance of the variable across all groups.

When conducting a fixed effects regression, researchers must choose between the least squares dummy variable (LSDV) and de-meaned model approaches.Both models produce unbiased estimates of the coefficients, but the LSDV model has an advantage in that it provides more flexibility when dealing with interactions between fixed effects and time-varying covariates. On the other hand, the de-meaned model is preferred for reasons of computational efficiency and it can handle certain types of data that the LSDV model cannot (such as panel data with a small number of time periods).

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We have a formula to it, given the points  (x, y) and (xo, yo)

\(dist = \sqrt{(x-xo)^2+(y-yo)^2}\)

So,

\(dist = \sqrt{(6-2)^2+(8-5)^2}\)

\(dist = \sqrt{4^2+3^2}\)

\(dist = \sqrt{25}\)

\(dist = 5\)

Answer:

The distance between the two points is 5

Step-by-step explanation:

For this problem, we are given the dimensions of a garden and the cost of planting seeds per square meter in this garden. We need to determine the total cost of planting the seeds.

The first step is to calculate the area of the garden, for which we need to multiply the length and width:

Now we need to multiply the area by the cost of the seeds per square meter. We have:

The total cost is 21.5x² + 40.85x -32.25

The equation of the problem is \(5(n+7)\)

The sentence is asking 5 times the sum of n+7, so you are multiplying (n+7) by 5.

By using the "disp" function, we can show the value of a variable on the screen.

With MATLAB's "disp" function, you can show the value of a variable on the screen. The "disp" function prints the variable's or expression's value as text on the screen. The syntax for employing the "disp" function is as follows: CSS copy code displayed (variable)

The variable that you want to display is called "variable" in this case. MATLAB will show the value of the variable in the Command Window when the "disp" function is called with the variable as an argument.

Assume, for instance, that you've created the variable "x" and given it the value of 5. The following code can be used to show the value of "x": scss Coding example: x = 5; disp(x); When this code is executed, MATLAB will show that.

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The options that can be used as indices for the array are option A (i) and option E ((int)(Math.random() * 100)).

To determine which expressions can be used as an index for the array double[] t = new double[100], let's evaluate each option :

A. i: Since i is an integer variable with a value of 5, it can be used as an index because it falls within the valid index range of the array (0 to 99).

B. I + 6.5: This expression adds 6.5 to the variable i. Since array indices must be integers, this expression would result in a double value and cannot be used as an index.

C. 1 + 10: This expression evaluates to 11, which is an integer value and can be used as an index.

D. Math.random() * 100: The Math.random() function returns a double value between 0.0 (inclusive) and 1.0 (exclusive). Multiplying this value by 100 would still result in a double value, which cannot be used as an index.

E. (int)(Math.random() * 100): By multiplying Math.random() by 100 and casting the result to an integer, we obtain a random integer between 0 and 99, which falls within the valid index range and can be used as an index.

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