Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number

We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Both f(t) and g(t) are of exponential order.

To show that a function f(t) is of exponential order, we need to find positive constants M and k such that:

|f(t)| <= M * e^(k*t) for all t >= t0, where t0 is some arbitrary constant.

Let's start by considering f(t) = t³ * sin(t). We can use the fact that |sin(t)| <= 1 to obtain an upper bound for f(t):

|f(t)| = |t³ * sin(t)| <= t³ for all t

Now we need to find k such that t³ <= M * e^(k*t) for all t >= t0. Taking logarithms of both sides yields:

ln(t³) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

3 ln(t) <= ln(M) + k*t

Now we can choose M = 1 and k = 1 to obtain:

3 ln(t) <= ln(1) + t

3 ln(t) <= t

This inequality holds for all t >= 1, so we have shown that f(t) is of exponential order with M = 1 and k = 1.

Next, consider g(t) = t² * e^t. We can once again obtain an upper bound using the fact that e^t >= 1:

|g(t)| = |t² * e^t| <= t² * e^t for all t

To find M and k such that t² * e^t <= M * e^(k*t) for all t >= t0, we can again take logarithms of both sides:

ln(t² * e^t) <= ln(M * e^(kt)) = ln(M) + kt

Simplifying the left-hand side:

2 ln(t) + t <= ln(M) + k*t

Now we can choose M = 1 and k = 2 to obtain:

2 ln(t) + t <= ln(1) + 2t

2 ln(t) + t <= 2t

This inequality holds for all t >= 1, so we have shown that g(t) is of exponential order with M = 1 and k = 2.

Therefore, both f(t) and g(t) are of exponential order.

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The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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Answer:

790

Step-by-step explanation:

The volume equals: Height * Width * Length

Therefore, the volume = 22.9*7.5*4.6 = 790 cubic meters.

Answer:

I think first one

Step-by-step explanation:

because 1 3 1 are to separate

10 3 4 too

and 5 2 3

Use an alternative method such as the binomial test or the exact test for proportions when np is less than five.

When the product of the sample size (n) and the population proportion (p) is less than five (np < 5), the conditions for applying the normal approximation to the binomial distribution are not met. In such cases, it is recommended to use alternative methods to perform a valid hypothesis test.

One common approach is to utilize the exact test or Fisher's exact test. This method calculates the probabilities directly based on the binomial distribution, providing more accurate results when the sample size is small or np is low.

By employing the exact test, you consider all possible outcomes and calculate the exact probabilities of observing the data under the null hypothesis. This allows for a reliable hypothesis test, even when the normal approximation is not suitable.

Therefore, to perform a valid hypothesis test when np is less than five, you should opt for the exact test or Fisher's exact test rather than relying on the normal approximation.

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Answer:

yeah

Step-by-step explanation:

They do not intersect???

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

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Step-by-step explanation:

the answer is in the above image

adjacent side:

using Pythagoras

hypo² = oppo² + adja²

(√13)² = 2² + adja²

adja²= 13 -4

adja²=9

adjacent side = 3

so tan A= oppo/adja

tan A=2/3

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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Answer:

im not sure but i think the answer is 1,983.31

Step-by-step explanation:

Answer:

D. -2

Step-by-step explanation:

19 = x + 12 + 11 + x

Solve for x

Combine like terms

x + x = 2x

12 + 11 = 23

We now have

19 = 23 + 2x

Subtract 23 from both sides

19 - 23 = -4

23 - 23 cancels out

We now have -4 = 2x

Divide both sides by 2.

-4/2 = -2

2x/2 = x

x = -2

The inverse function of g(x) is g⁻¹(x) = 11x + 13. And the value of the (g · g⁻¹)(1) and h⁻¹(9) will be -288/11 and -5, respectively.

Given that:

Function, g(x) = (x - 13) / 11

h = {(-9, 1), (-5, 9), (6, 8), (8, 5), (9, 4)}

To determine the inverse function of the function f will be given by swapping x with y and y with x.

The inverse function of g(x) is calculated as,

x = (y - 13) / 11

11x = y - 13

y = 11x + 13

g⁻¹(x) = 11x + 13

The product of function and inverse function is given as,

(g · g⁻¹)(x) = (x - 13) (11x + 13) / 11

(g · g⁻¹)(x) = [11x² - 130x - 169] / 11

(g · g⁻¹)(1) = [11(1)² - 130(1) - 169] / 11

(g · g⁻¹)(1) = -288/11

The value of h⁻¹ is calculated as,

h⁻¹(9) = -5

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Answer:

angle 2

Step-by-step explanation:

Corresponding angles are angles that are on the same side of the transversal and are congruent.

To visualize this kindly view the attatched image.

Based off of the attatched image, the angle corresponding to angle 1 whould be angle 2.

We are not given enough information to find the measure of this angle but we do know ∠1 ≅ ∠2

Answer: B

Step-by-step explanation:

Answer:

x is greater than or equal to 4

Step-by-step explanation:

divide both sides by two, treating it as an equation

so x is greater than or equal to 4

The sample percentage (p) represents the proportion of people in a sample who have a particular attribute or trait. The correct option is A.

The sample percentage (p) represents the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or objects) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

Given there are 36 successful outcomes in a sample with a size of 80. Therefore, the sample proportion is,

Sample proportion = 36/80 = 0.45

Hence, the correct option is A.

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Answer:ask your teacher bc thats confusing

Step-by-step explanation:

For exercise 1, the derivative of F(x) = 2x^3 - 3x^2 + 3/x^2 is f'(x) = 6x^2 - 6x + 6/x^3, obtained by applying the power rule. For exercise 2, the derivative of F(x) = (x^2 + 2x)(3x^2 - 4) is f'(x) = 12x^3 - 8x + 18x^2 - 8, obtained by expanding and differentiating each term separately using the power rule.

Exercise 1:

Given: F(x) = 2x^3 - 3x^2 + 3/x^2

To find the derivative f'(x), we first rewrite F(x) as a polynomial:

F(x) = 2x^3 - 3x^2 + 3x^(-2)

Applying the power rule to find f'(x), we differentiate each term separately:

For the first term, 2x^3, we apply the power rule:

f'(x) = 3 * 2x^(3-1) = 6x^2

For the second term, -3x^2, the power rule gives:

f'(x) = -2 * 3x^(2-1) = -6x

For the third term, 3x^(-2), we use the power rule and the chain rule:

f'(x) = -2 * 3x^(-2-1) * (-1/x^2) = 6/x^3

Combining these derivatives, we get the overall derivative:

f'(x) = 6x^2 - 6x + 6/x^3

Exercise 2:

Given: F(x) = (x^2 + 2x)(3x^2 - 4)

To find the derivative f'(x), we expand the expression first:

F(x) = 3x^4 - 4x^2 + 6x^3 - 8x

Applying the power rule to find f'(x), we differentiate each term separately:

For the first term, 3x^4, we apply the power rule:

f'(x) = 4 * 3x^(4-1) = 12x^3

For the second term, -4x^2, the power rule gives:

f'(x) = -2 * 4x^(2-1) = -8x

For the third term, 6x^3, we apply the power rule:

f'(x) = 3 * 6x^(3-1) = 18x^2

For the fourth term, -8x, the power rule gives:

f'(x) = -1 * 8x^(1-1) = -8

Combining these derivatives, we get the overall derivative:

f'(x) = 12x^3 - 8x + 18x^2 - 8

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Hence, a shift register with a minimum of 8 stages would be necessary to generate the given sequence.

To determine the minimal number of stages of a shift register necessary for generating the given sequence, we need to find the length of the shortest feedback shift register (FSR) capable of generating the sequence.

Looking at the sequence 0 1 0 1 0 1 1 0, we can observe that it repeats after every 8 bits. Therefore, the minimal number of stages required for the shift register would be equal to the length of the repeating pattern, which is 8.

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Answer:

3.) x= 1 y= -3    4.) x= 10 y= -10

Step-by-step explanation:

Step-by-step explanation:

In x you can put the value which can given in question.

Answer:

5 people JUST jog

Step-by-Step Explanation:

150 PEOPLE

150-85=65 (85=swim)

65-60(swim/jog) =5 (jog)

THAT MEANS 5 PEOPLE JUST JOG

OR 65 PEOPLE JOG OVERALL

The number of people who jogs are 90.

We can solve this problem using the Rule of Inclusion/Exclusion.

The Rule of Inclusion/Exclusion states that if you want to find the number of elements in both sets, subtract the number of elements in the intersection from the sum of the number of elements in each set.

Therefore, in this problem, the number of people who jog is equal to the total number of people who either swim or jog, 150, minus the number of people who both swim and jog, 60, which is equal to 90 people.

Therefore, 90 people jog.

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Answer:

r=24

Step-by-step explanation:

Answer:

x = 98

Step-by-step explanation:

x = 53 + 45

x = 98

note: the measure of an ext. angle of a triangle is equal to the sum of the two non-adjacent interior angles.

Answer:

98

sum of angle in this triangle = 180

180-(53+45) = 82

so, the third angle is 82 degrees.

moving forward, the third angle (82 degrees) and angle x are straight line angle,

therefore, x + 82 = 180

x =180-82

x=98

Answer:

150 total eggs cracked

Step-by-step explanation:

I don't know how others do it but this is my way (fast and easy)

1,350/18

= 75

75*2

=150 total eggs cracked

Answer:

150 eggs expect to be cracked if there are a total of 1,350 in the grocery store.

Step-by-step explanation:

18 eggs - 2 cracked  = 16 eggs were good condition at  grocery story

1,350 eggs  / 18 eggs = 75

75 x 2 = 150

1,350 - 150 = 1200

Out of 1350 eggs,  1200 eggs  were good condition at  grocery story

150 eggs expect to be cracked if there are a total of 1,350 in the grocery store.

Fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The x axis label is Time in seconds, and the x axis values are from 0 to 10 in increments of 2 for each grid line.

The y axis label is Number of Balls, and the y axis values from 0 to 60 in increments of 12 for each grid line

A line is shown connecting points on ordered pair (2, 12) and (4, 24) and (6, 36) and (8, 48)

m=24-12/4-2

m=12/2

Hence,  fraction 12 over 2 can be used to calculate the rate per second at which the machine launches the balls

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Answer:

The answer is Nitrogen

Hope this helps :)

The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

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The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

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To find two positive numbers whose product is 81 and whose sum is a minimum, we can use the concept of the arithmetic mean-geometric mean inequality. The two positive numbers whose product is 81 and whose sum is a minimum are 3 and 27.

Step 1: Let's call the two positive numbers x and y.

Step 2: We know that the product of x and y is 81, so we can write the equation: x * y = 81.

Step 3: To find the sum of x and y, we can use the formula for the arithmetic mean, which is (x + y)/2.

Step 4: To minimize the sum, we want to minimize the arithmetic mean.

Step 5: According to the arithmetic mean-geometric mean inequality, the arithmetic mean is always greater than or equal to the geometric mean.

Step 6: The geometric mean of x and y is the square root of their product, so we can write the equation: √(x * y) = √81.

Step 7: Simplifying, we get √(x * y) = 9.

Step 8: Taking the square root of both sides, we find that x * y = 9.

Step 9: Since the product of x and y is the same as before, we know that x * y = 81.

Step 10: So, we have two equations: x * y = 9 and x * y = 81.

Step 11: Solving these equations, we find that the values of x and y are (3, 27) or (27, 3).

Step 12: Therefore, the two positive numbers whose product is 81 and whose sum is a minimum are 3 and 27.

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