Derive the following result "algebraically" using the properties listed in Theorem 6.2.2. Give a reason for every step that exactly justifies what was done in the step For all sets A.B.and C.(AU C-B=(A-B)u(C-B)

The given statement, "B. If t is a real number that corresponds to the point on the unit circle that lies along the positive y-axis, then tant is undefined" is not true because, Tant is undefined if t is a real integer corresponding to the point on the unit circle that lies along the positive y-axis..

Statement (B) is false: "If t is a real integer corresponding to the point on the unit circle that is along the positive y-axis, then tant is undefined."

The following is an explanation for the aforementioned answer: For 90° and 270° angles, the tangent (tan) function is undefined. It is a standard angle on the unit circle and sits on the positive y-axis, it equates to 90 degrees or pi/2 in radians. The tangent function is not undefined at this angle, as shown below:

tan(pi/2) = undefined

Therefore, statement (B) is not true.

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Answer:

50 and 20 that is the answer Thank you

For a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.

To find the relationship between a small change in x (dx) and the corresponding change in y (dy) for the function f(x) = 2x³ - 4x, we can differentiate the function with respect to x.

f(x) = 2x³ - 4x

Differentiating both sides with respect to x:

f'(x) = d/dx (2x³ - 4x)

f'(x) = 6x² - 4

Now, we can express the relationship between dx and dy in the form of dy = f'(x)dx:

dy = (6x² - 4)dx

Therefore, for a small change in x (dx), the corresponding change in y (dy) is given by the equation dy = (6x² - 4)dx.

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Answer:

See Below

Step-by-step explanation:

Put -5 in place of x

18(-5)-42 does not equal 7(-5)

-90-42 does not equal -35

-90-42=-132, not -35

The value x = -5 is a solution to the inequality 18x − 42 ≠ 7x.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

For showing x =-5 is a solution of the inequality 18x − 42 ≠ 7x put x =-5 in the solution if it satisfies the condition then it is a solution of the given inequality.

18x − 42 ≠ 7x

18 x ( -5 ) - 42 ≠ 7 x ( -5 )

-132 ≠ -35

The value x = -5 is satisfying the given inequality. Hence, x = -5 is a solution to the inequality 18x − 42 ≠ 7x.

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Answer:

answer = 15.1 cm

Step-by-step explanation:

The user cost of capital for that machine over one year is \(\$1,700.\)

The user cost of capital represents the economic cost incurred by a company for using a machine or capital asset. It takes into account both the opportunity cost of the capital invested and the depreciation of the asset over time.

In this scenario, the machine initially costs \(\$10,000\) in constant dollars, which means it is the real price adjusted for inflation. The real rate of interest is given as \(12\%\), which represents the cost of borrowing or the opportunity cost of using the capital for other investments.

The machine is expected to increase in price by \(2\%\) due to inflation, and the rate of depreciation is \(5\%\) which represents the decrease in the value of the machine over time.

To calculate the user cost of capital over one year, we add the real rate of interest and the rate of depreciation, and multiply it by the initial machine value:

\(User cost of capital = (0.12 + 0.05) * \$10,000 = 0.17 * \$10,000 = \$1,700\)

Therefore, the user cost of capital for that machine over one year is \(\$1,700.\)

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Answer:

x=38 degrees

Step-by-step explanation:

Vertical angles are congruent. In the image, angle x is vertical to the angle that is given. Therefore, x=38 degrees

Answer:

Ten thousands

Step-by-step explanation:

Replace all other digits with zero

This gives 40,000

Ten thousand (10,000) has the same amount of digits

Since the bond is a discount bond, it's only payment is the repayment of the par value at maturity, i.e., in one year.Yield to maturity = 25%

Yield to maturity (YTM) is the total rate of return a bond will have achieved after all interest payments and principal repayments have been made.

In essence, YTM represents the internal rate of return (IRR) on a bond if held to maturity.It can be difficult to calculate yield to maturity because it makes the assumption that the bond's rate of return is applicable to all interest and coupon payments.

800 = \(\frac{1000} {1 + \:\:yield \:\:to \:maturity}\)

1 + Yield to maturity = 1.25

Yield to maturity = 25%

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the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Answer:

24.25

Step-by-step explanation:

The minimum admission score is at the 70th percentile of the normal distribution which, according to a z-score table, corresponds to a z-score of 0.524.

The z-score, for any given value X, is determined by:

\(z=\frac{X-\mu}{\sigma}\)

If the mean score is 21 and the standard distribution is 6.2, the minimum required score for admission is:

\(0.524=\frac{X-21}{6.2}\\X=24.25\)

The minimum score required for admission is 24.25.

Answer:

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3orx∈(−∞,3)

The lines y=3x−2 and y=2x+1 both will intersect at x=3

Clearly, the dark line shows the solution of 3x−2<2x+1.

solution

Step-by-step explanation:

Answer:

To find the measure of each interior angle of any regular polygon, we use the formula {(n - 2) × 180} / n degrees, where n is the number of sides of the polygon.

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Since we know that equal number of dashes will always be equal to another we can easily solve the question. They said AB=8 and as you can see 8 is represented by two dashes here and if we take in what i said earlier,, that means DC= 8 too. They also said AD= 5. Since 5 is represented by one dash we can easily see that since BC also has one dash,, it is going to be equal to AD which concluded to the answer of 5.

Answer:

try 2+2 that should work

The width of a 90 percent confidence interval for the proportion of California medical school graduates who plan to specialize in family practice is approximately 0.138. This can be solved by the concept of Probability.

To find the width of the confidence interval, we first need to calculate the margin of error. The formula for the margin of error is:

Margin of error = Z* (sqrt(p*(1-p)/n))

Where:

Z* = the critical value for the desired level of confidence (in this case, 90% confidence corresponds to a Z* value of 1.645)

p = the sample proportion (48/120 = 0.4)

n = the sample size (120)

Plugging in these values, we get:

Margin of error = 1.645 * (sqrt(0.4*(1-0.4)/120)) = 0.069

So the margin of error is 0.069.

To find the width of the confidence interval, we need to double the margin of error:

Width of confidence interval = 2 * margin of error = 2 * 0.069 = 0.138

Therefore, the width of the 90% confidence interval for the proportion of California medical school graduates who plan to specialize in family practice is approximately 0.138. This means that we can be 90% confident that the true proportion of graduates who plan to specialize in family practice falls within a range of 0.4 ± 0.069, or between 0.331 and 0.469.

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Answer:

y=2x

Step-by-step explanation:

14/7= 2

16/8=2

if you try at least two, and they are the same number than its probs that.

Answer:

1 on 3

Step-by-step explanation:

The red dice has 6 faces. The number you have to obtain is less than 3. So your answers must be 1 and 2. The numbers 1 and 2 are two solutions out of six. Now the same goes with the white dice. Two solutions out of six. You combine them and obtain 4 on 12. Then, you reduce the answer in minimal terms and finally obtain 1 on 3.

The opportunity cost is merely the expense of not making a decision.

As a result, if you chose Project P placed above a white Project Q, the opportunity cost for such a decision is 75,000 times the estimated NPV of Project Q.

The distinction between current value of money over time value of cash outflows over time is defined as net present value (NPV).

Some key features regarding the Net Present Value (NPV) are-

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The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.

The amplitude of the canonical function is determined by the Pythagorean theorem:

A' = √(2² + 5²)

A' = √ 29

The angular frequency C  is the constant within the trigonometric functions from the non-canonical formula:

C = 4π

Then, we find the initial position of the weight in time: (t = 0)

y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)

y(0) = 5

And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)

5 = √ 29 · sin (4π · 0 + D)

5 / √ 29 = sin D

D ≈ 0.379π rad

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

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In summary, F(x) does not satisfy the properties of a CDF due to the discontinuity at x = 5.

The given function F(x) is not a valid cumulative distribution function (CDF) because it violates one of the properties of CDFs.

A valid CDF must satisfy the following properties:

F(x) is non-decreasing for all x.

F(x) approaches 0 as x approaches negative infinity.

F(x) approaches 1 as x approaches positive infinity.

F(x) is right-continuous.

Let's analyze the given function, F(x):

F(x) =

0.25 if x ≤ 5

0.5 if 5 < x ≤ 10

1 if x > 10

The function violates the property of right-continuity. Specifically, at x = 5, there is a jump from F(5) = 0.25 to F(5+) = 0.5, which means the function is discontinuous at that point. In a valid CDF, there should be no jumps or discontinuities.

Since F(x) is not a valid CDF, we cannot directly find the corresponding probability density function (PDF) for this function.

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The farmer is undertaking an experiment to see which type of apple tree, fuji or gala, would yield more fruit in his orchard, and the plots are the experimental units in this investigation. So, the plots are the solution.

Based on the given conditions,

The plots are the experimental units as they are the objects subjected to the measurements. The variety of apple trees is the explanatory variable since they promote change in the experimental unit through two different treatments (Fuji or Gala variety). The farmer is the one conducting the experiment and the number of apples is the result to be analyzed. The orchard as a whole does not interfere in the experiment since each plot is being studied.

Therefore,

The plots are experimental units in this study, then the farmer is conducting an experiment to determine which variety of apple tree, fuji or gala, will produce more fruit in his orchard. So ,the answer is the plots.

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Answer:

-9w^2-90w

Step-by-step explanation:

You just use the distributive property and watch the negatives and positives.

\(\huge\boxed{-9w^2-90w}\)

Distribute \(-9w\) to both \(w\) and \(10\) as shown in the attached image. Then, just simplify the terms with multiplication.

\((-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}\)

Answer:

ur welcoem

Step-by-step explanation:

Applying the pythagroean theorem, the formula to find the horizontal distance, d, is: \(\mathbf{d = \sqrt{h^2 - R^2} }\)

The pyhagroean theorem is given as, c² = a² + b², where h is the longest side of the right triangle.

Given  the following:

The formula derived would be:

h² = d² + R²

Make d the subject fo the formula

\(\mathbf{d = \sqrt{h^2 - R^2} }\)

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