Destiny is asked about her age. She answers as follows. "My age is 3 years more than twice the age of my
younger brother. The sum of our ages is 42 years."

Answer:

C: 5.625

Step-by-step explanation:

Answer:

C) 34.375

Step-by-step explanation

C) 34.375

Answer:

the first

Step-by-step explanation:

The net amount of imports is RM 175 million of GDP of Country A. Option  C is the correct answer.

The total amount of money spent during a specific time period by firms, consumers, and the government may be used to compute GDP.

Calculation:

GDP = personal consumption + gross investment + govt consumption + net exports + imports

Therefore, Import = 175

Here the total amount of imports is RM 175 million. Therefore, Option  C is the correct answer.

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The complete question is, "The information below contains information on Country A.

                                                  RM(in millions)

Gross Domestic Product              1250

Consumer Spending                    500

Investment Spending                   350

Govt Spending                              350

Export                                             225

What is the amount of imports?

A. RM 800 million

B. RM 135 million

C. RM 175 million

D. RM 575 million"

Answer:

13 ug

Step-by-step explanation:

Victoria is designing an image to be projected onto a screen. Her design is shown

below.

Victoria's Design

What is the total area, in square centimeters,

of Victoria's design?

8 cm

4 cm

4 cm

4 cm

10 cm

14 cm

146 centimeters squared

188 centimeters squared

118 centimeters squared

Answer:

x = -9, y = 5

Step-by-step explanation:

Since we need to solve this system of linear equations by substitution, let's transform the second equation into the form, x = ay + b. We start off with x - 3y = -24, subtract 3y from both sides, and we get x = 3y - 24. Then, substitute the expression 3y - 24 for y in 2x + 9y = 27.

2(3y - 24) + 9y = 27    Substitute 3y - 24 for x.  

6y - 48 + 9y = 27        Distribute 2.

15y = 75                      Add & subtract to combine the like terms.

y = 5                            Divide by 15.

Now that we have the value of y, we can find x by substituting 5 for y in any of the equations. Let's use 2x + 9y = 27 for example.

2x + 9(5) = 27             Substitute 5 for y.

2x + 45 = 27               Multiply.

2x = -18                       Subtract.

x = -9                          Divide by 2.

Answer:

1. Equation: x/-9=-16

solution: x=144

2. Equation:15*x=-75

solution: x=-5

3.Equation:0.75n=36

solution: n=48

Step-by-step explanation:

The given function is given by:

f′(x) = 4x(x2 − 1) − 2x2 · 2x (x2 − 1)2.

To find the interval(s) on which the function is continuous, we need to first check for the existence of the function f(x). The function is continuous over its domain if and only if f(x) exists over the entire domain. Thus, we need to check if the denominator is zero or not.

If the denominator is zero, the function is not defined at that point and hence there is a discontinuity at that point. If the denominator is not zero, then the function is defined at that point and thus the function is continuous at that point.

Here, the denominator is (x2 − 1)2. The denominator is never zero for any value of x. Hence, the function is defined and continuous for all real values of x.

Thus, the function is continuous for all real values of x. The function f(x) is continuous for all real values of x. There are no discontinuities in the given function. Hence, the answer is DNE.

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(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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The derivative and domain of the function f(x) = x²-2x³  is :\((-\infty, \infty)\).

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

\(\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}\)

       \(\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}\)

       \(=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}\)

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      \(\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}\)

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :\((-\infty, \infty)\).

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The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

Betty's "average" speed for the triathlon was approximately 20 miles per hour.

Let's start by converting the different distances and times to a common unit. Since we want to calculate the speed in miles per hour (mph), we'll convert the swimming distance from miles to hours by dividing it by Betty's swimming speed of 1 mile per 25 minutes (or 0.04 miles per minute):

Swimming time = 25 minutes = 0.42 hours (since there are 60 minutes in an hour)

Swimming distance = 1 mile ÷ 0.04 miles per minute = 25 minutes = 25 miles per hour

We can do the same thing for the biking and running portions of the race:

Biking time = 45 minutes = 0.75 hours

Biking distance = 30 miles ÷ 0.75 hours = 40 miles per hour

Running time = 40 minutes = 0.67 hours

Running distance = 6 miles ÷ 0.67 hours = 8.96 miles per hour

Now we can find the total distance and total time for the race:

Total distance = 1 mile + 30 miles + 6 miles = 37 miles

Total time = 0.42 hours + 0.75 hours + 0.67 hours = 1.84 hours

Finally, we can calculate Betty's average speed for the race by dividing the total distance by the total time:

Average speed = Total distance ÷ Total time = 37 miles ÷ 1.84 hours = 20.11 miles per hour

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Answer:

3. It is both a function of x and a relation i think

Step-by-step explanation:

Answer:

reeee

Step-by-step explanation:

Answer:

the answer would be: -27bk

10 goes on top of the b

4 goes on top of the k

Answer: 20%

Step-by-step explanation:

The probability that a randomly selected marble will be pink can be found by the formula:

= Number of pink marbles / Number of total marbles

= 4 / 20

= 20%

There is a 20% chance that if you pick a marble, it will be pink.

Answer:

28 in

Step-by-step explanation:

Use Pythagoras Theorem

\( {a}^{2} + {b}^{2} = {c}^{2} \)

Where c is the hypotenuse of the right angle triangle ,and a and b the other sides. Just substitute the values and get your answer.

Equation of a line:

9x - 7y = -63

To find the x-intercept we have to substitute y = 0 into the equation, as follows:

9x - 7*0 = -63

9x = -63

Dividing by 9 at both sides of the equation:

9x/9 = -63/9

x = -7

To find the y-intercept we have to substitute x = 0 into the equation, as follows:

9*0 - 7y = -63

-7y = -63

Dividing by -7 at both sides of the equation:

-7y/(-7) = -63/(-7)

y = 9

Answer

x-intercept: −7; y-intercept: 9

Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

<95141404393>

Answer:

0.0275

Step-by-step explanation:

The predicate in the conditional statement checks whether the value of variable "a" is less than or equal to 1. However, it does not directly determine if "a" is of type double.

In this specific case, let's break down the code:

1. The expression `(2 + 1) / 2` is evaluated first. Since both 2 and 1 are integers, the division operation `/` results in a floating-point value, specifically 1.5.

2. The result of the expression is then assigned to variable "a" with the statement `a = (2 + 1) / 2`. The value of "a" becomes 1.5.

3. The conditional statement `if (a <= 1)` is evaluated. The comparison `1.5 <= 1` is false because 1.5 is greater than 1.

Therefore, the predicate result for the variable "a" to be a double primitive type in this case is false.

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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Answer:

Step-by-step explanation:

-1

a. There are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The value of parameter α for  P(|X| < 1) = P(|X| > 2) is 4

a. We know that for a uniform distribution over (−α,α), the probability density function is given by f(x) = 1/(2α) for −α ≤ x ≤ α and zero otherwise. Thus, the probability of the event (-1 < X < 2) can be computed as:

P(-1 < X < 2) = ∫(-1)²/(2α) dx + ∫2²/(2α) dx

= (1/2α) ∫(-1)² dx + (1/2α) ∫2² dx

= (1/2α) [x]₋₁¹ + (1/2α) [x]²₂

= (1/2α) (2α - 1) + (1/2α) (4 - α²)

= (3 + α²)/(4α)

We want this probability to be 0.75. So, we solve the equation (3 + α²)/(4α) = 0.75 for α:

(3 + α²)/(4α) = 0.75

=> 3 + α² = 3α

=> α² - 3α + 3 = 0

This is a quadratic equation in α with discriminant:

Δ = b² - 4ac

= (-3)² - 4(1)(3)

= 9 - 12

= -3

Since Δ is negative, there are no real solutions to the equation. Therefore, there is no value of α for which P(-1 < X < 2) = 0.75.

b. The pdf of a uniform distribution is given by:

f(x) = 1/(b-a), for a ≤ x ≤ b

In this case, a = -α and b = α. Therefore,

f(x) = 1/(2α), for -α ≤ x ≤ α

Now we can calculate the probabilities as follows:

P(|X| < 1) = P(-1 < X < 1) = ∫(-1 to 1) f(x) dx = ∫(-1 to 1) 1/(2α) dx = 1/(2α) * [x]_(-1 to 1) = 1/α

P(|X| > 2) = P(X < -2 or X > 2) = P(X > 2) + P(X < -2) = ∫(2 to α) f(x) dx + ∫(-α to -2) f(x) dx = ∫(2 to α) 1/(2α) dx + ∫(-α to -2) 1/(2α) dx = 1/4

Therefore, we need to find α such that P(|X| < 1) = P(|X| > 2) = 1/4.

From P(|X| < 1) = 1/α, we get α = 1/P(|X| < 1) = 1/(1/4) = 4.

From P(|X| > 2) = 1/4, we get the same value of α = 4.

Hence, α = 4 satisfies both conditions.

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The probability that either event will occur is 0.83

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

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes

To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.

Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.

Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax.  Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.

Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows.  If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.

Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,

CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080.  NPV ≈ $824,179.  Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.

Therefore, the answers are:

a. Total outflows: $2,007,901

b. Total inflows: $827,080

c. Net present value: $824,179

d. Should the old issue be refunded with new debt? Yes

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This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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The two equation that represents the information is x + y = 150

y = 3x

let

the number of rock music = x

the number of alternative music = y

Therefore,

x + y = 150

y = 3x

The two equation that represent the information are as follows:

x + y = 150

y = 3x

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Answer:

P=30

W=12

T=16

Step-by-step explanation:

If the limit of the function f(x) as x approaches a is equal to the value of f(a), then we can say that the function is continuous at the point a. This means that the graph of the function has no abrupt changes or breaks at the point a.

To understand this concept, we can imagine the graph of the function as a continuous curve. If the limit of the function as x approaches a is equal to f(a), then the curve does not have any gaps or jumps at the point a. This means that we can draw the graph of the function without lifting our pen off the paper at the point a.

This property of continuity is important in many areas of mathematics and science, as it allows us to make predictions and draw conclusions based on the behavior of a function. For example, if we know that a function is continuous at a certain point, we can use this information to find the value of the function at nearby points, or to make predictions about its behavior in the future.

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