what is angle BCD
A. 80°
B. 90°
C. 100°
D. 110°

Total time required to grow investment of $35,000 to $50,000 if compounded continuously at the interest rate 4.75% is equal to 3.26  years .

Present Value = $35,000

Future Value = $50,000

r  = 4.75%

  = 0.0475

Formula used to calculate the future value of an investment with compounded continuously is,

Future Value = Present Value × e^(r × t)

r = annual rate of interest

t = time (years)

e = exponential constant

  = 2.71828

Substitute the value in the formula we get,

$50,000 = $35,000 × e^( 0.0475 × t )

⇒ e^(0.0475 ×t) = 1.42857

Take logarithm of both the sides,

⇒0.0475 × t = log(1.42857)

⇒t = log(1.42857) / 0.0475

⇒ t = 0.15490152569 / 0.0475

⇒ t ≈ 3.26 years

Therefore, approximate time taken for the given investment to grow to $50,000 with compounded continuously is equal to 3.26  years .

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(a)the body temperature of the 1601 lb man will increase by approximately 3.0 °C.(b)the body temperature of the 160 lb man will increase by approximately 2.4 °C.

The specific heat of a human is given as 3.47 J/°C. Using this information, we can calculate the increase in body temperature when a certain number of calories are converted into heat energy. In the first scenario, a 1601 lb man consumes a candy bar containing 287 Cal. In the second scenario, a 160 lb man consumes a roll of candy containing 41.9 Cal. We will calculate the increase in body temperature for each case.

(a) To calculate the increase in body temperature for a 1601 lb man who consumes a candy bar containing 287 Cal, we need to convert calories to joules. Since 1 Calorie (Cal) is equal to 4184 joules, we have:
Energy = 287 Cal × 4184 J/Cal = 1.2 × \(10^6\) J
Now, using the specific heat formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat, and ΔT is the change in temperature, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Assuming the mass of the man is converted to kilograms, we have:
ΔT = (1.2 × \(10^6\) J) / (1601 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 3.0 °C
Therefore, the body temperature of the 1601 lb man will increase by approximately 3.0 °C.
(b) For a 160 lb man who consumes a roll of candy containing 41.9 Cal, we repeat the same calculation:
Energy = 41.9 Cal × 4184 J/Cal = 1.75 × \(10^5\) J
ΔT = (1.75 × \(10^5\) J) / (160 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 2.4 °C
Thus, the body temperature of the 160 lb man will increase by approximately 2.4 °C.

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The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.

According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.

In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.

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For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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hiStep-by-step explanation:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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The minimum amount of paint needed for two coats will be 297 square centimeters.

The shape is a combination of the rectangle and the triangle. Then the area of the shape is calculated as,

A = 1/2 x 18 x 9 + 18 x 12

A = 81 + 216

A = 297 square centimeters

Hence, the minimum amount of paint needed for two coats will be 297 square centimeters.

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Answer:

46

Step-by-step explanation:

Since we know the value of the variable c, we can substitute 20 for c

2c + 6

2(20) + 6

40 + 6

46

Answer:

$2,898.00

Step-by-step explanation:

FV=2500(1.03)^5

FV=2500(1.159274)

FV=$2,898.00

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Katie should buy at least 8 rolls of crepe paper to decorate the perimeter and diagonals of her 20 ft x 20 ft square ceiling.

What is perimeter and diagonal of a square ?

The perimeter of a square is the sum of the lengths of all its sides. If the length of each side of the square is "s", then the perimeter is equal to 4s.

Perimeter = 4s

The diagonal of a square is the length of a straight line that connects two opposite corners of the square. If the length of each side of the square is "s", then the diagonal is equal to s times the square root of 2 (i.e., diagonal = s√2).

Calculating the number of crepe paper :

The perimeter of a square is equal to the sum of the length of all four sides. In this case, the ceiling is a 20 ft x 20 ft square, so its perimeter is:

20 ft + 20 ft + 20 ft + 20 ft = 80 ft

To hang crepe paper around the perimeter, Katie needs 80 ft of crepe paper.

The length of the diagonal of a square can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse (the diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal of the square ceiling forms the hypotenuse of two 20 ft x 20 ft right triangles, so we can use the Pythagorean theorem to find its length:

diagonal² = 20² + 20²

diagonal² = 400 + 400

diagonal² = 800

diagonal = sqrt(800) = 28.28 ft (rounded to two decimal places)

To hang crepe paper from each corner to the opposite corner, Katie needs four diagonals, so she needs a total of:

4 x 28.28 ft = 113.12 ft

of crepe paper.

The total length of crepe paper needed is:

80 ft + 113.12 ft = 193.12 ft

To determine the minimum number of rolls of crepe paper Katie needs to buy, we divide the total length of crepe paper required by the length of each roll:

193.12 ft / 25 ft per roll = 7.7248 rolls

Katie cannot buy a fraction of a roll, so she should round up to the nearest whole number. Therefore, she should buy at least 8 rolls of crepe paper.

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a) The probability that his weight is greater than 175 lb is approximately 0.4602 (b) the probability that the mean weight of 20 randomly selected men is greater than 175 lb is approximately 0.6772.

To determine the minimum score for admission consideration at George Mason University, we need to find the 90th percentile score of the normally distributed college entrance examination scores. The mean score is 550 and the standard deviation is 100.

Using a standard normal (Z) table, we find that the Z-score corresponding to the 90th percentile is 1.28. To calculate the required minimum score (X), we can use the formula: X = μ + Zσ, where μ is the mean, Z is the Z-score, and σ is the standard deviation. Thus, X = 550 + (1.28)(100) = 550 + 128 = 678. An applicant must score at least 678 to be considered for admission.

For the second question, a) the probability that a randomly selected man weighs more than 175 lb can be determined using the Z-score formula: Z = (X - μ) / σ. Plugging in the values, Z = (175 - 172) / 29 ≈ 0.10. Checking the Z-table, we find the probability to be approximately 0.4602.

b) To find the probability that the mean weight of 20 randomly selected men is greater than 175 lb, we first determine the standard error (SE) of the sample mean using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size. In this case, SE = 29 / √20 ≈ 6.48. Now, we calculate the Z-score: Z = (175 - 172) / 6.48 ≈ 0.46. Referring to the Z-table, the probability is approximately 0.6772.

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Answer:

0.123

Step-by-step explanation:

.151 - .028

since you cannot take 8 from 1 you must borrow from the tens unit (the 5)

the 5 becomes a 4 and the 1 becomes 11

11-8 = 3

4-2 = 2

1-0 = 1

so the difference is .123

Answer:

x = 9.6 meters

y = 20.98 meters

Shadow length = 11.38 meters

Step-by-step explanation:

By applying tangent rule in right triangle ABD,

tan(21)° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(21) = \(\frac{x}{25}\)

x = 25(tan 21)

x = 9.5966

x ≈ 9.60 meters

Similarly, by applying tangent rule in ΔABC,

tan(40)° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(40)° = \(\frac{BC}{AB}\)

tan(40)° = \(\frac{y}{25}\)

y = 25(tan 40°)

y = 20.98 meters

Length of the shadow of the man = y - x

                                                        = 20.98 - 9.60

                                                        = 11.38 meters

If you know the rules for differentiation, then

\(f(x)=\dfrac7x\implies f'(x)=-\dfrac7{x^2}\implies f'(1)=-7\)

If you don't, you can use the definition of the derivative to first find \(f'(x)\):

\(f'(x)=\displaystyle\lim_{h\to0}\frac{\frac7{x+h}-\frac7x}h=\lim_{h\to0}\frac{7x-7(x+h)}{hx(x+h)}=-\lim_{h\to0}\frac7{x(x+h)}=-\dfrac7{x^2}\)

Plug in \(x=1\) to get the same result.

Or, you can directly compute the value of the derivative using the limit definition:

\(f'(1)=\displaystyle\lim_{x\to1}\frac{\frac7x-7}{x-1}=\lim_{x\to1}\frac{7(1-x)}{x(x-1)}=-\lim_{x\to1}\frac7x=-7\)

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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Step-by-step explanation:

Answer:

Minimum Unit Cost = $14,362

Step-by-step explanation:

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.6

b = -108

c = 19,222

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

-(-108)/2(0.6) = 108/1.2 = 90

Plugging this value into original function would give us the minimum (unit cost):

The area of the quilt is 1127/20 square feet. This can also be written as a mixed number, which would be 56 7/20 square feet.

To find the area of the quilt, we need to multiply the width by the length. Let's calculate it step by step:

Width: 9 4/5 ft. We can convert the mixed number to an improper fraction by multiplying the whole number (9) by the denominator (5) and adding the numerator (4). Then we divide the result by the denominator.

9 * 5 = 45. 45 + 4 = 49.

So, the width is 49/5 ft.

Length: 5 3/4 ft. We can convert the mixed number to an improper fraction using the same method.

5 * 4 = 20. 20 + 3 = 23.

So, the length is 23/4 ft.

Now, we can calculate the area:

Area = Width * Length.

Area = (49/5 ft) * (23/4 ft).

To multiply fractions, we multiply the numerators together and the denominators together:

Area = (49 * 23) / (5 * 4) ft².

Area = 1127/20 ft².

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The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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Answer:

18 feet

Step-by-step explanation:

The solution to the equation 5x = 55 can be found by dividing both sides by 5. This gives x = 11. However, the problem asks to round the answer to two decimal places. Therefore, the correct answer is option B, x = 2.49.

To solve the equation, we use the inverse operation of multiplication, which is division. Dividing both sides of the equation by 5 gives x = 11/5. To round this to two decimal places, we look at the third decimal place, which is 8. Since 8 is greater than or equal to 5, we round up the second decimal place, which gives x = 2.49. Therefore, option B is the correct answer.

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To solve the equation, we need to isolate the variable x on one side of the equation. We can start by dividing both sides of the equation by 5:

x = 55/5 = 11

Therefore, the solution to the equation is x = 11.

Explanation: The equation 5x = 55 means that we have 5 times some number (x) equal to 55. To solve for x, we need to find the value of x that makes this statement true. We can do this by dividing both sides of the equation by 5, which gives us x = 55/5 = 11. This tells us that if we multiply 11 by 5, we get 55, which confirms that 11 is the solution to the equation.

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The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

To draw the state diagram of a PDA that accepts the language L = {w ∈ {a, b}^∗ | w has twice as many a's as b's}, we can design a simple PDA with two states.

State 1: Initial state

Transition: (a, ε, a) -> State 1

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

State 2: Secondary state

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

Accepting state: Final state to indicate that the input string is accepted.

Here is the state diagram representation of the PDA:

Note: Find the attached image for the state diagram representation of the PDA.

In this PDA, State 1 is the initial state, and State 2 is the secondary state. The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).

The PDA works as follows:

This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

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a. The power contained in the air swept by 40-meter blades is 1,769,292.45 watts.; b. The turbine's power output is 353.86 kW.; c. The annual revenue generated is $185,925.60.

a. To calculate the power contained in the air swept by the 40-meter blades, we can use the formula for wind power: P = 0.5 × ρ × A × V^3, where P is power, ρ is air density, A is the swept area of the blades, and V is wind speed.

First, we need to find the swept area (A). Since the blades are 40 meters long, the area can be calculated as A = π × r^2, where r is the length of the blades (radius). A = π × (40)^2 = 5,026.55 m^2.

Now we can find the power contained in the air: P = 0.5 × 1.225 kg/m³ × 5,026.55 m^2 × (9 m/s)^3 = 1,769,292.45 watts.

b. If the turbine has an efficiency of 20%, its power output would be 20% of the energy contained in the wind: 0.2 × 1,769,292.45 watts = 353,858.49 watts or 353.86 kW.

c. To find the annual revenue, we first need to calculate the annual energy production in MWh: 353.86 kW × 24 hours × 365 days / 1,000 (to convert to MWh) = 3,098.76 MWh.

Now, multiply the energy production by the selling price: 3,098.76 MWh × $60/MWh = $185,925.60 in revenue per year.

In summary:
a. The power contained in the air swept by 40-meter blades is 1,769,292.45 watts.
b. The turbine's power output is 353.86 kW.
c. The annual revenue generated is $185,925.60.

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Answer

The midpoint of AB is -4

ANSWER:

y=2x-3

HOPE IT HELPS

Step-by-step explanation:

Add the system of equations each one by one.

I added them all downwards until i found the 4th one to be correct

y = 2x - 3

y = 2x - 3

--------------

2y = 4x - 6

y = 2x - 3.

To find the value of y in each coordinates given above, substitute their respective x values.

1......y = 2(5) - 3

= 10 - 3

= 7.

2......y = 2(8) - 3

= 16 - 3

= 13.

then write the value you substituted in x on the left side of each bracket & the value you got when you substituted them on the right.

(5 , 7) (8 , 13)

Answer:

The answer is 50%.

Step-by-step explanation:

I did the question on IXL, and got it right.

The amount of fiber asked by the doctor to be consumed is 30 grams .

Method to calculate percentages :

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100 .

Let the amount of fiber asked by the doctor to be consumed be x .

According to question ,

40 % of x = 12

Solving the equation ,

( 40 / 100 ) * x = 12

x = 1200 / 40

x = 30

Hence ,  the amount of fiber asked by the doctor to be consumed is 30 grams .

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Answer:

30

Step-by-step explanation:

Answer:

6.1

Step-by-step explanation:

because the 3 is below 5 so it sticks to 1

\(\sqrt[5]2x^{6} }\) is equivalent to expression .

What does a math expression mean?

An expression is a group of terms joined together with the operations +, -, x, or, such as 4 x 3 or 5 x 2 3 x y + 17. An equation is a claim that two expressions have values that are equal, as in the example 4 b 2 = 6. This claim is made in a sentence that contains the equals symbol.

                                Expressions are made up of a number of phrases with operators in between. A mathematical equation is a pair of statements joined together by the symbol "equal to" (=). For instance, 3x-8.

expression = (2x³)²/₅

             = 2x³ ˣ ²/₅

              = 2x⁶/₅

              = \(\sqrt[5]2x^{6} }\)

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