sum of numbers 12-111

1. Surface area:

We need to split trinagular prism into 5 different polygons. Then calculate the area for each of them, and finally add up the five results to find the total surface area.

We have 2 triangles and 3 rectangles.

Both triangles are equal, so, we only need to find the area for one of them:

- Triangle:

We know h (h = 5 in), but we don't know b, and here is where the Pythagorean theorem comes in:

For our trinagle, we know the hypotenuse length (13 in) and one side length (5 in), so:

And so, going back to the triangle area, we have:

- "Front" rectangle area:

- "Right" rectangel area:

- "Left" rectangle area:

Finally, the surface area of the triangle prism is:

30 + 30 + 260 + 100 + 240 = 660 in^2

2. Volume

The volume is just the area of the base triangle times the height of the prism. So:

The height of the building is 16 meters.

What is right triangle?

A right triangle is a type of triangle that has one of its angles measuring 90 degrees (π/2 radians). The side which is opposite to the right angle is the hypotenuse, while the other two sides are called the legs.

We can solve this problem using the Pythagorean theorem, which relates the sides of a right triangle. Let h be the height of the building. Then we can draw a right triangle with one leg of length h and the other leg of length 12m, representing the height and length of the shadow, respectively. The hypotenuse of this triangle is the distance from the top of the building to the tip of the shadow, which is 20m. So we have:

h² + 12² = 20²

Simplifying and solving for h, we get:

h² = 20² - 12²

h² = 256

h = sqrt(256)

h = 16

Therefore, the height of the building is 16 meters.

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The probability that at most three grafts fail is 0.98 and the probability that at least two grafts fail is 0.1.

To find the probability that at most three grafts fail, we need to find the sum of the probabilities for x = 0, 1, 2, and 3.

Using the given values of f(x), we get:

P(X <= 3) = f(0) + f(1) + f(2) + f(3)

= 0.7 + 0.2 + 0.05 + 0.03

= 0.98

So the probability that at most three grafts fail is 0.98.

To find the probability that at least two grafts fail, we need to find the sum of the probabilities for x = 2, 3, and 4 and subtract it from 1.

Using the given values of f(x), we get:

P(X >= 2) = 1 - (f(0) + f(1)) = 1 - (0.7 + 0.2) = 0.1

So the probability that at least two grafts fail is 0.1

--The question is incomplete, answering to the question below--

"Grafting the uniting of the stem of one plant with the stem or root of another; is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with hardy root system: Most Florida sweet oranges grow on trees grafted to the root of sour orange variety. The density for X, the number of 'grafts that fail in series of five trials.

For the values of x = 0, 1, 2, 3, and 4 value of f(x) is 0.7, 0.2, 0.05, 0.03, and 0.01 respectively.

Use f(x) to find the probability that at most three grafts fail; that at least two grafts fail."

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Answer:

Step-by-step explanation: 122x2=144

Answer: x = 12, - 12

Step-by-step explanation:

Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.

The given functions are:

y = f(x) = - sin x + 2 and

y = g(x) = - 2cos x.

To sketch the graphs of these functions on the same set of axes, we need to construct a table of values and plot them on a coordinate plane.

Let's begin with function f(x).

Table of values for f(x):x f(x)0° 32° 1.87° 2.45° 2.83° 2.97° 2.85° 2.5° 1.95° 1.18° 0.3° 0°

The values of f(x) were obtained by substituting the corresponding values of x in the given function and evaluating the resulting expression.

Note that we chose values of x in increments of 30° to make it easier to plot the points on the graph.

However, any values of x within the given interval [0°; 180°] could be used.

Table of values for g(x):

x g(x)0° -20.00° -1.80° -1.17° -0.53° -0.13° 0.00° -0.13° -0.53° -1.17° -1.80° -2.00°

The values of g(x) were obtained in the same way as for f(x).

Note that the amplitude of f(x) is 1 and the amplitude of g(x) is 2.

Also, the period of both functions is 360° or 2π radians since they are both sin and cos functions respectively and the coefficient of x is 1.

Therefore, we can use these values to draw the graphs of the two functions on the same set of axes.

The graph of y = f(x) = - sin x + 2 and y = g(x) = - 2cos x for x is an element [0°; 180°] is shown below.

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Answer:

C 61,705

Step-by-step explanation:

10.9% of 35,000 = 3,815

3,815 x 7 = 26,705  (interest is added per year and 3,815 is the interest amount)

35,000 + 26,705 = 61,705 ( the original loan plus the interest for 7 years)

Answer:

hich number line shows the solution set for StartAbsoluteValue StartFraction s Over 2 EndFraction + 4 EndAbsoluteValue less-than 2.? A number line going from negative 14 to positive 10. Open circles are at negative 12 and negative 4. Everything between the points is shaded. A number line going from negative 14 to positive 10. Open circles are at negative 12 and negative 4. Everything to the left of negative 12 and to the right of negative 4 is shaded. A number line going from negative 14 to positive 10. Closed circles are at negative 4 and positive 4. Everything to the left of negative 4 and to the right of positive 4 is shaded. A number line going from negative 14 to positive 10. Closed circles are at negative 4 and positive 4. Everything between the points is shaded.

Step-by-step explanation:

Answer:

GRAPH C

Step-by-step explanation:

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

\(\sin(50^o) = \frac{3}{c}\)

Step-by-step explanation:

Given

See attachment for triangle

Required

Expression to solve c

To solve for c, we simply calculate the sine of angle at B

i.e.

\(\sin(50^o) = \frac{Opposite}{Hypotenuse}\)

This gives:

\(\sin(50^o) = \frac{3}{c}\)

Make c the subject

\(c = \frac{3}{\sin(50^o)}\)

Answer: \(\frac{1}{16}\)

Step-by-step explanation:

1. Original Equation: \(4^4(4^-^7)(4)\)

2.Simplify: \(4^4(4^-^7)(4) ----> 4^4* 4^-^7 * 4\\\)

3.Apply exponent rule: \(4^4^-^7^+^1\)

4. Simplify: \(4^-^2\\\)

5.Apply exponent rule: \(\frac{1}{4^2}\)

6.Simplify: \(\frac{1}{16}\)

answer is 115

hope that helped lol

Answer:

Choice A. The shading in the Venn Diagram shown in the first attachment represents the set \((K \cup M) \; \cap \; (K \cup L)\).

Step-by-step explanation:

Let \(A\), \(B\), and \(C\) be sets. By the distributive law of sets, \(A \cup (B \cap C)\) and \((A \cup B) \cap (A \cup C)\) refer to the same set.

Apply this property to simplify the given expression:

\(\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}\)

\(M \cap L\) refers to the intersection between the two lower circles. The union of that intersection with set \(K\) (the upper circle) would be the shaded region seen in choice A.

Answer:

-15/16

Step-by-step explanation:

Both of the 7/16's cancel each other out.

Answer:

7/15

Step-by-step explanation:

easy as 1 2 3 na na naaaaaa he he he

Answer:

3°

Step-by-step explanation:

33 +19x = 90     subtract 33 from both sides of the equation

19x = 57             divide both sides by 19

x = 3°

Answer:

9

Step-by-step explanation:

(a) The supply when the price is $10 is 18 units. (b) The demand when the price is $10 is 21 units. (c) The equilibrium price is $7, and both the quantity supplied and demanded at this price are 9 units. (d) The supply curve crosses the horizontal axis at the point (4, 0), indicating that at a price of $4, there is no supply of CDs.

(a) To find the supply when the price is $10, substitute p = 10 into the supply equation:

q = 3p - 12

q = 3(10) - 12

q = 30 - 12

q = 18

Therefore, the supply when the price is $10 is 18 units.

(b) To find the demand when the price is $10, substitute p = 10 into the demand equation:

q = -2 + 23

q = 21

Therefore, the demand when the price is $10 is 21 units.

(c) To find the equilibrium price, set the supply equal to the demand and solve for p:

3p - 12 = -2 + 23

3p = 21

p = 7

The equilibrium price is $7. To find the corresponding quantity supplied and demanded, substitute p = 7 into either the supply or demand equation:

For supply:

q = 3p - 12

q = 3(7) - 12

q = 21 - 12

q = 9

For demand:

q = -2 + 23

q = 21

Therefore, at the equilibrium price of $7, both the quantity supplied and demanded are 9 units.

(d) To find where the two lines cross the horizontal axis, set q = 0 and solve for p in each equation:

For supply: q = 3p - 12

0 = 3p - 12

3p = 12

p = 4

For demand: q = -2 + 23

0 = -2 + 23

2 = 23 (not possible)

The economic interpretation of the point (4, 0) on the horizontal axis for the supply equation is that at a price of $4, there is no supply of CDs. This could indicate that the cost of production or other factors make it unprofitable to supply CDs at that price.

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The distance it will reach to  x, = 46.6 feet

acc to our question-

hence,The distance it will reach to  x, = 46.6 feet

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Answer:

plot between 1/3 and 2/3 or 1/2.

Answer: 14

Step-by-step explanation:

9-(2-7)

9-(-5)

14

As per the double integral, the flux of the vector is 2√11(6z + 1) + 176

What is double integral small definition?

In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.

And it is calculate by the formula as Flux= ∫∫F⋅ndS

Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.

And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.

As per the formula of flux of vector, it can be written as,

=>Flux =  ∫∫(1i + 1j + 3k) . 2 dS

When we integrate this one the we get,

=> Flux = 2√11(6z + 1) + 176

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The order of the product ab in the abelian group is lcm(m, n).

In an abelian group, the order of the product of two elements can be determined using the concept of the least common multiple (LCM) of their individual orders.

Let a and b be elements of an abelian group, where the order of a is m and the order of b is n. The order of an element in a group is defined as the smallest positive integer k such that the element raised to the power of k yields the identity element.

In this case, the order of the product ab can be determined by considering the LCM of m and n, denoted as lcm(m, n). The LCM is the smallest positive integer that is divisible by both m and n.

Therefore, the order of the product ab in the abelian group is lcm(m, n).

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The least squares estimator performs on a simultaneous equation model with an endogenous regressor by being (b) biased but consistent in large samples.

It is a statistical approach that is commonly used to estimate unknown parameters in regression analysis. The least squares estimator works well when applied to the simultaneous equation model with an endogenous regressor, but it is biased in some cases.

What is a least squares estimator?

The least squares estimator is a technique used to estimate the parameters of a statistical model, as the name suggests. The method finds the parameter estimates by minimizing the sum of the squared residuals, which are the differences between the observed values and the predicted values of the model.The unbiased and consistent estimator of the least squares is a statistical method that works well for large samples. It is biased but consistent in the simultaneous equation model with an endogenous regressor. It is unbiased, but it becomes inconsistent unless it is collected via random sampling.The least squares estimator is widely used in econometrics to estimate the parameters of a model. It is also used in linear regression analysis, which is one of the most common applications of the least squares estimator. It is a powerful tool that can be used to estimate the parameters of a model and to make predictions based on those estimates.

The use of the least squares estimator has revolutionized the way researchers approach statistical analysis.

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Answer: x-6, x+3, x-3

Step-by-step explanation;

Split the equation into two.

x2(x-6)-9(x-6)

(x-6) is seen as one of the tiles. Now work on x2-9

x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).

Answer:

y = 2x - 3 is the anwser i think

Answer:

if you need help on 40 the answer is

xy=1

if the number is going throguh the y axis when its parelle.

tell me if im wrong

The first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

For given question,

We have been given a sequence \(a_n=\frac{n^2-9}{n^3+3}\)

We need to find the first five terms, a1, a2, a3, a4, a5, of the sequence.

For n = 1,

\(a_1=\frac{1^2-9}{1^3+3} \\\\a_1=\frac{-8}{4} \\\\a_1=-2\)

For n = 2,

\(a_2=\frac{2^2-9}{2^3+3}\\\\ a_2=\frac{-5}{11}\)

For n = 3,

\(a_3=\frac{3^2-9}{3^3+3} \\\\a_3=\frac{0}{30}\\\\ a_3=0\)

For n = 4,

\(a_4=\frac{4^2-9}{4^3+3} \\\\a_4=\frac{7}{67}\)

For n = 5,

\(a_5=\frac{5^2-9}{5^3+3} \\\\a_5=\frac{16}{128}\\\\ a_5=\frac{1}{8}\)

Given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

Therefore, the first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

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Answer:

45.) 45

46.) 2

47.) 16

48.) 8

49.) 10

50.) 11

51.) 16

52.) 6

53.) 55

54.) 14

Step-by-step explanation:

Answer:

3r^2t^3

Step-by-step explanation:

A. Characteristics of Nigerian and Japanese Population Pyramids:

B. Challenges and Opportunities for Nigeria and Japan:

A. Characteristics of Nigerian and Japanese Population Pyramids:

Nigerian Population Pyramid:

Nigeria is a country in West Africa with a rapidly growing population. According to the 2017 estimate you provided, Nigeria had a population of approximately 201 million people.

The Nigerian population pyramid is likely to exhibit a broad base, indicating a high proportion of young individuals in the population.

There may be a relatively larger proportion of dependents, both young and old, compared to the working-age cohorts.

Gender disparities may exist within specific cohorts, potentially reflecting cultural or socioeconomic factors.

It is important to note that specific observations regarding the Nigerian population pyramid would require visual reference to the actual data and age cohorts.

Japanese Population Pyramid:

Japan, on the other hand, is a developed country in East Asia with a more mature population structure.

The Japanese population pyramid may exhibit a narrower base and a larger proportion of older individuals, indicating a declining birth rate and an aging population.

The working-age cohorts may be relatively smaller in comparison to the dependent cohorts, both young and old.

Gender disparities within specific cohorts may be less prominent compared to Nigeria.

Again, visual reference to the actual data is necessary for more accurate observations.

B. Challenges and Opportunities for Nigeria and Japan:

Nigeria:

Challenges: Nigeria's rapid population growth poses challenges in providing essential services such as healthcare, education, and infrastructure to meet the needs of a growing population. Additionally, high youth unemployment rates and income inequality can lead to social and economic challenges.

Opportunities: Nigeria's large and youthful population can be a potential demographic dividend if properly harnessed. Investing in education, skills training, and job creation can lead to increased productivity, innovation, and economic growth.

Japan:

Challenges: Japan's aging population presents challenges such as increased healthcare and pension costs, labor force shortages, and a decline in economic productivity. The shrinking working-age population may strain social welfare systems.

Opportunities: Japan can focus on technological advancements, automation, and attracting skilled foreign workers to address labor shortages. They can also encourage policies to enhance productivity and promote active aging to tap into the potential of older workers.

Please note that the challenges and opportunities described above are general observations and should be supplemented with specific data and research on the respective countries.

C. Rate of Natural Increase (RNI) and Ecological Impact:

Unfortunately, I don't have access to the specific table in the Bjelland textbook or the appendix you mentioned. However, I can provide some general information about the regions you mentioned:

South Asia: South Asia is one of the world's most densely populated regions. It includes countries like India, Pakistan, Bangladesh, and others. The RNI in South Asia is relatively high, indicating significant population growth. The ecological impact of the region depends on various factors such as resource consumption, industrial development, urbanization, and environmental policies.

East Asia: East Asia is home to densely populated countries like China, Japan, and South Korea. While China's population growth has slowed down due to its one-child policy, other countries in the region also face challenges related to aging populations. The ecological impact of East Asia depends on factors such as industrialization, urbanization, energy consumption, and environmental regulations.

Europe: Europe has a relatively low RNI and, in some countries, faces population decline or stagnation. The ecological impact of Europe depends on factors such as energy consumption, waste management, transportation systems, agricultural practices, and environmental policies.

Africa: Africa has the highest RNI among the regions mentioned. It is experiencing rapid population growth, which can have significant ecological impacts in terms of resource consumption, land use, urbanization, deforestation, and biodiversity loss. However, it's important to note that the ecological impact of a region is not solely determined by population size or growth rate but also by consumption patterns, technological advancements, and sustainable practices.

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