n alternating series is a ---select--- whose terms are ---select--- . (b) under what conditions does an alternating series converge?

The height of the building from which the angle of elevation is 32 degrees is 127.87m.

The angle of elevation is found to be 32 degrees and when moving 50 closer to the building, the angle of elevation is 53.

Let us say that the height of the building is X.

Now, let us say the distance between the building and the person is Y.

So, we write,

tan(32°) = X/Y

Also, tan(53°) = X/(Y-50)

0.62 = X/Y and 1.32 = X/(Y-50)

0.62Y = 1.32Y - 66

66 = 0.32Y

Y = 206.25 m

Now, we know, X = 206.25m x 0.62

X = 127.87m

So, the height of the building is 127.87m.

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The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Substituting the given values, we get:

A = π(2.1 m)^2 = 13.85 m^2

So the total cost of the glass with a price of $7.10 per square meter is:

Cost = Price per square meter x Total area

Cost = $7.10/m^2 x 13.85 m^2 = $98.24

Therefore, the cost of the glass is $98.24.

The equation of line is y = 12x and the number of boxes the shipping company can pack in 18 hour period is 216 boxes

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of hours be x

Let the number of boxes be y

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 5 , 60 )

Now , the slope of the line m = y/x

Substituting the values in the equation , we get

Slope m = 60 / 5 = 12

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 60 = 12 ( x - 5 )

y - 60 = 12x - 60

y = 12x

Now , when x = 18 hours

y = 12 ( 18 ) boxes

y = 216 boxes

Hence , the number of boxes is 216 boxes

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Answer:

the answer is c

toatally unrealated:

if you find yourself stumbbled like this again in multiple chice questions, there is a 60% chance the answer is c

Maximum 8A/144 people are allowed to entire the park.

The entire space taken up by the surface of the park is called area.

If the park is rectangular shaped, then the area is the product of length and breadth. If it is square shaped, area can be determined by the square of the side length.

Given, length of unused space = 12 foot

    breadth of unused space = 12 foot

Area of unused space = 12 x 12 = 144 square feet

Maximum 8 people is allowed for every 144 squares feet space

Let, area of the entire park is A square feet

Now maximum number of people allowed = (8 × A)/ 144

hence, 8A/144 people is allowed.

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Answer:

B

Step-by-step explanation:

\( - 1 - 5x + 6 - 30x \leqslant - 65\)

\( - 35x + 5 \leqslant - 65\)

Factoring -5

\( - 5(7x - 1) \leqslant - 65\)

Divided sides by -5

##############################

Point :

If the sides of an inequality are multiplied by or divided by a negative number, the direction of the inequality changes and returns.

##############################

\( \frac{ - 5}{ - 5}(7x - 1) \geqslant \frac{ - 65}{ - 5} \\ \)

\(7x - 1 \geqslant 13\)

Plus sides 1

\(7x - 1 + 1 \geqslant 13 + 1\)

\(7x \geqslant 14\)

Divided sides by 7

\( \frac{7}{7}x \geqslant \frac{14}{7} \\ \)

\(x \geqslant 2\)

Done ♥️♥️♥️♥️♥️

The total costs of the SC would be the total amount of money that s needed for a company or individual to purchase goods and services.

The concept of Sum of Costs ( SC ) refers to the total amount of money needed to produce or provide a good or service. It includes all the costs associated with production, such as the cost of materials, labor, overhead, and other expenses.

Sum of costs is an important concept in business and economics because it helps companies to determine the profitability of their products or services and make informed decisions about pricing, production, and investment.

The question is not complete so I gave you a summary of the concept of the sum of costs.

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Answer:

I think it is 7

Step-by-step explanation:

Because 3*4= 12 and 3+4=7 and those are the numbers that make the smallest sum that I can think of

Please Mark Brainlest

Answer:

36

Step-by-step explanation:

9x-31+7x-2+4x+33=360

x=18

7(18)-2

124

180-124=36

According to the question The maximum area that Farmer Garrett can enclose in the corral is:

\(\[A = L \cdot W = 600 \cdot 300 = 180,000 \text{ square feet}.\]\)

Let's assume the length of each half of the corral is \(\(L\)\) feet. Since the divider runs parallel to the shorter sides, it does not contribute to the perimeter.

The perimeter of each half of the corral is equal to the sum of the length and two times the width. So, the perimeter of each half is:

\(\[P = L + 2W\]\)

Since Farmer Garrett has a total of 2400 ft. of fencing, the total perimeter of the corral is \(\(2P: 2P = 2400\)\). Dividing both sides by 2, we get:

\(\[P = 1200\]\)

Now, we can express the width \(\(W\)\) in terms of the length \(\(L\)\):

\(\[W = \frac{{P - L}}{2}\]\)

Substituting the value of \(\(P\)\), we have:

\(\[W = \frac{{1200 - L}}{2}\]\)

The area \(\(A\)\) of each half of the corral is given by:

\(\[A = L \cdot W\]\)

Substituting the value of \(\(W\)\), we get:

\(\[A = L \cdot \left(\frac{{1200 - L}}{2}\right)\]\)

To find the maximum area, we need to find the value of \(\(L\)\) that maximizes the area \(\(A\)\). We can do this by taking the derivative of \(\(A\)\) with respect to \(\(L\)\), setting it equal to zero, and solving for \(\(L\).\)

\(\(\frac{{dA}}{{dL}} = \frac{{1200 - 2L}}{2}\)\)

Setting  \(\(\frac{{dA}}{{dL}} = 0\)\), we have:

\(\[1200 - 2L = 0\]\)

\(\[2L = 1200\]\)

\(\[L = 600\]\)

Now we can calculate the corresponding width \(\(W\):\)\(\[W = \frac{{1200 - L}}{2} = \frac{{1200 - 600}}{2} = \frac{{600}}{2} = 300\]\)

Therefore, the maximum area that Farmer Garrett can enclose in the corral is \(\[A = L \cdot W = 600 \cdot 300 = 180,000 \text{ square feet}.\]\)

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Answer:

Short and simple: 625

Answer:

x = -b/a

Step-by-step explanation:

ax+b = 0

Subtract b from each side

ax+b-b=0-b

ax = -b

Divide each side by a

ax/a = -b/a

x = -b/a

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer: the larger number is 59 and the smaller number is 17.

Step-by-step explanation:

Answer: D. Mrs. Bell has the lower interest rate, because both decimals have a 4 in the ones place, and 1 the third is less than 2 tenths.

Answer:

D

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

dgshdbahdbdbsbdbdbdbdbebdbdhdhd

Answer:

m(WXY) = 224°

Step-by-step explanation:

Measure of inscribed angle = ½ the measure of intercepted arc

Therefore:

m<C = ½*m(WXY)

112° = ½*m(WXY) (substitution)

Multiply both sides by 2

2*112° = m(WXY)

224° = m(WXY)

m(WXY) = 224°

Probability is simply how likely something is to happen, so the probability of landing heads up on the next flip is 1/2.

The probability is obtained by dividing the total number of outcomes by the entire number of potential ways an event may occur. Odds are a separate concept from probability. The probability of an event happening is divided by the probability that it won't, and the result is the odds.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value among 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

P(H)= Probability of getting  head while flipping a coin is 1/2

and,

P(T)= Probability of getting  tail while flipping a coin is 1/2

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Answer:

x = -2 hope it helped

As per question,

\(19x+15=8x−7\)

Solving it,

\(19x - 8x = - 7 - 15\)

\( = > 11x = - (7 + 15)\)

\( = > 11x = - 22\)

\( = > x = - \frac{22}{11}\)

\( = > x = - 2\)

Hence, Value of x is -2

-------------------☆-------------------

( If it shows that the answer isn't -2, then it is some technical error with the system. The answer will however come as -2 only. )

The true statements are:

Thus, the correct option is B.

Here the exponential equation is:

2^x = 8

To solve this, we can apply the logarithm function in both sides, then we will get:

log(2^x) = log(8)

x*log(2) = log(8)

x = log(8)/log(2) =3

Also remember the rule:

log(x)/log(n) = logₙ(x)

Then:

x = log₂(8).

Then the true statements are:

x = log(8)/log(2)

x = log₂(8).

x =3

So the correct statements are:

II, III, and IV

The correct option is B.

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The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

\(S_n =\frac{n}{2}(2a+(n-1)d)\)

The sum of the first ten terms of a linear sequence is 145

⇒ \(S_{10} =\frac{10}{2}(2a+(10-1)d)\)

⇒ 145 = 5 (2a+9d)

⇒ \(\frac{145}{5} =2a+9d\)

⇒ 29 = 2a + 9d  ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ \(S_{20} =\frac{20}{2}(2a+(20-1)d)\)

⇒ 590 = 10 (2a + 19d)

⇒ \(\frac{590}{10}=2a+19d\)

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = \(\frac{30}{10}\)

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = \(\frac{2}{2}\)

⇒ a = 1

Thus, sum of first four terms is

⇒ \(S_4 =\frac{4}{2}(2(1)+(4-1)(3))\)

⇒ \(S_4 =2(2+(3)(3))\)

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

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Answer: 96°

Step-by-step explanation:

If a triangle is being drawn, Angle A and C will be the two remote interior angles in the triangle. The sum of the two interior angles has to equal to the exterior angle.

Set them equal each other and solve for x.

(3x-6) + (6x +12) = 12x - 24     Combine like terms

9x + 6 = 12x - 24          Subtract 6 from both sides

    - 6             -6  

   9x = 12x - 30             Subtract 12x from both sides

-12x       -12x  

    -3x = -30               Divide both sides by -3    

 x = 10      

Now since  x is 10 degrees we will need to input the value into in for x in the exterior angle expression and break it down.  

   Exterior :  12(10) - 24

                    120 - 24  = 96

    This means the measure of the exterior angle at vertex B is  96 degrees.

Answer:

Step-by-step explanation:

2 hours/x speed

2.25 hours/x+5 speed

.25 hours/5 speed

20 mph

20 miles/1 hour

40 miles/2 hours

Answer:

I think it is 9

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use cosine:

Answer:

Step-by-step explanation:

Here we will use cosine to find the value..

We need to know how to solve different time zone problems to solve this problem. The time in Newark when Harry began the flight is 11:30 am, option (F) is the correct answer.

In this question we have two cities Newark and Denver that have a time difference of 2 hours. Newark is 2hrs later than the time in Denver. The flight from Newark to Denver takes 5 hrs. Harry arrived at 2:30 pm, we need to find out at what time the flight left Newark. If we subtract 5 hrs from 2:30 pm we get 9:30 am, so when the flight left Newark it was 9:30 am in Denver, since the time in Newark is 2 hrs later than Denver, so it was 11:30 am in Newark.

Therefore the time when the flight left Newark is 11:30 am, option (F) is the correct answer.

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