Alberto sights the top of a building at an angle of elevation of 70°.

With a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

When calculating the circumference (C) of a circle, the formula 2 * π * radius (R) is employed.

Taking into consideration R = 20 feet, we shall arrive at the following figure:

C = 2 * π * 20

C ≈ 2 * 3.14159265359 * 20

C ≈ 125.66 feet

If we use this calculation to determine the total distance covered after running 10 laps around a track, our equation morphs into Circumference (C) multiplied by the Number of laps (L).

When L equals 10, it follows that:

Total distance ≈ 125.66 feet * 10

Total distance ≈ 1256.6 feet

Therefore, with a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

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What is the total distance covered after running 10 laps around a circular track with a radius of 20 feet?

The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.

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The missing term of the factorization equation is A = ( -15x - 1 ) ( x + 2 )

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -15x² - 31x - 2

On simplifying , we get

The expanded form of the expression ( -15x - 1 ) ( x + 2 ) can be calculated using the distributive property of multiplication over addition

So , on factorizing , we get

A = ( -15x - 1 ) ( x + 2 )

Hence , the factorized equation is A = ( -15x - 1 ) ( x + 2 )

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The complete question is attached below :

Fill in the missing terms to complete the factorization. 15x² + x - 2 = (? -1) (? + 2)

a- 3x, 5x

b- x, 15x

c- 5x, 3x

d- 15x, x

The value of the side length h is 19.1 cm.

The figure in the image is a right triangle:

Angle θ = 47 degrees

Opposite to angle θ = 14cm

Hypotenuse = h

To solve for side length h, we use trigonometric ratio.

Note that: sine = opposite / hypotenuse

Plug in the values and solve for h.

sin( 47° ) = 14 / h

h = 14 / sin( 47° )

h = 19.1 cm

Therefore, the value of h is 19.1 cm.

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The value of cost of the perimeter of the lid is, $32.625

Given that;

Dylan is putting a gold ribbon around the lid of a rectangular box. The lid ha a width of 6(1/4) inches and a length of 4(5/8) inches.

Hence, The value of perimeter of the lid is,

⇒ P = 2 (6 1/4 + 4 5/8)

⇒ P = 2 (25/4 + 37/8)

⇒ P = 2 (50/8 + 37/8)

⇒ P = 2 (87/8)

⇒ P =  87/4 inches

Since, The ribbon costs $1.50 per Inch.

Hence, Total cost for lid is,

⇒ 1.50 × 87/4

⇒ $32.625

Thus, The value of cost of the perimeter of the lid is, $32.625

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Answer:B

Step-by-step explanation:i did the quiz

In total, Christian had 62 customers in the last week.

The value of the angle y is 86 degrees

To determine the value of the variable, we need to take note of the properties of a parallelogram. They include;

Also, note that angles on a straight line is equal to 180 degrees.

From the information shown on the diagram, we have;

y + 94 = 180

collect the like terms

y = 180 - 94

Subtract the terms

y =86 degrees

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Answer:g=g(9)

Step-by-step explanation:

The answer is : No, this time there is not a fixed number of trials,

Fixed Number of Trials (n): Established beforehand, the experiment consists of a specified set of trials or repetitions.

Binary Outcomes: Every trial possess just two feasible outcomes typically referred to as "success" and "failure."

Independent Trials: The result of a single trial will not affect the outcome of any subsequent trials.

Constant Success Probability (p): Per trial, the chances of success remain unchanging.

Taking into account the given circumstances, Ms. Lee intends on giving out another homework pass consequently, she will keep pulling names until concluding with a statistics student. She rearranges and shuffles the papers which contain the names in-between each trial.

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Answer:

By using the formula down below you can find the area of a trapezoid

A = [tex]\frac{a+b}{2}[/tex]h

↑ Area

A = Base

B = Base

H = Height

Example.

A = 12

B = 4

H = 2

First “ A “ + “ B “ =

12 + 4 = 16

16 / 2 = 8

8 x “ h “

8 x 2 = 16

Answer is 16

Thus the answer is, above

So if you look that up then it will show you how to find the area of a trapizoid

The approximate value of the median is 25

The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.

To find the median, calculate the value mean by adding together the middle values and dividing them by two.

Hence, the approximate value of the median is Median

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What is the approximate value of the median?

A 18

B 20

C 25

D 27

To order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

If we consider each "drop-in" guest as half a guest, then the total number of guests becomes:

40 + 0.5x, where x is the number of "drop-in" guests.

To determine how much of each food item to order, we can use the recommended amounts as a guide and scale them up based on the total number of guests:

So, to order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

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Answer:

  (a)  x = -4y +19

Step-by-step explanation:

You want to know a good first step for solving the system of equations in an efficient manner.

One way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.

Here, a useful first step is to solve the second equation for x:

  x = -4y +19

__

Additional comment

Then the solution proceeds with substitution for x:

  3(-4y +19) +2y = 17

  -10y +57 = 17

  -10y = -40

  y = 4

  x = -4(4) +19 = 3

The solution is (x, y) = (3, 4).

Another reasonable first step is to subtract the second equation from twice the first:

  2(3x +2y) -(x +4y) = 2(17) -(19)

  5x = 15

  x = 3

  3 +4y = 19 . . . . . . substitute for x in the second equation

  y = (19 -3)/4 = 4

The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.

Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time

We have,

To determine which savings account has more money after 9 years, we can evaluate the amount of money in each account using the given equations.

For Savings Account A, the equation is:

A = 21.09t + 1125

Substituting t = 9 (since we're interested in the amount after 9 years), we get:

A = 21.09(9) + 1125 = 1300.81

So, after 9 years, Savings Account A will have $1300.81.

For Savings Account B, the equation is:

A = 1125(1 + 0.01875/2)^(2t)

Substituting t = 9, we get:

A = 1125(1 + 0.01875/2)^(2(9)) = 1318.98

So, after 9 years, Savings Account B will have $1318.98.

Therefore,

Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time

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Answer:

2x2+x+5

Step-by-step explanation:

Answer:

1st one is b.  2nd one is A

Step-by-step explanation:

i did the quiz

Answer:

To find the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper, we need to use Bayes' theorem:

P(Under 40 | Read paper) = P(Read paper | Under 40) * P(Under 40) / P(Read paper)

where

P(Under 40 | Read paper) is the probability that a person is under 40 given that he or she gets the news by reading the paper

P(Read paper | Under 40) is the probability that a person under 40 reads the paper (36/80)

P(Under 40) is the overall probability of selecting a person under 40 (40/80)

P(Read paper) is the overall probability of selecting a person who reads the paper, calculated as the sum of those who are under 40 and read the paper and those who are 40 or older and read the paper (36+24)/(80)

Plugging in the values, we get:

P(Under 40 | Read paper) = (36/80) * (40/80) / ((36+24)/80)

P(Under 40 | Read paper) = 0.6

So the probability that a person surveyed is under 40, given that he or she gets the news by reading the paper, is 60%.

The 99% confidence interval for the proportion of Americans who believe that the minimum wage should be raised is: 0.56 < P < 0.64

We are given:

Sample size: n = 1000

Sample proportion: p = 600/1000 = 0.6

Formula for confidence interval for proportion is:

CI = p ± z√(p(1 - p)/n)

where:

p is sample proportion

n is sample size

z is z-score at confidence level

z at 99% CL = 2.576

Thus:

CI = 0.6 ± 2.576√(0.6(1 - 0.6)/1000)

CI = 0.6 ± 0.04

CI = (0.56, 0.64)

CI = 0.56 < P < 0.64

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The magnitude of the vector 4v is 4 times the magnitude of v, which is equal to 4 √29.

Given the vector v = 5i - 2j, we can find the magnitude or norm of the vector ||v|| using the formula:

||v|| = √(v · v)

where · denotes the dot product of the vector with itself.

Substituting the values of the vector v, we have:

||v|| = √((5i - 2j) · (5i - 2j))

Expanding the dot product using the distributive law, we get:

||v|| = √(25i² - 20ij + 4j²)

Since i² = j² = 1 and ij = ji = 0, we can simplify this expression to:

||v|| = √(25 + 4) = √29

Thus, the magnitude of the vector v is √29.

Now, we need to find the magnitude of the vector 4v. Using the property that ||kv|| = |k| ||v|| for any scalar k and vector v, we have:

||4v|| = |4| ||v|| = 4 √29

In summary, the magnitude of the vector v is √29, and the magnitude of the vector 4v is 4 √29.

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The simplified expression is 120x³ + 120x².

To simplify the expression 5x(2x+2)12x, we can use the distributive property of multiplication over addition and simplify the resulting terms.

First, we distribute 5x to the expression (2x+2), which gives us:

5x(2x+2) = 10x² + 10x

Next, we can multiply the result by 12x:

12x(10x² + 10x) = 120x³ + 120x²

Therefore, the simplified expression is 120x³ + 120x².

We can see that the original expression was a multiplication of three factors, and we used the distributive property to simplify it by expanding and multiplying the resulting terms. The final expression has a common factor of 120x², which we can factor out to get 120x²(x+1).

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Answer: 550.320 to the nearest whole number is 550.

Step-by-step explanation: If the number if five or more, it rounds up, but if it is four or less, it stays the same. Therefore, because 3 is less than four, the answer is 550. Hope this helps! :)

Answer:

550

Step-by-step explanation:

If we look at the number we see .320, as we can see the number in the front is 3 and behind that is 2, when we are rounding the key thing to always remember is if its greater than 5 we round up if not go down so sense 3 doesn't go over 5 we don't change the number in front of it 0 and the same thing with 2 but we wouldn't change the 3 instead. so sense .320 doesn't qualify as a whole number we do not need it so we get the answer,

550.

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HAVE A NICE DAY :)

Answer:

Step-by-step explanation:

[tex]\sf -24=8(y-8)-4y[/tex]

[tex]\sf 8\left(y-8\right)-4y=-24[/tex]

Expand:-

[tex]\sf 4y-64=-24[/tex]

Add 64 to both sides:-

Divide both sides by 4:-

________________________

The rate of car is 35 mph.

Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.

Let c be the rate of wind.

215 + c = rate of plane with wind

215 - c = rate of plane against wind

Therefore, the travel time =distance/rate

⇒ 750/(215+c) = 540/(215-c)

Cross multiplying we get,

540(215+c) = 750(215-c)

116100+540c = 161250-750c

1290c = 45150

c=35

Hence, the rate of car is 35 mph.

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The student is correct because we can factorize x² - x - 56 to get (x - 8)(x + 7).

How to Factorize an Expression?

In order to determine if -56 is the integer that can replace the box in the expression, we can try to factorize the expression and see if it works.

Factorize x² - x - 56 using the sum-product pattern:

x² - x - 56

Take out the common factors from each pair:

(x² + 7x) - (8x - 56)

x(x + 7) -8(x + 7)

Rewrite in factored form:

(x - 8)(x + 7)

Thus, this shows that the student is correct.

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Answer:

a₈₁ = - 482

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 2 and d = a₂ - a₁ = - 8 - (- 2) = - 8 + 2 = - 6 , then

a₈₁ = - 2 + (80 × - 6) = - 2 + (- 480) = - 2 - 480 = - 482

If 5 is subtracted from the square of a number, the positive solution is √5.

In this exercise, you are required to determine or solve for an unknown number as follows. First of all, we would assign a variable to the unknown number and then translate the word problem into an algebraic expression as follows;

Assuming the unknown number is represented by the variable x.

Therefore, the required algebraic expression is given by;

x² - 5

In order to determine the positive solution, we would have to equate the algebraic expression to zero as follows;

x² - 5 = 0

x² = 5

x = ±√5

x = √5 (positive solution)

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