2. Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the
observers to the top of the pole are 19 and 21°. Find the height of the flagpole. Round to the nearest
foot.

The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

The cubic function is given in the question, as follows:

f(x) = 64x³ + 27

The above expression can be rewritten as:

f(x) = (4x)³ + (3)³

Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get

f(x) = (4x + 3)(16x² − 12x + 9)

Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).

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Answer:

2,2 but i could be wrong

Just wanted to say he's correct, it's 2, 2

Answer:10

Step-by-step explanation:

5.5 equals 25.then you subtract 25 by 25 and get zero.

Check the picture below.

On solving the provided question we can say that by bodmas ((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

The acronym BODMAS helps children learn the hierarchy of math operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms:

B Bracket, O Degrees (Power/Exponent or Square Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also known as PDMAS in some areas. It symbolizes exponents, division, multiplication, addition and subtraction. It also represents brackets. The BODMAS rule states that parentheses must be handled first, then powers or roots (that is, of), division, multiplication, addition, and finally subtraction. Known as BODMAS in India and the UK, PEMDAS is primarily used in the US. However, they are identical to each other. The parentheses, order, and order of addition, subtraction, multiplication, and division are the same for the two rules.  

by bodmas

((4 / 3) / (1/4)) + ((2 / 5) / (1/4)) + ((4 / 15) / (1/4)) =8

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There are 50 ways for Marvin to reach his destination without passing through the forbidden point.

To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.

In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).

There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.

Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)

We can visualize this by drawing another grid and counting the paths:

In total, there are

=> 5 x 10 = 50

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Answer: [tex]8d^{2} (8d^3 - 3)[/tex]

Step-by-step explanation:

8d^2 is the GCF for this binomial

Answer:

Below

Step-by-step explanation:

L X W is area of rectangle ...this figure can be viewed as a rectangle on top of a rectangle

top rectangle is 3x-2   wide   and   (2x+5) - (3x-2)  length

   area =  (3x-2)(  (2x+5) - (3x-2) )

             = (3x-2) ( -x + 7)  = - 3x^2 + 23x -14     units^2

The bottom is then    (3x-2 + 2) * (3x-2)

                             area = (3x)(3x-2) = 9x^2 - 6x  units^2

Add the two areas together      (-3x^2+23x-14) + (9x^2 -6x)

                                                     6x^2 + 17x -14    and this = 25 cm^2  (given)

      6x^2 + 17x -14 = 25

      6x^2 + 17x - 39 = 0   Use Quadratic Formula to find x = 1.5

then find the longest side   using this value of x

        3x-2 + 2  = 4.5 cm

    2x+5 = 8  cm    <=====longest side

3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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Answer: about 1587 cm^2

Step-by-step explanation: The equation for area of circle is A= πr^2 OR A= (pi/4)d^2

Given the diameter is 46.7, the radius would be half of that which is 23.35.

Simply plug it into the equation

A =  π23.35^2

OR

A= (π/4)46.7^2

Since you are using 3 in place of pie, it would be 3(23.35)^2  OR (3/4)46.7^2

the answer i got was 1,635 cm^2 so your closest choice to that is 4

the answer is 66

its easy... you posted this as high-school... this is 6th grade work

Area is 69 km2

………..,……….

a) The histogram for the data is illustrated below.

b) The cumulative percentage polygon is define in the histogram

c) The amount does the monthly electricity cost seem to be concentrated is 128 - 152

A histogram is a graphical representation of a frequency distribution. It consists of a set of bars that represent the frequency of data within certain intervals, also known as bins. The height of each bar represents the frequency or count of data points that fall within that bin.

To create a histogram for the electricity cost data, we need to first decide on the number and size of the bins. One common rule is to choose the number of bins as the square root of the sample size. In this case, we have 50 data points, so we can choose about 7 bins. The size of the bins can be determined by dividing the range of the data by the number of bins.

Once we have determined the number and size of the bins, we can create the histogram by drawing a set of bars with heights proportional to the number of data points that fall within each bin. The histogram can be further enhanced by adding labels for the x and y-axes, a title, and a legend.

As per the histogram, the amount does the monthly electricity cost seem to be concentrated is 128-152

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The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.

Given;

Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.

The addition of the internal angles of triangle is 180

So, let vertex angle be x

The other two sides will be x+10,

x+x+10+x+10=180

3x+20=180

x=160/3

x=53.3

Therefore, the vertex angle of the triangle will be 53.3degrees.

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375 different combinations of pizza Grayson and his friends can create.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

They can pick thick, hand-tossed, or deep-dish crust.

Here, n=3 r=1

So, C(n, r) = 3!/1!(3-1)!

= 3

They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

Number of ways = 5×5×3×5

= 375

Hence, in 375 ways they can choose pizza.

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An inverse relationship is also known as a negative relationship, because the correlation coefficient, is negative in an inverse relationship. Correct option is B.

An inverse relationship is a type of relationship between two variables in which they move in opposite directions. As one variable increases, the other variable decreases. In other words, when one variable changes, the other variable changes in the opposite direction.

For example, in the context of physics, the distance between two objects and the gravitational force between them have an inverse relationship. As the distance between the objects increases, the gravitational force between them decreases, and vice versa.

An inverse relationship is also known as a negative relationship. This is because the correlation coefficient, which measures the strength and direction of the relationship between two variables, is negative in an inverse relationship.

A correlation coefficient of -1 indicates a perfect inverse relationship, while a correlation coefficient of 0 indicates no relationship, and a correlation coefficient of 1 indicates a perfect positive relationship.

In contrast, a direct relationship, also known as a positive relationship, is a type of relationship between two variables in which they move in the same direction. As one variable increases, the other variable also increases, and vice versa.

In summary, an inverse relationship is a negative relationship in which two variables move in opposite directions, while a direct relationship is a positive relationship in which two variables move in the same direction.

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Answer:

y = 3x + 10

Step-by-step explanation:

slope intercept form​ is y = mx + b

y - 4 = 3(x+2)

y - 4 = 3x + 6

y = 3x + 10

So, the answer is y = 3x + 10

Answer:

9 - y

Step-by-step explanation:

less than means Subtraction

The angle congruence property illustrated is given as follows:

Symmetric Property of Angle Congruence.

The symmetric property of angle congruence states that if if one geometric shape is congruent to a second shape, than the second shape is also congruent to the first.

The shapes in this problem are given as follows:

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The actual amount of sale for each bake is $214. As Miguel said it is $215 which is very close to the actual amount, it is reasonable.

To determine if Miguel's estimate of $215 per bake sale is reasonable, we can start by calculating the average amount of money the scout troop made per bake sale. We do this by dividing the total amount they earned by the number of sales they had, as follows:

Total amount earned = $1,498

Number of bake sales = 7

Average amount earned per bake sale = Total amount earned ÷ Number of bake sales

= $1,498 ÷ 7

= $214

This calculation shows that the average amount the scout troop made per bake sale was $214. This means that if they had charged a consistent price for all of their baked goods at each sale, they would have made an average of $214 per sale.

Now, we can compare this average to Miguel's estimate of $215 per bake sale. Since his estimate is very close to the actual average, we can conclude that it is reasonable.

It is possible that the scout troop charged slightly different prices for their baked goods at each sale, which could explain the small discrepancy between the actual average and Miguel's estimate. However, given that the difference between the two values is only $1, it is likely that Miguel's estimate is a good approximation of the actual amount.

Moreover, it is reasonable to assume that the scout troop earned the same amount at each bake sale, especially if they had a set price for their baked goods.

If they had charged different prices at each sale, it would have been more difficult to estimate the average amount they earned per sale, and it would have been less likely that Miguel's estimate of $215 per bake sale would have been close to the actual average.

Therefore, based on the calculation and the context of the problem, we can conclude that Miguel's estimate of $215 per bake sale is reasonable.

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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the errors come from a normal distribution.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, implying that data closer to the mean occur more frequently than data further away from the mean.

The normal quantile plot of the residuals in a simple linear regression model is used to establish if it is reasonable to think the errors are normal.

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Step-by-step explanation:

1000ml=1 litre

800 divided by(1000 multiplied by 5)=16%

The obtuse angle such that has the same sine as -275° is θ = 95°

We want to find an obtuse angle (with a measure larger than 90°) in the range 0 ≤ θ ≤ 2π (or 0 < θ < 360°, after that we can change the units from degrees to radians) such that sin(θ) = sin(-275°)

First, remember that the sine function has a periodicity of 360°, then:

sin(-275°) = sin(-275° + 360°) = sin(85°)

Now we know that the sine function is symmetric around x = 90°

Then:

sin(90° + x) = sin(90° - x)

if we take x = 5° we will get:

sin(90° + 5°) = sin(90° - 5°)

sin(95°) = sin(85°) = sin(-275°)

Thus we can conclude that θ = 95°

That is the obtuse angle.

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a) The probability of being dealt a flush is approximately 0.00198, or about 0.2%.

b) The probability of being dealt one pair is approximately 0.422, or about 42.2%.

a. To find the probability of being dealt a flush, we need to first determine how many possible flush hands there are, and then divide that by the total number of possible hands. There are 4 suits in a deck of cards, so there are 4 ways to choose which suit the flush will be in.

Once we have chosen a suit, there are 13 cards of that suit, and we need to choose 5 of them. The number of ways to choose 5 cards from 13 is given by the combination formula: C(13,5) = 1287. Therefore, there are 4 x 1287 = 5148 possible flush hands.

The total number of possible hands is given by the combination formula for choosing 5 cards from a deck of 52: C(52,5) = 2598960. Therefore, the probability of being dealt a flush is 5148/2598960, which simplifies to approximately 0.00198, or about 0.2%.

b. To find the probability of being dealt one pair, we need to first determine how many possible one pair hands there are, and then divide that by the total number of possible hands. There are 13 denominations in a deck of cards, so there are 13 ways to choose which denomination will form the pair.

Once we have chosen a denomination, there are 4 cards of that denomination, and we need to choose 2 of them. The remaining 3 cards must each be a different denomination from the pair, so there are 12 denominations left to choose from, and 4 cards of each denomination.

We need to choose 3 of these 12 denominations, and then 1 card from each of those 3 denominations. The number of ways to choose 2 cards from 4 is given by the combination formula: C(4,2) = 6. The number of ways to choose 3 denominations from 12 is given by the combination formula: C(12,3) = 220.

The number of ways to choose 1 card from each of 3 denominations is 4 x 4 x 4 = 64. Therefore, the total number of possible one pair hands is 13 x 6 x 220 x 64 = 1,098,240. Dividing this by the total number of possible hands gives us the probability of being dealt one pair, which is 1,098,240/2598960, or approximately 0.422, or about 42.2%.

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The area of the rectangle can be expressed as a fraction by multiplying 3/4 and 5/12. The answer is 5/16, which represents the area of the rectangle.

1. Multiply the length and width of the rectangle: 3/4 x 5/12 = 15/48

2. Reduce the fraction to its simplest form: 15/48 = 5/16

3. The answer is 5/16, which represents the area of the rectangle.

To find the area of a rectangle, you need to multiply the length and width of the rectangle together. In this case, the rectangle is 3/4 of a foot long and 5/12 of a foot wide. To express the area as a fraction, you need to multiply the two fractions together. 3/4 x 5/12 = 15/48. Since 15 and 48 have a common factor of 3, the fraction can be reduced to its simplest form, 5/16. Therefore, the area of the rectangle can be expressed as 5/16. This fraction represents the area of the rectangle.

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The complete question is

A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle of a feet wide.

The correct option is B, the system of equations has infinitely many solutions.

When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.

In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.

Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.

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Answer:

x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.

Step-by-step explanation:

5x <= 15

Next, we'll solve for x by dividing both sides by 5:

x <= 3

So, the possible values for the number are any value less than or equal to 3, including negative numbers.

x <= 3 represents all values such as: -∞, -100, -4, -3, -2, -1, 0, 1, 2, 3.

Answer: this app should be freer

Step-by-step explanation:

To double, the population must increase by a factor of 2, which would take ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.

To solve for the time it took for the bacterial population to double, we need to use the exponential growth formula:

[tex]N(t) = N_0 * e^{(kt)[/tex]

where N0 is the initial population, N(t) is the population at time t, k is the growth rate, and e is the base of the natural logarithm (approximately 2.71828).

Since the population is increased sixfold in 10 hours, we can set up the equation as:

[tex]N_0 * e^{(kt)} = 6 * N_0[/tex]

Taking the natural logarithm of both sides gives:

kt = ln(6).

Dividing both sides by k and using the fact that the natural logarithm of 2 is approximately 0.693,

ln(2) / ln(6) = ln(2) / ln(6) * 10 hours = 2.817 hours.

So it took approximately 2.817 hours for the population to double.

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Work Shown:

i = P*r*t

900 = 6000*r*1

r = 900/6000

r = 0.15

That converts to 15% after moving the decimal point 2 spots to the right. It's the same as multiplying by 100.