two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?

Answer:

x = 4

Step-by-step explanation:

Alternative interior angles means these angles are equal in magnitude and sign

[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]

In data analytics, a population refers to all possible data values in a certain dataset.

Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.

The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.

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The expected value of cases in which juries got the right decision is 150, and the variance is 375.

1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.

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Answer:

Isiah Thomas

Step-by-step explanation:

I amazing fact

Answer:

the correct answer is 4

Step-by-step explanation:

yea sorry i don’t know step-by-step

The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.

As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.

We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:

Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:

Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)

Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)

(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)

Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)

(b), we can use the just-proven formula:

A = ln(1, 2,...) + ln + ln (89)

= ln(j=1 to 89) prod

sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).

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Answer:

"9 more than A" is a verbal expression.

Answer:

Step-by-step explanation:

To solve this problem, we need to find out how many seats there are in total, and then multiply that by the price per ticket.

To find the total number of seats, we need to add up the number of seats in each row. We can use the formula for an arithmetic sequence to do this:

S = n/2 * (a + l)

where S is the sum of the sequence, n is the number of terms, a is the first term, and l is the last term.

In this case, we have:

n = 20 (since there are 20 rows)

a = 25 (since there are 25 seats in the first row)

d = 2 (since the difference between each row is 2 seats, the common difference is 2)

We can use d to find the last term as well:

l = a + (n-1)*d

l = 25 + (20-1)*2

l = 25 + 38

l = 63

Now we can plug these values into the formula:

S = 20/2 * (25 + 63)

S = 10 * 88

S = 880

So there are 880 seats in total.

To find the total sales, we just need to multiply by the price per ticket:

total sales = 880 * $32

total sales = $28,160

Therefore, the total sales for a one-night concert with all seats taken would be $28,160.

Answer:

Starting with the left side of the equation:

cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)

= cosθ + sinθ

Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.

Answer:15 percent

Step-by-step explanation:

The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

The acceleration vector can be found from the following formula:

[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]

Next, we need to normalize the velocity vector using the following formula:

[tex]T(t) = v(t) / ||v(t)||,[/tex]

Where ||v(t)|| is the magnitude of the velocity vector.

[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]

Then, the tangential component of a(1) is:

[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]

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Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436

The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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Answer: 12.84

Step-by-step explanation:

if x = 3.2 and y = 6.1  and Z = 0.2

then plug in the numbers

(3.2)(0.2) + (6.1)(2)

0.64 + 12.2 = 12.84

Any variable next to a number means multiplication.

if I was wrong lmk

In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.

The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.

Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.

Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.

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The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

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The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

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The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.

To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.

Let's consider a cross section of the solid taken at a distance x from the center of the circle.

Since the cross section is an equilateral triangle, all its sides have the same length.

Let  this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:

[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]

Therefore, the area of the cross section at a distance x from the center of the circle is:

[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]

Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):

[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]

To find the limits of integration for y, we need to consider the equation of the circle:

[tex]x^2 + y^2= 3^2[/tex]

Solving for y, we get:

[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]

Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:

[tex]y = 3*\sqrt{3}[/tex]

Substituting this into the integral, we get:

[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]

[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]

Integrating, we get:

[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]

[tex]= 81/2*\sqrt{3}[/tex]

Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units

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The upper bound of a + b can be found by adding the upper bounds of a and b.

For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.

For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.

So the upper bound of a + b is:

5.5 + 3.5 = 9

Therefore, the upper bound of a + b is 9cm.

The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0

Given that

Center = (5, 0)

Point on the circle = (5. 9/2)

The equation of a circle can be expressed as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x - 5)² + (y - 0)² = r²

Calculating the radius, we have

(5 - 5)² + (9/2 - 0)² = r²

Evaluate

r = 9/2

So, we have

(x - 5)² + (y - 0)² = (9/2)²

Expand

x² - 10x + 25 + y² = 81/4

Multiply through by 4

4x² - 40x + 100 + 4y² = 81

So, we have

4x² + 4y² - 40x + 19 = 0

Hence, the equation is 4x² + 4y² - 40x + 19 = 0

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Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.

Inequality is an algebraic statement that two or more mathematical expressions are unequal.

Inequalities can be represented as:

The total amount received by the island = $32,000

The daily receipt of donations = $4,500

Let the number of days = x

Let the funds raised for aid = y

y ≤ 32,000 + 4,500x

Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.

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Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).

In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:

final amount = 5.00 - 5.00 - (5.00 * 0.045)

final amount = 5.00 - 5.00 - 0.225

final amount = 4.775

Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.

Answer: x=211/1296

Step-by-step explanation:

The probability of getting tails in the three coins would be 0.125 or 12.5%.

To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.

Probability of getting tails in any of the three coins:

1 / 2 = 0.5

Total probabilityy:

0.5 x 0.5 x 0.5 = 0.125 or 12.5%

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Answer:

a=1/3

Step-by-step explanation:

First, expand the brackets by doing multiplication:

2+6a+3=3a+6

Then, move the unknown to the left and the numbers to the right:

3a=6-5

3a=1

a=1/3

The solution to the given equation is -1.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 2+3(2a+1)=3(a+2)

2+6a+3=3a+2

6a+5=3a+2

6a-3a=2-5

3a=-3

a=-1

Therefore, the solution to the given equation is -1.

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After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.

Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.

The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.

If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.

The number of generations (n) in seven hours is calculated as:

n = t/g

n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations

The number of cells in the cream pie after 7 hours is calculated as :

N = N₀ × 2ⁿ

N = 6 cells × 2⁷

N = 768 cells

Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.

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