an arctic explorer reached the north pole and decided to erect the national flag . his eyes was 1.6 m from the ground and the angle of elevation to the top of the 3 m flagpole was 28. how far from the base of the flagpole did he stand?

Simplifying the expression (x)(6 + x)−2x gives x^2 + 4x

Information given in the question

the expression (x)(6 + x)−2x

The expression is simplified by first expanding

(x) (6 + x) − 2x

6x + x^2 - 2x

x^2 + 4x (products as powers when possible)

The result here is a quadratic equation without the constant variable. it can be simplified further to give

x(x + 4)

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Answer: D. 5.38 > 5.271 > 5.217

The values of [tex]D, D_x, D_y[/tex] are, [tex]D = 13, D_x = 8, D_y = 19[/tex].

What is Cramer's rule?

One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.

Consider, the given system of equations

-3x + 4y = 4             ...(1)

2x = 7y - 9               ...(2)

equation (2) can be written as,

2x - 7y = -9             ..(3)

Using Cramer's rule, we have to find the determinant of the coefficient matrix

matrix,

D= [tex]\left[\begin{array}{ccc}-3&4\\2&-7\end{array}\right][/tex]  = (-3)(-7) - 8 = 21 - 8 = 13

Secondly, find the determinant of x coefficient matrix,

[tex]D_x[/tex] =  [tex]\left[\begin{array}{ccc}4&4\\-9&-7\end{array}\right][/tex] = (4)(-7) - (4)(-9) = -28 + 36 = 8

Similarly, find the determinant of y coefficient matrix,

[tex]D_y[/tex] = [tex]\left[\begin{array}{ccc}-3&4\\2&-9\\\end{array}\right][/tex] = (-3)(-9) - (4)(2) = 27 - 8 = 19

Hence, values of the determinants are, [tex]D = 13, D_x = 8, D_y = 19[/tex].

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The equation of the circle is x² + y² - 41 =0.

A circle is a round-shaped 2-dimensional geometrical figure in which the points on the boundary are equidistant from a fixed point called a center.

Given, a circle centered at O(0,0)and has a point B (4,5) on its circumference.

The radius of the circle is the distance between the points O(0,0) and B (4,5), therefore,

r = √((4-0)² + (5-0)²)

r = √(16+25)

r = √41

The equation of a circle, centered at the origin with a radius of r =√41  units, is given by,

x² + y² = √41²

x² + y² = 41

x² + y² - 41 =0

Hence, the equation of the circle is x² + y² - 41 =0.

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Answer:

????? you did not show the net of the prism

Step-by-step explanation:

Answer:

b) it's a polyhedron

I don't know what else to say

The percentage of pediatricians that work more than 70 h per week is; 2.275%

The formula for z-score of a normal distribution is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

sample mean; x' = 70 hours

population mean; μ = 40 hours

standard deviation; σ = 15 hours

Thus;

z = (70 - 40)/15

z = 2

From online p-value from z-score calculator, we have;

p-value =  0.02275 = 2.275%

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g(x) is a vertical dilation of f(x), then the x-value of the vertex does not change, using that we will see that the vertex of g(x) is (-4, 24)

We know that there is a parabola graphed called f(x), such that the vertex of f(x) is at (-4, 6).

We also have a vertical dilation of this function defined as:

g(x) = 4*f(x)

Notice that because this is a vertical dilation, the x-value of the vertex does not change, then the vertex is at x = -4, like on f(x).

Evaluating there we get:

g(-4) = 4*f(-4)

And because the vertex of f(x)  is (-4, 6), then we know that:

f(-4) =6

Replacing that we get:

g(-4) = 4*f(-4) = 4*6 = 24

Then the vertex of g(x) is at (-4, 24)

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Answer:false

Step-by-step explanation:

Answer:

[ D ] 140

Step-by-step explanation

4 x 265 = 1060

1060 - 1200 = -140

the answer is 140  i hope this helped <3

The startup company needs to sell 68 skateboards in order to break even

To solve this problem, we have to find the profit of the company and what is required to break-even from total sales.

C(x) = 10x + 500

r(x) = -x² + 70x

Profit = revenue - cost

profit = (-x² + 70x) - 10x + 500

profit = -x² + 70x - 10x + 500

profit = -x² + 60x + 500

Solving the quadratic equation

x = 67.4 ≅68

For the startup to break even, they need to sell at least 68 skateboard.

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Answer:

Nick

Step-by-step explanation:

Nick: 39 miles / 2 hours = 19.5 miles per hour

Jane: 34 miles / 5 hours = 6.8 miles per hour

Nick is biking faster!

Answer:

The answer would be the first one because when you factor -3 out, inside of the parentheses should be all positive because negative times negative is positive.

Answer:

[tex]w=\frac{y+1}{a+2}[/tex]

Step-by-step explanation:

[tex]y-aw=2w-1 \\ \\ y+1=2w+aw \\ \\ y+1=w(a+2) \\ \\ w=\frac{y+1}{a+2}[/tex]

Answer: (-2, -2)

Step-by-step explanation:

Right now, the coordinates of point C are (1, -3).

It is first moved 3 units to the left, so the point C would change to (1 - 3, -3) = (-2, -3)

It is then moved 2 units up, so point C would change to (-2, -3 + 2) = (-2, -1)

1. The hypothesis are given as follows:

2. The critical value is of: t = 2.3974.

3. The test statistic is of: t = 2.35.

4. The decision is: Reject the null hypothesis.

5. The conclusion is: There is enough evidence to conclude that the mean is greater.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean in Los Angeles is greater, that is:

[tex]H_0: \mu \leq 178258[/tex]

At the alternative hypothesis, it is tested if there is enough evidence, hence:

[tex]H_1: \mu > 178258[/tex]

The t-distribution is used, as we have the standard deviation for the sample but not for the population. Using a t-distribution calculator, with 55 - 1 = 54 df, a right-tailed test, as we are testing if the mean is greater than a value and a significance level of 0.01, the critical value is:

t = 2.3974.

Hence the decision rule is defined as follows:

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 191790, \mu = 178258, s = 42627, n = 55[/tex]

Hence the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{191790 - 178258}{\frac{42627}{\sqrt{55}}}[/tex]

t = 2.35.

The test statistic is greater than the critical value, hence:

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The simplified point-slope form is y = 2x -12

A simple definition of point-slope form is a line equation written with only one point on the line and the slope of the line. (x, y) is the point form, and the slope is the rise over run or the ratio of the change in y values to the change in x values.

Given points (2,-8) and (-1,4)

We have to determine the answer in point-slope form

The slope formula provides the slope of the line:

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

m = (4 -(-8))/(-1-2) = 12/-3 = -4

the point-slope formula is given by

y-y1 = m(x-x1)

In terms of this formula:

m = 2

y1 = -8

x1 = 2

Let's simplify by plugging these values into the point-slope formula:

y - y1 = m (x - x1)

y - (-8) = (2)(x - 2)

y + 8 = 2(x - 2)

y + 8 = 2x -4

y = 2x -12

Therefore the simplified point-slope form is y = 2x -12

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Answer:

First by using inverse operations, subtract 12 on both sides.

Now it will become

Now divide 6 to isolate x

Hence, the answer is

a) The expected value of each $1 bet in roulette is of: -$0.988.

b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.

The expected value of a discrete distribution is obtained as the sum of each outcome multiplied by it's respective probability.

The three-number bet is when one sequence of three numbers has to be correctly chosen, hence the probability of winning is of:

p = 1/(10³) = 1/1000.

(as there is only one correct sequence, and for each number, there are 10 outcomes).

The payout is given as follows:

11:1.

That is, if you win, you earn 11 times the amount you bet.

Considering a bet of $1, the distribution of earnings is given as follows:

Hence the expected value of the bet is:

E(X) = 11/1000 - 999/1000 = -$0.988.

Which is the amount you are expected to lose for every dollar you bet.

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Answer:

ez hi

Step-by-step explanation:

ez

Equation of line c parallel to line d and passing through points  (2, -6) is

The equation of line d will be written in the slope intercept form of the form just like line c,

the slope intercept form is as below

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

y = -5x + 3

slope

m = -5

slope of parallel lines are equal hence slope of line d = -5

using the formula for the slope intercept the equation is written

(y - y₁) = m (x - x₁)

point (2, -6) and m = -5

(y - -6) = -5 (x - 2)

y + 6 = -5x + 10

y = -5x + 4

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The equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

The coordinates of the point = (-7, -4)

The slope of the line = 10/7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Where [tex](x_1,y_1)[/tex] is the coordinates of the point

Substitute the values in the equation

y -(-4) = 10/7(x - (-7))

y + 4 = (10/7)(x + 7)

Convert to slope intercept form

y +4 = (10/7)x + 10

y = (10/7)x + 10 - 4

y = (10/7)x + 6

Hence, the equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

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Answer: 12

Step-by-step explanation: When multiplying (in this case finding a product,) by one, the number you are multiplying will always be the answer.

The size of the bacterial population after 80 minutes is  19048.81

The size of the bacterial population after 7 hours is  49152000.

Given,

A bacterial culture initially contains 3000 bacteria and doubles every half hour.

we are asked to determine the size of the bacterial population after 80 minutes.

The exponential growth law for this problem is

p(t) = 3000 (2)^t/30

where t is the time in minutes. To find the population after 80 minutes, plug in t=80 and evaluate P(80).

p(80) = 3000 (2)^80/30

p(80) = 3000(2)^8/3

p(80) = 19048.81

now, we are asked to determine the size of the bacterial population after 7 hours.

To find it after  hours, plug in t=420 minutes (since 7 hrs equals 420 minutes) and evaluate p(420).

p(420) = 3000(2)^420/30

p(420) = 3000(2)^14

p(420) = 49152000

hence we get the required size of the population.

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The sum of n terms of geometric sequence with n=5, a₁ =4, r=3 is given by = 484.

Given that the sequence is geometric.

First term is = a₁ = 4

Common ratio is = r = 3

The number of terms for which the sum to be determined = n = 5

So the required sum of n terms of given geometric sequence is given by,

S [tex]=a_1\times\frac{r^n-1}{r-1}[/tex]

S [tex]=4\times\frac{3^5-1}{3-1}[/tex]

S = 4*((243-1)/2)

S = (4*242)/2

S = 484

Hence the sum of the given geometric sequence is 484.

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To find the set of numbers with a given mean we can assume them as consecutive terms, Zina did the same thing.

Mean or Arithmetic mean is the average of the given set of numbers. It is also denoted as the equal distribution of values for a given data. To calculate the mean of data, we can use the following formula  

Mean/Average = Sum of observations ÷ Number of observations

Here we have

The average of 5 numbers is 85

Let's assume that the 5 numbers are 5 consecutive numbers and the five numbers are x, x+1, x+2, x+3, x+4, and x+5  [ for simple calculations ]  

Average of 5 numbers = Sum of numbers / 5

⇒ 85 = (x+ x+ 1 + x+2 + x+3 + x+4 ) /5

⇒ 425 = 5x + 10  

⇒ 5x = 415

⇒ x = 83

Then the 5 numbers are 83, 84, 85, 86, and 87

Therefore,

To find the set of numbers with a given mean we can assume them as consecutive terms and we can calculate the mean, Zina did the same thing.  

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The joint relative frequency of students who use a mobile device in an online class is approximately 32%.

The joint relative frequency of students who use a mobile device in an online class, we need to divide the frequency of the intersection of the "Mobile device" and "Online" categories by the total number of students (200 in this case) and express it as a percentage.

From the given two-way frequency table, we can see that the frequency for the intersection of "Mobile device" and "Online" is 64.

The joint relative frequency can be calculated as:

Joint Relative Frequency = (Frequency of intersection / Total number of students) × 100

Joint Relative Frequency = (64 / 200) × 100

Joint Relative Frequency ≈ 32%

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