A surveyor measures the angle of elevation to a point on a mountain to be 18 degrees the point on the mountain is horizontally 4 miles away from the surveyor the vertical change in elevation from the point where the surveyor is standing to the point on the mountain is___ miles?

Answer:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We assume that the die is fair and the probability of obatin a one is 1/6.

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=12, p=1/6)[/tex]

And we want to find this probability:

[tex] P(X=12)[/tex]

And if we replace we got:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

Answer:

The answer is rotational symmetry.

Step-by-step explanation:

The Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane. A shape is said to possess rotational symmetry when it still looks the same after we rotate it.                                            

Answer:

Step-by-step explanation:

$228

The LCM of P and Q is found by taking the highest powers of the common prime factors from both numbers, which results in LCM(P, Q) = 37 x 73 x 112.

To find the Least Common Multiple (LCM) of P and Q when given as products of prime factors, we look for the highest powers of the prime factors that appear in either P or Q. In this case:

For prime factor 3, the highest power in P and Q is 37. For prime factor 11, the highest power is 112 (from P). Since prime factor 7 only appears in Q, we include it in its highest power, which is 73. Combining these, the LCM of P and Q as the product of prime factors is:

LCM(P, Q) = 37 x 73 x 112

there are 10 numbers ( 0-9)

there are 26 letters ( A-Z)

10 x 26 x 26 x 10 x 10 x 10 x 10 =67,600,000 possible combinations

Area = 1039.23 square units

 Round answer as needed. See picture for equation

Answer: a=100 and b=5

Step-by-step explanation:

Given: A school typically sells 500 yearbooks each year for $50 each.

The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.

Let x represents the number of $5 decreases in price.

Then the new price (in dollars)=50-5x

Total yearbook sold=500+100x

If the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.

Then the revenue function will be [tex]R(X)=(500+100x)(50-5x)[/tex]

On comparing this with the given revenue expression we get

a=100 and b=5.

In this exercise we have to calculate the values ​​of A and B, so we have to:

[tex]A=100\\B=5[/tex]

Since the equation is:

[tex]R(X)=(500+ax)(50-bx)[/tex]

And the following information was given:

So knowing that by increasing 100 more books sold this is equal to A and the decrease in value is going to be equal to b.

[tex]R(X)=(500+100x)(50-5x)[/tex]

See more about equation at brainly.com/question/2263981

To solve this problem, all you have to do is to subtract 360 degrees (equivalent to 1 rotation) from the given angle until the answer is less than 360 degrees.

1st subtraction: 750 – 360 = 390 degrees

2nd subtraction: 390 – 360 = 30 degrees

Therefore the positive angle less than one rotation that is coterminal with 750 degrees is 30 degrees.

The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.

This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.

Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.

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Final answer:

A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.

Explanation:

In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.

A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.

A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.

Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.

Given these definitions, the correct answer to the question would be:

D. i, ii, iii, v, vi

Final answer:

The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).

Explanation:

If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.

Answer:  The required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

Step-by-step explanation:  We are given to write the following inequality in the slope-intercept form :

[tex]-6+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope intercept form of a straight line with slope m and y-intercept c is given by

[tex]y=mx+c.[/tex]

Writing equation (i) in slope-intercept form, we have

[tex]-6+2y\leq 42\\\\\Rightarrow 2y\leq 42+6\\\\\Rightarrow 2y\leq 48\\\\\Rightarrow y\leq 24\\\\\Rightarrow y\leq 0\times x+24,[/tex]

where slope, m = 0  and  y-intercept, c = 24.

Thus, the required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

The variance of the five bedroom house is 864.

σ²

[tex]=\frac{X^2}{N} -u^2[/tex]

To get the value of X²

= 100²+100²+120²+120²+180²

= 81200

The number is N = 5

u = mean

[tex]u = \frac{100+100+120+120+180}{5}[/tex]

u = 124

The values in the variance formula

[tex]\frac{81200}{5} -124^2[/tex]

16240-15376

= 864

The variance is 864

Read more on variance here:

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we have

[tex] f(x) = 2x^{2}- x -6 [/tex]

using a graph tool

see the attached figure

we know that

1) the domain of the function is all real numbers-------> interval (-∞,∞)

2) The range of the function is the interval [-6.125,∞)

3) The vertex of the function is the point (0.25,-6.125)

4) The function has two x-intercepts-----> ( -1.5,0) and (2,0)

5) The function is increasing over the interval (0.25,∞) and decreasing over the interval (-∞,0.25)