AP STATISTICS

You've taken a random sample of beaches in the United States and measured their lengths. A hypothetical probability distribution for beach length is represented in the table below. What's the probability of a randomly selected beach having a length of 12 miles?
Answer Choices:
A) .35
B) .10
C) 0
D) .45
E) None of the above

Answer:

line MN

Step-by-step explanation:

If two planes intersect, then the intersection is a line.

Answer: line MN

Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.

It is found using a calculator, with three inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value is of is of Tc = 2.8609.

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Answer: 3 1/4

Step-by-step explanation: you started with 8 1/4 subtract the 1/4 now ur left with 8-3 which equals 5

Answer:

9/25 or -1/11

Step-by-step explanation:

2 outcome

1; 7x-5=18x-4

2;-(7x-5)=18-4

Answer:

D.

Step-by-step explanation:

We can solve by simply isolating x:

[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]

You can check by plugging in any value greater than -8

-122<-3(-2-8(-7))-8*-7

-122<-3(-2+56)+56

-122<-3(54)+56

-122<-162+56

-122<-106

The responses include:

In mathematics, a real number simply means a value of a continuous quantity which can represent a distance along a line.

In this case, real numbers are the numbers that include both rational and irrational numbers. Here, Rmrational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and the irrational numbers such as √3, π(22/7), etc., are all real numbers.

In conclusion, the correct options are A, B, and C.

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Answer:

X-intercepts:

[tex] (\frac{3}{7} ,0)[/tex]

Y-intercepts:(0,3)

Step-by-step explanation:

Hello!

given expression

[tex]y = - 7x + 3[/tex]

x-intercept is the point on the graph where y=0

solve

[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]

Thus, x-intercept

[tex]( \frac{3}{7} ,0)[/tex]

y-intercept is the point on the graph where x=0

solve

[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]

Thus, y-intercept (0,3)

Hope it helps!

The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

We want to solve the algebraic fraction equation given as;

3a³ - 5b³ + (3/a) + b³

Rearranging the algebra to get;

(3a³ + (3/a)) + b³ - 5b³

Factorizing out 3/a and simplifying gives;

(3/a)(a⁴ + a) - 4b³

This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

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Answer:

[tex]52\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}(11+15)(4\sqrt{3})=52\sqrt{3}[/tex]

Answer:

y = 1/2 x  + 3

Step-by-step explanation:

Find slope, m = (y1-y2)/(x1-x2) =  (7-0) / (8- - 6)  = 7/14 = 1/2

   ( does not matter which one you assign as point 1 or point 2)

Point (-6,0)  slope form ( you can use either point)

(y-0) = 1/2 (x- -6)

y = 1/2 x +3

Answer:

C

Step-by-step explanation:

The correct answer is the option A because in one-to-one functions, each y value corresponds to only one x value.

Let z=a+bi, w=c+di

[tex]|z+w|^2 -|z-w|^2 \\ \\ = |(a+c)+i(b+d)|^2 -|(a-c)^2 +i(b-d)|^2\\\\=(a+c)^2 +(b+d)^2-(a-c)^2 -(b-d)^2\\\\=a^2 +2ac+c^2 +b^2 +2bd+d^2 -a^2 +2ac-c^2 -b^2+2bd-d^2\\\\=4ac+4bd\\\\=4Re(z)Re(w)+4Im(z)Im(w)[/tex]

The number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

When fractions are represented on a number line, we can plot them on a number line just like we do with whole numbers and integers. Parts of a whole are represented by fractions. As a result, fractions on the number line are represented by splitting a whole into equal parts, ranging from 0 to 1, and the number of those equal parts would match the denominator of the fraction.

To graph the given fractions on the number line, we first convert them to like fractions.

3/6, 3/4, and 3/12

= 6/12, 9/12, and 3/12, which are like fractions.

Now we divide the number line with the minimum mark as 1/12, the least fraction, with 12 as denominator.

Now, we can mark the points 6/12, 9/12, and 3/12, as shown.

Thus, the number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

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Answer: 6x[tex]6x{2}+93x-126andx{2}+84[/tex]

Step-by-step explanation: The only thing you do is just to keep multiplying until you get your answer.

The conclusion for p, from the confidence interval, using an absolute value inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:

[tex]|p - E| \leq M[/tex]

For this problem, the estimate and the margin of error are:

E = 0.27, M = 0.019.

Hence the inequality is:

[tex]|p - 0.27| \leq 0.019[/tex]

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The arc length of the circle is 5π/9 units

From the question, we have the following parameters

Angle, ∅ = 5π/9

Radius, r = 1 unit

The arc length (x) is calculated as

x = r∅

Substitute the known values in the above equation

x = 5π/9 * 1

Evaluate the product

x = 5π/9

Hence, the arc length of the circle is 5π/9 units

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The graph is shown in the attached image.

Answer:

A = 8000

B = 4000

C = 12000

Step-by-step explanation:

$24000 = A,B and C

A = 2B

B = 1/3C

solve for the letter that gets described the most

that letter is B

A =2B

B = 1/3C -> C = 3B

24000 = A + B + C

24000 = 2B + B + 3B

24000 = 6B

B = 4000

A =2B = 8000

C = 3B = 12000

Answer:

[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]

Step-by-step explanation:

Horizontal Major Axis:

   [tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]

Vertical Major Axis:

   [tex]\frac{(y-k)^2}{a^2}+\frac{(x-h)^2}{b^2}+[/tex]

So these two expressions are essentially the same with the only difference being the location of "a" and "b". The length of the major axis will be "2a" and the length of the minor axis will be "2b". The way I remember this is because when you have the horizontal major axis the "a" value is in the denominator of the (x-h) and I think of "x" as a horizontal value, since it moves a point horizontally. When you have a vertical major axis the "a" value is in the denominator of (y-k) and I think of "x" as a vertical value, since it moves a point vertically.

So just by looking at the graph, you can easily determine that the eclipse has a horizontal major axis. This can be further proven, since the distance from the origin on the right side is 28, and the distance from the the top to the origin is only 20.

So you could set up an equation to solve for a, since 2a = length of major axis, but since we're given the two points, the "a" value is really just the length from the origin to the right/left side, and combining these together you get the value of 2a/major axis, but you don't have to do that. So by looking at the graph you'll see the distance from the origin to the right side is 28. This means "a=28"

You can do the same thing here for the "b" value, and since the top is 20 units away from the origin, "b = 20"

So now let's set up the equation:
[tex]\frac{x^2}{28^2} + \frac{y^2}{20^2}=1[/tex]

Square the values in the denominator

[tex]\frac{x^2}{784}+\frac{y^2}{400}=1[/tex]

there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

In this case, we know that the area is:

[tex]A = 4x^2 + 12x[/tex]

We can factorize that expression into:

[tex]A = x*(4x + 12)[/tex]

So there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

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The domain of the functions are:

The domain of a function is the set of input values the function can take i.e. the set of values the independent variable can assume?

Function 1

The function is given as:

f(x) = √4x + 6

Set the radicand greater than 0

4x + 6 > 0

Subtract 6 from both sides

4x > -6

Divide by 4

x > -3/2

Express as interval notation

[-3/2, ∞)

Hence, the domain of f(x) = √4x + 6 is [-3/2, ∞) or x >-3/2

Function 2

The function is given as:

g(x) = -4√-20x - 6

Set the radicand greater than 0

-20x - 6 > 0

Add 6 to both sides

-20x > 6

Divide by -20

x < -6/20

Simplify

x < -3/10

Express as interval notation

(-∞, -3/10]

Hence, the domain of g(x) = -4√-20x - 6 is (-∞, -3/10] or x < -3/10

Function 3

The function is given as:

f(x) = 15 + √5x - 16

Set the radicand greater than 0

5x - 16 > 0

Add 16 to both sides

5x > 16

Divide by 5

x > 16/5

Express as interval notation

[16/5, ∞)

Hence, the domain of f(x) = 15 + √5x - 16 is [16/5, ∞) or x >16/5

Function 4

The function is given as:

p(x) = √20x + 6

Set the radicand greater than 0

20x + 6 > 0

Subtract 6 from both sides

20x > -6

Divide by 20

x > -6/20

Simplify

x > -3/10

Express as interval notation

(-3/10, ∞]

Hence, the domain of p(x) = √20x + 6 is (-3/10, ∞] or x > -3/10

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Comparing A and B we find the value of the variables as

x = radius

Centre (-2,0)

Radius 2

The sketch of the image is attached below

Generally, the equation for is mathematically given as

x = -4 cos -(i)

Multiply -(i) both sides by & we

x^2= -4xcos\theta

We know that and

x= x cos\theta

y = rsino

x² + y² = x² (cos²∅ + sin²∅).

x² + y² = x² ....sin² ∅ + cos 2∅=1

so, putting rates in (ii) we get

x²+y² = -4x

x²+4²  +4 + y²=4

(2 + 2)² + y² =4

The rectangular form of

x = -4cos∅  is (x + 2)² + y² = 4 ---- A

We can see that A is a graph of circles. The general equation of a circle is

= (x-h)² + (y)² = x² ----B

where (h, k) = centre

Comparing A and B we find

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Answer:

x = 15°

Step-by-step explanation:
165 and x are on a straight line which means they are supplementary.
Set up the equation and solve for x:

165 + x = 180

x = 180 - 165

x = 15

Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.

The chemist wants to end up with 72 L of solution, so

[tex]x+y+z=72[/tex]

while using twice as much of the 60% solution as the 30% solution, so

[tex]z = 2y[/tex]

The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means

[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]

Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.

[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get

[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]

By elimination,

[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]

so that

[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]

and

[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 35 people, out of which 17 are female and 5 are male that prefer mint chocolate chip, hence:

p = (17 + 5)/35 = 22/35 = 0.6286.

There is a 0.6286 = 62.86% probability that a randomly selected person is female or prefers mint chocolate chip.

Out of the same 35 people, 11 people prefer cookie and cream and 2 people prefer vanilla, hence:

p = (11 + 2)/35 = 13/35 = 0.3714

There is a 0.3714 = 37.14% probability that a randomly selected person prefers cookie and cream or vanilla.

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Given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.

Given the data in the question;

Since the scenario depicts a right angle triangle, we use trigonometric ratio.

tanθ = Opposite / Adjacent

We height of the building from the eye level x

Substitute given into the equation,

tan( 35 ) = x / 80ft

x = tan( 35 ) × 80ft

x = 0.7002075 × 80ft

x = 56ft

Now, to get the height of the building, we add the height of the person and the height of the building from the eye level of the person.

Height of building = x + 4ft

Height of building = 56ft + 4ft

Height of building = 60ft

Therefore, given the height of the person, angle of elevation and distance from the building, the height of the building is 60 feet.

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Answer:

[tex] \pmb{ \pink{QUESTION�}}[/tex]

Find the midsegment of the triangle which is parallel to CA.

[tex] \pmb{ \pink{ANSWER:-}}[/tex]

Tip

[tex] \frak{Explanation:-} [/tex]

We have to find the segment which is parallel to CA.

From the given data,

The segment EG is the midsegment of the triangle[tex]\triangle[/tex] ABC.

So we have,

A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side.

[tex]\implies\rm{midsegment \: EG \: parallel \: to \: CA}[/tex]

[tex]\frak{RainbowSalt}[/tex]~

Answer:

[tex]\fbox {EG}[/tex]

Step-by-step explanation:

Based on the given diagram, we can clearly see the midsegment (lies in the middle of the figure) that is parallel to AC is EG

I hope it helped you solve the problem.

Good luck on your studies!

Answer:

Step-by-step explanation:

parallel lines are the same so they dont touch u-u

perpendicular lines do touch eachother and intersect

The required two differences between constructing parallel lines and constructing perpendicular lines are,
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

Parallel lines are defined as the pair of lines in which points on both the lines are equidistant from each other, and the line never intersects each other.

The differences between constructing parallel lines and constructing perpendicular lines are as follows.

1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.

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Answer:0.08333333....

Step-by-step explanation:

Answer:

4x²

Step-by-step explanation:

Normally you would use the exponent → roots rule, but this one simplifies easier without that

[tex](8x)^{\frac{2}{3} }[/tex]

8 = 2³

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}}[/tex]

then the threes cancel, since one is a 3 and the other one is [tex]\frac{1}{3}[/tex]

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2[/tex]

then just square the 2 and the x

[tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2 = 4x^2[/tex]