Shape of sampling, distribution, CLT application and proportion

Answer:

\(\frac{3}{8}\) miles

You have to walk \(\frac{3}{8}\) more miles to get to the shoe store.

Step-by-step explanation:

So first, we have to convert the \(\frac{1}{4}\) to a fraction that has a denominator of 8, which we are going to multiply 2 on both top & bottom. Equation-

\(\frac{1}{4}\) * \(\frac{2}{2}\) = \(\frac{2}{8}\)

And then, the house to shoe store is \(\frac{5}{8}\) miles as we know from the question. We subtract the distance by  \(\frac{2}{8}\), because that is how much we've walked already. And we know that when we are subtracting fraction, we need to make sure the denominators are the same and we ONLY subtract the numerator. So the equation would be like this-

\(\frac{5}{8}\) - \(\frac{2}{8}\) = \(\frac{3}{8}\)

And we got the answer- \(\frac{3}{8}\) miles

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Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

  f(3) = 1

Step-by-step explanation:

The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, so ...

  f(3) = 1

__

The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).

_____

Additional comment

When the polynomial is written in Horner Form:

  f(x) = ((x -6)x +13)x -11

the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.

The equation for g(x) is g(x) = x²-3

When x=0, f(x)= 0 and so has a vertex at (0,0)

Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.

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Answer:

155

Step-by-step explanation:

∠QOR= 25

∠POQ = x

here sum of both angles is 180 ( by linear pair)

therefore,

∠QOR + ∠POQ =180

25 + x = 180

x=180-25

x=155

hence, ∠POQ= 155

The surface area of the rectangular prism is 46m²

Surface area of a rectangular prism = 2(width×length + height×length + height×width)

SA = 2(wl + hl + hw)

= 2(2.5×4 + 2×4 + 2×2.5)

= 2(10 + 8 + 5)

= 2(23)

= 46m²

Therefore, the surface area of a rectangular prism is 46m²

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To solve this equation, first get rid of the fractions.

We do this by multiplying both sides by the denominator, 2.

So we have (2)(1/2s) = (7/2)(2).

On the left, we have s and on the right, we have 7.

So we have s = 7.

Answer:

he got right

Step-by-step explanation:

The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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A segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .

Given :

given a segment ab, construct the point p on the segment that divides it into two segments such that the shorter is to the longer as the longer is to the whole .

You are asked to construct P such that :

PB / AP = AP / AB

This ratio is the reciprocal of the Golden Ratio.

( AP )^2 = PB * AB

( AP )^2 = PB * ( AP + BP )

( AP )^2 = PB ( AP ) + ( BP )^2

Divide by PB^2 on both sides

ф^2 = ф + 1

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(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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The required value of 4/ 27 to tenth decimal places is 0.1.

To determine the 4/ 27 to the tenth decimal place.

Decimals is defined as one of the digits, which has a number and the fractional part separated by a decimal point after the whole number.

Recurring Decimal is defined as also named repeating decimal, is a decimal number that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.

Here,
= 4 / 27
dividing 4 by 27
4/27 = 0.148148148148148
now round of the above digit to tenth decimal place means place after the decimal is tenth place. So,
= 0.1

Thus, the required value of 4/ 27 to tenth decimal place is 0.1.

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Answer:

(x+3) and (x-2) are the correct factors

Step-by-step explanation:

If we expand (x-3)(x-2), we see that it equates to x²-5x+6, which is not what we want. The correct factors would be (x+3)(x-2) since the middle term's coefficient becomes 1 as 3-2=1 whereas -3-2=-5.

Answer:

V = 4576 m^3

Step-by-step explanation:

length l = 26 m

width w = 22 m

height h = 8 m

diagonal d = 34.9857114 m

total surface area S_tot = 1912 m^2

lateral surface area Sl_at = 768 m^2

top surface area S_top = 572 m^2

bottom surface area S_bot = 572 m^2

volume V = 4576 m^3

Agenda: l = length

w = width

h = height

d = diagonal

S_tot = total surface area

S_lat = lateral surface area

S_top = top surface area

S_bot = bottom surface area

V = volume

Volume of Rectangular Prism:

V = lwh

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

The statements that are true about the reflectional  symmetryof a regular heptagon are:

It has only one line of reflectional symmetry.

The line of reflectional symmetry passes through the center of the heptagon.

A regular heptagon is a polygon with seven equal sides and angles. Each vertex of the heptagon is equidistant from the center of the heptagon, and the lines connecting the center to the vertices divide the heptagon into seven congruent triangles.

To understand the reflectional symmetry of the regular heptagon, we need to define what it means. Reflectional symmetry is a type of symmetry where a figure is symmetric with respect to a line. In other words, if we fold the figure along this line, one half will coincide with the other half.

In the case of the regular heptagon, we can observe that if we draw a line passing through the center of the heptagon and perpendicular to any of its sides, we obtain a line of reflectional symmetry. This line divides the heptagon into two congruent halves. However, if we draw any other line of reflectional symmetry, it will not coincide with the sides of the heptagon, and therefore, it will not divide the heptagon into congruent halves.

Therefore, we conclude that the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

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Answer:

With speed of 18 feet per second the distance between the twins change.

Step-by-step explanation:

v1 is 10

v2 is -8

So, the difference is (10)-(-8)

which is 18.

Answer:

The distance of 2 feet with a speed of 10 feet per second.

The polynomials 2(- 4g + 7g + 8) - (3g² - 4g - 5) is -3 g^2+10 g+21.

What is polynomials?

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

\($$\begin{aligned}& 2(-4 g+7 g+8)-\left(3 g^2-4 g-5\right) \\& -4 g+7 g+8=3 g+8 \\& -\left(3 g^2-4 g-5\right)=-3 g^2+4 g+5 \\& =2(3 g+8)-3 g^2+4 g+5\end{aligned}$$\)

Expand \($2(3 g+8): \quad 6 g+16$\)

=6 g+16-3 g^2+4 g+5

Group like terms

=-3 g^2+6 g+4 g+16+5

Add similar elements: 6 g+4 g=10 g

=-3 g^2+10 g+16+5

Add the numbers: 16+5=21

=-3 g^2+10 g+21

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Answer: To solve the inequality x^2 + 3x - 4 > 0, we can use the method of factoring.

First, we can factor the quadratic expression:

x^2 + 3x - 4 = (x + 4)(x - 1)

Now we can find the values of x that make the expression greater than zero by looking at the sign of the expression for each factor and applying the sign rules of multiplication:

Using this method, we can create a sign chart:

x x + 4 x - 1 x^2 + 3x - 4

-4 0 -5 +6

-1 + - -

1 + + +

0 + - -

2 + + +

From the sign chart, we can see that the expression is greater than zero for x < -4 or x > 1. Therefore, the solutions to the inequality are all real numbers x such that x < -4 or x > 1. We can write this as:

x < -4 or x > 1

Answer:

(-1, -4)

Step-by-step explanation:

y = -x is the 45° diagonal through the origin from top left to bottom right.

a reflection across that line brings anything that is in quadrant 1 (x and y are positive) to quadrant 3 (x and y are negative) like this point. and vice versa.

points in quadrant 2 stay in quadrant 2, points in quadrant 4 stay in quadrant 4.

but in every case x and y are exchanged and both signs are flipped like (-1, 2) turns into (-2, 1).

or for our point : (4, 1) turns into (-1, -4)

Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

Answer:

y = 4x + 5

Step-by-step explanation:

3y - 12x = 15

Add 12x to both sides.

3y = 12x + 15

Divide by 3 to isolate y.

y = 4x + 5

Answer:

ACTUALLY IT'S, y=4x-5

Step-by-step explanation:

12x-3y=15                          - Get y alone

-12x   =12x                          

-3y=-12x+15

-3y=-12x+15     - Divide.            

__________

-3           -3

y=12/3x-15/3                  -  Distribute division. Negative over a negative is positive. Positive over a negative is a negative.

y=4x-5     - Reduce fractions.

The types of rotation are:

In this case:

 ⇒ it is reflection since the graph is inverted and each point is the same distance from the line of reflection

Answer: reflection

Hope that helps!

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

12

Step-by-step explanation:

P = is you add Length (L) plus Legnth (L) plus Width (W) plus Width (W)

4+4+2+2

Answer:

The equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14

Step-by-step explanation:

It is given that the line that is parallel to the group in each equation and passes through the given point 7y= -2x + 5; (3,-7) and we need to write the equation in slope intercept form of the same line.

Now,

The slope of parallel lines is the same. By changing the equation to slope-intercept form, get the slope in the first line;

=> 7y= -2x + 5

=> y= -2/7x + 5/7

So, the slope = -2/7

Further,

Given the point and the knowledge that the second line would similarly have a slope of -2/7 and the point is (3, -7). With these numbers, we can construct an equation in the slope-intercept form and apply it to get the y-intercept;

=> y = mx + b

=> -7 = -2/7 × 3 + b

=> -7 + 2/7 × 3 = b

=> b = -6.14

Now, put the value of y-intercept back into the equation;

=> y = -2/7x - 6.14

Therefore, the equation in slope intercept form of the line that is parallel to the group in each equation and passes through the given point (3,-7) is y = -2/7x - 6.14

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A.)the annual rate of change is  $1,266.67 per year

B)the rate of change as a percentage is 3.7235%.

C)   the car value be in the year 2011 is $8,350.

A percentage is a way of expressing a portion or fraction of a whole as a number out of 100. The term "percent" comes from the Latin per centum, which means "by the hundred."

A) To calculate the annual rate of change between 1991 and 2006, we need to first calculate the total decrease in value over that time period, and then divide that decrease by the number of years.

The total decrease in value is:

$34,000 - $15,000 = $19,000

The number of years between 1991 and 2006 is:

2006 - 1991 = 15 years

So the annual rate of change is:

$19,000 / 15 years = $1,266.67 per year

B) To express the rate of change as a percentage, we need to divide the annual rate by the initial value and then multiply by 100:

($1,266.67 / $34,000) x 100% = 3.7235%

Rounding this to 4 decimal places, we get: 3.7235%.

C) To calculate the value of the car in the year 2011, we need to continue the depreciation using the same annual rate of change.

From 2006 to 2011 is a period of 5 years.

The value in 2011 will be:

$15,000 - ($1,266.67 x 5) = $8,333.35

Rounding to the nearest $50, we get: $8,350.

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The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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