Two poles on the ground are 90 feet apart. The shorter pole is 7.5 feet tall. The angle of depression
from the top of the taller pole to the top of the shorter pole is 28°. How tall is the longer pole? Round
to the nearest tenth.

Let's use the variable x to represent the list price of the car.

The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.

We can write this as an equation:

Total cost = List price + 0.07(List price) + 450

We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:

12,755 = x + 0.07x + 450

Simplifying the right side:

12,755 = 1.07x + 450

Subtracting 450 from both sides:

12,305 = 1.07x

Dividing both sides by 1.07:

x = 11,500

Therefore, the list price of the car your cousin bought was $11,500.

The list price of the car your cousin bought was $11,500.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's start by setting up an equation to represent the total cost of the car:

Total cost = List price + 7% of List price + $450

We know that the total cost is $12,755, so we can substitute that in:

$12,755 = List price + 0.07(List price) + $450

Simplifying this equation, we get:

$12,755 = 1.07(List price) + $450

Subtracting $450 from both sides, we get:

$12,305 = 1.07(List price)

Dividing both sides by 1.07, we get:

List price = $11,500

Therefore,

The list price of the car your cousin bought was $11,500.

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The alternative hypothesis can be written as H₁: pA < pB.

The alternative hypothesis would be that there is a difference in the proportion of Republicans (Group A) and Democrats (Group B) who favor the government investing billions of dollars to improve the country's train system. Expressly, it would state that the proportion of Republicans who favor this investment is less than the proportion of Democrats who favor it:

H₁: pA < pB

where pA denotes the proportion of Republicans who favor the investment and pB denotes the proportion of Democrats who favor the investment.

In the alternative hypothesis, we actually create the relationship between the variables which are being tested in that situation. According to these, we come across the comparison among the variables and how much they differ from each other. The alternative hypothesis is the statement the researcher tries to prove by conducting a statistical analysis.

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libraries is approximately normal

Yes, the conditions for use of a t-model are met. The sample size is large enough (100) and the distribution of time spent at university libraries is approximately normal.

The ball will hit the ground after 4 seconds (x2 = 4).

Given the formula h(x) = -16x^2 + v0x + h0, we can plug in the values for the initial velocity (v0) and the initial height (h0) to find the equation that describes the ball's height as a function of time.

v0 = 64 ft/s (initial velocity)

h0 = 12 ft (initial height)

Now, we can write the function for the ball's height:

h(x) = -16x^2 + 64x + 12

To find when the ball hits the ground, we need to solve for x when h(x) = 0:

0 = -16x^2 + 64x + 12

This is a quadratic equation, and we can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -16, b = 64, and c = 12.

x = (-64 ± √(64^2 - 4*(-16)12)) / 2(-16)

First, we find the discriminant (b^2 - 4ac):

64^2 - 4*(-16)*12 = 4096 + 768 = 4864

Now we can plug the discriminant back into the quadratic formula:

x = (-64 ± √4864) / (-32)

We have two possible solutions:

x1 = (-64 + √4864) / (-32)

x1 = (-64 + 64) / (-32)

x1 = 0

x2 = (-64 - √4864) / (-32)

x2 = (-64 - 64) / (-32)

x2 = 128 / 32

x2 = 4

Since x1 = 0 represents the initial time when the ball is kicked, we discard this solution.

Therefore, the ball will hit the ground after 4 seconds (x2 = 4).

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The height, in feet, after x seconds of an object launched straight up can be found by the function h(x)=−16x2+v0x+h0, where v0 is the initial velocity of the object and h0 is the initial height.

A ball is kicked straight up into the air from a height of 12 ft with an initial velocity of 64 ft/s. After how many seconds does the ball hit the ground?

If the value of the 2022 Jeep Wrangler Rubicon depreciates at a rate of 9.7% per year, then its value after t years can be modeled by:

V(t) = 67,035(1 - 0.097)^t

Simplifying the right side:

V(t) = 67,035(0.903)^t

Therefore, the function that models the car's value, V, t years since 2022 is V(t) = 67,035(0.903)^t.

1. Mean = 54

2. Standard Deviation = 6.3

3. Probability = 0.077

4. Probability = 0.845

5. Probability = 0.155

6. Probability = 0.323

The Number of atoms ≈ 5.119 x 10^24 atoms

The Mass ≈ 248.0 g

Mass ≈ 248.0 g

To find the number of atoms, we use Avogadro's number, which is 6.022 x 10^23 atoms/mole.

Number of atoms = (8.500 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 5.119 x 10^24 atoms

To find the mass, we need the molar mass of oxygen, which is 16.00 g/mole.

Mass = (15.50 moles) * (16.00 g/mole)

Mass ≈ 248.0 g

Determine the number of moles of helium in 1.953 x 10^8 g of helium.

To find the number of moles, we need the molar mass of helium, which is 4.00 g/mole.

Number of moles = (1.953 x 10^8 g) / (4.00 g/mole)

Number of moles ≈ 4.883 x 10^7 moles

Calculate the number of atoms in 147.82 g of sulfur.

To find the number of atoms, we first need to find the number of moles of sulfur, and then use Avogadro's number. The molar mass of sulfur is 32.07 g/mole.

Number of moles = (147.82 g) / (32.07 g/mole)

Number of moles ≈ 4.609 moles

Number of atoms = (4.609 moles) * (6.022 x 10^23 atoms/mole)

Number of atoms ≈ 2.772 x 10^24 atoms

Determine the molar mass of Co.

The molar mass of cobalt (Co) is 58.93 g/mole.

Determine the formula mass of Ca3(PO4)2.

To find the formula mass, we need to add up the molar masses of all the elements in the compound.

Ca3(PO4)2 contains 3 calcium (Ca) atoms, 2 phosphorus (P) atoms, and 8 oxygen (O) atoms.

Molar mass of Ca = 40.08 g/mole

Molar mass of P = 30.97 g/mole

Molar mass of O = 16.00 g/mole

Formula mass = (3 * 40.08) + (2 * 30.97) + (8 * 16.00)

Formula mass = 120.24 + 61.94 + 128.00

Formula mass ≈ 310.18 g/mole

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The answers to the following prompts are give as follows:

9 (c) the time taken for rocket to hit the ground is 5

10 (c) the maximum height is 4

11 (b) the solutions of 16x² - 64 = 0  are  -4 and 4

9) To find the time it takes the rocket to hit the ground, we need to find the value of s when h(s) = 0 since h(s) represents the height of the rocket.

So we need to solve the equation: -3s^2 + 6s + 45 = 0.

Factoring, we get -3(s - 5)(s + 3) = 0. So s = 5 or s = -3. Since time cannot be negative, we take s = 5.

Therefore, the answer is (c) 5.

10 ) The maximum height of the rocket occurs at the vertex of the parabola given by the function h(s) = -3s^2 + 6s + 45. The s-coordinate of the vertex is given by s = -b/2a, where a = -3 and b = 6. So s = -6/-6 = 1. Therefore, the answer is (a) 1.

11) We can solve the equation 16x² - 64 = 0 by factoring out the greatest common factor, which is 16: 16(x² - 4) = 0.

Then, we can factor the quadratic expression as a difference of squares: 16(x + 2)(x - 2) = 0. Therefore, the solutions are x = -2 and x = 2, and the answer is (b) -4 and 4.

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Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.

Sample 1:[tex]17/25 = 0.68[/tex]

Sample 2: [tex]12/25 = 0.48[/tex]

Sample 3: [tex]14/25 = 0.56[/tex]

Sample 4: [tex]9/25 = 0.36[/tex]

Next, we calculate the deviation of each observation from its respective sample mean:

Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|

Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|

Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|

Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|

where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.

The MAD is the average of these deviations:

MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100

Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.

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Answer:

x<-1/5

Step-by-step explanation:

Imma assume the _ is a - soo

3x-1<-2x

5x<-1

x<-1/5

Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

[tex]\frac{11}{2}[/tex] ÷ 4 = [tex]\frac{11}{2}[/tex]  x [tex]\frac{1}{4}[/tex] = [tex]\frac{11}{8}[/tex]

So, the answer is [tex]\frac{11}{8}[/tex]

The outcome of given exponential expression [tex]{(7^4)}^4[/tex] will be  [tex]{(7)}^{16}[/tex].

A number raised to a specific power is represented mathematically by an exponential expression. It is drafted in the style of "a" is the base, and "b" is the exponent. The base "a" is b times multiplied by itself.for eg:

                      In  [tex]5^{9}[/tex] => 5 is base and 9 is exponent

In mathematics, exponential expression or exponential notation is frequently employed to conveniently and succinctly describe big or tiny quantities. Also, it is employed in fields where exponential growth or decay are important, such as computer programming and finance.

Now, Given:

[tex]{(7^4)}^4[/tex]

we know,

[tex]{(a^b)}^c = {(a)}^{b\cdot c}[/tex]

Hence, for given exponential expression, we get,

[tex]{(7^4)}^4 = {(7)}^{4\cdot4[/tex]

[tex]{(7)}^{4\cdot4} = {(7)}^{16[/tex]

Thus, option a.) is correct answer.

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Complete Question: What is the outcome of multiplying 7 raised to the power of 4 by itself, raised to the power of 4  or [tex]{(7^4)}^4[/tex]?

a.)[tex]{(7)}^{16}[/tex]

b.)[tex]{(7)}^{8}[/tex]

c.)[tex]{(7)}^{4^4}[/tex]

d.)[tex]{(7)}^{4}[/tex]

The final absolute value inequality that represents the solution set x ≤ -9 or x ≥ -5 is |x + 7| ≥ 2.

If the absolute value expression is greater than or equal to a number (e.g. |x| >= 5).

We can write it as two separate inequalities: x >= 5 or x <= -5.
The absolute value expression is less than or equal to a number (e.g. |x| <= 3)

We can write it as the single inequality: -3 <= x <= 3.
Using these rules:

We can write an absolute value inequality that has the solution set x <= -9 or x >= -5200 as follows:
| x + 2604 | >= 5193
To see why this works,

Let's first look at the case where x is less than or equal to -9. In this case, we have:
x + 2604 <= -9
x <= -2613
Plugging this into our inequality:
| -2613 | >= 5193
Which is true, since |-2613| = 2613 >= 5193.
Now let's look at the case where x is greater than or equal to -5200. In this case, we have:
x + 2604 >= -5200
x >= -7804
Plugging this into our inequality, we get:
| -7804 | >= 5193
Which is also true, since |-7804| = 7804 >= 5193.
Therefore, the inequality | x + 2604 | >= 5193 has the solution set x <= -9 or x >= -5200, as desired. I hope this helps! Let me know if you have any other questions.
Midpoint = (-9 + (-5)) / 2 = -7
The absolute value inequality will have the form |x - (-7)|.
|x + 7| ≥ 2, since the distance between -9 and -7 is 2.
|x + 7| ≤ -2, since the distance between -5 and -7 is -2.
However,

An absolute value cannot be negative, so the second inequality doesn't make sense. Therefore, we'll only use the first inequality.
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angle opposite 16 = [tex]sin-1(\sqrt(1 - cos2(angle opposite 16))[/tex] angle opposite 16 = [tex]sin-1(\sqrt(1 - (-0.442)2)[/tex]angle opposite 16 = 118.7 degrees

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a kind of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four distinct shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The internal angles on the same side of the horizontal line are also angles. The total number of internal angles is 360.

To calculate the area of a parallelogram, multiply the base by the height. Nevertheless, the height is not mentioned in this situation. Alternatively, we may use the following formula to calculate the area of a parallelogram:

The area is defined as follows: base x height x sin (angle between base and height)

[tex]16^2 = 13^2 + 13^2 - 2(13)(13) (13)[/tex]

cos(opposite angle 16) 256 = 338 − 338

cos(opposite angle 16) cos(opposite angle 16) = -0.442

We know the angle is between 90 and 180 degrees since the cosine is negative. To get the angle in that range, we may use the inverse sine function:

angle opposite 16 = [tex]sin-1(\sqrt(1 - cos2(angle opposite 16))[/tex] angle opposite 16 = [tex]sin-1(\sqrt(1 - (-0.442)2)[/tex]angle opposite 16 = 118.7 degrees

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The image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin is a smaller square with vertices J'(-0.4, 0.4), K'(0.4, 0.4), L'(-0.4, -0.4), and M'(0.4, -0.4).

A graph is a visual representation of data, relationships or functions, typically consisting of points, lines, and curves plotted on a coordinate system.

To graph the image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin, we need to perform the following steps:

Plot the vertices of the square JKLM.

Draw lines connecting the vertices to form the square.

Find the coordinates of the image vertices after dilation with a scale factor of 1/5 centered at the origin.

Plot the image vertices and connect them to form the image square.

Here's a step-by-step guide to performing each of these steps:

Plot the vertices of square JKLM:

J(-2, 2)    K(2, 2)

    +------+

    |      |

    |      |

    +------+

L(-2, -2)   M(2, -2)

Draw lines connecting the vertices to form the square:

      J(-2, 2)    K(2, 2)

          +------+

          |      |

          |      |

          +------+

L(-2, -2)         M(2, -2)

Find the coordinates of the image vertices after dilation with a scale factor of 1/5 centered at the origin:

To find the coordinates of the image vertices, we need to multiply the coordinates of each vertex by the scale factor of 1/5:

[tex]J' = (-2 * 1/5, 2 * 1/5) = (-0.4, 0.4)\\K' = (2 * 1/5, 2 * 1/5) = (0.4, 0.4)\\L' = (-2 * 1/5, -2 * 1/5) = (-0.4, -0.4)\\M' = (2 * 1/5, -2 * 1/5) = (0.4, -0.4)\\[/tex]

Plot the image vertices and connect them to form the image square:

        J'(-0.4, 0.4)    K'(0.4, 0.4)

            +------+

            |      |

            |      |

            +------+

L'(-0.4, -0.4)         M'(0.4, -0.4)

The image of square JKLM after a dilation with a scale factor of 1/5 centered at the origin is a smaller square with vertices J'(-0.4, 0.4), K'(0.4, 0.4), L'(-0.4, -0.4), and M'(0.4, -0.4).

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The image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin, is a smaller square centered at the origin.

To graph the image of square JKLM after a dilation with a scale factor of 1/5, centered at the origin, we can follow these steps:

Draw the original square JKLM.

Draw a line segment from the origin to each vertex of the square.

Multiply the length of each line segment by 1/5.

Draw a new square centered at the origin, with side lengths equal to the lengths of the new line segments.

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Answer:

Add 1 1/4 x 1 1/4

Step-by-step explanation:

The equation that will tell us measure of additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground is given option 155 - 110 = a.

Highest kick went when Ranim started karate from the ground is

= 110 degrees

Highest kick limit given by instructor from the ground = 155 degrees

This equation represents the difference between the final desired angle of 155 degrees and the initial angle of 110 degrees.

Which Ranim's kick went when she started karate.

The result of this subtraction will give us the measure of the additional angle, a.

That Ranim needs to add to her kick to reach the new desired angle.

Therefore, equation representing the measure of the additional angle a, of Ranim karate kick is equal to 155 - 110 = a.

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The above question is incomplete, the complete question is:

When Ranim started karate, her highest kick went 110 degrees from the ground. Her instructor asked her to practice until her highest kick goes 155 degrees from the ground. Which equation will tell us the measure of the additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground?

155−110=a

155+110=a

180−110=a

155+90=a

A year is approximately 365.24 days long, so without leap years, our calendar would slowly become out of sync with

the Earth's orbit around the sun.

The reason why we need to have leap years is because the year does not contain an exact multiple of 24-hour days.

This would eventually cause the seasons to occur at different times of the year.

To keep the calendar aligned, we add an extra day (February 29th) to the calendar every four years, making the year

366 days long.

A year is approximately 365.24 days long, so without leap years, our calendar would slowly become out of sync with

the Earth's orbit around the sun.

This ensures that the calendar year stays in sync with the astronomical year.

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It will take John approximately 17 months to pay off the balance.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:

Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:

Monthly interest rate = 19% / 12 = 0.01583

Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:

Monthly finance charge = $2000 x 0.01583 = $31.66

Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:

Payment applied to balance = $150 - $31.66 = $118.34

Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:

Number of months to pay off balance = $2000 / $118.34 = 16.9

(rounded up to the nearest whole number)

Therefore, it will take John approximately 17 months to pay off the balance.

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The second time when harry feel like consuming 17 kg of sheep after he wakes up is equal to 39.7 hours ( round to nearest tenth of an hour).

Function is equal to

H (t) = 12 sin (2/24t) +15

Where  H(t) models the weight of sheep in kg that Harry like to swallow in 't' hours after wakes up.

't' in radians.

Harry wants to consumes 17kg

⇒ H(t) = 17 for t.

Substituting the given expression for H(t), we get,

⇒ 12 sin(2/24 t) + 15 = 17

⇒ 12 sin(2/24 t) = 2

⇒ sin(2/24 t) = 1/6

⇒ 2/24 t = sin^(-1)(1/6)

We know that sin^(-1)(1/6) = 0.167

Substitute the value we get,

⇒ t = 12 × 0.167

⇒ t = 2.004 radians

This gives us the first time after Harry wakes up that he feels like consuming 17 kg of sheep.

For the second time,

Add one full period to the first time, since the function H(t) has a period of 12π/2 = 6π.

The second time is,

t = 2.004 + 6π

  = 2.004 + 6×3.14

 = 20.844 radians

To round to the nearest tenth of an hour,

Since there are 12 hours in a full revolution.

Convert radians to hours by dividing by 2π and then multiplying by 12.

t = 20.844/(2π) ×  12

 = 3.31 × 12 hours

 = 39.69

  = 39.7 (rounded to the nearest tenth)

Attached graph.

Therefore, the second time after Harry wakes up that he feels like consuming 17 kg of sheep is approximately 39.7 hours after he wakes up.

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The significance test is a test that claim on the basis of p-value and cannot check if the observed effect and it is the observed effect due to chance. So, the right choice for the answer is option(b).

We have to determine the statement that reflects the test of significance in a number of statements. We check the each option one by one. A significance test tests the claim made. This test used to investigate the claim by considering the null and alternate hypothesis. It cannot used to check about the sample or the experiment are properly design or not. Now, the significance test determines that the observed effect is due to chance. Because it measures the observed difference between the group using the p-value ( probability or chance).

A significance test, tests the claim. It cannot say if the observed effect is important or not. It is only based on test the claim on the basis of p-value and cannot check if the observed effect is important. Hence, option( b) is right.

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The distance between the points (2, -4) and (2, 7) is 11 units.

What is distance?

In mathematics, the distance between two points is a numerical value that represents the amount of space between them. The distance between two points is calculated using the Pythagorean theorem, which applies to any two points in a two-dimensional or three-dimensional space.

The two points have the same x-coordinate of 2, so they lie on a vertical line. To find the distance between them, we need to find the difference between their y-coordinates.

The y-coordinate of the first point is -4 and the y-coordinate of the second point is 7. Therefore, the difference between the y-coordinates is:

7 - (-4) = 7 + 4 = 11

So the distance between the two points is 11 units.

Therefore, the distance between the points (2, -4) and (2, 7) is 11 units.

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The area of the figure is 39ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

Area of a rectangle is expressed as ;

A = l × w

where l is the length and w is the width.

Dividing the shape into two;

The area of shape 1 = l× w

= 3× 7 = 21ft²

The area of shape 2 = l× w

= 6 × 3 = 18 ft²

therefore the total area = 21+18 = 39 ft²

therefore the area of the figure is 39ft²

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The complete table is:

x (weeks since 5 years ago)         y (in $)

260                                                 150.01

259                                                 150.06

256                                                 149.42

234                                                 142.03

208                                                 152.79

104                                                   97.65

0                                                       70.43

The coordinates are given by (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

The X axis suggests the weeks since 5 years ago and Y axis suggests the closing price at each time.

Number of weeks in a year is 52 weeks.  

Most recent time suggests, x = 52*5 = 260

when x = 260, then y = 150.01

7 days ago that is 1 weeks ago, x = 260 -1 = 259

The value of y then = $ 150.06

1 months ago that is 4 weeks ago, x = 260 - 4 = 256

The closing price then is, y = 149.42

6 months ago, x = 260 - 52/2 = 260 - 26 = 234

The closing price then is, y = 142.03

1 year ago that is 52 years ago, x = 260 - 52 = 208

The closing price was then, y = 152.79

3 years ago, x = 260 - 52*3 = 260 - 156 = 104

The closing price was then, y = 97.65

5 years ago, x = 260 - 52*5 = 260 - 260 = 0

The closing price was then, y = 70.43.

Then the coordinates are (260, 150.01), (259, 150.06), (256, 149.42), (234, 142.03), (208, 152.79), (104, 97.65), (0, 70.43).

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Answer:

mean= 56.9

median= 55.5

mode= 64

If a sample of 100 Americans is taken that same week, then the probability that "sample-proportion" has between a 42% and a 47% approval rating is 0.7693 or 76.93%.

To calculate the probability that the sample-proportion falls between 42% and 47% for a sample of 100 Americans, we use the standard normal distribution.

The Sample size (n) is = 100,

The Sample proportion (p) = 46% or 0.46,

The "Standard-deviation" (σ) = √(p×(1-p)/n) = √(0.46×(1-0.46)/100) ≈ 0.0497,

We now calculate the "z-scores" corresponding to the lower and upper bounds of the desired range,

We know that, the value of "z" is (x - μ)/σ,

where x = desired proportion, μ = mean proportion, and σ = standard deviation,

So, The probability that the sample proportion has between a 42% and a 47% "approval-rating", is written as :

⇒ P(0.42 < x < 0.47) = P[(0.42 - 0.46)/0.0497 < z < (0.47 - 0.46)/0.0497],

⇒ P(0.42 < x < 0.47) = P[-0.807 < z < 2.015],

⇒ P(0.42 < x < 0.47) = 0.9783 - 0.209,

⇒ P(0.42 < x < 0.47) = 0.7693,

Therefore, the required probability is 0.7693 or 76.93%.

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The 3 trigonometric ratios of the right triangle with respect to angle A are as follows:

sin A = 12 / 13

cos A = 5 / 13

tan A = 12 / 5

The side of a right angle triangle can be found using trigonometric ratios as follows:

Therefore, let's find the 3 trigonometric ratios with respect to angle A.

sin A = opposite / hypotenuse

sin A =  36 / 39

sin A = 12 / 13

cos A = adjacent  / hypotenuse

cos A = 15 / 39

cos A = 5 / 13

tan A = opposite / adjacent

tan A = 36 / 15

tan A = 12 / 5

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Sam still needs to walk 7/8 of a mile to reach his goal.

To find out how many miles Sam has already walked, we add the distance he walked before lunch (1 1/8 miles) to the distance he walked after resting (3/4 mile):

1 1/8 + 3/4 = 9/8 + 3/4 (since we need a common denominator of 8)

= 18/8 + 3/8

= 21/8

So Sam has already walked 2 5/8 miles.

To find out how much further he needs to go to reach his goal of 3 1/2 miles, we subtract what he's already walked from his goal:

3 1/2 - 2 5/8 = 7/2 - 21/8 (again, we need a common denominator of 8)

= 28/8 - 21/8

= 7/8

So Sam still needs to walk 7/8 of a mile to reach his goal.

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