1. Solve for x in the inequality t 1-4x +52 3x-2 and illustrate + lo the answer 5 the number line.​

The probability that exactly one out of six randomly chosen female cats weighs more than 4.5 kg is approximately 0.3487, or 34.87%.

a) To find the proportion of female cats with weights between 3.7 and 4.4 kg, we need to calculate the z-scores for these weights and then find the corresponding probabilities using the standard normal distribution.

For a weight of 3.7 kg:

z = (3.7 - 4.1) / 0.6 ≈ -0.67

For a weight of 4.4 kg:

z = (4.4 - 4.1) / 0.6 ≈ 0.50

Using a standard normal table or a calculator, we can find the probabilities associated with these z-scores. The probability of a z-score less than -0.67 is approximately 0.2514, and the probability of a z-score less than 0.50 is approximately 0.6915.

Therefore, the proportion of female cats with weights between 3.7 and 4.4 kg is approximately 0.6915 - 0.2514 = 0.4401, or 44.01%.

b) To find the proportion of female cats that are heavier than a certain cat with a weight 0.5 standard deviations above the mean, we can find the probability associated with the z-score of that weight.

z = (4.1 + 0.5 * 0.6 - 4.1) / 0.6 ≈ 0.50

Using the standard normal distribution, the probability of a z-score greater than 0.50 is approximately 0.3085.

Therefore, the proportion of female cats that are heavier than the cat in question is approximately 0.3085, or 30.85%.

c) The 80th percentile corresponds to a z-score that has an area of 0.80 to its left under the standard normal distribution. Using a standard normal table or calculator, we find that the z-score associated with the 80th percentile is approximately 0.84.

To find the weight corresponding to this z-score:

z = (weight - 4.1) / 0.6 ≈ 0.84

Solving for the weight, we have:

weight ≈ 0.84 * 0.6 + 4.1 ≈ 4.604 kg

Therefore, a female cat whose weight is at the 80th percentile weighs approximately 4.604 kg.

d) To find the probability that a randomly chosen female cat weighs more than 4.5 kg, we need to calculate the z-score for a weight of 4.5 kg and find the probability associated with that z-score being greater than zero.

z = (4.5 - 4.1) / 0.6 ≈ 0.67

Using the standard normal distribution, the probability of a z-score greater than 0.67 is approximately 0.2514.

Therefore, the probability that a randomly chosen female cat weighs more than 4.5 kg is approximately 0.2514, or 25.14%.

e) The probability that exactly one out of six randomly chosen female cats weighs more than 4.5 kg can be calculated using the binomial distribution.

Let p be the probability of a cat weighing more than 4.5 kg, which we found to be 0.2514. The probability of one cat weighing more than 4.5 kg and the other five weighing less can be calculated as:

P(X = 1) = (6 choose 1) * p^1 * (1-p)^5

Using this formula, we can substitute the values and calculate the probability. The result is approximately 0.3487, or 34.87%.

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Given that sin(x) = -5/13 and the condition is to provide the answer without using sin, cos, or tan, I assume you are looking for the value of cos(x).

We can use the Pythagorean identity: sin²(x) + cos²(x) = 1

Substitute the given value of sin(x):
(-5/13)² + cos²(x) = 1

Solve for cos²(x):
cos²(x) = 1 - (-5/13)²

cos²(x) = 1 - (25/169)

Now find the common denominator (169) and subtract:
cos²(x) = (169/169) - (25/169)

cos²(x) = 144/169

Since we need the value of cos(x), we take the square root of both sides:
cos(x) = ±√(144/169)

cos(x) = ±12/13

Since the value of sin(x) is negative, we are in the third or fourth quadrant, where the cosine is also negative. Therefore, we choose the negative value for cos(x):

cos(x) = -12/13

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Maya can expect to pay $252 to replace the glass window in her restaurant. This can be found by calculating the area of the window and multiplying it by the price per Square foot of the glass

The cost of replacing the glass window, we first need to determine the area of the window. Since the window is in the shape of a square and its side lengths are 6 feet, we can calculate the area as:

Area = side length x side length

Area = 6 feet x 6 feet

Area = 36 square feet

Next, we can calculate the cost of the glass needed to replace the window. We are given that the cost of the glass is $7 per square foot, so we can use the formula:

Cost = price per square foot x area

Substituting the values we have, we get:

Cost = $7/square foot x 36 square feet

Cost = $252

Therefore, the cost of the glass needed to replace the window is $252.

Maya can expect to pay $252 to replace the glass window in her restaurant. This can be found by calculating the area of the window and multiplying it by the price per square foot of the glass.

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To find two solutions for Ax = 0, we first need to understand the relationship between the given solutions, x1 and x2, for Ax = b. Since Ax = b has two solutions, the matrix A must not be invertible.

Step 1: Find the vector d that connects x1 and x2.
d = x2 - x1

Step 2: Add d to both x1 and x2 to create new solutions for Ax = b.
x3 = x1 + d
x4 = x2 + d

Step 3: Observe that the difference between x3 and x4 is also d.
x4 - x3 = d

Step 4: Scale d by a scalar factor k to find two solutions to Ax = 0.
y1 = k * d
y2 = -k * d

Now we have found two solutions (y1, y2) for Ax = 0, and a new solution (x3) for Ax = b using the given solutions x1 and x2.

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It is difficult to accurately predict the number of days a favorite radio or TV station will correctly forecast whether it will be cloudy over the next 30 days.

Forecasting weather accurately is a challenging task, and even the most advanced weather models are subject to errors. The accuracy of a station's forecasts depends on various factors such as the quality of their data sources, the skill and experience of their forecasters, and the complexity of the weather patterns in the region. Therefore, it is not possible to determine the exact number of days a station will make correct forecasts about whether it will be cloudy or not. However, it is important to note that modern weather forecasting has come a long way in recent years, and many stations now provide fairly accurate predictions. It is always a good idea to consult multiple sources and use personal judgment when making plans based on weather forecasts.

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The tourist had $1200.91 in US dollars when he left the country.

The American tourist exchanged 80% of $8175 to local currency, which is:

0.8 x $8175 = $6540

To calculate how much local currency the tourist received for $6540, we can use the buying rate of Kshs.83.25 per US dollar:

Amount in local currency = $6540 x Kshs.83.25 per US dollar = Kshs.544335

After spending Kshs.443,595, the tourist had Kshs.544,335 - Kshs.443,595 = Kshs.100,740 left.

To calculate how much US dollars the tourist can buy with Kshs.100,740, we can use the selling rate of Kshs.84.05 per US dollar:

Amount in US dollars = Kshs.100,740 / Kshs.84.05 per US dollar = $1200.91

Therefore, the tourist had $1200.91 in US dollars when he left the country.

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The Histogram is explained in the solution below.

To create a histogram of the given data, we need to determine the frequency of each value and represent it graphically.

Here's a histogram for the provided data:

Number of Customers   Frequency

0 - 5                                        **

5 - 10                                       ***

10 - 15                                     ****

15 - 20                                    *****

20 - 25                                      **

In this histogram, the x-axis represents the ranges of the number of customers (e.g., 0-5, 5-10, etc.), and the y-axis represents the frequency of occurrence for each range.

The asterisks (*) indicate the frequency of customers falling within each range.

To generate the histogram, you count the occurrences of each value within the given ranges.

For example, there are 2 occurrences () of values between 0-5, 3 occurrences (*) between 5-10, and so on.

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Yes, triangles VWX and ZYX are congruent.

Congruent triangles are triangles having corresponding sides and angles to be equal. This means for two triangles to be congruent, their corresponding angles and sides must t be equal.

angle YXZ = angle VXW ( vertically opposite angles)

XZ = VX ( a line bisected into two)

therefore angle W = angle Z

therefore since angle W = angle Z , angle V will also be equal to angle Y.

Therefore we can say that triangles VWX and ZYX are congruent.

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Not enough information.  One one corresponding pair given (at best, 2).  However, we need info about at least 3 corresponding pairs to use one of our Triangle congruence theorems.

We could prove triangle congruence with only one more piece of information (guaranteeing congruence of 2 more corresponding parts), if we had that X was also the midpoint of WY.

With only the given information, we only have 1 pair of corresponding sides that we can prove congruent, because if X is the midpoint of VZ, then VX is congruent to XZ, by the definition of midpoint.

Which corresponding parts MAY be congruent

From the picture, the three points W, X, and Y appear collinear (but this  is not explicitly given, so this would be an assumption, and may be assuming too much).  If W, X, and Y are not collinear, then there is a bend, and angle VXW and angle ZXY would not form a vertical angle pair.  IF W, X, and Y are collinear, then angle VXW, and ZXY form a vertical angle pair, and angle VXW and angle ZXY would be congruent.

Even then, you still only have two corresponding part pairs congruent, one Side and one Angle.  This is insufficient to prove that the two triangles are congruent.

Why the triangles aren't necessarily congruent from the given information:

(See attached picture)  In the attached picture, I have drawn two triangles.

X is clearly the midpoint of VZ, and I've even taken the liberty of including the assumption that W, X, and Y are collinear, allowing the vertical angles to be congruent.

However, since we were not given that X was a midpoint, or that WX is congruent to XY, I've exaggerated that those two sides might not be congruent, and thus the triangle are not congruent, even though it met all of the given criteria.

Given that we only have one side pair guaranteed, we need two angle pairs, or another side pair and the angle between them.

W, X, Y collinear

To pick up one angle, if we had that W, X, and Y were collinear, as described above, that would be sufficient to prove that angle VXW and angle ZXY would be congruent as a vertical angle pair.

But that's only one part, we'd still need one more, so even after that, you'd need one more angle to prove congruence:

If you got the vertical angle pair, you could prove the triangles congruent with one more side, but specifically it must be the two sides contain the angle, so WX congruent to XY to prove that the triangles are congruent using SAS.

Some concepts that would lead to either one more angle pair being congruent or the sides WX and XY being congruent are as follows:

Parallel lines

If VW was parallel to ZY, since VZ is a line, it is a transversal to WV and YZ.  Since Angle V and Angle Z form alternate interior angles, and given that the line are parallel, Angle V and Angle Z would be congruent.  Then, apply ASA.

X is a midpoint of WY -- smallest amount of info needed to prove triangle congruence

If X was a midpoint to WY, then that guarantees that W, X, and Y are collinear (something which was not explicitly given originally).  This would guarantee that the vertical pair was congruent, and would give us that the sides WX and XY were congruent (by definition of midpoint).  This would be the smallest amount of information needed that would allow us to prove the triangle congruence.

Answer:

Step-by-step explanation:

, (-7/8 - 5/12) + 3/16 = -53/48.

Answer:

Step-by-step explanation:

p(x) = (2x - 3)^2 - 25
 a)     = (2x - 3)^2 - 5^2

          = (2x - 3 + 5) (2x - 3 - 5)
 b)         = (2x + 2) (2x - 8)

 c) (2x + 2) (2x - 8) = 0               |             (2x + 2) (2x - 8) = -16
      4x^2 - 12x - 16 = 0                |             4x^2 - 12x - 16 = -16
      x^2 - 3x - 4 = 0                      |             x^2 - 3x = 0
       x^2 + x - 4x - 4 = 0               |              x(x - 3) = 0
       x(x + 1) - 4(x + 1) = 0             |              x = 0 or x = 3
       (x - 4) (x + 1) = 0

        x = 4 or x = - 1
d)   p(5) = (2(5) + 2) (2(5) - 8) | p(2root3) = (2(2root3) + 2)(2(2root3) - 8)
             = 12 x 2                       | = (4root3 + 2)(4root3 - 8)

             = 24                             | = 48 - 16 - 24root3
                                                  | = 32 - 24root3

The correct option is c, the fraction with repeating decimals is 3/11.

A fraction in lowest terms with a prime denominator other than 2 or always produces a repeating decimal.

Here the options are:

a) 3/25

b) 3/16

c) 3/11

d) 3/8

If you know the prime numbers, you can see that there is only one option with a prime number in the denominator.

That option is the third one, where the denominator is 11, that fraction will have repeated decimals

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Answer:

How many modes does the set {2, 8, 4, 10, 7, 3, 1} have?

Step-by-step explanation:

What is a mode?

You're welcome.

Answer:

No modes

Step-by-step explanation:

A mode is the most repeated number in the set. in this case, none of the numbers are repeated. If each number is used once, there is no repetition, so there is no mode.

The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

From the question, we have the following parameters that can be used in our computation:

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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Answer:

Step-by-step explanation:

A

Generally when you're solving systems of equations like this you want one variable to be by itself and have no coefficient (it's not being multiplied by anything)

In question A, the x variable is by itself but it has a coefficient of 4 (not 1)

if f(x, y, z) = 4[tex]x[/tex][tex]y^{2}[/tex][tex]z^{3}[/tex] arcsin (xz) , the value of fₓzᵧ is "24xyz²√(1-x²z²)".

To find fₓzᵧ, we differentiate f(x,y,z) partially with respect to x, then z, and finally y.

First, we take the partial derivative of f with respect to x:

fₓ = 4y²z³(arcsin(xz)) + 4xy²z³(1-x²z²)⁻ᵐ

where m = 1/2 * (1 - x²z²)⁻ⁿ, n = -1/2

Next, we take the partial derivative of fₓ with respect to z:

fₓz = 12xyz²(arcsin(xz)) + 4y²z²(1-x²z²)⁻ᵐ + 8xy²z²x(1-x²z²)⁻ⁿ

Finally, we take the partial derivative of fₓz with respect to y:

fₓzᵧ = 24xyz²√(1-x²z²)

Therefore, fₓzᵧ = 24xyz²√(1-x²z²) is the solution, where x, y, and z are the values of the given function f.

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To determine the linear regression equation and the correlation coefficient, we need the data provided in the table. Unfortunately, the table you mentioned is missing from your question. Without the data, it is not possible to calculate the linear regression equation or the correlation coefficient.

In a scenario where an insurance agent is examining the relationship between a driver's age and the percentage of accidents caused by speeding, the linear regression equation would allow us to predict the percentage of accidents caused by speeding based on the driver's age. The correlation coefficient would indicate the strength and direction of the relationship between these two variables. A correlation coefficient of 1 would indicate a perfect positive relationship, -1 would indicate a perfect negative relationship, and 0 would indicate no linear relationship.

If you can provide the data from the table, I'll be able to assist you further in determining the linear regression equation and the correlation coefficient.

The perimeter and the area of each composite figure are, respectively:

Case A: p = 25 m, A = 28.72 m²

Case B: p = 62 cm, A = 182 cm²

Case C: p = 57.5 cm, A = 186.48 cm²

Case D: p = 67.4 in, A = 485.280 in²

In this problem we must determine the perimeter and the area of four composite figures. The perimeter is the sum of all sides of the figure and the area is the sum of areas according to the following area formulas:

Rectangle / Parallelogram

A = b · h

Triangle

A = 0.5 · b · h

Quarter of a circle

A = 0.25π · r²

Where:

Case A

Perimeter

p = 2 · (6.1 m) + 2 · (1.2 m) + 2 · (5.2 m)

p = 25 m

Area

A = (5.2 m) · (2.1 m) + (2.5 m) · (4.0 m) + (1.5 m) · (5.2 m)

A = 28.72 m²

Case B

p = 16 cm + 2 · (7 cm) + 6 cm + 2 · (8 cm) + 10 cm

p = 16 cm + 14 cm + 6 cm + 16 cm + 10 cm

p = 62 cm

A = (10 cm) · (7 cm) + (16 cm) · (7 cm)

A = 182 cm²

Case C

p = 3 · (11.1 cm) + 2 · (12.1 cm)

p = 57.5 cm

A = (11.1 cm)² + 0.5 · (11.1 cm) · (11.4 cm)

A = 186.48 cm²

Case D

p = 12.1 in + 10.1 in + 2 · (11.5 in) + 22.2 in

p = 67.4 in

A = 0.5π · (12.1 in)² + (22.2 in) · (11.5 in)

A = 485.280 in²

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The volume of fruit punch that fits in Brian's drink bottle is 4 cups.

To determine how many cups of fruit punch fits in Brian's drink bottle need to first calculate the total volume of fruit punch in the cooler before he filled his drink bottle.

We are told that the cooler contained 5 gallons of fruit punch initially.

Since 1 gallon is equivalent to 16 cups then 5 gallons will be equal to:

5 x 16 = 80 cups

The cooler contained a total of 80 cups of fruit punch initially.

After Brian fills his drink bottle there are 76 cups of fruit punch left in the cooler. T

his implies that Brian took 80 - 76 = 4 cups of fruit punch.

Based on the assumption that Brian's drink bottle can only hold 4 cups of fruit punch.

Brian's drink bottle has a larger or smaller capacity, then the answer will change accordingly.

It is also worth noting that the volume of fruit punch that fits in Brian's drink bottle may vary depending on the shape and size of the bottle and how much space is left after the fruit punch is poured into it.

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When the interval [3, 11] is divided into 16 subintervals of equal length, each of the subintervals has length (a) 2. (b)4. (b) 4. () c. 1/2

When the interval [3, 11] is divided into 16 subintervals of equal length, we can use the formula:
length of each subinterval = (length of the interval) / (number of subintervals)
Therefore, the length of each subinterval would be:
(11 - 3) / 16 = 8 / 16 = 1/2
So the answer is (c) 1/2.
This means that each of the 16 subintervals would have a length of 1/2. It's important to note that the number of subintervals does not affect the length of the interval itself, only the length of each subinterval.
It's also worth mentioning that if we had divided the interval [3, 11] into a different number of subintervals of equal length, the length of each subinterval would have been different. This formula is specific to dividing an interval into a certain number of subintervals.

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The null hypothesis for testing a correlation coefficient is h0: rhoxy = 0, indicating no correlation between the variables.

The null hypothesis (h0) in hypothesis testing represents the assumption of no relationship or correlation between the variables under investigation. In the case of testing a correlation coefficient (rhoxy), the appropriate null hypothesis would be h0: rhoxy = 0.

This null hypothesis suggests that there is no linear relationship between the variables. In other words, the correlation coefficient is expected to be zero, indicating no correlation or dependence between the variables being studied.

When conducting hypothesis testing, the alternative hypothesis (h1) typically represents the alternative scenario where a relationship or correlation is expected. In this context, the alternative hypothesis for testing a correlation coefficient would be h1: rhoxy ≠ 0 or h1: rhoxy > 0, depending on the specific research question and the direction of the expected relationship.

In summary, the null hypothesis for testing a correlation coefficient is h0: rhoxy = 0, indicating no correlation between the variables, while the alternative hypothesis can vary depending on the expected relationship.


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The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based on given indicator information, is called b. posterior probability

Bayes' theorem is a formula used to calculate the conditional probability of an event or hypothesis based on prior knowledge or information. It allows us to update our prior beliefs or probabilities based on new evidence or information.

The probability of the states of nature, after using Bayes' theorem to adjust the prior probabilities based on given indicator information, is called the posterior probability. It represents the revised probability of each state of nature, given the observed indicator or evidence.

To calculate the posterior probability, we multiply the prior probability by the likelihood of the evidence given the state of nature, and then divide by the marginal probability of the evidence. The resulting probability represents the updated probability of the state of nature, given the observed evidence or indicator.

Therefore,

The probability of the states of nature, after use of Bayes' theorem to adjust the prior probabilities based on given indicator information, is called b. posterior probability

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Answer:

it is calculating the average of their score

The measures are given as follows:

The area of a rectangle is given by the multiplication of the base by the height, as follows:

A = bh.

The dimensions are given as follows:

b = 5 in, h = 2 in.

Hence the area is given as follows:

A = 5 x 2 = 10 in².

The area of a triangle is given by half the multiplication of the base by the height, as follows:

A = 0.5bh.

The dimensions are given as follows:

b = 1 in, h = 1 in.

Hence the area is given as follows:

A = 0.5 x 1 x 1 = 0.5 in².

Hence the area of plastic is given as follows:

10 - 0.5 = 9.5 in².

The diagram is given by the image presented at the end of the answer.

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The general indefinite integral of ([tex]5x^4 + 8x + 7[/tex]) dx can be found by using the power rule of integration.

According to the power rule, we add one to the exponent and divide the entire term by the new exponent. Therefore, integrating [tex]5x^4[/tex] yields [tex](5/5)x^5[/tex] or [tex]x^5[/tex], integrating 8x yields (8/2)x² or 4x², and integrating 7 yields 7x. Hence, the general indefinite integral of [tex](5x^4 + 8x + 7)[/tex] dx is [tex]x^5 + 4x^2 + 7x + C[/tex], where C is the constant of integration. It is important to note that the constant of integration is added to the end of the integrated function because it is not possible to determine the exact value of the constant. Therefore, it is represented by the letter C. When solving problems that require the evaluation of a definite integral, the constant of integration is eliminated as the limits of integration determine the value of C.

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Answer:

y ≈ 11.04 ft

Step-by-step explanation:

We know that the formula for volume of a cylinder is

[tex]V=\pi r^2h[/tex] where

Thus, we must solve for the height, y by plugging in 3000 for V, and 9.3 for r into the volume formula:

[tex]3000=\pi (9.3)^2y\\3000=86.49\pi y\\3000/(86.49\pi )=y\\11.04092564=y\\11.04=y[/tex]

The area of triangle ABC is 27 square units.

To determine the area of triangle ABC, we can use the formula for the area of a triangle given its coordinates:

Area = 1/2 × x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|

Given the coordinates of points A(-2, 5), B(4, 2), and C(-8, -1), we can substitute these values into the formula:

Area = 1/2 × (-2)(2-(-1)) + (4-(-2))( -1-5) + (-8)(5-2)

Simplifying the expression, we have:

Area = 1/2 × (1-6-24-24)

Area = 1/2 × (-53)

Area = -26.5

Since area cannot be negative, we take the absolute value to obtain the area of triangle ABC as 26.5 square units. Therefore, the area of triangle ABC is 26.5 square units.

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You need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

First, 5% of the total cost for four years.

= 0.05 x ($14,895.00/yr x 4 years)

= 0.05 x $59,580.00

= $2,979.00

Second, Divide the total amount you need to pay over four years by the number of years.

= $2,979.00 / 4

= $744.75

Therefore, you need to pay $744.75 for each year of attending college.

Now, the total contribution goal.

= Amount to pay each year x 4 years

= $744.75 x 4

= $2,979.00

and, Monthly savings required

= Total contribution goal / 48 months

= $2,979.00 / 48

= $62.06

Therefore, you need to save $62.06 each month for four years to achieve your total contribution goal before starting college.

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Name of the two-dimensional figure that is a cross-section of both the cube and pyramid is square and triangle.  A cross section is the intersection of a three-dimensional object or form with a plane in mathematics.

By slicing the object with the plane, it may be acquired, exposing a two-dimensional illustration of the junction. Cross sections are useful tools for visualizing and comprehending an object's underlying structure, such as that of a complicated form or a geometric solid.

They aid mathematicians and scientists in the analysis and prediction of properties, the measurement of areas or volumes.

In many disciplines, including geometry, mathematics, physics, engineering, and computer graphics, cross sections are significant because they allow us to understand the intricate details of three-dimensional objects through their two-dimensional projections.

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C. If there is no variability (all the scores of the variables have the same value), measures of dispersion will equal zero.

Measures of dispersion are used to describe the spread of data. They include the range, variance, and standard deviation. When all the scores of a variable have the same value, there is no spread or variability in the data. This means that the distance between the minimum and maximum value (range) is zero, and the variance and standard deviation are also zero.

In this case, there is no need to calculate measures of dispersion because they will all equal zero. This is because the data points do not differ from each other in any way, and there is no variation to describe. Therefore, when there is no variability in a set of data, measures of dispersion will always equal zero.

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In ΔRST, the measure of angle R is  73.1°

Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T

i.e., r = side ST and t = side RS

We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

i.e., for triangle ABC,

sinA/a = sinB/b = sinC/c

Using sine law for ΔRST,

sinR/r = sinS/s = sinT/t

Consider equation,

79 × 0.8481 = sin(R) × 70

sin(R) = 66.99 / 70

sin(R) = 0.9571

∠R = arcsin(0.9571)

∠R = 73.1°

Thus, measure of angle R = 73.1°

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complete question:

In ΔRST, r = 79 inches, t = 70 inches and ∠T=58°. Find all possible values of ∠R, to the nearest 10th of a degree