Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 3. 4. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 6. 8. Boris scored a 55 on the knowledge test and 106 on the aptitude test. Callie scored 67 on the knowledge test and 119 on the aptitude test. (a) Which test did Boris perform better on? Use z-scores to support your answer. (b) Which test did Callie perform better on? Use z-scores to support your answer. (c) Boris also took a logic test. His z-score on that test was -0. 43. Does this change the answer to which test Boris performed better on? Explain your answer using z-scores

Chaz builds a connection between points on circle Q and points on circle P by carrying out these two translations while maintaining the size and shape of the circles.

Chaz may apply two translations sequentially to map circle Q onto circle P, demonstrating that they are comparable following a similarity transformation followed by a rigid transformation.

The center of circle Q can first be translated to the center of circle P by Chaz. The two circles' centers will match thanks to this translation.

After that, Chaz can do another translation to line up a point on circle Q's circumference with a similar point on circle P's circumference. The matching points on the circles are aligned as a result of this translation.

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A.  the company should charge approximately $18.08 per unit to sell 2500 units.

B.  Q is measured in thousands, this means the company will sell about 6350 units (rounded to the nearest integer) when the price is set at $8.50 per unit.

(a) To find the price for each unit to sell 2500 units, we need to plug Q = 2.5 (since Q is in thousands) into the demand function P = 26e^(-0.04Q):

P = 26e^(-0.04 * 2.5)

After calculating the value, we get:

P ≈ 18.08

So, the company should charge approximately $18.08 per unit to sell 2500 units.

(b) To find how many units will sell if the price is $8.50, we need to solve the equation P = 26e^(-0.04Q) for Q:

8.50 = 26e^(-0.04Q)

First, we need to isolate the exponential term:

(8.50 / 26) = e^(-0.04Q)

Now, take the natural logarithm (ln) of both sides:

ln(8.50 / 26) = -0.04Q

Next, divide both sides by -0.04:

Q = ln(8.50 / 26) / -0.04

After calculating the value, we get:

Q ≈ 6.35

Since Q is measured in thousands, this means the company will sell about 6350 units (rounded to the nearest integer) when the price is set at $8.50 per unit.

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The mean of this distribution is 26.5. The standard deviation is 8.0623. The probability that the number will be exactly 36 is P (x = 36) = 0.0286. The probability that the number will be between 21 and 23 is P (21 < x < 23) = 0.0400. The probability that the number will be larger than 26 is P (x > 26) = 0.2857. P (x > 16 | x < 18) = undefined. The 49th percentile is 29.3700. The minimum for the lower quartile is 19.75.

a. The mean of a uniform distribution is the average of the maximum and minimum values, so in this case, the mean is:

mean = (12 + 41) / 2 = 26.5

Therefore, the mean of this distribution is 26.5.

b. The standard deviation of a uniform distribution is given by the formula:

sd = (b - a) / sqrt(12)

where a and b are the minimum and maximum values of the distribution, respectively. So in this case, the standard deviation is:

sd = (41 - 12) / sqrt(12) = 8.0623

Therefore, the standard deviation of this distribution is 8.0623.

c. Since the distribution is uniform, the probability of getting any specific value between 12 and 41 is the same. Therefore, the probability of getting exactly 36 is:

P(x = 36) = 1 / (41 - 12 + 1) = 0.0286

Rounded to four decimal places, the probability is 0.0286.

d. The probability of getting a number between 21 and 23 is:

P(21 < x < 23) = (23 - 21) / (41 - 12 + 1) = 0.0400

Rounded to four decimal places, the probability is 0.0400.

e. The probability of getting a number larger than 26 is:

P(x > 26) = (41 - 26) / (41 - 12 + 1) = 0.2857

Rounded to four decimal places, the probability is 0.2857.

f. The probability that x is greater than 16, given that it is less than 18, can be calculated using Bayes' theorem:

P(x > 16 | x < 18) = P(x > 16 and x < 18) / P(x < 18)

Since the distribution is uniform, the probability of getting a number between 16 and 18 is:

P(16 < x < 18) = (18 - 16) / (41 - 12 + 1) = 0.0400

The probability of getting a number greater than 16 and less than 18 is zero, so:

P(x > 16 and x < 18) = 0

Therefore:

P(x > 16 | x < 18) = 0 / 0.0400 = undefined

There is no valid answer for this question.

g. To find the 49th percentile, we need to find the number that 49% of the distribution falls below. Since the distribution is uniform, we can calculate this directly as:

49th percentile = 12 + 0.49 * (41 - 12) = 29.37

Rounded to four decimal places, the 49th percentile is 29.3700.

h. The lower quartile (Q1) is the 25th percentile, so we can calculate it as:

Q1 = 12 + 0.25 * (41 - 12) = 19.75

Therefore, the minimum for the lower quartile is 19.75.

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Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.

First, we need to find the total number of cups of M&Ms Jen has

5 1/2 cups = 11/2 cups

Then, we divide the total number of cups by the number of cups needed to fill each bag

(11/2 cups) ÷ (1 1/4 cups/bag)

To divide by a fraction, we can multiply by its reciprocal

(11/2 cups) x (4/5 cups/bag)

= 44/10 cups

Simplifying, we get

= 4 2/10 cups

= 4 1/5 cups

So, Jen can fill 4 bags completely.

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To find the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to find the probability of getting NNNNN as the first five patients. Since the success rate is 0.3 and the failure rate is 0.7, the probability of getting NNNNN is:

0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807

Therefore, the estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is 0.16807.

To find the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can select three patients out of four and multiply it by the probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively. The number of ways to select three patients out of four is:

4C3 = 4

The probability of getting EEE and NEEE for the selected patients and non-selected patients, respectively, is:

(0.7)^3 x (0.3) x (0.7) = 0.1029

Therefore, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is 4 x 0.1029 = 0.4116 (rounded to 4 decimal places).

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Answer: Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.

Step-by-step explanation:

The functions S(t) and P(t) represent the value of the sedan and pickup truck, respectively, as a function of time t in years since the purchase. Let's analyze each function:

For S(t)=24,400(0.82)^t, the coefficient 24,400 represents the initial value or starting point of the function. This means that the value of the sedan at the time of purchase was $24,400.

The base 0.82 represents the rate of depreciation or decrease in value of the sedan over time. Specifically, the sedan's value decreases by 18% per year (100% - 82%).

For P(t)=35,900(0.71)^t/2, the coefficient 35,900 represents the initial value or starting point of the function.

This means that the value of the pickup truck at the time of purchase was $35,900. The base 0.71 represents the rate of depreciation or decrease in value of the pickup truck over time.

Specifically, the pickup truck's value decreases by approximately 29% every two years, since the exponent is divided by 2.

Comparing the two functions, we can see that the initial value of the pickup truck was higher than the initial value of the sedan.

However, the rate of depreciation of the pickup truck is greater than that of the sedan. This means that the pickup truck will lose its value at a faster rate than the sedan.

For example, after 5 years, we can evaluate each function to see the values of the sedan and pickup truck at that time:

S(5) = 24,400(0.82)^5 ≈ $10,373.67

P(5) = 35,900(0.71)^(5/2) ≈ $15,864.48

We can see that after 5 years, the pickup truck is still worth more than the sedan, but its value has decreased by a greater percentage. Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.

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An equation of the tangent plane to the surface at the given point is x + 2y + 3z = 14. A set of symmetric equations for the normal line to the surface at the given point is (x-1)/2 = (y-2)/4 = (z-3)/6.

The gradient of the surface is given by

∇f(x, y, z) = <2x, 2y, 2z>

At point (1, 2, 3), the gradient is

∇f(1, 2, 3) = <2, 4, 6>

The equation of the tangent plane can be found using the formula

f(x, y, z) = f(a, b, c) + ∇f(a, b, c) · <x-a, y-b, z-c>

Plugging in the values we have

x + 2y + 3z = 14

The direction vector of the normal line is the same as the gradient of the surface at the given point

<2, 4, 6>

To find symmetric equations for the line, we can use the parametric equations

x = 1 + 2t

y = 2 + 4t

z = 3 + 6t

Eliminating the parameter t, we get the symmetric equations

(x-1)/2 = (y-2)/4 = (z-3)/6

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Maximum Height of the ball: 6.25 units

To find the initial and maximum height of the ball following the function f(x) = -0.25(x-3)^2 + 6.25, we need to evaluate the function at the initial position and find the vertex of the parabola.

Initial height:
When the ball is initially thrown, it's at position x=0. Plug this value into the function:

f(0) = -0.25(0-3)^2 + 6.25
f(0) = -0.25(-3)^2 + 6.25
f(0) = -0.25(9) + 6.25
f(0) = -2.25 + 6.25
f(0) = 4

The initial height of the ball is 4 units.

Maximum height:
The maximum height corresponds to the vertex of the parabola. Since the function is in the form f(x) = a(x-h)^2 + k, the vertex is at the point (h, k). In our case, h = 3 and k = 6.25.

The maximum height of the ball is 6.25 units.

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Using the fundamental counting principle, the total number of outcomes given m outcomes and n outcomes will be m*n. A helpful way to think about this is by using a tree.

Say we have 2 shirts and 3 pairs of pants. We can show all possible outcomes using a tree like this in the picture attached.

So, by looking at the tree, we can see that every different shirt has 3 different pairs of pants that can go with it to make a combination. Thus, the total amount of combinations is the number of pants (3) that can go with each type of shirt (2). So, 3*2 is 6 total combinations.

In this example, m was 2 and n was 3. Applied to any number of individual outcomes, the total amount will be m*n.

The area of the circle is  12. 56 square units

The formula for calculating the area of a circle is expressed as;

A = πr²

This is so such that the parameters of the equation are;

From the information given, we have that;

Area = unknown

Radius = 2 units

Now, substitute the values into the formula, we have;

Area = 3.14 ×2²

Find the square

Area = 3.14 × 4

Multiply the values, we have;

Area = 12. 56 square units

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To prove the trigonometric identity csc(x) - sin(x) - cos(x)cos(x), we will start by simplifying the left-hand side of the equation using trigonometric definitions and identities.

Recall that csc(x) = 1/sin(x). We will use this definition to rewrite the left-hand side of the equation:

1/sin(x) - sin(x) - cos(x)cos(x)

Now, we will find a common denominator for the terms in the equation. In this case, the common denominator is sin(x). To do this, we will multiply sin(x) to the second term:

(1 - sin^2(x) - cos(x)cos(x)sin(x)) / sin(x)

Next, we will use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to replace sin^2(x) in the expression:

(1 - (1 - cos^2(x)) - cos(x)cos(x)sin(x)) / sin(x)

Simplifying the expression, we get:

(cos^2(x) - cos(x)cos(x)sin(x)) / sin(x)

Now, we can factor out cos(x) from the numerator:

cos(x)(cos(x) - sin(x)) / sin(x)

This expression is equivalent to the given identity, so we have proven the trigonometric identity:

csc(x) - sin(x) - cos(x)cos(x) = cos(x)(cos(x) - sin(x)) / sin(x)

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To simplify the given function F(x) = x(x^2 - 4) - 3x(x - 2), we need to use the distributive property and combine like terms.

First, we distribute x in the first term, and we get:

F(x) = x^3 - 4x - 3x^2 + 6x

Next, we can combine like terms:

F(x) = x^3 - 3x^2 + 2x

Therefore, the simplified form of the given function F(x) = x(x^2 - 4) - 3x(x - 2) is F(x) = x^3 - 3x^2 + 2x.

a) Two different twin circles for five pair of twins are ( 5,2,4,2,3,5,4,3,1,1,3) and ( 3,1,1,3,4,5,3,2,4,2,5).

b) No twin circles in 3 pair of twins because any of arrangement of them cannot fulfil the condition of twin circle.

c) The partial twin circle ( third circle) present in above figure can't be completed because 4 positions are fixed there and after that number of persons more than seats.

We have a pair twins are numbered 1, 1, 2, 2, 3, 3, and so on. They all seated in a circle so that the least number of gaps between two twins always

equals their assigned number. This is called a twin circle. That is Number of persons between 1 and 1 twins = 0

Number of persons between 2 and 2 twins = 1,

so on.. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same.

a) We have to make two twin circles for five pair twins. The arrangement of pair twins in two different ways with the satisfaction of conditions. So, first arrangement is ( 5,2,4,2,3,5,4,3,1,1,3) and

other arrangement is ( 3,1,1,3,4,5,3,2,4,2,5).

b) There is no twin circle between the arrangement of 3 twin pairs. Because in case of 3 twin pair total members = 3×2 = 6 and number of members can be seat between pairs are 3( 1+2+0). As we know, it is fixed that no person between (1,1). So, we cannot be arrange the 2 pairs with desirable 3 gaps that is 1 person between (2,2) and 2 persons between (3,3).

c) There is total 12 positions to seat in circles. The position of 6 and 1 is fixed. According to above scenario, position next to 1 is for 1 (clockwise) and 5th position from given 1 position in (clockwise) is other member of twin 6. Now, four positions are fixed. Eight positions are left and 4 twin pairs (2,2) , (3,3), (4,4),(5,5). Number of persons seat between 4 pairs are 10 in counts ( greater than position ) so, no such arrangement is possible. Hence, this partial circle can't be completed.

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Complete question:

The above figure complete question.

Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated in a circle so that the least number of gaps between two twins always

equals their assigned number. This is called a twin circle. Note that this means there is no person between the twins numbered 1 and 1, there is just one person between the twins numbered 2 and 2, and so on. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same. For example, the following are the same twin circles for 4 pairs of twin.

a) Find two twin circles for five pairs of twin

b) Explain why no twin circles in 3 pairs of twin

c) explain why this partial twin circle can't be completed ? ( third circle)

The given radian measure -1.7 pi is equivalent to -306 degrees.

The correct answer is option (b), Negative 306 degrees. This conversion takes into account the negative sign of the radian measure, resulting in a negative degree measure to convert a radian measure to a degree measure, we use the conversion factor that 180 degrees is equal to π radians.

Given the radian measure -1.7π, we can calculate the corresponding degree measure by multiplying -1.7π by the conversion factor:

Degree measure = (-1.7π) * (180 degrees / π)

The π in the numerator and denominator cancels out, resulting in:

Degree measure = -1.7 * 180 degrees

Calculating the value, we have:

Degree measure = -306 degrees

Therefore, the correct answer is option b) Negative 306 degrees.

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Answer:

The percentage of stainless steel used to make the two ends of the tank cannot be determined without additional information. Please provide more details about the tank and its construction.

Step-by-step explanation:

To calculate the percentage of stainless steel used to make the two ends of the tank, we need to know the total amount of stainless steel used to make the entire tank, as well as the amount used to make the ends. Without this information, it is impossible to determine the percentage of stainless steel used for the ends.

For example, if the tank is made entirely of stainless steel, then the percentage of stainless steel used to make the ends would be 100%. However, if the tank is made of multiple materials, then the percentage of stainless steel used for the ends would depend on the amount of stainless steel used for the entire tank and the amount used for the ends.

Therefore, to calculate the percentage of stainless steel used for the ends of the tank, we need additional information about the tank's construction and materials.

19.29 cubic feet  is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet

Without knowing the specific shape of the composite figure, it is impossible to give an exact answer. However, we can provide a general formula for the volume of a cylinder with height h and diameter d, and assume that the composite figure consists of a cylinder and some other shape.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder. The diameter of the cylinder is given as 2.5 feet, which means the radius is 1.25 feet.

If the height of the cylinder is also 2.5 feet, then the volume of the cylinder is:

V_cylinder = π(1.25)^2(2.5) = 6.15π cubic feet (exact)

To approximate to two decimal places, we can use the approximation π ≈ 3.14:

V_cylinder ≈ 6.15(3.14) = 19.29 cubic feet (approximate to two decimal places)

However, since we do not know the specific shape of the composite figure, we cannot give an exact answer for its volume.

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At a significance level of 0.05, the critical value is typically chosen as 1.96 for a two-tailed test. Comparing this critical value with the obtained p-value of 0.067, which is greater than 0.05, indicates that the result is not statistically significant.

At 0.05 level of significance, when we fail to reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis. In this case, the null hypothesis states that the mean filling weight of the population is equal to 20 ounces. Since the data does not provide strong evidence to suggest otherwise, we conclude that the mean filling weight is not significantly different from 20 ounces.

Hence, the answer is (b) "Not significantly different than 20 ounces."

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The length of the diagonal is c = √269 feet.

To get the length of the diagonal of a rectangular patio, we can use the Pythagorean theorem, which states that for a right triangle with legs of length a and b, and hypotenuse of length c, a² + b² = c². In this case, the legs of the right triangle are the length and width of the rectangular patio, which are 10 feet and 13 feet, respectively. Let's use a and b to represent these lengths.
a = 10 feet
b = 13 feet
We want to find the length of the diagonal, which is the hypotenuse of the right triangle. Let's use c to represent this length.
a² + b² = c²
10² + 13² = c²
100 + 169 = c²
269 = c²
Now we need to find the square root of 269 to get the length of the diagonal.
c = √269
c ≈ 16.4 feet
So the length of the diagonal of the rectangular patio is approximately 16.4 feet. We can also find the ratio of the length, width, and diagonal of the rectangular patio.
length:width = 10:13
width:length = 13:10
length:diagonal = 10:√269
width:diagonal = 13:√269
diagonal:length = √269:10
diagonal:width = √269:13

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Probability of Janie winning game = (2⁴⁷ - 1)/2⁴⁷  or approximately 0.999999999999978, using binomial distribution with given information.

We can solve this probability by using the binomial distribution. Let X be the random variable representing the number of heads in the remaining tosses until one of the players wins the game. Since Luka has 24 points, Janie needs to win X heads before Luka wins one more.

We want to find the probability that Janie wins the game, which is the probability that X is greater than or equal to Luka's remaining points needed to win(25 - 24 = 1).

Let p be the probability of the coin landing heads up, and q be the probability of the coin landing tails up, so that p + q = 1. Since the coin is fair, p = q = 1/2.

Using the binomial distribution, the probability that Janie wins the game is:

P(X >= 1) = 1 - P(X = 0)

where

P(X = k) = [tex](47 - 24 choose k) (1/2)^k (1/2)^(47 - 24 - k)[/tex]

= (23 + k choose k) (1/2)⁴⁷

where k = 0, 1, 2, ..., 23.

Therefore,

P(X = 0) = (23 choose 0) (1/2)⁴⁷ = 1/2⁴⁷

P(X >= 1) = 1 - P(X = 0) = 1 - 1/2⁴⁷

Simplifying,

P(X >= 1) = (2⁴⁷ - 1)/2⁴⁷

Therefore, the probability that Janie wins the game is (2⁴⁷ - 1)/2⁴⁷ or approximately 0.999999999999978.

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The graph representing the ice sheet's thickness (y) over time (x, in weeks) is a linear equation with a negative slope.

We are given the initial thickness of the ice sheet (2 meters) and its thickness after 3 weeks (1.25 meters). The rate of decrease in thickness is constant.

To find the slope, we can use the formula: (change in y) / (change in x). Here, the change in y is (1.25 - 2) = -0.75 meters, and the change in x is 3 weeks.

Therefore, the slope is -0.75 / 3 = -0.25 meters/week. The graph will be a straight line with a negative slope, indicating that the ice sheet's thickness is decreasing at a constant rate over time.

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Answer:

Step-by-step explanation:

Of means to multiply

So to find .3 of the 10.38 pounds up apples:

.3 x 10.38

=3.114 pounds of apples were used

The value of the given triple integral is ∫∫∫ (4z^3 + 3y^2 + 2x) dv = 1/2.

To evaluate the given triple integral, we need to determine the limits of integration for x, y, and z. As there are no specific bounds given, we can assume that the region of integration is the entire space. Therefore, the limits of integration for x, y, and z will be from negative infinity to positive infinity.

Thus, we have:

∫∫∫ (4z^3 + 3y^2 + 2x) dv = ∫∫∫ 4z^3 dv + ∫∫∫ 3y^2 dv + ∫∫∫ 2x dv

Using the fact that the integral of an odd function over a symmetric interval is zero, we can see that the integral of 2x over the entire space is zero.

Hence, we are left with evaluating the integrals of 4z^3 and 3y^2 over the entire space.

∫∫∫ 4z^3 dv = 4 ∫∫∫ z^3 dxdydz

Using the fact that the integral of an odd function over a symmetric interval is zero, we can see that the integral of z^3 over the entire space is zero.

Thus, we have ∫∫∫ 4z^3 dv = 0.

Similarly, we can evaluate ∫∫∫ 3y^2 dv as follows:

∫∫∫ 3y^2 dv = 3 ∫∫∫ y^2 dxdydz

Since the limits of integration are from negative infinity to positive infinity, the integrand is an even function. Therefore, we can write:

∫∫∫ y^2 dxdydz = 2 ∫∫∫ y^2 dx dz dy

Now, using cylindrical coordinates, we can express y^2 as r^2 sin^2 θ and the differential element dv as r dz dr dθ.

Therefore, we have:

∫∫∫ y^2 dxdydz = 2 ∫∫∫ r^4 sin^2 θ dz dr dθ

Using the fact that the integral of sin^2 θ over a full period is π/2, we can evaluate the integral as follows:

∫∫∫ y^2 dxdydz = 2 π/2 ∫0∞ ∫0^2π ∫0^∞ r^4 sin^2 θ dz dr dθ

Simplifying the integral, we get:

∫∫∫ y^2 dxdydz = (π/2) (2π) (1/5) = π^2/5

Hence, we have:

∫∫∫ (4z^3 + 3y^2 + 2x) dv = 0 + π^2/5 + 0 = π^2/5

Finally, we can simplify the result as π^2/5 = 1/2. Therefore, the value of the given triple integral is 1/2.

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The set of dimensions for the largest box is: 4 in x 4 in x 3.8 in.

We know that the smallest box must hold 8 fluid ounces or 15 in³ of soup. Let's assume the dimensions of the smallest box to be x, y, and z.

Then, we have:

[tex]x * y * z = 15[/tex]

Now, the largest box will be a dilation of the smallest box using a scale factor of 2. This means that every dimension of the smallest box will be multiplied by 2 to get the dimensions of the largest box.

So, the dimensions of the largest box will be 2x, 2y, and 2z.

Now, we need to find the dimensions of the smallest box. We can start by solving the equation x * y * z = 15 for one of the variables, say z:

[tex]z = 15 / (x * y)[/tex]

Substituting this value of z in the expression for the dimensions of the largest box, we get:

[tex]2x * 2y * (15 / (x * y))[/tex]

Simplifying this expression, we get:

[tex]4 * 15 = 60[/tex]

So, the dimensions of the largest box are approximately 4 in by 4 in by 3.8 in (rounded to the nearest tenth).

Therefore, the set of dimensions for the largest box is: 4 in x 4 in x 3.8 in.

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Therefore, an initial deposit of $37,728.66 is required to have a college fund of $110,000 in 17 years with quarterly compounding and an APR of 4.9%.

An amount held in an account is referred to as a deposit. It might be put up in a bank as collateral for goods that are being rented out or bought. A deposit is used in many different sorts of economic transactions.

Compound interest can be calculated using the following formula to determine the required down payment:

A = P(1 + r/n)(nt)

where:

A = the future value of the account (in this case, $110,000)

P = the principal or initial deposit

r = the annual interest rate (4.9%)

n = the number of times the interest is compounded per year (4 for quarterly compounding)

t = the number of years (17)

When we enter the specified numbers into the formula, we obtain:

$110,000 = P(1 + 0.049/4)(4*17)

$110,000 = P(1.01225)⁶⁸

$110,000 = P * 2.9126

Dividing both sides by 2.9126, we get:

P = $37,728.66

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The law of sines is solved and the triangle is given by the following relation

Given data ,

From the law of sines , we get

a / sin A = b / sin B = c / sin C

a)

C = 135° C = 45₁ B = 10°

So , the measure of triangle is

A/ ( 180 - 35 - 10 ) = A / 35

And , a/ ( sin 135/35 ) = sin 35 / a

On simplifying , we get

a = 36.50

Hence , the law of sines is solved

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