Rob bought a 1965 Fender Jazzmaster vintage electric guitar in 1980 for a price of $150. In 2010 it was appraised for $4,200. Suppose $150 was deposited in a variable-rate certifi cate of deposit for 30 years with interest compounded daily. A. If the CD paid 12. 3% interest for the fi rst 7 years, what would the balance be after the fi rst 7 years? Round to the nearest cent. B. If the CD paid 6% interest for the next 10 years, what would the balance be after the fi rst 17 years? Round to the nearest cent. C. If the CD paid 4. 1% interest for the remaining 13 years, what would the balance be after 30 years? Round to the nearest cent. D. What is the difference between the appraised value of the guitar and the amount the original $150 would have earned in the CD?

The value of the expression 5 + 5 × 5 ÷ 5 ÷ 5 is equal to 10.

The order of operations in mathematics is to perform the operations in the following order:

Using this rule, we can simplify the expression:

First, we perform the multiplication and division from left to right:

5 x 5 = 25

25 ÷ 5 = 5

Then, we add the remaining terms:

5 + 5 = 10

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The probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

There are 36 possible outcomes when two standard six-sided dice are rolled. Each die has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.

To find the probability of rolling a sum of 6, we need to count the number of ways we can get a sum of 6. There are five possible ways to get a sum of 6:

- Roll a 1 on the first die and a 5 on the second die

- Roll a 2 on the first die and a 4 on the second die

- Roll a 3 on the first die and a 3 on the second die

- Roll a 4 on the first die and a 2 on the second die

- Roll a 5 on the first die and a 1 on the second die

So, the probability of rolling a sum of 6 is 5/36.

Therefore, the probability of rolling a sum of 6 when two standard six-sided dice are rolled is 5/36, or approximately 0.139.

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AnswerAnswer:

Step-by-step explanation:

To determine the materials cost for the brooch, we need to know the area of each material used in the brooch. Let's say that the brooch is made up of a 5 cm x 5 cm square of silver, a 2 cm x 2 cm square of copper, and a 3 cm x 1 cm rectangle of stone.

The area of the silver sheet is 5 cm x 5 cm = 25 cm^2, so the cost of the silver is 25 cm^2 x $9.75/cm^2 = $243.75.

The area of the copper sheet is 2 cm x 2 cm = 4 cm^2, so the cost of the copper is 4 cm^2 x $3.25/cm^2 = $13.

The area of the stone is 3 cm x 1 cm = 3 cm^2, so the cost of the stone is 3 cm^2 x $1.75/cm^2 = $5.25.

Therefore, the total materials cost for the brooch is $243.75 + $13 + $5.25 = $262.

C(12) represents the total cost (in dollars) of renting the industrial cleaning unit for 12 hours.

The problem gives us a function C(t) = 60 + 24t, where t represents the number of hours that an industrial cleaning unit is rented for. The function tells us that the total cost (in dollars) of renting the unit is equal to $60 plus $24 per hour.

Now, we are asked to find what C(12) represents. To do so, we substitute t = 12 into the function, which gives us:

C(12) = 60 + 24(12)

We can simplify this expression by multiplying 24 by 12, which gives us:

C(12) = 60 + 288

Adding 60 and 288 together, we get:

C(12) = 348

So, C(12) represents the total cost (in dollars) of renting the industrial cleaning unit for 12 hours. Therefore, the correct answer to the question is: The cost of renting the unit for 12 hours.

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About 10,676 gallons of paint were used to paint the 157 newly built homes in the subdivision, assuming each house required exactly 68 gallons of paint and 13 paint brushes.

The statement problem states that there are 157 newly built homes in a subdivision, and that 68 gallons of paint and 13 paint brushes were used for each house. This means that each house required 68 gallons of paint and 13 paint brushes.

To find the total amount of paint used for all 157 houses, we need to multiply the amount of paint used per house (68 gallons) by the number of houses (157):

Total amount of paint = 68 gallons/house x 157 houses

Total amount of paint = 10,676 gallons

Therefore, approximately 10,676 gallons of paint were used for the 157 newly built homes in the subdivision.

It's worth noting that this calculation assumes that each house required exactly 68 gallons of paint and 13 paint brushes. In reality, there may be some variation in the amount of paint and brushes used for each house, so the actual total may be slightly different.

However, this calculation provides a reasonable estimate of the total amount of paint used

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The problem involves finding the radius of a cylindrical can that will minimize the cost of the metal to make the can, given that the can must hold one liter of oil.

Specifically, we need to find the radius of the can that will minimize the surface area, and hence the cost, of the metal required to make the can.

To solve the problem, we need to first write an expression for the surface area of the can in terms of its radius, and then differentiate this expression with respect to the radius to find the critical point. We then need to check that the critical point corresponds to a minimum value of the surface area, which will give us the optimal radius for the can. Optimization problems like this one are used in many fields, including engineering, economics, and physics, to find the best course of action given certain constraints and objectives.

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Answer:  10/12

Step-by-step explanation:

since they give you adjacent to angle m and hypotenuse use

cos x = opp/hyp

cos M = 10/12

Answer:

x=3, Adding and dividing. (Im not too sure how to answer that question, Are there some options that you learned in class?)

Step-by-step explanation:

4x-5=7

+5       +5

4x=12

/4      /4

x=3

We will be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.

To find the missing angle and arc measures, follow these steps:

1. Look at the given diagram to identify the angles and arcs involved.

2. Use the angle sum property of a circle to find the measure of the missing angle. This property states that the sum of the angles in a circle is equal to 360 degrees. So, if you know the measures of the other angles in the circle, you can subtract their sum from 360 to find the missing angle.

3. Use the arc angle formula to find the measure of the missing arc. This formula states that the measure of an arc is equal to the measure of its corresponding central angle. So, if you know the measure of the missing angle, you can use it to find the measure of the missing arc.

4. Check your answer by making sure that the sum of all the arc measures in the circle is equal to the circumference of the circle.

Overall, be sure to take your time and carefully consider the given information in order to find the missing angle and arc measures accurately.

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The minimum value of a - b is around 2.2 with a = 8.4 rounded to one decimal place and b = 6.19 rounded to two decimal places.

We must first subtract b (lower bound) from a (upper bound) to determine the least value of a - b, which is equal to 8.4 - 6.19 = 2.21. 2.21 is the difference between a and b. However, the question requests that we round off this number to the nearest tenth.

We remove the first decimal point because 1 is

less than 5, giving us 2.2. Hence the minimum value of a -b to the nearest decimal is found to be 2.2.

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The complete question is:

Given a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places, find the minimum value of a - b rounded to 1 decimal place.

The depreciation for the first year of the truck's useful life is $7,467 by the straight-line method and $2,720 by the units-of-output method.

Depreciation per year = (Cost - Salvage value) / Useful life

Depreciation per year = (40,000 - 5,000) / 5 = $7,000

Depreciation for the first year = (16,000 / 15,000) x $7,000 = $7,467

Depreciation per mile = (Cost - Salvage value) / Total miles expected to be driven

Depreciation per mile = (40,000 - 5,000) / (5 x 15,000) = $0.17/mile

Depreciation for the first year = 16,000 x $0.17 = $2,720

Therefore, the depreciation for the first year of the truck's useful life is $7,467 by the straight-line method and $2,720 by the units-of-output method.

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The exact length of the curve is 112/3(√3 + 1), or approximately 96.666.

To find the exact length of the curve, we can use the formula for arc length:

L = ∫a^b √(1 + [f'(x)]²) dx

where f(x) = (x² - 4)^(3/2)/6, 5 ≤ x ≤ 9.

First, we find f'(x):

f'(x) = 3x(x² - 4)^(1/2)/12 = x(x² - 4)^(1/2)/4

Then we substitute f'(x) into the formula for arc length:

L = ∫5^9 √(1 + [x(x² - 4)^(1/2)/4]²) dx

L = ∫5^9 √(1 + x²(x² - 4)/16) dx

L = ∫5^9 √(16 + 16x²(x² - 4)/16) dx

L = ∫5^9 √(16x² + x^4 - 4x²) dx

L = ∫5^9 √(x^4 + 12x²) dx

L = ∫5^9 x²√(x^2 + 12) dx

We can use the substitution u = x^2 + 12, which gives du/dx = 2x and dx = du/2x, to simplify the integral:

L = (1/2)∫37^93 √u du

L = (1/2) [(2/3)u^(3/2)]_37^93

L = (1/3)[(125 + 108√3) - (13 + 36√3)]

L = (1/3)(112√3 + 112)

L = 112/3(√3 + 1)

Therefore, the exact length of the curve is 112/3(√3 + 1), or approximately 96.666.

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At the point P(2,2), the unit vector for the direction of steepest ascent is  (-i + j)/√2, and the unit vector for the direction of steepest descent is (i - j)/√2. A vector that points in the direction of no change in the function at P is (2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k.

To find the unit vectors that give the direction of steepest ascent and steepest descent at P, we need to find the gradient of F at P and normalize it to obtain a unit vector.

First, we find the partial derivatives of F with respect to x and y

Fx = -2x e^(-x^2/(16-y^2))/((16-y^2)^2)

Fy = 2y e^(-x^2/(16-y^2))/((16-y^2)^2)

Plugging in the coordinates of P, we get

Fx(2,2) = -2e^(-1/3)/49

Fy(2,2) = 2e^(-1/3)/49

Therefore, the gradient of F at P is

∇F(2,2) = (-2e^(-1/3)/49) i + (2e^(-1/3)/49) j

To obtain the unit vector in the direction of steepest ascent, we normalize the gradient

u = (∇F(2,2))/||∇F(2,2)|| = (-i + j)/√2

To obtain the unit vector in the direction of steepest descent, we take the negative of u

v = -u = (i - j)/√2

To find a vector that points in a direction of no change in the function at P, we need to find a vector orthogonal to the gradient of F at P. One way to do this is to take the cross product of the gradient with the vector k in the z-direction

w = ∇F(2,2) x k = (2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k

Therefore, the vector that points in a direction of no change in the function at P is

(2e^(-1/3)/49) i + (2e^(-1/3)/49) j + (2/7) k

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The complete equation of two squares to find the product of 22 and 18 is (22 + 18)(22 - 18) = 396

When we can interpret an expression as the difference of two perfect squares, i.e. a2-b2, we can factor it as (a+b)(a-b).

To use the difference of two squares to find the product of 22 and 18:

First, find the average of the two numbers:

(22 + 18) ÷ 2 = 20

Then, find the difference between the two numbers:

22 - 18 = 4

Now we can write:

(20 + 4)(20 - 4) = 24 × 16 = 384

But we need to add the extra 12 to get 396:

(20 + 4)(20 - 4) + 12 = 396

So the completed equation is:

(22 + 18)(22 - 18) = 396

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The integral ∫8(1-tan²(x)/sec² dx Note Use an upper-case "C" for the constant of integration is ∫8(1-tan²(x)/sec²(x)) dx = 8 tan(x) + C where C is the constant of integration.

To evaluate the integral ∫8(1-tan²(x)/sec²(x)) dx, we need to use trigonometric identities to simplify the integrand.

First, we use the identity tan²(x) + 1 = sec²(x) to rewrite the integrand as follows:

8(1 - tan²(x)/sec²(x)) = 8(sec²(x)/sec²(x) - tan²(x)/sec²(x))

Simplifying this expression by canceling out the common factor of sec²(x), we get:

8(sec²(x) - tan²(x))/sec²(x)

Next, we use the identity sec²(x) = 1 + tan²(x) to simplify the expression further:

8(sec²(x) - tan²(x))/sec²(x) = 8((1 + tan²(x)) - tan²(x))/sec²(x)

Simplifying the expression inside the parentheses, we obtain:

8/ sec²(x)

Therefore, the integral simplifies to:

∫8(1-tan²(x)/sec²(x)) dx = ∫8/ sec²(x) dx

We can now use the substitution u = cos(x) and du/dx = -sin(x) dx to transform the integral into a simpler form:

∫8/ sec²(x) dx = ∫8/cos²(x) dx = 8∫cos(x)² dx

Using the power-reducing formula cos²(x) = (1 + cos(2x))/2, we get:

8∫cos(x)² dx = 8/2 ∫(1 + cos(2x))/2 dx = 4(x + 1/2 sin(2x)) + C

Substituting back u = cos(x), we obtain:

∫8(1-tan²(x)/sec²(x)) dx = 8 tan(x) + C

where C is the constant of integration.

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Answer: I believe the answer would be 38/5x - 3

Answer:

IT depends on how many kids there are per group.

Step-by-step explanation:

1) To find the differentials of z = x^2 - xy^2 + 4y^5, we can use the total differential formula:

dz = (∂z/∂x)dx + (∂z/∂y)dy

Taking the partial derivatives of z with respect to x and y:

∂z/∂x = 2x - y^2

∂z/∂y = -2xy + 20y^4

Substituting these into the total differential formula:

dz = (2x - y^2)dx + (-2xy + 20y^4)dy

2) To find the differentials of f(x,y) = (3x-y)/(x+2y), we can again use the total differential formula:

df = (∂f/∂x)dx + (∂f/∂y)dy

Taking the partial derivatives of f with respect to x and y:

∂f/∂x = (y-3)/(x+2y)^2

∂f/∂y = (3x-2y)/(x+2y)^2

Substituting these into the total differential formula:

df = [(y-3)/(x+2y)^2]dx + [(3x-2y)/(x+2y)^2]dy

3) To find the differentials of f(x,y) = xe^x3y, we can once again use the total differential formula:

df = (∂f/∂x)dx + (∂f/∂y)dy

Taking the partial derivatives of f with respect to x and y:

∂f/∂x = e^(x3y) + 3xye^(x3y)

∂f/∂y = 3x^2e^(x3y)

Substituting these into the total differential formula:

df = (e^(x3y) + 3xye^(x3y))dx + (3x^2e^(x3y))dy

Here are the results:

1) For z = x^2 - xy^2 + 4y^5, the partial derivatives are:
∂z/∂x = 2x - y^2
∂z/∂y = -2xy + 20y^4

2) For f(x,y) = (3x-y)/(x+2y), the partial derivatives are:
∂f/∂x = (3(x+2y) - 3(3x-y))/(x+2y)^2
∂f/∂y = (-1(x+2y) + (x+2y))/(x+2y)^2

3) For f(x,y) = xe^(x^3y), the partial derivatives are:
∂f/∂x = e^(x^3y) * (1 + 3x^2y)
∂f/∂y = xe^(x^3y) * x^3

These partial derivatives represent the differentials for each respective function.

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The distance the boat travels to get to the beach is approximately 5.0 miles.

To see why, we can draw a right triangle on the coordinate plane, with one leg along the x-axis (going 3.5 miles east) and the other leg along the y-axis (going 4 miles south). The hypotenuse of this triangle is the straight distance from the marina to the beach, which is the distance the boat travels.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c^2 = a^2 + b^2

c^2 = (3.5)^2 + (4)^2

c^2 = 12.25 + 16

c^2 = 28.25

c ≈ 5.0

Therefore, the distance the boat travels to get to the beach is approximately 5.0 miles.

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The only line on the graph with a unit rate less than 2 is the horizontal line passing through y=8.

To identify the unit rates on the graph, we need to find the slope of the line connecting each pair of points. We can use the formula:

slope = (change in y) / (change in x)

For example, the slope between the first two points (7,8) and (14,16) is:

slope = (16-8) / (14-7) = 8/7

Similarly, we can find the slopes for the other pairs of points:

- between (7,8) and (21,24): slope = (24-8) / (21-7) = 16/14 = 8/7
- between (14,16) and (21,24): slope = (24-16) / (21-14) = 8/7

Notice that all three slopes are equal, which means the graph represents a line with a constant unit rate of 8/7.

To find lines with unit rates less than 2, we need to look for steeper lines on the graph. Any line with a slope greater than 2/8 (or 1/4) will have a unit rate greater than 2.

One way to see this is to note that a slope of 2/8 means that for every 2 units of increase in y, there is 8 units of increase in x. This is equivalent to saying that the unit rate is 2/8 = 1/4. If the slope is greater than 2/8, then the unit rate is greater than 1/4, and therefore greater than 2.

Looking at the graph, we can see that the steepest line has a slope of 2/3, which means it has a unit rate of 2/3. Therefore, any line with a slope greater than 2/3 will have a unit rate greater than 2, and any line with a slope less than 2/3 will have a unit rate less than 2.

To summarize:

- The graph represents a line with a constant unit rate of 8/7.
- Any line with a slope greater than 2/3 has a unit rate greater than 2.
- Any line with a slope less than 2/3 has a unit rate less than 2.

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The p-value is less than the significance level so reject the null hypothesis and concluded percentage of the students volunteer their time is different from receiving financial aid students.

Percentage of college students who volunteer their time = 20%

Perform a hypothesis test.

Null hypothesis H₀: p = 0.20,

where p is the proportion of college students who volunteer their time.

The alternative hypothesis is Hₐ: p ≠ 0.20.

Indicating that the proportion of college students who volunteer their time is different for students receiving financial aid.

57 out of 381 randomly selected students who receive financial aid volunteered their time.

Test the hypothesis,

Calculate the sample proportion of volunteers among the students receiving financial aid,

p₁ = 57 / 381

    = 0.149

Using Test statistic,

which follows a normal distribution under the null hypothesis .

Mean = 0  

Standard deviation σ = √(p(1-p)/n),

where p = 0.20 is the proportion under the null hypothesis

n = 381 is the sample size.

z

= (p₁ - p) /√(p×(1-p)/n)

= (0.149 - 0.20) / √(0.20(1-0.20)/381)

= -2.55

Using attached table of p-value from z-score.

Calculated test statistic of -2.55 corresponds to a p-value of 0.0054,

which is less than the significance level α = 0.01.

Reject the null hypothesis .

Therefore, we conclude that there is evidence to suggest that the percentage of college students who volunteer their time is different for students receiving financial aid.

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The above question is incomplete, the complete question is:

20% of all college students volunteer their time. is the percentage of college students who are volunteers different for students receiving financial aid? of the 381 randomly selected students who receive financial aid, 57 of them volunteered their time. what can be concluded at the α = 0.01 level of significance?

The average number of vehicles registered in each borough of NYC is 4.2 x 10^5.

To find the average number of vehicles registered in each borough of NYC, we need to divide the total number of registered vehicles by the number of boroughs. Therefore, the average number of vehicles registered in each borough can be calculated as:

Average number of vehicles = Total number of vehicles registered / Number of boroughs

= 2.1 x 10^6 / 5

= 4.2 x 10^5

Therefore, the average number of vehicles registered in each borough of NYC is 4.2 x 10^5.

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Answer:

y=4x+4

Step-by-step explanation:

The slope formula is:
[tex]y=mx+b[/tex]

with m being the slope and b being the y-intercept

Given: slope=4, y-intercept=4

We can substitute the slope and the y-intercept into the question:

y=4x+4

Hope this helps! :)

The equation of the line in slope-intercept form of a line with slope 4 and y-intercept 4 is [tex]\text{y} = 4\text{x} + 4[/tex].

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\text{m}=\dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]

[tex]\text{m}=\dfrac{(\text{y}\bar{\text{a}}-\text{y}\bar{\text{a}})}{(\text{x}\bar{\text{a}}-\text{x}\bar{\text{a}})}[/tex]

It is given that:

A line with slope 4 and y-intercept 4.

The linear equation in one variable can be made:

As we know,

The standard equation of the line is:

[tex]\text{y} = \text{mx} + \text{c}[/tex]

Here m is the slope and c is the y-intercept.

[tex]\text{m} = 4[/tex]

[tex]\text{c} = 4[/tex]

[tex]\boxed{\bold{y = 4x + 4}}[/tex]

Thus, the equation of the line in slope-intercept form of a line with slope 4 and y-intercept 4 is [tex]\text{y} = 4\text{x} + 4[/tex].

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When dealing with absolute value expressions, we must consider both the positive and negative values of the argument.

In this case, we are asked to simplify[tex]|x÷3| if x<0[/tex], which means that x is a negative number.

To simplify this expression, we must first evaluate x÷3, which gives us a negative number divided by a positive number, resulting in a negative quotient.

However, since we are only interested in the absolute value of this quotient, we must ignore the negative sign and write the expression as:

[tex]|x÷3| = -(x÷3)[/tex]

Note that the negative sign in front of the expression serves to cancel out the negative sign of the quotient, thus giving us a positive result.

Therefore, the simplified expression for[tex]|x÷3| if x<0 is -(x÷3)[/tex]. This expression can be used to evaluate the value of |x÷3| for any negative value of x, by simply plugging in the corresponding value for x.

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Annette's average speed was 40 mph if Annette drives her car 115 miles and has an average of a certain speed.

What is Average speed ?

Average speed is the total distance traveled divided by the total time taken to travel that distance. It is a measure of the overall speed of an object or person over a certain period of time.

Let's call Annette's original average speed "x". We can use the formula:

distance = speed x time

to set up two equations based on the given information.

For the first part of the trip:

115 = x * t1 (where t1 is the time it took Annette to travel 115 miles at speed x)

For the second part of the trip:

138 = (x + 8) * t2 (where t2 is the time it would have taken Annette to travel 138 miles at a speed of x + 8)

Since Annette traveled the same amount of time for both parts of the trip, we can set t1 equal to t2:

t1 = t2

We can solve for t1 in the first equation:

t1 = 115 : x

And we can solve for t2 in the second equation:

t2 = 138 : (x + 8)

Since t1 = t2, we can set the two expressions for t equal to each other:

115 : x = 138 : (x + 8)

Now we can solve for x:

115(x + 8) = 138x

115x + 920 = 138x

920 = 23x

x = 40

Therefore, Annette's average speed was 40 mph.

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The angle of depression from the man to the building below is approximately 39.81°.

To find the angle of depression from the man to the building below, we'll use the tangent function and the given information.

Given:
- The man is 40,000 feet away from the building horizontally.
- The man's altitude is 33,000 feet.

Step 1: Identify the opposite and adjacent sides in relation to the angle of depression.
- The opposite side is the altitude (33,000 feet).
- The adjacent side is the horizontal distance (40,000 feet).

Step 2: Use the tangent function to find the angle of depression.
tan(angle) = opposite/adjacent
tan(angle) = 33,000/40,000

Step 3: Find the inverse tangent of the ratio to get the angle.
angle = arctan(33,000/40,000)

Step 4: Calculate the angle.
angle ≈ 39.81°

The angle of depression from the man to the building below is approximately 39.81°.

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It would take Jose approximately 3232 minutes (or about 53.87 hours) to read 2020 pages at the same rate of 2.5 pages every four minutes.

To determine how long it would take Jose to read 2020  runners at the same rate of2.5  runners every four  twinkles, we can use a proportion.   Let x be the number of  twinkles it would take Jose to read 2020  runners. also, we can set up the following proportion:

2.5 pages / 4 minutes = 2020 pages / x minutes

To solve for x, we can cross-multiply and simplify:

2.5 pages * x minutes = 4 minutes * 2020 pages

2.5x = 8080

x = 8080 / 2.5

x = 3232

Therefore, it would take Jose approximately 3232 minutes  to read 2020 pages at the same rate of 2.5 pages every four minutes.

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Therefore, the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high is approximately 28.7 feet.

In order to find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high, we will use the angle of elevation and the tangent function.

1. Given the lowest angle of elevation of the sun in winter is 20 degrees, we will use this angle in our calculations.

2. Set up a right triangle with the fence as the vertical side (opposite side), the distance x as the horizontal side (adjacent side), and the angle of elevation (20 degrees) at the point where the fence meets the ground.

3. Use the tangent function to find the distance x:

tan(angle) = opposite side / adjacent side

4. Plug in the values we have:

tan(20) = 10.5 / x

5. Solve for x:

x = 10.5 / tan(20)

6. Calculate the value of x:

x ≈ 28.7 feet

Therefore, the distance x is approximately 28.7 feet.

Note: The question is incomplete. The complete question probably is: In one area, the lowest angle of elevation of the sun in winter is 20 degrees. Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.

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The length of side a is 50 if the angle ∠bac is 50° and the length of side b is 20 and side c is 35 using cosine law.

Length of side b = 20

Length of side c = 35

Angle ∠bac =  50°

To calculate the length of the side a, we need to use the cosine law. The formula is:

[tex]a^2 = b^2 + c^2 - 2bc cos(A)[/tex]

Substituting the given values in the formula, we get:

[tex]a^2 = 20^2 + 35^2 - 2(20)(35)cos(50°)[/tex]

[tex]a^{2}[/tex] = 400 + 1225 + (1400)*(0.642)

[tex]a^{2}[/tex] = 1625 + 898.8

a = [tex]\sqrt{2523.8}[/tex]

a = 50

Therefore we can conclude that the length of side a is 50 using cosine law.

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The evaluated probability that there have been 2 occurrences in ten minutes  is 0.0842, under the condition that the mean number of occurrences in ten minutes is 5.

Here we have to apply  the Poisson distribution formula. The formula is
[tex]P(X = k) = (e^{-g} * g^k) / k!,[/tex]
Here
X = number of occurrences,
k = number of occurrences we want to find the probability for,
e = Number of Euler's
g = mean number of occurrences in ten minutes.

For the given case, g = 5 since
Therefore,
P(X = 2) = (e⁻⁵ × 5²) / 2!
≈ 0.0842.

Hence,  after careful consideration the  evaluated probability that there are 2 occurrences in ten minutes is  0.0842.

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