Margie needs to know the square footage for the first floor of the condo her client wants to make an offer on. The kitchen is 10 feet by 15 feet, the living/dining combo is 20 feet by 25 feet, and the office and sunroom are each 10 feet by 10 feet. What’s the total square footage?

Answer:

Step-by-step explanation:

I think your question is lack of information, so here is my addition for it:

Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces. Calculate the probability of a defect and the expected number of defects for a 1000-unit production run in the following situations.

a,The process standard deviation is .15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

My answer:

As we know that

μ = 10

σ = 0.15

The standarlized score is the value z decrease by the mean and then divided by the standard deviation.

Z = (x- μ) / σ = [tex]\frac{9.85 -10}{0,15}[/tex] ≈-1

Z = (x- μ) / σ = [tex]\frac{10.15 -10}{0.15}[/tex] ≈1

Determine the corresponding probability using the table 1 of the appendix

P (x<9.85 or x>10.15) = P(z < -1.00 or z > 1.00) = 2P9z<-1.00) = 2*0.1587 = 0.3714

She probability of a defect and the expected number of defects for a 1000-unit production = 0.3714 *100% = 37.14%

Final answer:

The answer explains how to calculate the probability of defects in a production process with a specific mean weight using the normal distribution and standard deviations.

Explanation:

Probability

In a production process where the mean weight of items is 10 ounces, the probability of defects can be calculated using the normal distribution. For instance, in a scenario with a 10% defect rate, drawing a random sample of 100 items can help determine the number of defective items expected based on standard deviations.

Expected Number of Defects

Utilizing the 68-95-99.7 empirical rule, one can assess the number of defects in a sample of products. Additionally, standard deviations are useful in determining the probability of defects to ensure product quality and calibration needs in manufacturing processes.

Final answer:

The maximum height attained by the rocket is 134 meters.

Explanation:

To find the maximum height attained by the rocket, we can use the kinematic equation:

Final velocity squared = Initial velocity squared + 2 * acceleration * distance

First, convert the initial velocity from feet per second to meters per second. Then, plug in the values into the equation:

0² = (8.8 m/s²) * H + (288 ft/s)²

Solve for H, which represents the maximum height attained:

H = (288 ft/s)² / (2 * g)

Finally, convert the maximum height from feet to meters:

H = (288 ft/s)² / (2 * 8.8 m/s²) = 134 m

The expression that does not belong with the other three is −58+(−34) because it results in a more negative value compared to the other expressions.

The expression that does not belong with the other three is −58+(−34).

−58−34 and −34+58 are both addition expressions, while −34−58 is a subtraction expression. These three expressions involve adding or subtracting two numbers.

However, −58+(−34) is different because it involves adding a negative number to another negative number, which results in a more negative value. The other three expressions all result in a positive value.

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Answer:

Probability that at least three would be yellow = 0.556 .

Step-by-step explanation:

We are given that In Europe, 53% of flowers of the reward less orchid, Dactylorhiza sambucina are yellow.

The Binomial distribution probability is given by;

P(X = r) = [tex]\binom{n}{r}p^{r}(1-p)^{n-r}[/tex] for x = 0,1,2,3,.......

Here, n = number of trials which is 5 in our case

          r = no. of success which is at least 3 in our case

         p = probability of success which is probability of yellow flower of

                0.53 in our case

So, P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)

      = [tex]\binom{5}{3}0.53^{3}(1-0.53)^{5-3} + \binom{5}{4}0.53^{4}(1-0.53)^{5-4} + \binom{5}{5}0.53^{5}(1-0.53)^{5-5}[/tex]

      = [tex]10*0.53^{3}(0.47)^{2} + 5*0.53^{4}(0.47)^{1} + 1*0.53^{5}(0.47)^{0}[/tex]

      = 0.556

Therefore, the probability that at least three would be yellow is 0.556 .        

Answer:

17.6 feet

Step-by-step explanation:

If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot.

Let x be the distance between the building and Diana,

Tan theta = opposite / adjacent side

then tan 37 = 130/x

 [tex]tan(37)=\frac{130}{x} \\xtan(37)= 130\\x=\frac{130}{tan(37)} =172.5 feet[/tex]

Let y be  distance between the building and Diana after moving forward,

[tex]tan(40)=\frac{130}{y} \\ytan(40)= 130\\y=\frac{130}{tan(40)} =154.9 feet[/tex]

now find the distance by subtracting to find how much closer she is to the building

[tex]172.5 - 154.9 = 17.6 ft[/tex]

Answer:

[tex]2\dfrac{2}{3}[/tex] cups of flour

Step-by-step explanation:

Each batch uses 2/3 cup of flour.

If Eduardo makes 4 batches, he is going to need [tex]4X\frac{2}{3}[/tex] cups of flour.

[tex]4 X \dfrac{2}{3}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex]

Eduardo is going to need [tex]2\dfrac{2}{3}[/tex] cups of flour.

Final answer:

Eduardo will need 2 2/3 cups of flour for 4 batches.

Explanation:

To find the total cups of flour Eduardo needs for 4 batches:

Amount of flour for 1 batch: 2/3 cup

Total cups for 4 batches: (2/3 cup) x 4 = 8/3 cups = 2 2/3 cups

So, Eduardo will need 2 2/3 cups of flour for 4 batches.

Answer:

0.875

Step-by-step explanation:

This is a binomial distribution because a child can be either a boy or a girl. We denote the probability of being a boy as p and being a girl as q. Both are mutually exclusive. The questions both are equally likely. Hence, p = q = 0.5.

The event of having at least a boy is the complement of the event of having no boy. Now the probability of having no boy is the the probability of all children being girls. This is given by

[tex]P(3G) = 0.5\times0.5\times0.5 = 0.125[/tex]

Then, the probability of at least 1 boy, by the law of complements, is

[tex]P(\ge1B) = 1 - P(3G) = 1 - 0.125 = 0.875[/tex]

Answer:

The probability of having at least one is a boy = 0.875

Step-by-step explanation:

Let B represent boy and G represent Girl.

For a couple having three children with the probability of having a boy or a girl is the same, they are 8 possible outcomes which are [BBB, BBG, BGG, BGB, GGG, GGB, GBG, GBB] = 8

BBB means having a boy followed by a boy followed by a boy while BGB means having a boy followed by a girl followed by a boy.

The probability of having at least one is a boy, it can be [ BBB BBG BGG BGB GGB GBG GBB] = 7  

Probability is the ratio number of favorable outcomes to the total number of possible outcomes.

Therefore, The probability of having at least one is a boy = 7/8 = 0.875

Answer:

13) 0

Step-by-step explanation:

Answer:

#13:  0

#14:  -99

Step-by-step explanation:

#13:  g(x) = 2x^3 - 5x^2 + 4x - 1;  x = 1

Step 1:  Substitute 1 for x

2(1)^3 - 5(1)^2 + 4(1) - 1

2(1) - 5(1) + 4 - 1

2 - 5 + 4 - 1

0

Answer:  0

#14:  h(x) = x^4 + 7x^3 + x^2 - 2x - 6;  x = -3

Step 1:  Substitute -3 for x

(-3)^4 + 7(-3)^3 + (-3)^2 - 2(-3) - 6

81 + 7(-27) + 9 + 6 - 6

81 - 189 + 9 + 6 - 6

-99

Answer:  -99

Answer:

See explanation

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{2} - 5[/tex]

and

[tex]g(x) = f(x - 7)[/tex]

We substitute x-7, wherever we see x in f(x) to obtain:

[tex]g(x) = {(x - 7)}^{2} - 5[/tex]

This means g(x) is obtained by shifting f(x) 7 units to the right.

Also we can say g(x) is obtained by shifting the parent quadratic function, 7 units left and 5 units down.

You have not provided the options, but I hope this explanation helps you check the correct answers.

Answer:

Option A. 264 ft² ; 4 gallons

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

From the picture attached,

Area of the barn to be painted = Area of the (rectangular base + Triangular top) - Area of the window

Area of the rectangular base = 12 × 18

                                                = 216 ft²

Area of the triangular top = [tex]\frac{1}{2}(\text{Base}\times \text{Height})[/tex]

                                          = [tex]\frac{1}{2}(12)(28-18)[/tex]

                                          = 60 square feet

Area of the window = 3 ft × 4 ft

                                 = 12 ft²

Total area to be painted = 216 + 60 - 12

                                         = 264 ft²

∵ 70 square feet of the barn is covered by the amount of paint = 1 gallon

∴ 1 square feet will be covered by the amount = [tex]\frac{1}{70}[/tex] gallons

∴ 264 square feet will be painted by = [tex]\frac{264}{70}[/tex]

                                                             = 3.77 gallons

                                                             ≈ 4 gallons

Therefore, Option (A). 264 ft²; 4 gallons will be the answer.

Answer:

A) 264 ft2; 4 gallons

Step-by-step explanation:

Right answer on usatestprep

Answer:  The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

So, the total number of boys is:

x + 18  

Number of girls = y

Number of boys / number of girls = 5/4

(x+18) /y = 5/4

Solving for "y"

4 (x +18) =5 y

4x +72 = 5y

(4x +72) /5 = y

The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5

Answer: Lucas had $7

Step-by-step explanation:

Let x represent the amount of money that Lucas had initially.

Let y represent the weight of each type of oat that he bought.

Lucas bought a certain weight of oats for his horse at a unit price of .20 per pound. The total cost left him with one extra dollar. This means that

x - 0.2y = 1 - - - - - - - - - - - -- - 1

He wanted to buy the same weight for enriched oats instead, but at .30 per pound he was short 2 dollars. This means that

x - 0.3y = - 2- - - - - - - - - - - -- - 1

Subtracting equation 1 from equation 2, it becomes

0.1y = 3

y = 3/0.1

y = 30

Substituting y = 30 into equation 1, it becomes

x - 0.2 × 30 = 1

x - 6 = 1

x = 1 + 6

x = 7

Final answer:

By setting up equations based on the cost per pound of regular and enriched oats and the money Lucas had and was short, we deduce that Lucas wanted to buy 30 pounds of oats and he had $7 initially.

Explanation:

To solve for the amount of money Lucas had, we need to set up two separate equations based on the information given. If x is the weight of the oats in pounds and y is the total amount of money Lucas has, then:

Subtracting the first equation from the second gives us:

0.10x = 3

So, Lucas wanted to buy 30 pounds of oats. Substituting x back into either of the original equations gives us y:

Therefore, Lucas had $7 initially before making any purchase.

Answer:

[tex]\text{Unemployment rate}\approx 7.7\%[/tex]

[tex]\text{Labor force participation rate}\approx 92.9\%[/tex]

Step-by-step explanation:

We have been given that the number of employed persons equals 180 million. The number of unemployed persons equals 15 million, and the number of persons over age 16 in the population equals 210 million. We are asked to find the unemployment rate and the labor force participation rate.

[tex]\text{Unemployment rate}=\frac{\text{Number of unemployed person}}{\text{Labor force}}\times 100\%[/tex]

We know that labor force is equal to employed population plus unemployed population.

[tex]\text{Unemployment rate}=\frac{\text{15 million}}{\text{180 million + 15 million}}\times 100\%[/tex]

[tex]\text{Unemployment rate}=\frac{\text{15 million}}{\text{195 million}}\times 100\%[/tex]

[tex]\text{Unemployment rate}=0.0769230769\times 100\%[/tex]

[tex]\text{Unemployment rate}=7.69230769\%[/tex]

[tex]\text{Unemployment rate}\approx 7.7\%[/tex]

Therefore, the unemployment rate is approximately 7.7%.

[tex]\text{Labor force participation rate}=\frac{\text{Labor force}}{\text{Total eligible population}}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=\frac{\text{195 million}}{\text{210 million}}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=\frac{195}{210}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=0.9285714285714286\times 100\%[/tex]

[tex]\text{Labor force participation rate}=92.85714285714286\%[/tex]

[tex]\text{Labor force participation rate}\approx 92.9\%[/tex]

Therefore, the labor force participation rate is approximately 92.9%.

The unemployment rate is 7.69% and the labor force participation rate is 92.86%.

The unemployment rate can be calculated by dividing the number of unemployed persons by the labor force and multiplying by 100. In this case, the number of unemployed persons is 15 million and the labor force is the sum of employed and unemployed persons, which is 180 million + 15 million.

The labor force participation rate can be calculated by dividing the labor force by the total number of persons over age 16 and multiplying by 100. In this case, the total number of persons over age 16 is 210 million.

Unemployment rate: (15 million / (180 million + 15 million)) x 100 = 7.69%

Labor force participation rate: ((180 million + 15 million) / 210 million) x 100 = 92.86%

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Answer:

0, 1 , 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18

Step-By-Step Explanation:

i will go from 0 to 20:

0: 0

1: 1

2: 2

3: 3

4: 4

5: 5

6: 6

7: 7

8: 8

9: 9

10: A (10 is another 'digit')

11: B

12: 10 (12 = 1*12^1 + 0* 12^0)

13: 11 (13 = 1*12^1 + 1*12^0)

14: 12 (14 = 1*12^1 + 2*12^0)

15: 13

16: 14

17: 15

18: 16

19: 17

20: 18

Just remember to use the notation A and B after the digit nine, for example

22: 1A

23: 1B

24: 20

In other words, the answer is 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18

The first twenty counting numbers in base twelve are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, and 17.

In base twelve, the counting numbers are represented using the digits 0, 1, 2, 9, A, and B. The first twenty counting numbers in base twelve are:

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Answer:

Therefore, we have 36 different treatment groups.

Step-by-step explanation:

We know that the 7 subjects are selected from the 9 that are​ available, and the 7 selected subjects are all treated at the same​ time.

We calculate how many different treatment groups are​ possible.

We get:

[tex]C_7^9=\frac{9!}{7!(9-7)!}=\frac{9\cdot 8\cdot 7!}{7!\cdot 2\cdot 1}= 36[/tex]

Therefore, we have 36 different treatment groups.

Answer:

For this case we have the following notation:

y= the number of minutes that you read

x = the number of minutes that your brother read

And we have that you decide to read 30 minutes longer than your brother, so the equation would be:

y = x+30

And for the other part of the question if x =15 we got:

y = 15+30 = 45

Step-by-step explanation:

Assuming this complete question: "You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes.

How many minutes will you read if your brother reads for 15 minutes?"

Solution to the problem

For this case we have the following notation:

y= the number of minutes that you read

x = the number of minutes that your brother read

And we have that you decide to read 30 minutes longer than your brother, so the equation would be:

y = x+30

And for the other part of the question if x =15 we got:

y = 15+30 = 45

Answer:

The answer to your question is Perimeter = 24.1 u

Step-by-step explanation:

Data

F (-4, 5)

G (1, 10)

H (-9, 10)

Process

1.- Calculate the distance from FG

dFG = [tex]\sqrt{(1 + 4)^{2} + (10 - 5)^{2}}[/tex]

dFG = [tex]\sqrt{5^{2} + 5^{2}}[/tex]

dFG = [tex]\sqrt{25 + 25}[/tex]

dFG = [tex]\sqrt{50}[/tex]

dFG = [tex]5\sqrt{2}[/tex] = 7.07

2.- Calculate the distance from GH

dGH = [tex]\sqrt{(-9 - 1)^{2} + (10 - 10)^{2}}[/tex]

dGH = [tex]\sqrt{10^{2} + 0^{2}}[/tex]

dGH = [tex]\sqrt{100}[/tex]

dGH = 10

3.- Calculate the distance from FH

dFH = [tex]\sqrt{(-9 + 4)^{2} + ( 10 - 5)^{2}}[/tex]

dFH = [tex]\sqrt{-5^{2}+ 5^{2}}[/tex]

dFH = [tex]\sqrt{25 + 25}[/tex]

dFH = [tex]\sqrt{50}[/tex]

dFH = [tex]5\sqrt{2}[/tex] = 7.07

4.- Calculate the perimeter

Perimeter = 7.07 + 10 + 7.07

                 = 24.1 units

The computer algorithm executes twice as many operations when the input size increases by 1. By using this information and calculating the operations for each input size, we find that it executes 26,624 operations for an input size of 26.

To find out how many operations the computer algorithm executes when it is run with an input of size 26, we can use the given information. The algorithm executes twice as many operations when the input size increases by 1. So, if it executes 7 operations for an input size of 1, it would execute 14 operations for an input size of 2, 28 operations for an input size of 3, and so on.

Since the algorithm executes twice as many operations for each increase in input size, we can see that it follows a pattern of doubling. We can calculate the number of operations for an input size of 26 by doubling the number of operations for an input size of 25. Continuing this calculation, we get:

Input Size 1: 7 operations
Input Size 2: 14 operations
Input Size 3: 28 operations
...

Input Size 25: 13,312 operations
Input Size 26: 26,624 operations

Answer:

2115751

Step-by-step explanation:

Solution:

- The number of 5 letter words that contain x is the number of 5 letter words overall minus the number of 5 letter of words without x.

                  How many 5 letter words are there overall?

- The first letter could be one of 26 letters. The same could be said about the second letter, and the third, and the fourth and the fifth .. so on.

- So the number of 5 letter words overall is:

                        26x26x26x26x26 = 26^5 = 11881376

          How many 5 letter words are there that do not contain x?

- The first letter could be one of 25 letters (it could be one of any of the other 25 letters but not x). The second letter could also be one of 25 letters, and so could the third, and so could the fourth, and so could the fifth.

- So the number of 5 letter words that do not contain x is:

                        25x25x25x25x25 = 25^5 = 9765625

- So the number of 5 letter words that contain x is:

                      26^5 - 25^5 = 11881376 - 9765625 = 2115751.

Answer:

y = -2x + 4

Step-by-step explanation:

Slope: -2

Intercept: +4

Answer:

Option (c)

Chuy will save more than he needs and will meet his goal in less than 27 week.

Step-by-step explanation:

Given that, Chuy wants to buy a new television. The television cost is $1,350.

He decides to save the same amount of money each week.

After 8 weeks he saved $440.

Each week he saved [tex]=\$\frac{440}{8}[/tex]

                                 =$ 55

If he saved $55 each week.

At the end of 27 week he will save = $(27×55)

                                                          =$1485

Therefore he will save $1485 at the end of 27th week.

The saved money is more than the cost price of the television.

Therefore Chuy will meet his goal in less than 27 weeks.

Answer:

the awnser is the 27 week one

Step-by-step explanation:

Answer:

Therefore, the probability is P=0.000142.

Step-by-step explanation:

We have a weighted coin which lands on Heads with probability 0.17. You decide to toss it 5 times.

We calculate the  probability that the total number of times the coin lands on Heads. We get:

[tex]P=0.17^5\\\\P=0.000142[/tex]

Therefore, the probability is P=0.000142.

The answer involves using the binomial distribution to calculate the probabilities of getting different numbers of heads when tossing a weighted coin five times. The outcome of interest is the sum of probabilities of getting 0, 1, or 4 heads, as these are not prime numbers, unlike 2, 3, and 5.

The probability of a weighted coin landing on heads is given as 0.17. When tossing this coin 5 times, there are several outcomes, but we're interested in the probability that the total number of heads is not a prime number. To address the question, we need to calculate the binomial probabilities for obtaining 0, 1, 2, 3, 4, or 5 heads, since these cover all possible outcomes.

Then, we need to identify which of these are prime numbers, and which are not. Prime numbers within our range are 2, 3, and 5. Therefore, we want the probabilities of getting 0, 1, or 4 heads. These probabilities can be computed using the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where 'n' is the number of trials, 'k' is the number of successes (heads in this case), 'p' is the probability of getting a head on a single toss, and 'n choose k' is the binomial coefficient.

The probability of getting a total number of heads that is not a prime number is the sum of the probabilities of getting 0, 1, or 4 heads.

The length of the segment is 6.63 inches

Explanation:

Given that the radius of the circle is 12 inches.

The center of the circle to the endpoint and the midpoint of the chord forms a right angled triangle.

The hypotenuse is 12 inches.

One of the sides is [tex]\frac{20}{2}=10[/tex]

Applying the Pythagorean theorem, we have,

[tex]a^2+b^2=c^2[/tex]

Where [tex]a=x, b=10[/tex] and [tex]c=12[/tex]

Thus, we have,

[tex]x^{2} +10^2=12^2[/tex]

Simplifying, we get,

[tex]x^{2} =144-100[/tex]

[tex]x^{2} =44[/tex]

Taking square root on both sides of the equation, we have,

[tex]x=6.63[/tex]

Thus, the length of the line segment is 6.63 inches.

Answer:

The only x-intercept is x = 1

Step-by-step explanation:

The equation is:

[tex]r(x)=\frac{x-1}{x+4}[/tex]

We can substitute y for r(x), to write in the notation:

[tex]r(x)=\frac{x-1}{x+4}\\y=\frac{x-1}{x+4}[/tex]

To get y-intercept, we put x = 0

and

To get x-intercept, we put y =0

We want to find x-intercepts here, so we substitute 0 into y and solve for x. Shown below:

[tex]y=\frac{x-1}{x+4}\\0=\frac{x-1}{x+4}\\0(x+4)=x-1\\0=x-1\\x=1[/tex]

The only x-intercept is x = 1

Answer:

The probability of selecting a  person which is  self-employed but not married equals 1/8.

Step-by-step explanation:

Here, the given survey says:

Total number of people surveyed = 248

Number of people married = 156

The number of people are self employed = 70

Now, 25% of people who are married are SELF EMPLOYED.

Now, calculating 25% of 156 , we get:

[tex]\frac{25}{100} \times 156 = 39[/tex]

⇒ out of total 156 married people, 39 are self employed.

So, number of  self employed people but  not married

= Self employed people - Self employed people PLUS  married

=  70  -  39   =  31.

So, the probability that the person selected will be self-employed but not married = [tex]\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}[/tex] =  [tex]\frac{31}{248} = \frac{1}{8}[/tex]

Hence The probability of selecting a  person which is  self-employed but not married equals 1/8.

Answer:the mode is b

Step-by-step explanation:

B

Answer: 31

Step-by-step explanation:

the mode is the number that appears the most, in that case it would be 31. i also just did this in a quiz 2 seconds ago and was right.

Answer:

(a) [tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]

(b) 25,000

(c) 4.3068 min.

Step-by-step explanation:

Rate of change in the number of bacteria is proportional to the number present.

Let N is the population of bacteria.

[tex]\frac{dN}{dt}[/tex] ∝ N ⇒ [tex]\frac{dN}{dt}=kt[/tex] { k = proportionality constant}

initial population No. = 10,000

                          [tex]N(t_{1} )[/tex] = 20,000

         and [tex]N(t_{1}+10 )=100,000[/tex]

(a) For population growth

[tex]N(t)=N_{0}e^{kt}=10000e^{kt}[/tex]

[tex]N(t_1)=10,000e^{kt_1}=20,000[/tex]

[tex]e^{kt}=2[/tex]

[tex]ln(e^{kt_1})=ln(2)[/tex]

[tex]kt_1=ln(2)[/tex]

[tex]t_{1}=\frac{ln2}{k}[/tex] ----------(1)

[tex]N(t_1+t_{10})=100,000[/tex]

[tex]100,000=10,000e^{k(t_1+10)}[/tex]

[tex]10=e^{k(t_1+10)}[/tex]

[tex]ln10=ln[e^{k(t_1+10)}][/tex]

[tex]k(t_1+10)=ln10[/tex]

[tex]k(t_1)=ln10-10k[/tex]

[tex]t_1=\frac{ln10-10k}{k}[/tex] ----------(2)

from equation (1) and (2)

[tex]\frac{ln_2}{k}=\frac{ln10-10k}{k}[/tex]

[tex]ln10-ln2=10k[/tex]

[tex]k=\frac{ln5}{10}[/tex]

so expression will be

[tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]

(b) for t = 20

    [tex]N_{(20)}=10,000e\frac{ln5}{10}\times 20[/tex]

             =  [tex]10,000\times e^{2ln5}[/tex]

            = 10,000 × 25

            = 25,000

(c) Since [tex]t_1=\frac{ln2}{k}[/tex]   [from equation (1)]

                  [tex]=\frac{ln2}{\frac{ln5}{10} }[/tex]

                  [tex]=\frac{ln2}{ln5}\times 10[/tex]

                  = 4.3068

                 = 4.3068 min.

The interest expense for West Company in Year 1 is approximately $1,141, calculated using the principal of $38,000, the annual interest rate of 9%, and the time from the loan date to the end of Year 1, which is ⅓ of a year.

The student's question involves calculating the amount of interest expense to be reported on the income statement for West Company in Year 1, given that the company borrowed $38,000 on September 1, Year 1 at an annual interest rate of 9% with an 18-month term. To calculate the interest expense for Year 1, we need to consider the amount of time from the loan initiation date (September 1, Year 1) to the end of Year 1 (December 31, Year 1), which is 4 months or ⅓ of a year.

Interest Expense calculation:

Interest Expense = Principal Amount × Annual Interest Rate × Time in Years

Interest Expense for West's Year 1 = $38,000 × 9% × (⅓)

Interest Expense for West's Year 1 = $38,000 × 0.09 × 0.3333

Interest Expense for West's Year 1 = $1,141 (approximately)

Therefore, the interest expense appearing on West's Year 1 income statement would be approximately $1,141.

First problem: let [tex]b[/tex] and [tex]h[/tex] be the base and height of the rectangle, respectively. We know that [tex]b=11+h[/tex] (the base if 11 longer than the height), and that [tex]2(b+h)=58[/tex] (the perimeter is 58 centimeters).

So, we have the system

[tex]\begin{cases}b=11+h\\2(b+h)=58\end{cases}\iff\begin{cases}b=11+h\\b+h=29\end{cases}[/tex]

Use the first equation to substitute into the second:

[tex]b+h=11+h+h=2h+11=29 \iff 2h=18 \iff h=9[/tex]

And since the base is 11 centimeters longer, we have

[tex]b=11+h=11+9=20[/tex]

Second problem: Let [tex]m,n,o[/tex] be the number of cards owned by Mark, Norm and Oscar, respectively. We know that:

[tex]m+n+o=810[/tex] (they have 810 cards in total)

[tex]n=m+30[/tex] (Norm has 30 more than Mark)

[tex]o=2m[/tex] (Oscar has twice as much as Mark)

The second and third equation express [tex]n[/tex] and [tex]o[/tex] in terms of [tex]m[/tex], and substituting those expressions in the first equation we have

[tex]m+n+o=m+(m+30)+2m=810 \iff 4m+30=810 \iff 4m=780 \iff m=195[/tex]

And then we can use again the second and third equations:

[tex]n=m+30=195+30=225[/tex]

[tex]o=2m=2\cdot 195=390[/tex]