He takes a random sample of 49 recent charterholders and computes a mean salary of $172,000 with a standard deviation of $35,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.

Answer:

The distance between the cars is increasing at a rate of 65miles/hour

Step-by-step explanation: Please see the attachments below

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 4.75  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4.75  

Step-by-step explanation:

We are given that 260 people are randomly chosen at a shopping mall to taste-test a new brand of fruit drink. The results of the survey reveal that the average rating is 5.22 with a standard deviation of 2.31.

The marketing division of the fruit drink distributor is only interested in selling this drink if the true mean rating is more than 4.75.

Let [tex]\mu[/tex] = true mean rating.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 4.75  

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 4.75  

Here, null hypothesis states that the true mean rating is less than or equal to 4.75.

On the other hand, alternate hypothesis states that the true mean rating is more than 4.75.

Also, The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

                                T.S.  = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

Hence, the alternative hypothesis for testing whether the fruit drink distributor should sell this drink is  [tex]\mu[/tex] > 4.75.

The appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).

The appropriate domain for this situation can be determined by considering the values that the independent variable, t, can take in the given function. In this case, the function is h(t) = -16t^2 + 24t, where t represents the time since the ball was thrown.

Since time cannot be negative in this context, the domain of the function is t ≥ 0. This means that the appropriate domain for this situation is all non-negative real numbers or the interval [0, ∞).

Answer:

700 nanometers

Step-by-step explanation:

8 wavelengths had a combined length of 5,600 nanometers.

We want to find the wavelength (in nm) of 1 of those wavelengths.

We will assume all of them are same wavelength. So, we can basically divide the total of 8 wavelengths by 8 to get 1 wavelength. Thus:

5600/8 = 700

Hence,

1 wavelength distance is 700 nanometers (or 700 nm)

Answer:

The four in the hundreds place on the right is bigger because it is a whole number and the 4 behind the decimal on the left is smaller because it is a decimal.

Step-by-step explanation:

To find the length of the sides of squares cut from a piece of tin to create an open box, we use the dimensions of the tin and the area of the box's base to set up and solve a quadratic equation.

The student is asking for the length of the sides of the squares that are cut out from a piece of tin to create an open box. Given that the tin measures 30 cm by 70 cm, and the area of the base of the resulting box is 1536 cm2, we can set up an equation to solve for the side length of the squares.

Let's denote the side length of the squares as x. After the squares are cut out, the length and width of the base of the box will be (70 - 2x) and (30 - 2x) respectively. The area of the base is given by:

Area = length × width
1536 cm2 = (70 - 2x)(30 - 2x)

By expanding this and solving the quadratic equation for x, we can find the length of the sides of the squares cut from each corner of the tin.

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Answer:

DOGS is a parallelogram.

Step-by-step explanation:

Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4),  G(5, 6), and S(4,3).

To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:

Using the Distance Formula

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For D(1, 1) and O(2, 4)

[tex]|DO|=\sqrt{(2-1)^2+(4-1)^2}=\sqrt{1^2+3^2}=\sqrt{10} \:Units[/tex]

For G(5, 6), and S(4,3).

[tex]|GS|=\sqrt{(4-5)^2+(3-6)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{10}\:Units[/tex]

For O(2, 4) and G(5, 6)

[tex]|OG|=\sqrt{(5-2)^2+(6-4)^2}=\sqrt{(3)^2+(2)^2}=\sqrt{13}\:Units[/tex]

For S(4,3) and D(1, 1)

[tex]|SD|=\sqrt{(1-4)^2+(1-3)^2}=\sqrt{(-3)^2+(-2)^2}=\sqrt{13}\:Units[/tex]

Since:

Then, quadrilateral DOGS is a parallelogram.

The correct answer is c. 132 oz. To convert the cat's weight of 8 1÷4 pounds to ounces, multiply by 16.

Converting Pounds to Ounces

The cat weighs 8 1/4 pounds. To find out how many ounces this is, we need to convert pounds to ounces. We know from the conversion rate that 1 pound equals 16 ounces.

Step-by-Step Calculation

Thus, the cat weighs 132 ounces, so the correct answer is c. 132 oz.

The exponential equation that represents the growth of the bacteria over time, considering the given initial and future population sizes and the time that has passed, is P(t) = 360 × e^[(ln(1000/360)/15)t]. This formula adjusts the rate of growth to match the change from 360 bacteria to 1000 bacteria over a 15-minute period.

In this situation, we are dealing with a phenomenon commonly seen in biology called exponential growth which can be modeled mathematically. For this case, we can use the exponential growth formula, P(t) = P_0 × e^(rt), where P(t) is the future population size, P_0 is the initial population size, r is the growth rate, and t is the time that has passed.

Firstly, we know the initial population size (P_0) is 360 bacteria. The population size after 15 minutes (from 5 minutes to 20 minutes is 15 minutes) is 1000 bacteria. Therefore, if we plug in these values, we have 1000 = 360 × e^(15r).

To solve for r, we start by dividing both sides by 360 which results in 1000/360 = e^(15r). Taking the natural logarithm (ln) of both sides to isolate the exponential part, we get ln(1000/360) = 15r. Finally, divide by 15 yielding r = ln(1000/360)/15.

Therefore, the exponential equation representing this scenario is P(t) = 360 × e^[(ln(1000/360)/15)t], showing the population P(t) of the bacteria at any time t.

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Answer:68688

Step-by-step explanation:123 Thats EZ

The income remaining after taxes from last year is $68,688.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

To calculate the amount of income remaining after taxes, we need to subtract the total taxes paid from the gross income.

The total tax rate is the sum of the federal tax rate, FICA tax rate, and state tax rate.

Total tax rate = Federal tax rate + FICA tax rate + State tax rate

Total tax rate = 16.3% + 7.65% + 4.5%

Total tax rate = 28.45%

So the total amount of taxes paid is:

Total taxes = Gross income x Total tax rate

Total taxes = $96,000 x 28.45%

Total taxes = $27,312

To find the income remaining after taxes, we subtract the total taxes paid from the gross income:

Income after taxes = Gross income - Total taxes

Income after taxes = $96,000 - $27,312

Income after taxes = $68,688

Therefore, the income remaining after taxes from last year is $68,688.

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Answer:

12  29 /48  in mixed number form,

≈ 12.6 as a rounded decimal

Step-by-step explanation:

Multiply all three numbers together for the volume.

Answer:: D(t)= 50(4/5)^t

Step-by-step explanation: If 1/5 of the temperature difference is lost each minute, that means 4/5 of the difference remains each minute. So each minute, the temperature difference is multiplied by a factor of 4/5 (or 0.8).

If we start with the initial temperature difference, 50° Celsius, and keep multiplying by 4/5, this function gives us the temperature difference t minutes after the cake was put in the cooler.

Answer:

See answer below

Step-by-step explanation:

Hi there,

The prompt is trying to showcase exponential functions, and specifically exponential decay, where over the course of the independent variable (time in this example) the dependent variable (temp difference) exponentially drops.

To start, when a math prompt says something like "at the moment xyz begins" it usually means time zero. Thus, we have 1 point already, the y-intercept:

[tex]D(0)= 50 \ C[/tex]°

Now, we notice that it says it "loses 1/5 of its original value every minute" which is code for exp. decay.  So, to account for this, the remaining value is just b = 1 - 0.2 = 0.8.

Exponential Decay formula:

[tex]f(x) = a (1-r)^x[/tex]  where a is a constant, and constant r [tex]< 1[/tex]

[tex]D(t) = 50 * (0.8)^t \ C[/tex]°    where t is in minutes

thanks,

Answer:

[tex]H_o:\mu\geq 430\\\\H_a:\mu<430[/tex]

Step-by-step explanation:

-let [tex]\mu[/tex] denote the population mean in grams.

-The claim under investigation is that the machine is underfilling the bags.

-The investigator intends to determine whether or not the population mean is less than 430 grams.

#The stated hypotheses are:

The null hypothesis(mean gram of the bags is greater or equal to 430g):

[tex]H_o:\mu\geq 430\\\\[/tex]

-Alternative hypothesis is the population mean is less than 430g:

[tex]H_a:\mu<430[/tex]

Answer:

t = $4400 +/- $450

mean = $4400

standard deviation = $450

Step-by-step explanation:

Given;

Base salary b = $2000

Sales s = $8000 +/- $1500

Commission c = 30% sales = 0.3 × s

Total Salary t = base salary + commission = b + c

Commission c = 0.3×s = 0.3×($8000 +/-$1500)

c = $2400 +/- $450

Total salary t = b + c

Substituting the values;

t = $2000 + ($2400 +/- $450)

t = $4400 +/- $450

mean = $4400

standard deviation = $450

Answer:

The z statistic for this sample is -2.04.

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 7.44[/tex]

The alternate hypotesis is:

[tex]H_{1} \neq 7.44[/tex]

The z-statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the population mean(the hypothesis tested), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem:

[tex]X = 3.9, \mu = 7.44, \sigma = 10.98, n = 40[/tex]. So

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{3.9 - 7.44}{\frac{10.98}{\sqrt{40}}}[/tex]

[tex]z = -2.04[/tex]

The z statistic for this sample is -2.04.

Final answer:

Fitting a polynomial regression model involves determining coefficients that minimize the sum of squared differences between observed and predicted values. After plotting the data, the cubic model is fitted using statistical software. The coefficients, r-squared, and standard error of the estimate are then calculated to assess the model's accuracy.

Explanation:

The process of fitting a polynomial regression model involves finding the coefficients that minimize the sum of the squares of the differences between the observed values and the values predicted by the model. For a cubic equation, we will be fitting a model in the form y = a + bx + cx2 + dx3, where a, b, c, and d are the coefficients that need to be determined from the data.

To fit a cubic equation to the data and assess the goodness-of-fit, we usually perform the following steps:

The calculation of r2 (r-squared) is important because it tells us the strength of the relationship between the independent and dependent variables. An r2 value of 0.72, for instance, would indicate that 72% of the variability in the dependent variable can be explained by the model. The r2 value cannot be negative because it represents the proportion of variance explained, which is inherently non-negative.

Coefficient of determination is the square of the correlation coefficient (r), and since the correlation coefficient ranges between -1 and +1, its square will always be non-negative as well.

Answer:

-1r

Step-by-step explanation:

The value for the expression -10r + 9r is -1r.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

-10r+9r

Now, perform operations to solve

=-10 r + 9r

= r( -10 + 9)

Using properties of integers

(-) x (+ )= -

So,

= r( -1)

= -1r

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Answer:

The number of false positives is 108. The right answer is A

Step-by-step explanation:

According to the given data we have the following:

probability of negative results which are correcly identified =0.7

probability of negative results which are wrongly identified =1-0.7 =0.3

hence, probability of negative result = 1-0.1 =0.9

Therefore, in order to calculate the number of false positives we would have to use the following formula:

false positives =total number * probability of negative results which are wrongly identified * probability of negative result=400 * 0.9*(1-0.7) = 108

false positives = 400 * 0.9*(1-0.7)

false positives = 108

The number of false positives is 108

Answer:

24 Outcomes

Step-by-step explanation:

The sample space of an event is the set of all possible outcomes.

A jar contains 6 marbles numbered 1 through 6

Sample Space of Selecting a Marble from the Jar =6

A standard deck contains 4 Suits

Sample Space of Selecting a Card and Observing the Suit = 4

Theorem(The Fundamental Counting Principle)

If there are “x” ways for one event to happen, and “y” ways for a second event to happen, then there are “x * y” ways for both events to happen.

Therefore the Sample Space of randomly selecting a marble from the jar, observing the number drawn, and then randomly selecting a card from a standard deck and observing the suit of the card is given as:

Sample Space of Selecting a Marble X  Sample Space of Selecting a Card and observing the Suits

= 6 X 4

=24

There are 24 Outcomes in this experiment.

Answer:

8,20,32,44,56,68,80,92,104,116,128

Step-by-step explanation

Just keep adding 12

Answer: 620

Step-by-step explanation:

This is a progression but we need to find out whether it is Arithmetic Progression or an exponential or geometric progression.

From the quest, 8, 20, 32, 44, this is not an exponential function but an arithmetic progression because, when you subtract the first time from the second term , the common difference is 12.

20 - 8 = 12, so this is an arithmetic progression as said earlier. Now to find the sum of the first ten terms of the series, we apply the formula which is

S10 = n/2{(2a + ( n - 1 )d}, where n = 10, and a = 8 the first term and d the common difference = 12.. Now substitute for the values

S10 = 10/2{(2 x 8 + ( 10 - 1 )12}

= 5( 16 + 9 x 12)

= 5( 16 + 108 )

= 5( 124 )

= 620.

Therefore, the sum of the 10 terms of the series is 620.

But we can also solve it using other means . To solve this we first find the last term which is the 10th term using this formula

T10 = a + ( n - 1 )d

= 8 + (10 -1)12

= 8 + 9 x 12

= 8 + 108

= 116.

Now with this we could put this in the equation below.

S10 = n/2( a + L ) where L is the last term calculated above. Now we substitute to get the sum.

S10 = 10/2( 8 + 116)

= 5( 8 + 116 )

= 5( 124)

= 620.

I could have explained how we arrived at the formula above but the time could not permit, I will discuss that in the next lecture if I come across such question.

Answer:

The temperature that separates the lowest​ 59.5% of temperatures from the​ rest is 83.66 degrees Fahrenheit.

Step-by-step explanation:

Mean temperature = u = 77.9

Standard Deviation = [tex]\sigma[/tex] = 2.4

Since the distribution is normal and we have the value of population standard deviation, we will use the concept of z-score to find the desired value.

We have to find the value that separates lowest 59.5% of the temperature from the rest. This means our desired value is above 59.5% of the data values.

From the z-table we can find a z-score which is above 59.5% of the values and then convert it to its equivalent temperature using the formula.

From the z-table, the z-score which is above 59.5% of the value is:

z = 0.24

The formula for z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the values we have:

[tex]0.24=\frac{x-77.9}{2.4}\\\\ 5.76=x-77.9\\\\ x=83.66[/tex]

This is our data value equivalent to a z-score of 0.24. Just like 59.5% of z values were below 0.24, in the same manner, 59.5% of temperatures are below 83.66 degrees Fahrenheit.

Therefore, the temperature that separates the lowest​ 59.5% of temperatures from the​ rest is 83.66 degrees Fahrenheit.

Increasing the sample size in a statistical analysis, from n=3 to n=16, will likely lead to a decrease in the width of the confidence interval, making it more precise. Therefore, the most likely confidence interval after the change would be option C, 67.5 to 72.5.

In statistics, increasing the sample size reduces the standard error of the mean. The standard error defines the width of the confidence interval for a given sample size. If we increase the sample size from n=3 to n=16, the standard error and thus the width of the confidence interval will likely decrease, assuming all else stays the same. Hence, the confidence interval will be more precise.

Considering the given options, option C, a confidence interval of 67.5 to 72.5, represents a narrower interval and is therefore the most likely result after increasing the sample size from n=3 to n=16.

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Answer:

a)[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]\bar X = 112.75[/tex]

[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

[tex] s^2 = 540.5[/tex]

b) [tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]

And if we replace we got:

[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]

Step-by-step explanation:

Part a

For this case we have the following data: 111 113 145 105 90 100 150 88

We can calculate the mean with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X = 112.75[/tex]

And the sample variance can be calculated with this formula:

[tex]s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

And replacing we got:

[tex] s^2 = 540.5[/tex]

Part b

For this case we want to check is the true mean is equal to 102 or no, the t statistic is given by:

[tex] t = \frac{\bar X -\mu}{\frac{s}{\sqrt{n}}}[/tex]

And if we replace we got:

[tex] t = \frac{112.75-112}{\frac{23.249}{\sqrt{8}}}= 0.0912[/tex]

To answer the student's question, the sample mean of electrical energy usage is calculated to be 112.75 kwH. The sample variance requires computing the squared differences of each data point from the mean, summing them up and dividing by n-1. The t-statistic can then be calculated using the historical mean, the sample mean, and the sample standard deviation.

To calculate the mean of the sample data, we sum all the sample values and divide by the number of observations. The sample data for electrical energy usage in kwH per month are: 111, 113, 145, 105, 90, 100, 150, and 88. The sum of these values is 902 kwH, and with 8 residents in the sample, the mean (μ) is 902 kwH / 8 = 112.75 kwH.

The sample variance (s²) is calculated by taking the sum of squared differences from the mean and dividing by the sample size minus one. First, we find the squared differences for each data point: (111-112.75)², (113-112.75)², (145-112.75)², (105-112.75)², (90-112.75)², (100-112.75)², (150-112.75)², and (88-112.75)², which then summed up give us the total sum of squares. Dividing this total by 7 (n-1), we obtain the sample variance.

For the t statistic, we would need the hypothesized population mean to compare our sample mean against. However, we can calculate the t-value if we assume the historical mean provided (102 kwH) is the population mean we are testing against. The t-statistic is calculated using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(n)). In this scenario, n=8 and we would need the sample standard deviation, which is the square root of the variance we calculated earlier. Once these values are obtained, the t-statistic can be computed.

Answer:

LMN is not a right triangle.

Step-by-step explanation:

To verify that the lengths of a triangle for a right triangle, all we need to do is to check it they satisfy the Pythagoras Theorem.

Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

The Hypotenuse is always the longest side.

Since no angle is given, the two other sides can be alternated.

Given lengths of triangle LMN: 18.5 inches, 10, inches, and 15.5 inches

[tex]LHS=18.5^2=342.25\\RHS=10^2+15.5^2=100+240.25=340.25\\Since \: LHS\neq RHS,\\$The triangle is not a right triangle.[/tex]

Answer:

Step-by-step explanation:

A:  8

B:  15

C:  40

(A) The rides in 5 minutes are 8, (B) the time to cover 24 blocks is 15 minutes, and (C) in 25 minutes Jose rides 40 blocks.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

Jose rides his bicycle for 5 minutes to travel 8 blocks

Speed = distance cover / time taken

Speed = 8/5

Now, at the same speed

A) Distance covered in 5 minutes

8/5 = Distance/5 ⇒ Distance = 8 blocks.

B) Time taken in 24 blocks

8/5 = 24/Time ⇒ Time = 15 minutes.

C) Distance covered in 25 minutes

8/5 = Distance/25 ⇒ Distance = 40 blocks.

Hence "The rides in 5 minutes are 8, the time to cover 24 blocks is 15 minutes and in 25 minutes Jose rides 40 blocks".

Options are missing in the given question

Correct options are in the table and ask the same question as answered.

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The equivalent expression to log(2) - log(6) is D. log(1/3), since subtraction in logarithms indicates division, making the expression log(2/6) which simplifies to log(1/3).

The question asks which expressions are equivalent to log(2) - log(6). According to the properties of logarithms, the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log a - log b = log(a/b)). Therefore, log(2) - log(6) = log(2/6) = log(1/3).

Hence, the only equivalent expression from the given options is D. log(1/3). Option A is incorrect because log(2) + log(1/6) would imply multiplication, not division. Option B is just log(2) without subtraction. Option C, log(3), does not represent the given difference.

Answer:

[tex]y = 0.6215x[/tex]

Step-by-step explanation:

I am going to model an equation in the following format:

[tex]y = ax[/tex]

In which y is the number of miles, given the distance in kilometers x.

a is the slope, that is, how many miles each kilometer has.

5 kilometers is about 3.1075 miles.

So

5 km - 3.1075 miles

1 km - a miles

5a = 3.1075

a = 3.1075/5

a = 0.6215

So

[tex]y = 0.6215x[/tex]

Answer:

a and c

Step-by-step explanation:

The statements that are true are:

The area of the base of the pyramid, B, is 48 in.2

A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid.

The volume of the pyramid is 384 in.3

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

The area of the base of the pyramid is given by B = (1/2)bh, where b is the length of the base and h is the height of the pyramid.

We are not given the height of the pyramid, so we cannot determine the area of the base.

Therefore, the statement "The area of the base of the pyramid, B, is 64 in.2" is not true.

The area of the base of the pyramid is given as 48 in.2 in the problem statement. Therefore, the statement "

The area of the base of the pyramid, B, is 48 in.2" is true.

The volume of a square prism with dimensions 8 inches by 8 inches by 6 inches is V = lwh = 8 x 8 x 6 = 384 in.3.

The volume of the pyramid is also given as 384 in.3 in the problem statement.

Therefore, the statement "A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid" is true.

The correct statement is "A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume one-third the volume of this pyramid."

This statement is not true, since the volume of the pyramid is 384 in.3 and one-third of that volume is 128 in.3, which is not the volume of the prism given in the problem. Therefore, the statement is false.

Thus,

The statements that are true are:

The area of the base of the pyramid, B, is 48 in.2

A square prism with dimensions 8 inches by 8 inches by 6 inches will have a volume three times as large as this pyramid.

The volume of the pyramid is 384 in.3

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Answer:

a-area-22

a-perimeter-19

b-area-98

b-perimeter-42

Step-by-step explanation:

for the sides just add the numbers 2x

for the area multiply the numbers

hope this helps