help plz its about proportionality

We're given:

To find the area of the garden alone, we can subtract the area of the garden from the combined area of the garden and walkway:

\(4.5(8x + 4)-4(5.5x + 1.5)\)

Open up the parentheses:

\(= 36x +18 -22x - 6\)

Combine like terms:

\(= 36x +18 -22x - 6\\= 14x +18 - 6\\= 14x +12\)

The area of the walkway around the garden is 14x + 12.

Mr. Morgan has to pay a state tax of $ 38.4 in a biweekly basis on his $42000 yearly income.

State income taxes are a proportion of your income that you pay to the state government based on how much money you earn from your work, and they vary from state to state.

Tax exemption is the reduction or elimination of a requirement to make a required payment that would otherwise be imposed on individuals, properties, income, or transactions by a ruling power. Tax-exempt status might offer full tax exemption, reduced rates, or tax on only some things.

The more children you have, the more taxes you pay since children are exemptions or deductions on tax forms. Some non-profit organizations are tax-exempt, which means they don't have to pay any taxes. People are also exempt from participating in certain vocations and battles. You are excused if you have an exemption.

Personal Exemption is non taxable = $ 3600

Total income = $ 42000 yearly

Total taxable income = 42000 - 3600 = $ 38400

Total tax yearly = 2.6 % of 38400 = (2.6/100)*38400 = $ 998.4

Total tax generated biweekly is = (998.4/52)*2 = $ 38.4

Mr. Morgan has to pay a state tax of $ 38.4 in a biweekly basis on his $42000 yearly income.

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There are 15,504 possible 5 dip sundaes that can be made from the 20 flavors of ice cream available at the store.

To find the number of 5 dip sundaes that are possible if order is not considered and no flavor is repeated, we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of flavors (20 in this case), and r is the number of dips in the sundae (5 in this case).

So the number of 5 dip sundaes that are possible is:

20C5 = 20! / 5!(20-5)! = (20 x 19 x 18 x 17 x 16) / (5 x 4 x 3 x 2 x 1) = 15,504

Therefore, there are 15,504 possible 5 dip sundaes that can be made from the 20 flavors of ice cream available at the store.

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Answer:

-495

Step-by-step explanation:

-360-135= -495

Answer:

98

Step-by-step explanation:

the exterior angle is equal to the sum of the opposite interior angles

-Sumin <3

Answer:

98

Step-by-step explanation:

53+45+x = 180

53+45=98

180-98=82

82 (interior)

82+98=180

x = 98

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

Answer: 162.6cm

Step-by-step explanation:

4 boys have a mean height of 162cm. Their total height will be the average multiplied by the number of boys which will be:

= 162 × 4

= 648cm

A new boy with height of 165cm joined. This means that we now have 5 boys and their total height will be:

= 648cm + 165cm

= 813cm

The new mean height will be:

= Total height / Number of boys

= 813 / 5

= 162.6cm

The given series is convergent, and its sum is approximately 0.1524.

To determine whether the series ∑n=1∞ 1/(9+\(e^{(-n)}\)) is convergent or divergent, we can use the comparison test with the series 1/n.

Since for all n, \(e^{(-n)}\) > 0, we have \(9 + e^{(-n)}\) > 9, and so \(1/(9+e^{(-n)})\) < 1/9.

Now, we can compare the given series with the series ∑n=1∞ 1/9, which is a convergent p-series with p=1.

By the comparison test, since the terms of the given series are smaller than those of the convergent series 1/9, the given series must also converge.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a/(1-r)

where a is the first term and r is the common ratio. In this case, the first term is 1/10 (since \(e^{(-1)}\) is very small compared to 9.

We can approximate \(9+e^{(-n)}\) as 9 for large n), and the common ratio is \(e^{(-1)} < 1\). Therefore, the sum of the series is:

S = (1/10)/(1 - \(e^{(-1)}\)) = (1/10)/(1 - 0.3679) ≈ 0.1524

Therefore, the given series is convergent, and its sum is approximately 0.1524.

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The Cartesian coordinates of the spherical point M(4, 3π, π) are (0, 0, -4).  The Cartesian coordinates of the cylindrical point M(1, 2π, 2) are (1, 0, 2).

To determine the Cartesian coordinates of a point given in spherical or cylindrical coordinates, we can use the following conversions:

Spherical to Cartesian:

x = r * sin(θ) * cos(φ)

y = r * sin(θ) * sin(φ)

z = r * cos(θ)

Cylindrical to Cartesian:

x = r * cos(θ)

y = r * sin(θ)

z = z

Let's calculate the Cartesian coordinates for the given spherical and cylindrical points:

1. Spherical Coordinates (M(4, 3π, π)):

Using the conversion formulas, we have:

r = 4

θ = 3π

φ = π

x = 4 * sin(3π) * cos(π)

 = 4 * 0 * (-1)

 = 0

y = 4 * sin(3π) * sin(π)

 = 4 * 0 * 0

 = 0

z = 4 * cos(3π)

 = 4 * (-1)

 = -4

Therefore, the Cartesian coordinates of the spherical point M(4, 3π, π) are (0, 0, -4).

2. Cylindrical Coordinates (M(1, 2π, 2)):

Using the conversion formulas, we have:

r = 1

θ = 2π

z = 2

x = 1 * cos(2π)

 = 1 * 1

 = 1

y = 1 * sin(2π)

 = 1 * 0

 = 0

z = 2

Therefore, the Cartesian coordinates of the cylindrical point M(1, 2π, 2) are (1, 0, 2).

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The variance of the number of customers who will make a purchase is 2.4.

The variance of the number of customers who will make a purchase can be calculated using the formula:

Variance = n * p * (1 - p)

where n is the number of customers and p is the probability of a customer making a purchase.

In this case, n = 10 and p = 0.6. Substituting these values into the formula, we get:

Variance = 10 * 0.6 * (1 - 0.6)
Variance = 10 * 0.6 * 0.4
Variance = 2.4

Therefore, the variance of the number of customers who will make a purchase is 2.4.

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The solution to the initial value problem is \(y(t) = e^{(-5t)} + e^{(2t)} + 9e^{(-5t)} / 7\) using Laplace transforms.

To solve the initial value problem using the method of Laplace transforms, we will take the Laplace transform of both sides of the differential equation and then solve for the Laplace transform of y(t). Finally, we will take the inverse Laplace transform to obtain the solution in the time domain.

Step 1: Take the Laplace transform of both sides of the differential equation.

L[y" + 3y' - 10y] = L[0]

Using the linearity property of Laplace transforms, we can split the terms

L[y"] + 3L[y'] - 10L[y] = 0

Step 2: Apply the Laplace transform formulas.

According to the table of Laplace transforms, we have

L[y"] = s² Y(s) - s y(0) - y'(0)

L[y'] = sY(s) - y(0)

Using the initial conditions y(0) = 1 and y'(0) = 12, we can substitute the values

s² Y(s) - s(1) - 12 + 3(sY(s) - 1) - 10Y(s) = 0

Simplifying the equation

(s² + 3s - 10) Y(s) - s - 9 = 0

Step 3: Solve for Y(s).

Rearranging the equation

Y(s) = (s + 9) / (s² + 3s - 10)

Step 4: Find the inverse Laplace transform of Y(s).

To find the inverse Laplace transform, we can decompose the right side using partial fraction decomposition. Factoring the denominator, we have

s² + 3s - 10 = (s + 5)(s - 2)

Using the table of properties of Laplace transforms, we find the inverse Laplace transform

Y(s) = (s + 9) / [(s + 5)(s - 2)]

Applying the inverse Laplace transform, we get

\(y(t) = e^{(-5t)} + e^{(2t)} + 9e^{(-5t)} / 7\)

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measure of sum interior angle = (n-2)180 where n is the no. of sides

=(3-2)180

=180°

The first triangle :

110+45+y = 180

155+y = 180

y = 180-155

y = 25°

The whole triangle :

45+57+x = 180

102+x = 180

x = 180-102

x = 78°

Answer:

x = 78°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

110° is an exterior angle of the triangle on the right , then

x + 32°= 110° ( subtract 32° from both sides )

x = 78°

The probability that the mail arrival time is more than 20 minutes on a given day is 2/3.

It's nearly impossible to predict the outcomes of many events with a hundred percent certainty. However, we can still tell how likely the events are to happen.

Probability is how likely something is to happen. Probability can also mean a number that indicates the chance or likelihood that a particular event will occur. Probability is always between zero and one. Zero means impossible while one means certain. In most cases, the probability of something to happen is greater than zero and less than one.

Mathematically, we can express probability as P(A) = f/N where

Let P(A) represent the probability that the mail arrival time is more than 20 minutes on a given day, f represent the frequency (60 - 20), and N represent total number of possible outcomes, which is 60.

P(A) = (60 - 20)/60

P(A) = 40/60

P(A) = 4/6

P(A) = 2/3

There you have it! The probability is two-thirds.

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Step-by-step explanation:

so the answer is would be X = 15

To transform a system from the time domain to the frequency domain, you need to perform a Fourier transform.

The process of transforming a system from the time domain to the frequency domain involves the use of a mathematical operation called the Fourier transform. The Fourier transform allows us to represent a signal or a system in terms of its frequency components. Here are the steps involved:

Start with a signal or system that is represented in the time domain. In the time domain, the signal is described as a function of time.

Apply the Fourier transform to the time-domain signal. The Fourier transform mathematically converts the signal from the time domain to the frequency domain.

The result of the Fourier transform is a complex function called the frequency spectrum. This spectrum represents the signal in terms of its frequency components.

The frequency spectrum provides information about the amplitudes and phases of different frequency components present in the original time-domain signal.

The inverse Fourier transform can be used to convert the frequency spectrum back to the time domain if desired.

By performing the Fourier transform, we can analyze signals or systems in the frequency domain, which is particularly useful for tasks such as filtering, noise removal, and modulation analysis.

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The Median and IQR are most appropriate to describe the measures of center and variability of distribution. The histogram depicts the distribution of time is positively skewed. So, option(b) is right one.

We have a graph present in above figure, which showes the amount of time in hours spent on homework per week for a sample of students. We have to select correct measures of center and variability. The graph is a histogram. From the graph we can see that the data is positively skewed. Now for skewed distribution we prefer median over mean as mean is more sensitive to the outliers. As the data(time) is in ratio scale we can use any of the measures of dispersion; but for skewed distribution IQR is preferred because of its robustness. In a word both median and IQR can handle outliers. Thus the appropriate answer is Median and IQR, option (c).

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Complete question :

The above figure complete the question

the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices

a) mean and standard deviation

b) mean and iqr

c) median and standard deviation

d) median and iqr

e) median and range

The probability that a randomly selected score will be between 77 and 83 is 0.2841

The probability that a randomly selected score will be between 77 and 83 can be found using the Z-score formula and the standard normal distribution table.

First, we need to calculate the Z-scores for both 77 and 83 using the formula:

Z = (X - μ)/σ

Where X is the score, μ is the mean, and σ is the standard deviation.

For 77:

Z = (77 - 77.4)/7.8 = -0.05

For 83:

Z = (83 - 77.4)/7.8 = 0.72

Now, we can use the standard normal distribution table to find the probability for each Z-score. The table gives us the area to the left of the Z-score on the standard normal distribution curve.

For Z = -0.05, the probability is 0.4801.

For Z = 0.72, the probability is 0.7642.

To find the probability that a randomly selected score will be between 77 and 83, we need to subtract the smaller probability from the larger probability:

0.7642 - 0.4801 = 0.2841

Therefore, the probability that a randomly selected score will be between 77 and 83 is 0.2841.

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Answer:

The answer is 172.7 centimeters.

Step-by-step explanation:

1.) There are 12 inches in a foot. Multiply 5 feet by 12 inches, the answer would be 60 inches.

2.) Add the additional 8 inches to the 60 to get 68 inches total.

3.) Multiply 68 inches by 2.54 centimeters, the answer is 172.72 centimeters.

4.) Round off your answer to the tenths decimal place to get 172.7 centimeters total.

Answer:

1

Step-by-step explanation:

We use the top formula since x = -4

g(-4) = \(\sqrt[3]{-4+5}\)

g(-4) = \(\sqrt[3]{1}\)

g(-4) =1

The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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The order from least to greatest would be 12, 14, 18, 112, 114, 158 miles.

The order of the number of miles the girls run from least to greatest is 12, 14, 18, 112, 114, and 158 miles.

To solve the problem, we first need to find the least number of miles each of the girls ran. Eloise ran 12 miles, while Amelie and Kiki both ran 18 miles.

Therefore, the order from least to greatest would be 12, 14, 18, 112, 114, 158 miles.

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Answer:

the answer would be 21

Step-by-step explanation:

4+6 is 10 so divide 6 by 2 which is 3 and add three for each line 10+3+3+3=21

The area of the rectangle is 132

The area of the rectangle labelled 1 is 12

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

The rectangle (see attachment)

From the figure, we have the following dimensions

Length = 5 + 3 + 4 = 12

Width = 5 + 6 = 11

So, we have

Area = 12 * 11

Area = 132

For the rectangle labelled 1, we have

Length = 3

Width = 4

So, we have

Area = 3 * 4

Area = 12

Hence, the area is 12 square units

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Given that four ounces of a hamburger provides 316 calories and contains 32 grams of protein. We need to find the approximate percentage of calories from protein,

the percentage of calories from protein, we need to follow the steps below:

Step 1: Find the total calories from the given information.

Step 2: Calculate the number of calories from protein in the given quantity.

Step 3: Find the percentage of calories from protein.

Step 1: Find the total calories from the given information.4 ounces of hamburger provides 316 calories.

Step 2: Calculate the number of calories from protein in the given quantity. We know that 1 gram of protein provides 4 calories.

Therefore, 32 grams of protein provide 32 × 4 = 128 calories. So, the number of calories from protein in the given quantity of hamburger is 128 calories.

Step 3: Find the percentage of calories from protein. To find the approximate percentage of calories from protein, we need to divide the number of calories from protein by the total calories and multiply by 100.So, the approximate percentage of calories from protein is 128/316 × 100% = 40.5%.Approximate percentage of calories from protein is 40.5%.

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Answer:

eggs = $0.60

bacon = $0.50

Step-by-step explanation:

3 x .60 = 1.80

4 x .50 = 2.00    = 3.80

The set {(x, y): xy ≥ 1; x > 0; y > 0} is not convex because there exist line segments connecting two points within the set that extend outside the set.

To determine if the set is convex, we need to check if any two points within the set form a line segment that lies entirely within the set.

Consider two points A = (x1, y1) and B = (x2, y2) in the set, where xy ≥ 1, x > 0, and y > 0.

Let's assume A and B are distinct. Now, consider the midpoint M = ((x1 + x2)/2, (y1 + y2)/2) of the line segment AB.

To determine if M lies in the set, we need to check if (x1 + x2)/2 * (y1 + y2)/2 ≥ 1, x1 + x2 > 0, and y1 + y2 > 0.

However, it is possible to find points A and B in the set such that their midpoint M does not satisfy the above conditions. For example, if A = (1, 1) and B = (3, 1/3), the midpoint M = (2, 2/3) does not satisfy (x1 + x2)/2 * (y1 + y2)/2 ≥ 1.

Therefore, the set is not convex because there exist line segments connecting two points within the set that extend outside the set.

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Answer:

- \(\frac{1}{2}\)  

Step-by-step explanation:

1) 16

2) 16 ÷ ( - 2) = - 8

3) - 8 ÷ ( - 2) = 4

4) 4 ÷ ( - 2) = - 2

5) - 2 ÷ ( - 2) = 1

6) 1 ÷ ( - 2) =  - \(\frac{1}{2}\)

The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

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(c) Two assumptions necessary for the validity of the ANOVA are:

1. Independence: The observations within each group and between groups should be independent of each other. This means that the value of one observation should not be influenced by or related to the value of another observation.

2. Homogeneity of variances: The variances within each group should be roughly equal. This assumption, also known as homoscedasticity, ensures that the variability in the dependent variable is similar across all groups.

(d) The company uses leaflets of four different designs to promote its printers. To assess the impact of leaflet design on sales, an ANOVA is performed. The null hypothesis states that the mean sales are equal across all leaflet designs, while the alternative hypothesis suggests at least one mean is different.

By comparing the computed F-statistic with the critical F-value at a significance level of 0.05, the ANOVA determines whether there is sufficient evidence to reject the null hypothesis. If the p-value is less than 0.05, it indicates a significant difference among the leaflet designs.

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