Mila is one of South's top pitchers on the Girl's softball team. In a recent game against New Greer Academy, Mila's fastball was clocked to have traveled the 13.1m distance to home plate in 0.473 seconds.

What was the average speed of Mika’s pitch?

Average Speed: ___ m/s

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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Answer:

Greta is correct. The answer is y = 4x

Step-by-step explanation:

This is because one person is able to plant four trees and five people are able to plant 20 in the same amount of time which means 4 trees is to 1 person. In other words if you substitute the values into the equation you will see that x = 1 in the first scenario and x = 5 in second scenario.I will work out the second scenario below.

y = 4x (where y = 20)

20  = 4(x)

\(\frac{20}{4} = \frac{4x}{4}\)

5 = x

OR

y = 4x (where x = 5)

y = 4 * 5

y = 20

The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

An equation is a set of variables that are constrained through a situation or case.

As per the given,

1 person plants 4 trees.

x = 1 and y = 4

y/x = 4

5 people plant 20 trees

x = 5 and y = 20

y/x = 20/5 = 4

y = 4x

Thus, y = 4x will be correct.

Hence "The equation which represents the number of trees planted y for the x number of people will be y = 4x thus Greta will be right".

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There are 39 independent sets in the graph.

Given the question, an independent set in a graph is a set of mutually non-adjacent vertices in the graph. In this problem, we will count the number of independent sets in the given graph.

Using an adjacency matrix, we can calculate the degrees of all vertices, which are defined as the number of edges that are connected to a vertex.

In this graph, we can see that vertex 1 has a degree of 3, vertices 2, 3, 4, and 5 have a degree of 2, and vertex 6 has a degree of 1. 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1

The number of independent sets in the graph is given by the sum of the number of independent sets of size k, for k = 0,1,2,...,n.

The number of independent sets of size k is calculated as follows:

suppose that there are x independent sets of size k that include vertex i.

For each of these sets, we can add any of the n-k vertices that are not adjacent to vertex i.

Therefore, there are x(n-k) independent sets of size k that include vertex i. If we sum this value over all vertices i, we obtain the total number of independent sets of size k, which is denoted by a_k.

Using this method, we can calculate the number of independent sets of size 0, 1, 2, 3, and 4 in the given graph.

The calculations are shown below: a0 = 1 (the empty set is an independent set) a1 = 6 (there are six vertices, each of which can be in an independent set by itself) a2 = 8 + 6 + 6 + 6 + 2 + 2 = 30 (there are eight pairs of non-adjacent vertices, and each pair can be included in an independent set;

there are also six sets of three mutually non-adjacent vertices, but two of these sets share a vertex, so there are only four unique sets of three vertices;

there are two sets of four mutually non-adjacent vertices) a3 = 2 (there are only two sets of four mutually non-adjacent vertices) a4 = 0 (there are no sets of five mutually non-adjacent vertices)

The total number of independent sets in the graph is the sum of the values of a_k for k = 0,1,2,...,n.

Therefore, the number of independent sets in the given graph is a0 + a1 + a2 + a3 + a4 = 1 + 6 + 30 + 2 + 0 = 39.

Bonus Question : How many independent sets are there in the graph?

There are 39 independent sets in the graph.

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Problem 2:Solution:

Let G be a graph with six vertices, labelled A, B, C, D, E, F as shown below. There are no other edges except the ones shown.

Complete the table below showing the size of the largest independent set in each of the subgraphs of G.Given graph with labelled vertices are shown below,

Given Graph with labelled vertices

Now, the subgraphs of G are shown below.

Subgraph C

Graph with vertices {A, B, C, D}

The size of the largest independent set in the subgraph C is 2.Independent set in subgraph C: {A, D}

Subgraph D

Graph with vertices {B, C, D, E}

The size of the largest independent set in the subgraph D is 2.Independent set in subgraph D: {C, E}Bonus SubgraphGraph with vertices {C, D, E, F}

The size of the largest independent set in the subgraph formed by {C, D, E, F} is 3.Independent set in subgraph {C, D, E, F}: {C, E, F}

Hence, the required table is given below;

Subgraph

Size of the largest independent setC2D2{C, D, E, F}3

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Answer:

He spent on fruit after 5 months is $110.

In 15 months he spent $280.

Step-by-step explanation:

Fixed pay for membership is $25

And enrollment fee is $17 for each month.

The equation represents this situation is

y= 17 x + 25

He is going to stop receiving fruits once he spent $280.

Now, to find how much he spent on fruit after 5 months is plugin x as 5 into

y=17x+25 for x

y=17(5)+25

y=85+25

y=110 dollars

Now, to find how many months until $280 is to plug in y as 280 then solve the equation for x.

280 = 17 x+25

Subtract both sides 25

255 =17 x

Divide both sides by 17

x= 15 months

The area and the circumference of the circle with a radius 3 m are 28.26 m² and 18.84 m respectively.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle with a radius of 3 m, we need to find the area and the circumference of the circle,

Area = π×radius²

= 3.14×3²

= 28.26 m²

Circumference = 2π×radius

= 2×3.14×3

= 18.84 m

Hence, the area and the circumference of the circle with a radius 3 m are 28.26 m² and 18.84 m respectively.

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Answer:

Step-by-step explanation:

sin77=h/8

h=8sin77

h=8(0.9744)

h=7.7952ft

The Laplace transform of the function \(f(t) = 5t^3 - 5\sin(4t)\) is given by: \[F(s) = \frac{120}{s^4} - \frac{20}{s^2+16}\]

To find the Laplace transform of the given function \(f(t) = 5t^3 - 5\sin(4t)\), we can apply the properties and formulas of Laplace transforms.

The Laplace transform of a function \(f(t)\) is defined as:

\[

F(s) = \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st}\,dt

\]

where \(s\) is the complex frequency variable.

Let's find the Laplace transform of each term separately:

1. Laplace transform of \(5t^3\):

Using the power rule of Laplace transforms, we have:

\[

\mathcal{L}\{5t^3\} = \frac{3!}{s^{4+1}} = \frac{5\cdot3!}{s^4}

\]

2. Laplace transform of \(-5\sin(4t)\):

Using the Laplace transform of the sine function, we have:

\[

\mathcal{L}\{-5\sin(4t)\} = -\frac{5\cdot4}{s^2+4^2} = -\frac{20}{s^2+16}

\]

Now, we can combine the Laplace transforms of the individual terms to obtain the Laplace transform of the entire function:

\[

\mathcal{L}\{f(t)\} = \mathcal{L}\{5t^3 - 5\sin(4t)\} = \frac{5\cdot3!}{s^4} - \frac{20}{s^2+16} = \frac{120}{s^4} - \frac{20}{s^2+16}

\]

This is the Laplace transform representation of the function \(f(t)\) in the frequency domain. The Laplace transform allows us to analyze the function's behavior in the complex frequency domain, making it easier to solve differential equations and study the system's response to different inputs.

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It will take her approximately 2.76 years to decide.

The artist has 10 paintings, and there are 10 display locations. So, the total number of possible arrangements is 10! (10 factorial) which is equal to 3,628,800.

If she takes 1 minute to set up and view each arrangement, and she works 10 hours a day 6 days a week, she can work for 60*10=600 minutes in a day.

In a week, she can work for 600*6 = 3600 minutes.

Therefore, in a week, she can view 3600/1 = 3600 arrangements.

So, it will take her to view all possible arrangements is: 3,628,800/3600 = 1008 days

That's approximately 2.76 years.

So, it will take her approximately 2.76 years to decide.

Therefore, It will take her approximately 2.76 years to decide.

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The first game brought in more money than the last game.

Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.

According to question:

The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.

Therefore, the first game brought in more money than the last game.

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The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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Answer:

it is 6 inches

Step-by-step explanation:

Answer:

108

Step-by-step explanation:

Calculator

Answer:

108

Step-by-step explanation:

(45 * 240) / 100

(10,800) / 100 

108

The angle in the capital letter "L" measures 90°, making it a right angle.

A right angle is one that is exactly 90 degrees, or half of a straight angle. There is usually a quarter turn in it. The fundamental geometric forms, rectangle, and square, each have four angles that measure 90 degrees.

When two lines cross, and there is a 90-degree angle between them, the lines are said to be perpendicular. A few examples of 90-degree angles in real life include the angle between the hands of a clock at 3 o'clock, the angles between two neighboring sides of a rectangular door or window, etc.

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Here is an example of right skewed data:

Data: 1, 1, 1, 1, 2, 2, 2, 3, 3, 4

Mean: 2.5

Median: 2

Z-score of median: 0.5

As you can see, the mean is greater than the median. This is because the data is right skewed, meaning that there are a few extreme values on the right side of the distribution that are pulling the mean up.

The z-score of the median is positive because the median is greater than the mean.

Another example of right skewed data is the distribution of income. In most countries, most people earn a modest amount of income, but there are a few people who earn a very high income. This creates a right skewed distribution, with the mean being greater than the median.

In a right skewed distribution, the z-score of the median is positive because the median is closer to the mean than the mode. The mode is the most frequent value in the distribution, and it is usually located on the left side of the distribution in a right skewed distribution.

The mean is pulled to the right by the extreme values, but the median is not affected as much because it is not as sensitive to extreme values.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer: the answer is C

Step-by-step explanation:

Bernardo's probability of having a greater number than Silvia's is \($55 + 54 + 53 + \cdots + 1$\) =37/56.

From Bernardo's set, there are \($\binom{9}{3} = 84$\) numbers that he can randomly choose. From Silvia's set, there are \($\binom{8}{3} = 56$\)numbers that she can randomly choose. Since Bernardo and Silvia can choose their numbers independently, there are \($84 \cdot 56$\) pairs of numbers that you can compare. For example, if Bernardo chooses 321 and Silvia chooses 543, that is one pair. We can sort Bernardo's numbers from the greatest to the smallest. We can do the same for Silvia's numbers. So, Bernardo's greatest \($84 - 56 = 28$\) numbers are all bigger than Silvia's numbers. Here, we have \($28 \cdot 56$\) pairs satisfying that Bernardo's number will be greater than Silvia's. If Bernardo chooses the 29th greatest number, which is the same as Silvia's greatest number, hence there will be \($56 - 1 = 55$\) pairs satisfying that Bernardo's 29th greatest number will be greater than Silvia's. Similarly, if Bernardo chooses the 30th greatest number, there will be \($55 - 1 = 54$\) pairs satisfying that Bernardo's 30th greatest number will be greater than Silvia's. This pattern continues. So if Bernardo chooses the 29th greatest number or below, he will have \($55 + 54 + 53 + \cdots + 1$\) pairs where his number will be greater than Silvia's.

In total, Bernardo's probability of having a greater number than Silvia's is \($55 + 54 + 53 + \cdots + 1$\) =37/56.

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According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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To remove the single quotation marks ('') at the beginning and end of a string and remove the item at index 12, you can use Python's string manipulation methods and list slicing. First, you can use the strip() method to remove the surrounding single quotation marks. Then, you can convert the string into a list using the list() function, remove the item at index 12 using list slicing, and finally convert the list back into a string using the join() method.

To remove the single quotation marks at the beginning and end of a string, you can use the strip() method. This method removes any leading and trailing characters specified in the argument. In this case, you can pass the single quotation mark ('') as the argument to strip().

Here's an example:

string = "'example string'"

stripped_string = string.strip("'")

After executing this code, the value of stripped_string will be 'example string' without the surrounding single quotation marks.

To remove the item at index 12 from the string, you need to convert it into a list. You can use the list() function for this conversion. Then, you can use list slicing to remove the item at index 12 by excluding it from the list. Finally, you can convert the modified list back into a string using the join() method.

Here's an example:

string_list = list(stripped_string)

string_list.pop(12)

result_string = ''.join(string_list)

After executing this code, the value of result_string will be the modified string with the item at index 12 removed.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The nurse manager approves two staff nurses to attend a national conference.

The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.

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Answer:  

vertex= 4,-25

y coordinate of vertex = (x+4)2-25

x coordinate of vertex= x2-8x-9

Step-by-step explanation:

a. The number of passengers that will maximize the revenue received from that flight is 88 passengers. Let's suppose that the number of passengers for the charter flight is x.

Therefore, the total revenue from the flight is given by: Revenue = (83 × 581) + (x − 83) × (581 − 5)x. We can obtain the quadratic equation: Revenue = −5x² + 496x + 48,223 To get the maximum revenue, we need to find the x-value of the vertex using this formula:

x = −b/2a

= −496/2(−5)

= 49.6

≈ 88

The number of passengers that will maximize the revenue received from that flight is 88 passengers.

b. The maximum revenue is $ 51,328.00 The revenue function for the charter flight is given by: Revenue = −5x² + 496x + 48,223 Substituting x = 88, we get Revenue = −5(88)² + 496(88) + 48,223  

= 51,328

The maximum revenue is $51,328.00.

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Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

EXPLANATION

Since we have the function:

Vertical asymptotes:

Taking the denominator and comparing to zero:

The following points are undefined:

Therefore, the vertical asymptote is at x=-5

Horizontal asymptotes:

In conclusion:

The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

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Answer:

18.42 g

Step-by-step explanation:

Using the exponential growth / Decay function :

A = Pe^kt

A = final amount ; P = initial amount, t = number of years ; t = 20

A = 30e^-(0.0244 * 20)

A = 30e^-0.488

A = 30 * 0.6138528

A = 18.415586

Strontium present after 20 years will be :

18.42 g

Answer: I believe the answer would be g x $3.25 and f x $0.74

Step-by-step explanation:

If each pound of granola costs $3.25, then you would multiply however many pounds you’re buying, by the price per pound.

For example, if I was buying 6 pounds of granola then I would multiply six by $3.25.

6 x $3.25= $19.50

The Texas Star® Ferris wheel at the Texas State has diameter of 65 meters.

Circumference -- The distance around the circle (the perimeter of a circle).

Diameter -- The distance from the circle through the circle's center to the circle on the opposite side. (twice the radius)

Radius -- The distance from the center of a circle to the circle (half the diameter). Draw a line segment from the center of the circle to any part of the circle and you have the radius.

                 Circumference(C) = 2d

                 C=π*d

                 π*d=204.1

                 d=204.1/3.14

                 d=65

Hence, the diameter of the wheel is 65 meters .

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Answer:

Ratio of heights: 3 : 2

Ratio of surface areas: 9 : 4

Ratio of volumes: 27 : 8

Step-by-step explanation:

Since both cuboids are proportional, then we must derive expressions for the ratios of heights, surface areas and volumes from the following identities:

Perimeter

\(p' = k_{p}\cdot p\) (1)

Surface area

\(A'_{s} = k_{A_{s}}\cdot A_{s}\) (2)

Volume

\(V' = k_{V}\cdot V\) (3)

Where:

\(p\), \(p'\) - Perimeters of the small cuboid and the big cuboid, in inches.

\(A_{s}\), \(A'_{s}\) - Surface areas of the small cuboid and the big cuboid, in square inches.

\(V\), \(V'\) - Volumes of the small cuboid and the big cuboid, in cubic inches.

By means of geometry formulas we expand the system of equations below:

Perimeter

\(4\cdot (w' + h' + l') = k_{p}\cdot [4\cdot (w + h + l)]\)

\(4\cdot (k\cdot w'+ k\cdot h' + k\cdot l) = k_{p}\cdot [4\cdot (w+h+l)]\)

\(k_{p} = k\)

Surface area

\(2\cdot (w'\cdot h' + l'\cdot w' + l' \cdot h') = k_{A_{s}}\cdot [2 \cdot(w\cdot h + l \cdot w + l\cdot h)]\)

\(2\cdot [(k\cdot w')\cdot (k\cdot h') + (k\cdot l)\cdot (k\cdot w) + (k\cdot l)\cdot (k\cdot h)] = k_{A_{s}}\cdot [2\cdot (w\cdot h + l\cdot w + l\cdot h)]\)

\(k_{A_{s}} = k^{2}\)

Volume

\(w'\cdot h' \cdot l' = k_{V}\cdot (w\cdot h \cdot l)\)

\((k\cdot w)\cdot (k \cdot h)\cdot (k \cdot l) = k_{V}\cdot (w\cdot h \cdot l)\)

\(k_{V} = k^{3}\)

Where \(k = \frac{p'}{p}\).

If we know that \(p' = 30\,in\) and \(p = 20\,in\), then we proceed to calculate all the ratios:

\(k_{p} = \frac{30\,in}{20\,in}\)

\(k_{p} = \frac{3}{2}\)

\(k_{A_{s}} = \frac{9}{4}\)

\(k_{V} = \frac{27}{8}\)

Answer:

ratio of heights: (3/2)

Ratio of surface area: (9/4)

Ratio of volumes: (27/8)

Step-by-step explanation:

got this right, hope it helps :)