.Lesson 3: Modelling Data with a Curve of Best Fit 1. Liam was practising his shot put throws for an upcoming track meet. His coach took pictures of the ball with a time-lapse camera and measured the height of the ball versus time since the throw. The coach was hoping this information could help Liam to improve his throwing ability. The coach recorded the information in the following chart: Time (s) 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Height (cm) 152 272 358 402 405 366 297 181 a. What would be the most appropriate regression model to use in this situation? Answer: b. State an appropriate domain and range. What does each represent? Answer: c. Find the regression equation. Answer: d. Use your equation to find the height of the ball after 0.5 s. Answer: e. How long would it take for the ball to hit the ground? Answer:

The perimeter and the area of the composite figure are 29 centimeters and 49.5 square centimeters, respectively.

In this problem we have the representation of a composite figure, the result of the combination of a rectangle and a triangle. The perimeter of the figure is the sum of the sides and the area of the composite figure is the result of suming the areas of the rectangle and triangle:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

And the perimeter and the area of the composite figure are now computed:

Perimeter

p = 6 cm + 7 cm + 6.5 cm + 9.5 cm

p = 29 cm

Area

A = 0.5 · (6 cm) · (2.5 cm) + (6 cm) · (7 cm)

A = 7.5 cm² + 42 cm²

A = 49.5 cm²

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Answer:

Time, t = 2.44 seconds

Step-by-step explanation:

Logan is doing a handstand dive from a 12 meter platform. The equation that models the path of her dive is given by :

\(h=-4.9t^2+12t\)

It is required to find the time after which Logan will hit the ground. At this point, h = 0

\(-4.9t^2+12t=0\\\\t(-4.9t+12)=0\\\\t=\dfrac{12}{4.9}\\\\t=2.44\ s\)

So, after 2.44 seconds it will hit the water.

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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No 4 is not a factor of 93 :)

let me know if this helped<3

Explanation: a factor is whether or not a number can be multiplied with another number, 4 cannot be multiplied by any number to evenly come out as 93, the way you can check this is by dividing 93 by 4, if it comes out as a whole number with no decimal or remainder than the number is a factor if it has a decimal or remainder it is not a factor

Answer:

No.

Step-by-step explanation:

The first method entails simply listing all factors of 93 and then seeing if 4 is one of them. The factors of 93 are 1, 3, 31, and 93. Looking at the list, you see that 4 is not on the list, and the answer to "is 4 a factor of 93?" is therefore no. For the second and perhaps easier method, we divide 93 by 4 to see if the quotient is a whole number or fractional number. If the quotient is a whole number, then 4 is a factor of 93. If the quotient is a fractional number, then 4 is not a factor of 93. 93 divided by 4 is 23.25 which is a fractional number. Thus, once again, the answer to "Is 4 a factor of 93?" is no.

Answer:

19

Step-by-step explanation:

it’s the only one within Q3

Answer:

The formula for relative change is x = 100 * (final - initial) / initial  Using this concept, we can plug in our values. x = (3.95 - 3.45) / 3.45 = 0.5. 0.5 * 100 = 14.49%. Rounded to the nearest tenth would give us the value 14.5%.

Step-by-step explanation:

At the 5% significance level, we have sufficient evidence to conclude that the population mean is higher than 40 hours.

To test the null hypothesis that the population mean is 40 hours against the alternative that it is higher, we can perform a one-sample t-test.

The null hypothesis (H₀): μ = 40 (population mean is 40 hours)

The alternative hypothesis (H₁): μ > 40 (population mean is higher than 40 hours)

Given a sample of 10 students, the sample mean (x') is 45 hours and the sample standard deviation (s) is 10.5409.

Using the t-test, we calculate the test statistic t:

t = (x' - μ₀) / (s / √n)

Where x' is the sample mean, μ₀ is the null hypothesis population mean (40), s is the sample standard deviation, and n is the sample size (10).

Plugging in the values, we get:

t = (45 - 40) / (10.5409 / √10)

t ≈ 2.38

Next, we determine the critical value or the p-value associated with a significance level of 5%. For a one-tailed test (since we are testing if the mean is higher), the critical value is tc = t(α,n-1), where α is the significance level and n-1 is the degrees of freedom.

At a significance level of 5%, with 9 degrees of freedom (n-1), the critical value is tc = 1.833 (obtained from a t-table or statistical software).

Since the calculated t-value (2.38) is greater than the critical value (1.833), we reject the null hypothesis.

Therefore, at the 5% significance level, we have sufficient evidence to conclude that the population mean is higher than 40 hours based on the given sample data.

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The set A ∩ B = {3}

The intersection of sets, denoted as A ∩ B, refers to the set that contains elements that are common to both sets A and B. In this case, set A consists of the elements {1, 2, 3, 6}, and set B consists of the elements {3, 4, 5}.

The intersection of A and B, written as A ∩ B, represents the set of elements that appear in both sets simultaneously.

To find the intersection of sets A and B, we examine each element of set A and check if it is also present in set B. In this case, the element 3 is the only element that exists in both sets.

Therefore, the intersection of sets A and B is {3}.

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The system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

The given parameters are

Length = Not more than 12 inches

Perimeter = Less than 30 inches

"Not more than" means less than or equal to

So, we have

l ≤ 12

The perimeter of a rectangle is

P = 2l + 2w

So, we have

2l + 2w = Less than 30 inches

"Less than" is represented with <

So, we have

2l + 2w < 30

Hence, the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

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Answer:

a. I ≤ 12
    2l + 2w < 30

Step-by-step explanation:

i got it right on edge.

Answer:

$109.14

Step-by-step explanation:

This is correct!

Answer:

D/ $109.14

Step-by-step explanation:

i did the quiz

The scale that she can use for the vertical axis to maximize the difference in the heights of the bars is option c, 10-50.

To maximize the difference in the heights of the bars, she needs to choose a scale that covers the range of values represented by the data while minimizing the unused space on the vertical axis.

Option a, 0-50, would cover the entire range of values but may result in a lot of unused space if the data values are relatively small.

Option b, 0-40, would restrict the range of values and may not fully represent the differences between the heights of the bars.

Option c, 10-50, is a suitable choice as it covers the range of values and allows for differentiation between the heights of the bars. It eliminates unnecessary empty space below 10, focusing on the relevant range of data.

Option d and e, 25-40, restrict the range even further and may not adequately capture the differences between the heights of the bars.

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Step-by-step explanation:

Let t = time (in hrs) Linda rode her bike

Then (t-3) = Shana's time walking

:

Write a distance equation: dist = speed * time

:

Linda's dist + Shana's dist = 164

20t + 6(t-3) = 164

20t + 6t - 18 = 164

26t = 164 + 18

26t = 182

t = 182/26

t = 7 hrs, Linda is on the road

:

Time: 9 AM + 7 hrs = 4 PM, they will be 162 miles apart

:

Check using Linda's and Shana's distances:

20(7) + 6(7-3) =

140 + 24 = 164 mi

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The installing hardwood floors over a 1/2 inch thick plywood subfloor, it is recommended to use 2-inch L-shaped cleats with a flooring nailer. This will ensure that the hardwood planks are securely fastened to the subfloor and reduce the likelihood of squeaking or loose planks in the future.

When installing hardwood floors over a plywood subfloor, it is important to use the appropriate length of L-shaped cleats. The L-shaped cleats are nails used by a flooring nailer to attach the hardwood planks to the subfloor. In this case, the subfloor is a 1/2 inch thick plywood, while the hardwood planks are 3/4 inch thick.
The recommended length of L-shaped cleats to use when installing hardwood floors over a 1/2 inch thick plywood subfloor is 2 inches. This is because the 2-inch cleats will provide enough length to penetrate the subfloor and securely fasten the hardwood planks to the subfloor. Using shorter cleats may not provide enough grip and the hardwood floors may eventually become loose.
The flooring nailer shoots the L-shaped cleats in at a 45-degree angle, which helps to ensure that the cleats go in straight and do not damage the surface of the hardwood planks. It is important to use the appropriate length of cleats to avoid damaging the subfloor or the hardwood planks during installation.
In summary, when installing hardwood floors over a 1/2 inch thick plywood subfloor, it is recommended to use 2-inch L-shaped cleats with a flooring nailer. This will ensure that the hardwood planks are securely fastened to the subfloor and reduce the likelihood of squeaking or loose planks in the future.

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Answer:

they each got 1/5.there are five friends, if they share 1/5 then each gets 1/5 of nuts.

The fraction of the kilogram of nuts did each friend eat should be considered as the 1/5.

Since Five friends shared 1/5 kilogram of nuts equally

So here the fraction should be the same as shared by the five friends i.e. 1 by 5.

Therefore, The fraction of the kilogram of nuts did each friend eat should be considered as the 1/5.

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The critical value for a 99 confidence interval for a z interval is 2.576.

A confidence interval (CI) would be a range of values that, with a specific degree of certainty, are likely to encompass a population value. It is frequently stated as a percentage when a population mean falls between a higher and lower interval.

Some key features regarding the confidence interval are-

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The price of the rechargeable drill in the home improvement stores is P(m) = 1.2m + 4, where m is the manufacturing total cost.

P(m) = 1.2m + 4

P(m) = 1.2(manufacturing cost) + 4

P(m) = 1.2m + 4

The manufacturer of tools charges $4 more than its manufacturing cost for a rechargeable drill to a chain of home improvement stores. Following that, the chain sells each drill for 120 percent of what it paid the manufacturer.. Therefore, the price of the rechargeable drill in the home improvement stores can be represented by the function P(m), where m is the manufacturing cost of the drill. The equation P(m) = 1.2m + 4 shows that the price of the rechargeable drill in the home improvement stores is equal to 1.2 times the manufacturing cost plus $4. This equation indicates that the manufacturer of tools charges $4 more than its manufacturing cost and the home improvement stores then increase the price of the drill by 20% of the price they paid to the manufacturer. Therefore, the total cost of the rechargeable drill in the home improvement stores is 1.2m + 4, where m is the manufacturing cost of the drill.

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This relationship is observed in a sample of size 65. The value of 0.45 indicates that the relationship is moderately strong. Therefore, in the equation r(65) = 0.45, r represents an observed statistic.

The equation r(65) = 0.45 represents an observed statistic. Here's a long answer to support my explanation:Definition of a statisticA statistic is a value or measure that represents a sample. A statistic is calculated from the data that is obtained from the sample. A statistic is used to infer certain characteristics about the population based on the information obtained from the sample. The observed statistic is the statistic that is calculated using the sample data. Therefore, the observed statistic is the value that is observed when the statistic is calculated using the sample data. Definition of rThe letter r stands for the correlation coefficient.

The correlation coefficient is a measure of the strength of the linear relationship between two variables. The correlation coefficient can be calculated using the following formula:where x and y are the two variables, and n is the number of pairs of observations. Definition of the equation r(65) = 0.45The equation r(65) = 0.45 is a statement about the value of the correlation coefficient. The value of the correlation coefficient is 0.45 when the sample size is 65. This is an observed statistic because it is calculated using the sample data. Interpretation of the equation r(65) = 0.45The equation r(65) = 0.45 means that there is a moderate positive linear relationship between two variables.

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The value of SS for this population cannot be determined with the given information.

The sum of squares (SS) for a population is calculated by summing the squared differences between each individual score and the population mean.

However, the given information provides the population standard deviation (σx = 12) and the population variance (σx^2 = 54), but it does not provide the population mean (μ).

Without the population mean, we cannot accurately calculate the value of SS. Therefore, the value of SS for this population cannot be determined based on the given information.

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The plane's true bearing is $27.9°N of W, and its estimated ground speed is 473.3 mph.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's start with the airplane's speed.

A bearing of N25°W corresponds to a anticlockwise angle of 65° when measured from the westward direction (W).

As a result, the airplane's velocity vector can be divided into its north-south and east-west components as shown below:

V_A,north = 480 cos(65°) ≈ 200.5 mph (northward)

V_A,west = 480 sin(65°) ≈ 447.3 mph (westward)

V_W,north = 45 sin(75°) ≈ 43.5 mph (northward)

V_W,west = 45 cos(75°) ≈ 11.3 mph (westward)

To find the net velocity of the airplane, we can add the north-south and east-west components of the airplane velocity and wind velocity separately:

V_net,north = V_A,north + V_W,north ≈ 200.5 + 43.5 ≈ 244.0 mph (northward)

V_net,west = V_A,west + V_W,west ≈ 447.3 + 11.3 ≈ 458.6 mph (westward)

Now we can use the Pythagorean theorem to find the magnitude of the net velocity:

|V_net| = sqrt(V_net,north² + V_net,west²) ≈ 473.3 mph

To find the actual bearing of the airplane, we can use the inverse tangent function:

tan⁻¹(V_net,north / V_net,west) ≈ 27.9°

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Equilibrium points of the given system are u = c for d = 0 and u = 0 for d = 1.

An equilibrium point of a differential equation is a point where the derivative of the function is zero. In other words, an equilibrium point is a point where the function has no tendency to move. The equilibrium value of un+1 is given by u, when un+1 = u, the nu = c - du + 1= c(1-d). Here, the value of c does not affect the equilibrium point because it appears as a multiplier that applies to both sides of the equation.

Thus, the value of c has no effect on the equilibrium point. When d = 0, the equation becomes u = c(1-0) = c, hence the equilibrium point is u = c. When d = 1, the equation becomes u = c(1-1) = 0, hence the equilibrium point is u = 0. Thus, the equilibrium point of the given system is u = c for d = 0 and u = 0 for d = 1.

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(2.1) The equilibrium point for any value of c is u = c / (1 + d).

(2.2) The equilibrium point for any value of d is u = c / (1 + d).

(2.1) To determine the equilibrium points of the system un+1 = c - dun for all possible values of c, we need to find the values of u that satisfy the equation when un+1 = un = u.

Setting u = c - du, we can solve for u:

u = c - du

u + du = c

u(1 + d) = c

u = c / (1 + d)

So, the equilibrium point for any value of c is u = c / (1 + d).

(2.2) To determine the equilibrium points for all possible values of d, we set u = c - du and solve for u:

u = c - du

u + du = c

u(1 + d) = c

u = c / (1 + d)

Again, the equilibrium point for any value of d is u = c / (1 + d).

Therefore, the equilibrium points of the system for all possible values of c are u = c / (1 + d), where c and d can take any real values.

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Answer:

i believe it would be 7.2

Step-by-step explanation:

Answer:

p=1/4 or 0.25

Step-by-step explanation:

2p+3=5-6p Subtract 2p from both sides.

-2p       -2p

3=5-8p        Subtract 5 on both sides.

-5 -5

-2=-8p         Divide by -8 on both sides.

/-8  /-8

1/4=p or (as a decimal) 0.25=p

Hope this helps you out!! Have a great day c:

Answer:

105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

A = nh

A= 15x7

A = 105 inches squared

The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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Approximately, there are total 50 national parks is the United states.

The United States has approximately 50 national parks, which are congressionally designated procted areas operated by the National Park Service, an agency of the Department of the Interior.

National Parks are designated for their natural beauty, unique geological features, diverse ecosystems, and recreational opportitinies.

Some of the major national parks are Yesomite National Park, Bryce Canyon National Park, Acadia national park, National park of America Samona, Arches National park etc.

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Answer:

The answer is 50

Step-by-step explanation:

yes

The boat is approximately 4.12 miles from the marina and its direction is northeast. To head directly back to the marina, the boat must sail southwest.

To determine the boat's distance from the marina and the direction to head back, we'll use the Pythagorean theorem and some trigonometry.

After sailing 3 miles north and 2 miles northeast, the boat's total displacement is a right-angled triangle with legs of 3 miles (north) and 2√2 miles (east). The hypotenuse represents the straight-line distance back to the marina.

Using the Pythagorean theorem, distance^2 = (3^2) + (2√2)^2 = 9 + 8 = 17. So, the distance is √17 ≈ 4.12 miles.

To find the direction, we'll calculate the angle formed by the northward displacement and the straight-line path back to the marina. Using tangent, tan(angle) = (2√2)/3. The angle is arctan(2√2/3) ≈ 49.1 degrees.

So, the boat is approximately 4.12 miles from the marina and must sail 49.1 degrees west of south to head directly back to the marina.

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Answer:

Step-by-step explanation:

Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.

the total surface of the cone A = πrs+πr² and the volume is expressed as

V = 1/3πr²h

For the surface area of the cone;

Given parameters

radius = 8 cm and slant height s = 15 cm

Total surface area A = π(8)(15) + π(8)²

A = 90π+64π

A = 154π

If π = 3.14

A = 154(3.14)

A = 483.56cm²

A = 483.6cm²

Hence the total surface area of the cone to the nearest tenth is 483.6cm²

For the volume of the cone;

V = 1/3πr²h

Using pythagoras theorem to get the height of the cone;

l² = h²+r²

h² = l²-r²

h² = 15²-8²

h² = 225-64

h² = 161

h = √161

h = 12.69cm

V = 1/3π* (8)² * 12.69

V =  1/3π* 64 * 12.69

V =  1/3*3.14* 64 * 12.69

V = 2550.1824/3

V = 850.06 cm³

V = 850.1 cm³

Hence, the volume of the cone is  850.1 cm³ to the nearest tenth.

The length of AC in triangle BAC is equal 10.7 units

In trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The formula is given as

AC² = AB² + BC² - 2(AB)(BC) cos AC

AC² = 6² + 7² - 2(6)(7)cos110

AC = 10.7

Using cosine rule, the length of AC is 10.7 unit.

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