Question 3: The table below shows the result of an experimental study conducted by a group of civil engineering students on the coefficient of thermal expansion (a) of a steel structure. 60 50 40 -30 -40-50 -60 Temperature [°C] a [mm / mm °C] 30 20 10 0 -10-20 6.6 5.4 6.3 7.3 7.2 7.1 6.8 6.2 6.0 5.9 5.7 5.5 5.3 (a) Draw a scatter diagram of the coefficient of thermal expansion (a) against temperature (T). Comment the plot and suggest an equation that seems appropriate in relating a to T? [30%] (b) Using linear regression to determine the relation between thermal expansion and the temperature. [40%] (c) Using the regression equation from (b) to calculate the regression residuals for each experimental point and construct a run chart plot for these residuals. Discuss the residual plot commenting on relevant features. [30%]

Answer:

59 dollars

Step-by-step explanation:

you have to answer that for yourself

Answer:

\(your \: balance \: is : 80 - (3p + 4d).\)

Step-by-step explanation:

\(let \: the \: parakeet \: cost \: p \: each : \\ let \: the \: parrot \: cost \: d \: each : \\ let \: the \: total \: amount \: spent \: already \: be : \\ 3p + 4d \\\: then \: the \: balance \: left \: is \: given \: by : \\ 80 - (3p + 4d). \\ \\ note \: that : once \: you \: are \: provided \: with \: the \: value \\ \: of \: the \: various \: items \: each....then \: the \: actual \: balance \\ \: can \: be \: calulated \: using \: the \: above \: equaion.\)

♨Rage♨

In a perfectly symmetrical distribution with a mean (µ) of 30, there is no specific mode because all values occur with equal frequency.

In a perfectly symmetrical distribution, such as a symmetric bell-shaped curve or a uniform distribution, each value occurs with the same frequency. This means that there is no value that occurs more frequently than others, resulting in multiple modes or no mode at all.

The mode is typically used to identify the most common value in a dataset, but in a perfectly symmetrical distribution, all values have equal frequency, and there is no single mode. Instead, the distribution is characterized by its symmetry around the mean (µ). The mean represents the central tendency of the distribution, indicating the balance point of the data. In this case, with a mean of 30, the distribution is centered around this value, with equal numbers of observations on either side.

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The volume of the medication required, we subtract it from the nebulizer output to find the amount of saline needed.

To determine the amount of saline needed to make the medication last the full hour, we need to calculate the total volume of medication required and subtract it from the volume delivered by the nebulizer.

Given:

- Albuterol dose: 15 mg

- Atrovent dose: 0.5 mg

- Nebulizer output: 10 mL per hour

- Nebulizer flow rate: 4 LPM (liters per minute)

First, we need to convert the nebulizer flow rate to mL per hour:

4 LPM * 60 min = 240 mL per hour

Next, we calculate the total volume of medication required by adding the doses of albuterol and Atrovent:

Total medication volume = 15 mg + 0.5 mg

Now, we need to convert the total medication volume from milligrams to milliliters. To do this, we need to know the concentration of the medication (mg/mL) or the volume of the medication that corresponds to the given dose. Without this information, we cannot convert the dose to volume accurately.

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Answer:

12/4 is equal to 15/5

The next equality after 12/4 is 15/5.

Answer:

15

Step-by-step explanation:

12/4=3, so x/5=3.

5x3=15

Answer:

20% off 45.00 is 36.00

Step-by-step explanation:

The difference is $9.00

Answer:

$36

Step-by-step explanation:

20% of $45 is $9.

$45 - $9 = $36

The Integral Test The Integral Test states that if f is a positive, continuous, and decreasing function on the interval [a, ∞), and\(f(n) = a_n\), then the series \(∑a_n\) converges if and only if the integral from a to ∞ of f(x) dx is finite. This means that we can use the Integral.

Test to check the convergence of the series\(∑n=1[infinity]n^2e^(−n^3)\). We will use the function

\(f(x) = x^2e^(−x^3)\)for this, since it is positive, continuous, and decreasing on the interval [1, ∞). So, we have

\(a_n = n^2e^(−n^3)\)and

\(f(n) = n^2e^(−n^3).∫1[infinity]​x^2e^(−x^3) dx

= −1/3 e^(−x^3)|1∞.\)

Using substitution, let u = x^3. Then,

\(du/dx = 3x^2, so dx = du/3x^2.\) This gives us:

\(∫1[infinity]​x^2e^(−x^3) dx = ∫1[infinity]​e^−udu/3

=−1/3 e^(−u)|1∞

= −1/3 e^(−∞) − (−1/3 e^(−1))

= 1/3\)

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The valid solution within the context of the situation is A. (90, 25), where Trenton sells 90 boxes of 60-watt bulbs and 25 boxes of 100-watt bulbs.

To determine which solution is valid within the context of the situation, we need to substitute the values from each solution into the given inequalities and check if they satisfy the conditions.

Let's evaluate each solution:

A. (90, 25):

Substituting the values into the inequalities:

7(90) + 12(25) ≥ 1,000 ---> 630 + 300 ≥ 1,000 ---> 930 ≥ 1,000 (True)

90 + 25 > 100 ---> 115 > 100 (True)

B. (40, 64.50):

Substituting the values into the inequalities:

7(40) + 12(64.50) ≥ 1,000 ---> 280 + 774 ≥ 1,000 ---> 1,054 ≥ 1,000 (True)

40 + 64.50 > 100 ---> 104.50 > 100 (True)

C. (30, 80):

Substituting the values into the inequalities:

7(30) + 12(80) ≥ 1,000 ---> 210 + 960 ≥ 1,000 ---> 1,170 ≥ 1,000 (True)

30 + 80 > 100 ---> 110 > 100 (True)

D. (200, -10):

Substituting the values into the inequalities:

7(200) + 12(-10) ≥ 1,000 ---> 1,400 - 120 ≥ 1,000 ---> 1,280 ≥ 1,000 (True)

200 - 10 > 100 ---> 190 > 100 (True)

From the calculations, we can see that all of the given solutions satisfy both inequalities. However, it's important to note that the number of boxes of 100-watt bulbs (y) cannot be negative in the context of the situation.

Therefore, the valid solution within the context of the situation is A. (90, 25), where Trenton sells 90 boxes of 60-watt bulbs and 25 boxes of 100-watt bulbs.

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Answer:

This one doesn't have all the requirements so it doesn't work out at least how do I understand it  

Step-by-step explanation:

Data

• Morning: 156 times

• Lunch: x times

• Afternoon: 201 times

• Whole day: 562 times

Procedure

To know how many times did it ring at lunch, we have to build a relation, in which we know that the addition of the times in the morning, lunch, and afternoon equal the times it rang the whole day:

Then, we have to solve for x considering that it represents the times it rang during the lunch.

Answer: It rang 205 times during the afternoon.

Answer:

-330°

Step-by-step explanation:

just gotta trust it i guess

Given information: In the PGA, on par 3 holes, golfers hit the green in one shot 80% of the time. In fact, 20% of the time, they hit the green in one shot and then need only one putt to complete the hole. So 60% of the time, they hit the green in one shot but are unsuccessful on their putt.

Let G be the event that the golfer hits the green in one shot. Let P be the event that the golfer needs one putt to make the hole. Probabilities listed in the problem: Probability of hitting the green in one shot

.= 80% = P(G)Probability of hitting the green in one shot and needing only one putt = 20% = P(G ∩ P)Probability of hitting the green in one shot but are unsuccessful on the putt = 60% = P(G ∩ P')Where P' denotes not P or the complement of P. In other words, P' means that the golfer needs more than one putt to make the hole.

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Answer:

Step-by-step explanation:

The frame --  if it means the box on the outside which has 4 right angles, or the hexagon in the middle which has 0 right angles

Answer:

6.2 km x 1000 = 6200 m

Step-by-step explanation:

So, 6.2 kilometers = 6.2 × 1000 = 6200 meters. Conversion of 6.2 kilometers to other length, height & distance units -web

Answer:450ft2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the first two points to get a formula of the line E(5, 12), F(-1, 8)

m is found using two points as:

The formula becomes:

Then we find the value of b using one of the points. Let's use point E(5, 12)

So the formula now is:

To find the missing coordinate we substitute x with 2 and y with k:

Answer:

k = 10

Hope it helped:D

Answer: No

Explanation: A function is a relation in which each x-coordinate corresponds to exactly one y-coordinate.

In the relation shown here, notice that

the x-coordinate 2 appears twice.

In one case, 2 corresponds to -4 and in

the other case, 2 corresponds to -4.

Since the x-coordinate 2 corresponds to more than one

y-coordinate, no, this relation is not a function.

Answer:

Step-by-step explanation:

Option B. a = −5, b = −9, c = 12

The general form of the quadratic equation is as following

ax² + bx + c = 0

Where a, b and c are constants.

And the given equation is −5x2 − 9x + 12 = 0

Comparing the given equation to the general form

 ax² + bx + c = 0

−5x2 − 9x + 12 = 0

So, a = -5  , b = -9  and   c = 12

Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

So, the answer is option B: a = −5, b = −9, c = 12

Answer:

50 kg of green tea leaves and 50 kg of assam black tea leaves.

Step-by-step explanation:

Let x kg be the amount of green tea and y kg be the amount of Assam tea.

x+y=100 (1) [mass]

price for 1 kg of assam tea= 7.20/600×1000g

= $12/kg

total cost= 100×10

= $1000

8x+12y= 1000 (2) [cost]

(1)×8: 8x+8y= 800 (3)

(2)-(3): (8x+12y)-(8x+8y)= 1000-800

4y= 200

y= 50 (4)

sub (4) into (1):

x+50= 100

x= 50

Answer: 15/32

Step by step explanation:

The measure of the exterior angle to ∠x in triangle xyz is 92.05°.

The exterior angle of a triangle is the angle between any side of the triangle and the line extending from the opposite vertex. It is formed by extending one of the sides of the triangle past the vertex that is opposite to it.

The measure of the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

exterior to ∠x = ∠y + ∠z

exterior to ∠x = 63.25° + 28.8°

exterior to ∠x = 92.05°

Hence, the measure of the exterior angle to ∠x in triangle xyz is 92.05°.

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Answer:

1, 5 6 10 15 30 because these numbers times certain numbers can also give 30 for instance 1 by 30 is30, 5 by6 is 30 6 by 5 is 30 10 by 3 is 30 15 by 2 is 30 30 by 1 is 30

Answer:

2:5 is less than 7:15

Step-by-step explanation:

7:15 = 7/15 = .47 = .5

the other given ratios are,

9:15 = 3:5 = 3/5 = .6

2:5 = 2/5 = .4

3:5 =3/5 = .6

24:45 = 8:15 = 8/15 = .5

thus, the ratio which is less than 7:15 is 2:5

Answer:

you have to add 2 with the amount of y

Step-by-step explanation:

10 choose 3 with replacement gives you a mere 220 combinations. A “combination” lock uses permutations, so there would be 1000 possibilities.

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

Mathematically, a combination is a selection of things without regard for order.

The formula for “combination with replacement” is:

   \(C^{R} (n,r)=\frac{(n+r-1)!}{r! (n-r)!}\)

10 choose 3 with replacement gives you a mere 220 combinations.

The toss of three identical 10-sided dice would have 220 possible outcomes.

Hence, A “combination” lock uses permutations, so there would be 1000 possibilities.

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Answer:

To solve the problem, we need to create t-tables for each of the given functions for the x-values 2 through 6, and then compare the values of y to determine which function grows the fastest.

For function y = x:

|   x   |   y   |

|-------|-------|

|   2   |   2   |

|   3   |   3   |

|   4   |   4   |

|   5   |   5   |

|   6   |   6   |

For function y = x^2:

|   x   |   y   |

|-------|-------|

|   2   |   4   |

|   3   |   9   |

|   4   |  16   |

|   5   |  25   |

|   6   |  36   |

For function y = x^3:

|   x   |   y   |

|-------|-------|

|   2   |   8   |

|   3   |  27   |

|   4   |  64   |

|   5   | 125   |

|   6   | 216   |

For function y = 4x:

|   x   |   y   |

|-------|-------|

|   2   |  16   |

|   3   |  64   |

|   4   | 256   |

|   5   |1024   |

|   6   |4096   |

From the tables, we can see that the function y = 4x grows the fastest, as its values of y increase much more rapidly than the other functions as x increases. Therefore, the answer is D) y = 4x.

Step-by-step explanation:

Functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

a) L(A) = 1 - 1: This function is not a linear operator because it does not preserve scalar multiplication. Multiplying A by a scalar c would yield L(cA) = c - c, which is not equal to cL(A) = c(1 - 1) = 0.

b) L(A) = 1 + 17: Similar to the previous case, this function is not linear since it fails to preserve scalar multiplication. Multiplying A by a scalar c would result in L(cA) = c + 17, which is not equal to cL(A) = c(1 + 17) = c + 17c.

c) L(1) = C1 + AC: This function is a linear operator since it satisfies both the preservation of addition and scalar multiplication properties. Adding matrices A and B and multiplying the result by scalar c will yield L(A + B) = C(1) + AC + C(1) + BC = L(A) + L(B), and L(cA) = C(1) + cAC = cL(A).

d) L(1) = C°1: This function is a linear operator since it satisfies the properties of linearity. Addition and scalar multiplication are preserved, and L(cA) = C(0)1 = c(C(0)1) = cL(A).

e) L(1) = 1?C: This function is not a linear operator as it does not preserve scalar multiplication. Multiplying A by a scalar c would give L(cA) = 1?(cC), which is not equal to cL(A) = c(1?C).

In summary, functions (c) L(1) = C1 + AC and (d) L(1) = C°1 are linear operators on R^n, while functions (a), (b), and (e) do not satisfy the properties of linearity and therefore are not linear operators.

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Jessica purchased a DVD that was on sale for 12% off.

The sales tax in her county is 3%.

Let, y represent the original price of the DVD.

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will form an algebraic expression, according to the given data.

So,

The original price of the DVD = y

Discount on the original price :

y * 12/100

=3y/25

Price after discount :

y - 3y/25

=25y - 3y/25

=22y/25

Sales tax amount :

22y/25 * 3/100

11y/25 * 3/50

=33y/1250

Final price including the sales tax :

22y/25 + 33y/1250

1100y + 33y/1250

1133y/1250

(This will be considered as the final result.)

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