The equation of the line of best fit for the given data is y = -0.862026x + 8.
first we need to Calculate the mean of X and Y values
n = 7
mean_x = (3.5 + 6.9 + 2.1 + 0.6 + 5.3 + 8.2 + 4.7) / n = 4.5286
mean_y = (5.85 + 1.25 + 7.41 + 9.73 + 3.01 + 0.09 + 4.62) / n = 4.73
Calculate the deviation of X and Y values from their respective means:
x_dev = [x - mean_x for x in [3.5, 6.9, 2.1, 0.6, 5.3, 8.2, 4.7]]
y_dev = [y - mean_y for y in [5.85, 1.25, 7.41, 9.73, 3.01, 0.09, 4.62]]
x_dev = [-1.0286, 2.3714, -2.4286, -3.9286, 0.7714, 3.6714, 0.1714]
y_dev = [1.12, -3.48, 2.68, 5.0, -1.72, -4.64, -0.11]
Calculate the product of deviation of X and Y values:
xy_dev = [x_dev[i] * y_dev[i] for i in range(n)]
xy_dev = [-1.152432, -8.26272, -6.523568, -19.643, -1.32408, -17.02496, -0.018884]
Calculate the sum of deviation of X and Y values, and the sum of the product of deviation of X and Y values:
sum_x_dev = 0.0
sum_y_dev = 0.0
sum_xy_dev = -53.945584
Calculate the slope and y-intercept of the line of best fit:
slope = sum_xy_dev / sum([(x - mean_x)**2 for x in [3.5, 6.9, 2.1, 0.6, 5.3, 8.2, 4.7]])
y_intercept = mean_y - slope * mean_x
slope = -0.862026
y_intercept = 8.176187
we can now Write the equation of the line of best fity = -0.862026x + 8.176187
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Need the answer please, soon as possible
9514 1404 393
Answer:
(d) 27.4%
Step-by-step explanation:
The desired percentage is ...
(juniors for Kato)/(total juniors) × 100%
= 129/(129 +194 +147) × 100%
= (129/470) × 100% ≈ 27.4%
About 27.4% of juniors voted for Kato.
Here is a table classifying 116 thousand US households (in thousands) in
2013 by tenure and insurance status:
Insurance status Owns home Rents home
Insured
71
13
Uninsured
27
5
Find the relative frequency marginal distribution of insurance status.
Round to the nearest whole percent.
Insured: %
Uninsured: %
Insured = 72%.
Uninsured = 28%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Here is a table classifying 116 thousand US households (in thousands) in
2013 by tenure and insurance status:
Insurance status Owns home Rents home
Insured 71 13
Uninsured 27 5
Total house = 71 + 13 + 5 + 27 = 116
Insured = (71 + 13)/116 = 72%.
Uninsured = (5 + 27)/116 = 28%.
Therefore, 72% = insured and 28% = uninsured.
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in the illustration below ,The two lights are designed tc pperate at 6 volts, 5 amps each,
5
f the power source is12 volts, what will be the value of the Resistor?
Round to the tenth position. (0.00)
The value of the resistor needed in this scenario is approximately 1.2 ohms.
To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.
Using Ohm's Law, we have the formula:
V = I * R
Where:
V is the voltage across the resistor (12 volts in this case),
I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),
R is the resistance of the resistor (which we need to find).
Rearranging the formula, we have:
R = V / I
Plugging in the values:
R = 12 volts / 10 amps
R = 1.2 ohms
Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.
It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.
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you mix 1/2 cup of oats for every 1/4 cup of honey to make 12 cups of granol. How much oats and honey do you use?
Given that you mix 1/2 cup of oats for 1/4 cup of honey to make 12 cups of granol, we can write this as:
\(undefined\)Jamal and his dad went scuba diving. They went on a 54-foot dive, descending from a motor boat located on the Gulf of Mexico. The boat was located
at sea level.
Where on a number line would you plot a point to represent the boat's location?
What is the measure of AC? Thanks!!
Answer:
arc AC = 21 degrees
Step-by-step explanation:
2(3x-1.5) = 3x+9
6x-3 = 3x+9
3x = 12
x = 4
arc AC = 3(4) + 9 = 21
Christine is making chocolate chip cookies for a bake sale. She needs ¾ cup brown sugar for each batch of cookies she makes. She wants to make 3 batches of cookies. She has 3 cups of brown sugar. Does Christine have enough brown sugar to make 3 batches of cookies? Without actually solving the problem, explain why or why not.
what complex number has an absolute value of 5 ?
Answer:
the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}
please give me heart
The surface area of a piece of paper is 345 cm2. Use the fact that 10 mm = 1 cm to convert this area to mm2
Step-by-step explanation:
345cm²=34500mm²
:;
cm in mm(*10)
cm² in mm²(*100)
cm³ in mm²(*1000)
I'd appreciate the brainliest
W Over the last three months Ophelia, Aaron, Nathan, and Rebecca recorded their weight. The table shows their initial and final weights. Question: 2/5 Name Ophelia Aaron Nathan Rebecca Initial Weight, lbs 145 178 205 136 REVIEW Final Weight, lbs 157 163 217 128 Whose weight had the least absolute change? NOTES
The persons weight that had the least absolute change is: Rebecca
How to find the change in weight?We are given the initial and final weights of Ophelia, Aaron, Nathan and Rebecca.
Ophelia's change in weight = 157 - 145 = 12 lbs
Aaron's change in weight = 163 - 178 = -15 lbs
Nathan's change in weight = 217 - 136 = 81 lbs
Rebecca's change in weight = 128 - 136 = -8 lbs
The absolute value of a number or integer is the actual distance of the integer from zero, in a number line. Therefore, the absolute value is always a positive .
Thus, "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).
Therefore, the least absolute change is |-8 lbs| = 8 lbs
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What is the meaning of conditionally promoted in school
Determine if it is possible to form a triangle using the set of segments with the given measurements.
4.5 in., 5.6 in, 10 in.
a) No, adding all three sides does not add up to the correct measurements.
b) No, because two sides add up to less than the third one.
c) No, because two sides add up to more than the third one.
d) Yes, because two sides add up to less than the third one.
e) Yes, because two sides add up to more than the third one.
Answer:
e) Yes, because two sides add up to more than the third one.-------------------------
Apply the Triangle Inequality Theorem.
It states that:
For a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side.We'll take the sum of two shortest sides and compare with the longest:
4.5 + 5.6 = 10.1 > 10It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.
The matching answer choice is e).
Mona is four years older than Karly.
Alexis is twice as old as Mona. The
sum of their ages is 48. How old is
each girl?
Answer:
Let karly's age be x
mona is four years older
mona = 4+x
Alexis it twice as old as mona
alexis= 2(4+x)
alexis= 8+2x
the sum of their ages is 48
x + 4+x + 8+2x= 48
4x+12=48
4x=48-12
4x=36
x=9
katly is nine years old
mona = 4+x
mona = 4+9
mona = 13
mona is 13 years old
alexis = 8+ 2x
alexis = 8+ 2(9)
alexis = 8+18
alexis = 26
alexis is 26 years old
Please Help Will Give Points
Answer:
6.2cm
Step-by-step explanation:
I plotted values in the equation to get the rightful answer.
The approximate radius of the sphere with volume of 998 cm³ is 6.2 cm
Volume of a sphere:
V = 4 / 3πr³where
r = radius
V = 998 cm³
π = 3.14
V = 4 / 3 × 3.14 × r³
V = 12.56 r³ / 3
998 = 12.56 r³ / 3
cross multiply
998 × 3 = 12.56r³
2994 = 12.56r³
divide both sides by 12.56
r³ = 2994 / 12.56
r = ∛238.375796178
r = 6.20041444
r ≈ 6.2 cm
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A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is not yellow
P(not yellow)
The probability that it is not yellow candies will be 119/139.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A bag contains;
Number of red candies = 42
Number of green candies = 45
Number of yellow candies = 20
Number of purple candies = 32
Now,
Total number of candies in a bag = 42 + 45 + 20 + 32
= 139
And, The number of candies in a bag not contain yellow candy
= 139 - 20
= 119
Thus, The probability that it is not yellow candies will be;
Probability = Number of not yellow candies / Total candies
= 109 / 139
Therefore, The probability that it is not yellow candies will be 119/139.
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(6) In one game, a football quarterback
completed 17 passes for a total gain of 194 yards.
What was the average number of yards gained per
pass completion?
In football quarterback, a total gain of 11 yards was per pass.
Here we have been given that the football quarterback completed 17 passes for a total gain of 194 yards. This can be numerically stated as,
17 passes = 194 yards
We have been asked the number of yards gained in unit pass, that is,
1 pass = x yards
Where x = number of yards
Now by using unitary method we will get the average number of yards gained 1 per pass.
Therefore combining the equation (1) and (2) and solving them we will get,
17 pass = 194
1 pass = 194/17 yards
= 11.4 ≈ 11 yards
Thus, 11 yards were gained per pass.
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Find the perimeter of this L shape.
Answer: undefined, not enough information
Step-by-step explanation:
Answer:
15+19 =34 is the perimeter of the closed figure
hope it helped you
Your engineering position requires frequent travel to the west coast, typically through Chicago. In reviewing historical airline data, you have determined that over the last year flights into Chicago on Southwest have been normally distributed, arriving an average of 72.3 minutes late with a standard deviation of 9.8 minutes. Yesterday, a travel agent informed you that Southwest recently changed their scheduling into Chicago and has improved arrival times. To confirm this claim, you collect the arrival times for a random sample of 47 Southwest flights arriving into Chicago, and find a sample mean of 70.7 minutes and a sample standard deviation of 7.1 minutes. Has there been a change in the mean arrival times on Southwest
Answer:
The given data does not support the submission that there has been a change in the mean arrival times on Southwest
Step-by-step explanation:
The known mean late arrival time, μ = 72.3
The known standard deviation in late arrival time, σ = 9.8 minutes
The number of flights in the sample, n = 47
The sample mean late arrival time, \(\overline x\) = 70.7
The sample standard deviation late arrival time, s = 7.1
Using a significance level of 0.01
The null hypothesis is, H₀ ; μ = 70.7
The alternative hypothesis is, Hₐ ; μ ≠ 70.7
The test statistic is given as follows;
\(z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}\)
\(z=\dfrac{70.7-72.3 }{\dfrac{9.8 }{\sqrt{47}}} \approx -1.119290547\)
∴ z ≈ -1.12
p-value = 2 × P(z < -1.12) = 2 × 0.13136 = 0.26272
Given that the p-value of 0.26272 is larger than the significance level, 0.05, we fail to reject the null hypothesis
Therefore, there is not enough statistical evidence to show that there has been a change in the mean arrival times on Southwest
HELP MEEEEE PLZZZZZ!!!
Answer:
75.02 ft and 64.62 ft.
Where is the function 3(x + 4)(x – 7)^3 > 0?
Answer::
\((-\infty,-4)\cup(7,\infty)\)Explanation:
Given the function:
\(3\left(x+4\right)\left(x-7\right)^3\)We want to determine the interval in which the function is greater than 0.
First, solve for the critical values.
\(\begin{gathered} 3\left(x+4\right)\left(x-7\right)^3=0 \\ x+4=0,x-7=0 \\ x=-4,x=7 \end{gathered}\)So, the following are the possible intervals:
\(\begin{gathered} (-\infty,-4) \\ (-4,7) \\ (7,\infty) \end{gathered}\)We test each of the intervals:
\(\begin{gathered} (-\infty,-4),\text{ At }x=-5:3\left(x+4\right)\left(x-7\right)^3=5184>0 \\ (-4,7),\text{ At x}=0:3\left(x+4\right)\left(x-7\right)^3=-4116<0 \\ (7,\infty),\text{ At }x=8:3\left(x+4\right)\left(x-7\right)^3=36>0 \end{gathered}\)Therefore, the function is greater than zero in the intervals:
\((-\infty,-4)\cup(7,\infty)\)The result can be confirmed using the graph below:
What’s the perimeter of a square with a side of 9 cm
Answer:
32
Step-by-step explanation:
9+9+9+9 is 32 so thats your answer because all sides on a square are equal
Answer:
\(\boxed {\tt 36 \ centimeters}\)
Step-by-step explanation:
The perimeter is the sum of all the side lengths and a square has 4 equal sides.
The perimeter of a square can be found by adding the side length 4 times or multiplying the side length by 4.
\(p=4s\)
The side length is 9 centimeters.
\(s= 9 \ cm\)
Substitute the value into the formula.
\(p=4(9 \ cm)\)
Multiply
\(p= 36 \ cm\)
The perimeter of a square with a side length of 9 centimeter is 36 centimeters.
Solve.
3x+2y−z=8
2x+2z=−4
x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
How to resolve a system of linear equations
In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:
x = 4 - 3 · y
Second, substitute x in the first two equations:
3 · (4 - 3 · y) + 2 · y - z = 8
12 - 9 · y + 2 · y - z = 8
- 7 · y - z = - 4
2 · (4 - 3 · y) + 2 · z = - 4
8 - 6 · y + 2 · z = - 4
- 6 · y + 2 · z = - 12
Third, clear z in the first equation derived in the previous step:
z = 4 - 7 · y
Fourth, substitute z in the second equation derived in the second step:
- 6 · y + 2 · (4 - 7 · y) = - 12
- 6 · y + 8 - 14 · y = - 12
- 20 · y = - 20
y = 1
Fifth, calculate y and x:
z = 4 - 7 · 1
z = - 3
x = 4 - 3 · 1
x = 1
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
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Someone can help me please help #4
A landscaping company charges $48 per cubic yard of mulch plus a delivery charge of $28. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch.
The linear function for the total cost C is:
\(\text{C} = 28 + 48\text{x}\)What is a function?A function is an expression, rule, or law that defines a relationship between one variable.
Example:
\(f(\text{x}) = 2\text{x} + 1\)
\(f(1) = 2 + 1 = 3\)
\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Charge per cubic yard = $48Delivery charge = $28The total cost for x cubic yards.
\(\bold{C = 28 + 48x}\)
Thus, the function is C = 28 + 48x.
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Question 5 of 10
Mackenzie took out a payday loan for $1100 that charged a $95 fee. If the
loan matures in 2 weeks, what is the approximate effective interest rate of the
loan?
OA. 862%
OB. 86%
OC. 76%
OD. 762%
what is the GCF of 3 and 18
Answer:
3
Step-by-step explanation:
3 is a factor of 3 and of 18.
Answer: 3
Answer:
3 is the GCF!!!!!!HOPE THIS HELPS!!!
"A number decreased cubed by 24"
The expression that represents the sentence "A number cubed decreased by 24" is given as follows:
x³ - 24.
What is the algebraic expression that models the sentence?The sentence for this problem is defined as follows:
"A number cubed decreased by 24".
The number is unknown, hence the variable that represents the number is given as follows:
x.
The cube of the number is given as follows:
x³.
The number is then decreased by 24, hence we subtract the expression x³ by 24 to obtain the algebraic expression as follows:
x³ - 24.
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Using the information below, answer the next 3 questions: The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places)
Answer: 0.655
Step-by-step explanation:
Let X be a random variable that represents percent of fat calories that a person in America consumes each day.
As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).
Sample size : n= 16
The probability that the average percent of fat calories consumed is more than 35:
\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)
Hence, Required probability =0.655
Which of the following is the equation that represents the function given in the table?
x y
–2 16
–1 11
1 1
2 –4
1. Y= -1/5/x+6
2. Y=6x-1/5
3. Y=-5x+6
y=6x-5
Answer:
3. y=-5x+6.
Step-by-step explanation:
if to substitute given coordinates into equations and check equalities, then
y(-2)=-5*(-2)+6=16;
y(-1)=-5*(-1)+6=11;
y(1)=-5*1+6=1;
y(2)=-5*2+6=-4.
It means correct answer is 3.
Find the local maxima and local minima for the given function and also find the local maximum and local minimum values f(x)=x 3 −6x 2 +9x+15
The local maxima and local minima for the given function is x= 3 and
x= 1.
Here,
\(f(x) = x^{3} -6x^{2} +9x +15 = 0\\f(x) = 3x^{2} -12x +9\)
In order to have local maxima and minima, f′(x) must equal 0.
\(f(x) =0 = > 3(x^{2} -4x+3)=0\\=3(x-3)(x-1) = 0\\ x=3,x=1\)
1) When x = 3
In this instance, f′(x) = 3(x-3)9x-1) is negative when x is little less than 3 and positive when x is slightly more than 3.
Hence, when x rises through 3, f′(x) turns from negative to positive.
Hence, x=3 is a local minimum.
Case 2, x = 1,
In this instance, f′(x) = 3(x-3) (x-1) is positive when x is little less than 1 and f′(x) is negative when x is slightly greater than 1. As x rises through 1, f′(x) sign's shifts from positive to negative.
Hence, x=1 is a local maximum point.
the value of local maximum = f(1) = 19
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