The regression equation is:
y = 20.85 + 0.735 * x
How to solveYear Motor registration (000 nos.) No. of tyres sold (000 nos.)
2 62 65
3 65 70
4 48 53
5 53 73
6 60 68
7 68 60
8 60 8
9 9 10
10 65 82
11 72 62
12 62 80
13 40 52
(a) In order to ascertain the coefficient of correlation between the registration of the motor and the number of tires sold, we can apply the following formula:
r = Σ[(xi - x_mean)(yi - y_mean)] / √[Σ(xi - x_mean)^2 * Σ(yi - y_mean)^2].
To do this, we need to determine the mean values for the motor registration (x) and the number of tyres purchased (y).
[tex]x_m_e_a_n = (62 + 65 + 48 + 53 + 60 + 68 + 60 + 9 + 65 + 72 + 62 + 40) / 12 = 664 / 12 = 55.33\\y_m_e_a_n = (65 + 70 + 53 + 73 + 68 + 60 + 8 + 10 + 82 + 62 + 80 + 52) / 12 = 733 / 12 = 61.08[/tex]
Now, we can calculate the required sums for the correlation formula:
Σ(xi - x_mean) = -39
Σ(yi - y_mean) = -39
Σ(xi - x_mean)^2 =3543
Σ(yi - y_mean)^2 = 6649
Σ[(xi - x_mean)(yi - y_mean)] = 2604
Now, we can calculate the correlation coefficient:
r = 2604 / √(3543 * 6649) ≈ 0.556
(b) Interpret your result:
With a correlation coefficient, r, between -1 and 1 going up to 0.556, it shows up as a significant positive relationship.
So when the number of car registrations augments, the sales of tires will also go up.
(c) Test the significance of the result:
As the t-statistic is listed as 1.934, we can analyze it using the critical t-value from a t-distribution table which is around 2.228.
Consequently, since the t-statistic (1.934) is lower than the critical t-value (2.228), the correlation between them is not statistically significant at the 0.05 level.
(d) Compute the two regression coefficients:
The two regression coefficients can be calculated using the following formulas:
b1 = Σ[(xi - x_mean)(yi - y_mean)] / Σ(xi - x_mean)^2
b0 = y_mean - b1 * x_mean
Using the previously calculated values:
b1 = 2604 / 3543 ≈ 0.735
b0 = 61.08 - 0.735 * 55.33 ≈ 20.85
The regression equation is:
y = 20.85 + 0.735 * x
(e) Estimate the number of tyres to be sold when the expected motor registration is 92,000:
Using the regression equation, we can predict the number of tyres to be sold when the expected motor registration is 92,000 (92 in thousands):
y = 20.85 + 0.735 * 92 ≈ 87.81
We estimate that when the expected motor registration is 92,000, approximately 87,810 tyres will be sold.
It should be stated that the relationship was not considered to be statistically relevant so care is advised.
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help see photo on simple interest
The principal amount was £1260, and the annual interest rate is 5.5%.
Given that, Olivia gets £1606.50 and £1675.80 after 5 years and 6 years of investment in simple interest respectively.
SI = principal × rate × time / 100
So,
P + 5pr = £1606.50
P = £1606.50 - 5pr............(i)
P + 6pr = £1675.80
P = £1675.80 - 6pr.........(ii)
Therefore,
£1606.50 - 5pr = £1675.80 - 6pr
Pr = 69.3
Put the value of pr in eq(i)
P + 5(69.3) = 1606.50
P = 1606.5 - 346.5
P = 1260
Now,
(1260)r = 69.3
r = 0.055
The annual interest is 5.5%
Hence, the principal amount was £1260, and the annual interest rate is 5.5%.
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Find each angle and arc measure.
m∡RST = ______ degrees
m∡RUT = ______ degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
m∡RST angle is 146 degrees and m∡RUT is 157 degrees are the arc measures.
Let us find angle RVT
The sum of four angles should be 360 degrees
∠RVS +∠SVU+∠UVT+∠RVT=360
64+139+75+x= 360
278+x=360
x=360-278
x=82 degrees
Arc measure m∡RST =64+82
m∡RST = 146 degrees
m∡RUT = 82+75
m∡RUT = 157 degrees
Hence, m∡RST is 146 degrees and m∡RUT is 157 degrees are the arc measures.
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The expression V2 (V2Z) is called _________ ?
The expression [tex]V^2 (V^2_Z)[/tex] is called mean-square speed.
What is mean-square speed?In Mathematics and Science, mean-square speed is sometimes referred to as root-mean-square speed and it can be defined as a measure of the average value of square-speed of particles that are found in a molecule, gas, or liquid.
Mathematically, the mean-square speed of any particle is denoted or represented by this expression [tex]V^2 (V^2_Z)[/tex].
This ultimately implies that, mean-square speed is always calculated as the square root of the average value of the squares of the speeds (velocities) of each particles in thermodynamics and kinetic theory of gases.
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Complete Question:
The expression [tex]V^2 (V^2_Z)[/tex] is called ______?
Principle interviewed all math and english teachers and asked them to rank his school leadership on a scale of 1 to 10. He will use the result of the survey to report to his boss to show his school management abilities
1.Non response and household bias
2.Sampling and household bias
3.Response and non response bias
4.Response and sampling bias
The correct answer is 3. Response and non-response bias.
Response bias occurs when the way that questions are asked or worded, or the context in which they are asked, influences how respondents answer them. This can lead to inaccurate or incomplete information being collected.
Non-response bias occurs when some individuals selected to participate in a survey do not respond. This can happen for various reasons, such as being unavailable, unwilling, or unable to participate. Non-response bias can skew the results of a survey because the characteristics of those who do not respond may differ from those who do respond.
In this scenario, the principal has asked all math and English teachers to rank his school leadership on a scale of 1 to 10. If some teachers do not respond to the survey or are unavailable, unwilling, or unable to participate, this could lead to non-response bias.
Additionally, if the principal has a reputation for being well-liked or well-respected, some teachers may feel pressured to give a higher rating than they otherwise would, which could lead to response bias.
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The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 11654 and the sum of squares of regression (SSR) was 11405.0.
The value of R² (coefficient of determination) is 0.0214
We know that the formula for the coefficient of determination is,
R² = 1 - (SSR / SST)
where, R² is the coefficient of determination
SST is the total sum of squares
SSR is the sum of squares of regression
Here, the total sum of squares (SST) = 11654
and the sum of squares of regression (SSR) = 11405
Using above formula,
R² = 1 - (SSR / SST)
R² = 1 - (11405 / 11654 )
R² = 1 - 0.9786
R² = 0.0214
This is the required value.
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Find the complete question below.
A rectangle has an area of 54 square inches and a length of 6 inches. What is the width, in inches, of the rectangle?
Answer:
width = 9 in
Step-by-step explanation:
Area = A = length x width = w x l
w = A/l = 54 in²/6 in = 9 in
DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
skill code: 1604005
TT
The length BC of the bisected line segment is: 11.5
What is the length of the line after bisection?Usually a line that bisects a segment usually divides that segment into two equal parts.
Now, we are told that DE bisects Line AC at point B where AB = 3a + 4.
Thus, from the idea of a bisected segment, we can easily say that:
2(3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
6a = 15
a = 15/6
a = 5/2
a = 2.5
Thus:
AB = BC = 3(2.5) + 4
BC = 11.5
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Please someone help me. i really dont get this. If you help i give 40 POINTS Please help me
Answer:
Only Carla's
Step-by-step explanation:
I believe the answer is only Carla's because even though the left side is factored, there is still an 8 on the right side. To apply the zero product property rule, the equation needs to equal 0
Meanwhile Carla's works because then the equation would be x²=9 which we can easily take the square root of
Answer: Only Carla
Step-by-step explanation:
Only Carla
Carla said:
(x+1)(x-1)=8 FOIL
x²-1=8
x²=9
x=±3
Jordan said:
He will use 0 property rule but the factored portion must =0 It equals 8, so you can't use that property.
[tex]x^2=225[/tex]
Use the square root property to solve the equation. The equation has real number solutions.
The figures below are rectangles. What polynomial in standard form represents the area of the shaded region?
Answer:
A
Step-by-step explanation:
(x+5)(x-1)－(x+1)(x-4)=7x-1
Abigail is making a jewelry box and covering the entire box with decorative tape. How many square inches of tape will Abigail use to cover the jewelry box?
The amount of tape that Abigail will use to cover the jewelry box is given as follows:
298 in².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The dimensions of the box are given as follows:
6 in, 12.5 in and 4 in.
Hence the amount of tape, given by the surface area, is obtained as follows:
S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)
S = 298 in².
Missing InformationThe dimensions of the box are given as follows:
6 in, 12.5 in and 4 in.
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supply a polynomial, and a monomial
The monomials in the expression are given as follows:
x², xy, -8y².
The simplified polynomial is given as follows:
9x² + 9xy - 72y².
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
The expression for this term are given as follows:
9(x² + xy - 8y²).
The inner term is a polynomial composed by the sum/subtraction of the monomials presented as follows:
x², xy, -8y².
Applying the distributive property, the simplified polynomial is given as follows:
9x² + 9xy - 72y².
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5 ft:25 ft to fraction in its simplest form
Answer:
The answer is 1/5
Step-by-step explanation:
5ft:25ft=5ft/25ft=1/5
Answer:
1/2
Step-by-step explanation:
-x^2(x-4)
simplify the equation
Answer:
-x³ + 4x²
Step-by-step explanation:
-x^2(x-4)
Distribute
-x³ + 4x²
So, the answer is -x³ + 4x²
Use the diagram to complete the proportion. (Geometry)
FDBGEC
Answer:
The answer is
13)CE
14)EG
15)BD
16)BF
4. Use the formula found in Exercise #31 to calculate
the initial deposit of an account that is worth
$14,472.74 after earning 5.5% interest compounded
monthly for 5 years. (Round to the nearest dollar.)
The amount that was initially deposited is obtained as $10,100.
What is Compound interest?Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods.
The interest earned in each subsequent period is added to the principal, and the interest is then calculated on the new, larger amount.
We have that;
A = P (1 + r/n)^nt
Then we have;
A = amount
P = principal
r = rate
n = number of times compounded
t = time in years
Then;
14,472.74 = P(1 + 0.055/12)^12 * 5
P = $10,100
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If m∡KJL = (3x +2) degrees and ∡KLJ = (7x - 32) degrees, find mKL⌢.
mKL⌢=z____ degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
Answer:
angle m∠WXY intercepts the diameter WY.
Then,
m∠WXY = 90°
(13x - 1)° = 90°
13x - 1 = 90
Add 1 to each side.
13x = 91
Divide each side 13.
x = 7
Step-by-step explanation:
HOPE THIS HELPSSS
find f(g(4)) and g(f(4)) given f(x)=2x-3 and g(x)=5x^2-4x+1
Answer:
g(f(4)) = 106.
Step-by-step explanation:
To find f(g(4)), we first need to find
g(4):g(4) = 5(4)^2 - 4(4) + 1 = 80 - 16 + 1 = 65
Now that we know g(4) is 65, we can find
f(g(4)):f(g(4)) = f(65) = 2(65) - 3 = 127
Therefore,
f(g(4)) = 127.
To find g(f(4)), we first need to find f(4):f(4) = 2(4) - 3 = 5
Now that we know f(4) is 5, we can find g(f(4)):
g(f(4)) = g(5) = 5(5)^2 - 4(5) + 1 = 125 - 20 + 1 = 106
Therefore, g(f(4)) = 106.
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 2 ft by 2 ft by 12.5 ft. If the container is entirely full and, on average, its contents weigh 0.22 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answer:
38.81 pounds
Step-by-step explanation:
Considering the definition of right rectangular prism and its volume, the total weight of the contents is 38.81 pounds.
Right rectangular prism
A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.
Volume of right rectangular prism
To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.
That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.
Volume of the container
In this case, you know that:
the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.
So, the volume of the container is calculated as:
7.5 ft× 11.5 ft× 3 ft= 258.75 ft³
Then, the total weight of the contents is calculated as:
258.75 ft³× 0.15 pounds per cubic foot= 38.8125 pounds≅ 38.81 pounds
Finally, the total weight of the contents is 38.81 pounds.
if x=4 units, y=12 units, and h=8 units find the area of the parallelogram
The area of a parallelogram with the given base and height is 96 square units.
Given that, x=4 units, y=12 units, and h=8 units.
From the given figure,
Area of parallelogram = Base×Height
Here, b=4+12 =16 units and h=8 units
Now, area of parallelogram = 16×8
= 96 square units
Therefore, the area of a parallelogram with the given base and height is 96 square units.
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A bag contains 3 black balls, 2 blue balls, and 3 green balls. A
random sample of 4 balls is selected. Given that x is the number of
black balls. y is the number of blue balls.
a) Find the joint probability function f(x, y)
b) Find the joint probability distribution of f(x, y)
The requreid, the joint probability function f(x, y) is:
f(0,0) = 3/14
f(0,1) = 9/28
f(0,2) = 3/28
f(1,0) = 9/28
f(1,1) = 9/28
f(2,0) = 3/14
f(2,1) = 3/14
f(3,0) = 1/14
To evaluate the joint probability function f(x, y), we need to determine the probability of selecting x black balls and y blue balls out of a sample of 4 balls. We can do this using the hypergeometric probability distribution formula:
f(x,y) = P(X = x, Y = y) = (C(3, x) * C(2, y) * C(3, 4-x-y)) / C(8, 4)
where C(n, k) represents the number of combinations of k items chosen from a set of n items.
Plugging in the values, we get:
f(0,0) = (C(3,0) * C(2,0) * C(3,4-0-0)) / C(8,4) = 3/14
f(0,1) = (C(3,0) * C(2,1) * C(3,4-0-1)) / C(8,4) = 9/28
f(0,2) = (C(3,0) * C(2,2) * C(3,4-0-2)) / C(8,4) = 3/28
f(1,0) = (C(3,1) * C(2,0) * C(3,4-1-0)) / C(8,4) = 9/28
f(1,1) = (C(3,1) * C(2,1) * C(3,4-1-1)) / C(8,4) = 9/28
f(2,0) = (C(3,2) * C(2,0) * C(3,4-2-0)) / C(8,4) = 3/14
f(2,1) = (C(3,2) * C(2,1) * C(3,4-2-1)) / C(8,4) = 3/14
f(3,0) = (C(3,3) * C(2,0) * C(3,4-3-0)) / C(8,4) = 1/14
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(1/3)k=-4=7
what's k
The value of the variable k is 33
What are algebraic expressions?Algebraic expressions are simply described as the expressions that consist of variables, terms, coefficients, constants and factors.
These expressions also consist of certain mathematical operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationFrom the information given, we have that;
(1/3)k - 4=7
collect the like terns
1/3k = 7 + 4
Add the values
1/3k = 11
cross multiply the values, we have;
k = 11(3)
Multiply the values
k = 33
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confusing. someone please help! (there are 2 questions)
Answer:
Step-by-step explanation:
The rule for a triangle is that if you add the 2 shorter sides, it must be greater than the longest side (can't even be =, must be bigger.
A. 36+48>60 true yes triangle
B 6.2+5.7>9.4 yes triangle
C. 20+20 is not greater than 50 no not at triangle
D. 12+24>32 yes triangle
Vertical angles mean angles across from each other when 2 lines intersect.
So:
B, C, D are vertical angles
The vertices of a triangle are at (0,0), (8,8) and (4,12). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x ?
The volume of the figure that was created by the triangle being rotated, would be 94. 83 units ³
How to find the volume ?When a triangle is rotated about y = x, a right circular cone is created. The formula is:
= π r² h / 3
We need to find the height and radius. The coordinates for the right circular cone are:
(0,0) - (0,0)
(8,8) - (8,8)
(4,12) - (12,4)
Using this, we find that the radius is 4 units. The height can be found by using any point such as ( 12, 4).
= √ ( ( 12 - 8) ² + ( 4 - 8 ) ²)
= 5. 66 units
The volume would therefore be:
= π x 4² x 5. 66 / 3
= 94. 83 units ³
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Solve these 4 problems
The perimeter and the area of each composite figure are, respectively:
Case 1: p = 77.6 cm, A = 304 cm²
Case 2: p = 25.1 ft, A = 28 ft²
Case 3: p = 42 mi, A = 52.5 mi²
Case 4: p = 56.5 in, A = 179.424 in²
How to determine the perimeter and the area of a figure
In this problem we need to determine the perimeter and the area of four composite figures, that is, figures formed by combining triangles and rectangles, whose area formulas are listed below:
Triangle
A = 0.5 · b · h
Rectangle
A = b · h
Where:
A - Areab - Baseh - HeightNow we find the perimeter and the area of each figure:
Case 1
p = 2 · (18.8 cm) + 2 · (20 cm)
p = 77.6 cm
A = (15.2 cm) · (20 cm)
A = 304 cm²
Case 2
p = 10 ft + 8.1 ft + 7 ft
p = 25.1 ft
A = 0.5 · (10 ft) · (5.6 ft)
A = 28 ft²
Case 3
p = 17.5 mi + 6 mi + 18.5 mi
p = 42 mi
A = 0.5 · (17.5 mi) · (6 mi)
A = 52.5 mi²
Case 4
p = 20 in + 13.9 in + 15 in + 7.6 in
p = 56.5 in
A = (7.6 in) · (13 in) + 0.5 · √[(13.9 in)² - (13 in)²] · (13 in) + 0.5 · √[(15 in)² - (13 in)²] · (13 in)
A = 98.8 in² + 31.982 in² + 48.642 in²
A = 179.424 in²
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Analyze the diagram below and complete the instructions that follow.
Find the unknown side length, x. Write your answer in simplest radical form.
A. 4√32
B. 22
C. 16√5
D. 16√13
Answer:
C. 16√5
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]48^2 = 32^2 + x^2\\2304 = 1024 + x^2\\x^2 = 1280\\x = \sqrt{1280}\\[/tex]
[tex]\sqrt{1280}[/tex] is also equal to [tex]16\sqrt{5}[/tex].
Question 10 of 10
How does the graph of f (x) 3x +2 +4 relate to its parent function?
A. The parent function has been compressed.
B. The parent function has been translated up.
C. The parent function has been stretched.
D. The parent function has been translated to the left.
SUBMIT
The graph of f(x) relate to its parent function by B. The parent function has been translated up.
How does the graph of f(x) relate to its parent function?Given that
f(x) = 3x +2 +4
When evaluated, we have
f(x) = 3x + 6
The parent function of the above is
f(x) = 3x
When f(x) = 3x is compared to f(x) = 3x + 6, we have
Difference = 6
This means that the parant function is translated up by 6 units
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9. The prices of sweat shirts at five different stores are $6, $12, $11, $15, and $18. The mean price is $12.40 and the median price is $12. Identify the outlier and describe how the mean and median for this data set are affected by it.
The outlier in this data set is the sweatshirt priced at $18 since it is significantly higher than the rest of the prices.
How does the outlier affect the mean and median for the data set?The mean is affected more by outliers than the median.
In the provided data, the mean is higher than the median, which suggests that there may be an outlier pulling the average up. The outlier value of $18 is causing the mean to be higher.
If we remove the outlier value of $18, the mean price would be (6+12+11+15)/4 = $11, which is lower than the original mean of $12.40.
On the other hand, the median would remain the same since it is not affected by extreme values.
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n - 29 = -53
What is n????
17. The diameter of a cylinder is 7 yards. The height
is 12 yards. What is the volume, in terms of and
to the nearest cubic yard, of the cylinder?.7.GR.2.3
The volume of the cylinder that has a diameter of 7 yards and a height of 12 yards is: 147π cubic yard.
What is the Volume of a Cylinder?The volume of a cylinder can be determined by applying the volume formula which is given as:
Volume (V) = πr²h,
where "r" is the radius of the cylinder
"h" is the height of the cylinder
π is a constant
Given the following:
Diameter of cylinder = 7 yards, thus, radius (r) = 7/2 = 3.5 yards
Height (h) = 12 yards
Plug in the values:
Volume of the cylinder = π * 3.5² * 12 = 147π cubic yard.
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