The estimated slope is approximately 2.344
The given table is presented as follows;
[tex]\begin{array}{ccc}Number \ of Bids &&Price \ in \ Dollars\\1&&23\\2&&34\\4&&44\\9&&46\\10&&50\end{array}[/tex]
The regression line formula to be considered = [tex]\bar u = b_0 + b\cdot \bar x[/tex]
The required parameter is;
The estimated slope
The method to find the estimate slope;
The least squares regression formula (method) is presented as follows;
[tex]\bar u = b_0 + b\cdot \bar x[/tex]
Where;
b₀ = The y-intercept
[tex]\mathbf{ b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right) }{\sum \left(x_i - \bar x\right )^2 } = The \ estimated \ slope}[/tex]
From MS Excel, we have;
[tex]\bar x[/tex] = 5.2, [tex]\bar u[/tex] = 39.4
[tex]\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right)[/tex] = 156.6
[tex]{\sum \left(x_i - \bar x\right )^2 }[/tex] = 66.8
Therefore;
The estimated slope, b = 156.6/66.8 ≈ 2.344 (by rounding the answer to three decimal places)
Learn more about regression line here;
https://brainly.com/question/23528764
The weight of bags of fertilizer is normally distributed with a mean of 50 pounds and standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh:
a. Between 45 and 55 pounds?
b. At least 56 pounds?
c. At most 49 pound?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Normal Distribution:
[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]
For point a:
[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]
[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]
For point b:
[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]
For point c:
To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]
[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]
what is the length of AB? round to one decimal place
Answer:
A=0
Step-by-step explanation:
DAC=BAD
A=0
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92.
Round your answers to two decimal places.
(a) State the point estimate for the population mean cost of fast food bills at this restaurant $
(b) Calculate the 95% margin of error. $
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
$
≤ µ ≤ $
(d) What sample size is needed if the error must not exceed $1.00?
n =
First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.
Doing this, we get that:
a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
b) The 95% margin of error is $1.64.
c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
d) The sample size needed is 135.
Question a:
The point estimate for the population mean is the sample mean, which is of $18.21.
The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
Question b:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]
The 95% margin of error is $1.64.
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57
The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85
The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
(d) What sample size is needed if the error must not exceed $1.00?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.96*5.92[/tex]
[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]
[tex]n = 134.6[/tex]
Rounding up:
The sample size needed is 135.
For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328
To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000
10(2x-3)=10
find the value of x
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
10(2x-3)=1020x-30=1020x=10+3020x=40x=40/20X=2It is given that,
→ 10(2x-3) = 10
Then find required value of x,
→ 10(2x-3) = 10
→ 20x-30 = 10
→ 20x = 10+30
→ 20x = 40
→ x = 40/20
→ [x = 2]
Hence, the value of x is 2.
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism. Please explain.
a) 315 cm2 squared
b) 480 cm2 squared
c) 510 cm2 squared
d) 570 cm2
Answer:
Option (C)
Step-by-step explanation:
Surface area of a right prism = 2(Area of the triangular base) + Ph
Here, P = Perimeter of the base
h = Height of the prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the prism = 15 cm
Perimeter of the base = (5 + 12 + 13)
= 30 cm
Surface area of the right prism = 2(30) + 30(15)
= 60 + 450
= 510 cm²
Therefore, Option (C) will be the correct option.
Plz help
I will be giving extra 50 points
it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.
a. is simple, just put the terms in order
r² +6r -5
because:
[tex] {r}^{2} + {6r}^{1} + {5r}^{0} [/tex]
anything to the power of 0 equals 1,
because it's the same as r/r, and 5 * r/r = 5*1
b. same logic as above
a²b² -5ab +33
c.
-c³ +ab +d +9
d.
-9y^5 - 2x³y²z +4x² +10x +1
^5 = to the power of five, it's the fastest way to type it without the special math input tool.
hope it helps you
Answer:
I agree with the above one.
Find the fourth proportion to : 2,3,16
Answer is 24
Step by step:
2,3,16
Let the fourth proportion be x
2/3 = 16/x
or, 2x = 3×16
or, x = 3×16/2
or, x = 3×8
or, X = 24
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
31
?
40
Find the measure of the indicated angle to the nearest whole degree.
Answer:
51°
Step-by-step explanation:
Reference angle (θ) = ?
Opposite side length = 31
Hypotenuse length = 40
Apply SOH, which is;
Sin θ = Opp/Hyp
Plug in the values
Sin θ = 31/40
θ = sin^{-1}(31/40)
θ = 51° (neatest whole degree)
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
Please help! Question in image below:
Answers also below:
Answer:
11, 18, 25, 32, .....
Option D
Step-by-step explanation:
The formula for the nth term of an AP is a+(n-1)d
a+(n-1)d=a+(n-1-1)d+7
a+nd-d=a+nd-2d+7
d=7
As the common difference is 7.
The only option given which is in an AP is the 4th option
Which word MOST affects the tone of this sentence?
A slender woman walked into the room wearing a pink dress and a gaudy hat.
A- room
B- gaudy
C- woman
D- slender
Answer:
B
Step-by-step explanation:
Given f(x) = 6x + 2, find f(x – 3).
A. f(x – 3) = 6x – 1
B. f(x – 3) = 6x – 16
C. f(x - 3) = x - 1
D. f(x – 3) = 6x2 – 16x - 6
Answer: B. f(x - 3) = 6x - 16
Concept:
When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.
Solve:
Given function and value
f(x) = 6x + 2
f(x - 3)
Substitute the value into the given expression
f(x - 3) = 6 (x - 3) + 2
f(x - 3) = 6x - 18 + 2
f(x - 3) = 6x - 16
Hope this helps!! :)
Please let me know if you have any questions
A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.
Answer:
17d/20
Step-by-step explanation:
100-25=85
85/100×d
=17/20×d
=17d/20
I don't get this question i need some help please!!!
Answer:
2 sqrt(2) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/4
4 sin 45 = x
4 ( sqrt(2)/2) =x
2 sqrt(2) = x
Answer: D
Use sine to find the x-value:
[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]
30 POINTS PLEASE HELP
Answer:
Answer:
Solution given:
f(x)=5x-3
let
y=f(x)
y=5x-3
interchanging role of x and y
x=5y-3
x+3=5y
y=[tex]\frac{x+3}{5}[/tex]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
use complete sentences to describe the transformation of triangle ABC into its image.
Answer:
Move triangle ABC over 2 and up 1
Step-by-step explanation:
A transformation in geometry is to essentially move a shape. To move ABC onto A1B1C1 you would move triangle ABC over 2 and up 1.
Solve: 1/3a^2-1/a=1/6a^2
Step-by-step explanation:
there are two answers for a
Answer:
The ANSWER IS 1/6
Step-by-step explanation:
When the function f(x) = 4(2)x is changed to f(x) = 4(2)x − 13, what is the effect? (5 points)
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. The x-intercept is 13 spaces higher.
c. The y-intercept is 13 spaces lower.
d. All input values are moved 13 spaces to the left.
Answer:
C
If x = o then f(0) = 4(2) * 0 = 0
If f(x) = 4(2) 0 - 13
then f(x) = -13 at x = 0
Answer:
it will indeed be c
Step-by-step explanation:
deesnuts
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
Solve for x Round to the nearest tenth one place after the decimal !
Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
At a concession stand; three hot dogs and two hamburgers cost $9.75; two hot dogs and three hamburgers cost $10.25. Find the cost of one hot dog and the cost of one hamburger.
9514 1404 393
Answer:
hot dog: $1.75hamburger: $2.25Step-by-step explanation:
Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...
3x +2y -9.75 = 0
2x +3y -10.25 = 0
We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:
3, 2, -9.75, 3
2, 3, -10.25, 2
Now, we can form differences of cross-products in adjacent pairs of columns:
d1 = (3)(3) -(2)(2) = 9 -4 = 5
d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75
d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25
Then the solutions are found from ...
1/d1 = x/d2 = y/d3
x = d2/d1 = 8.75/5 = 1.75
y = d3/d1 = 11.25/5 = 2.25
The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.
_____
Additional comment
This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.
For a given pair of columns with coefficients ...
a b
c d
The cross-product we form is ad -cb.
What is the range of the function
Answer: [tex]-\infty < y < \infty[/tex] which is choice A
This is the set of all real numbers.
===========================================================
Explanation:
If you were to graph this function, then it spans infinitely upward and infinitely downward as well. That means that we can land on any y value we want, and that's why the range is the set of all real numbers.
Another approach we could take is to swap x and y to get [tex]x = \sqrt[3]{y+8}[/tex] which solves to [tex]y = x^3-8[/tex] . This is the inverse of the original function your teacher gave you. Recall that the domain and range swap roles when going from the original function to the inverse. What this means is that because the domain of
Domain of inverse = set of all reals
Range of original = set of all reals
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
The average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. Who is relatively taller based on their comparison to their gender, LeBron James at 81 inches or Candace Parker at 76 inches?
a) Candace is relatively taller because she has a larger z-score.
b) LeBron is relatively taller because he has a larger z-score.
c) LeBron is relatively taller because he has a smaller z-score.
d) Candace is relatively taller because she has a smaller z-score.
Answer:
b) LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
LeBron James:
Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81 - 69.5}{2.7}[/tex]
[tex]Z = 4.26[/tex]
Candace Parker:
Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 64.2}{3.2}[/tex]
[tex]Z = 3.69[/tex]
Who is relatively taller?
Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.
Consider the following sample space, S, and several events defined on it. S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}. FH is ___________.
Answer:
FnH = {Meagan}
Step-by-step explanation:
Given the following sets and events:
S = {Albert, Betty, Abel, Jack, Patty, Meagan}
F = {Betty, Patty, Meagan},
H = {Abel, Meagan}
P = {Betty, Abel}.
In order to get FnH
The intersection of F and H is the element that is common to both sets. Hence for the set given, we can see that Meagan is common to both sets, therefore:
FnH = {Meagan}
ASAP ! PLSSSQ!!!!!!!
Answer:
16
Step-by-step explanation:
