Answer: Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
Step-by-step explanation:
Equation of least-squares regression line for predicting y :
[tex]\hat{y}=b_1x+b_o[/tex]
, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] , [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]
Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]
Then,
[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]
Now,
[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]
Then, Regression line equation: [tex]\hat{y}=-1.008x+39.1704[/tex]
At the start of 2010 karim had rm5000
Step-by-step explanation:
Tell the whole question please
Classify the polynomial 2x^3+6x^2-4 by the number of terms. binomial. trinomial. cubic. quadratic.
Answer:
monomial
Step-by-step explanation:
Given that 243√3 =3^a, find the value of a
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
The area of a square is 64n36. What is the length of one side of the square?
Answer:
8n6
step by step explanation.
A sample of bacteria is growing at an hourly rate of 10% compounded continuously. The sample began with 4 bacteria. How many bacteria will be in the sample after 18 hours?
Answer:
24
Step-by-step explanation:
The computation of the number of bacteria in the sample after 18 hours is shown below:
We assume the following things
P = 4 = beginning number of bacteria
rate = r = 0.1
Now
We applied the following formula
[tex]A = Pe^{rt}[/tex]
[tex]= 4\times e^{18\times0.1}[/tex]
[tex]=4e^{1.8}[/tex]
[tex]= 4\times6.049647464[/tex]
= 24
We simply applied the above formula to determine the number of bacteria after the 18 hours
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answer:
what
Step-by-step explanation:
Hi any help is appreciated. Just wanna graduate:))
Answer: C
Step-by-step explanation:
h · k(x) = 2(3x - 5)(-2x + 1)
= (6x - 10)(-2x + 1)
= -12x² + 6x + 20x - 10
= -12x² + 26x - 10
Answer:
C
Step-by-step explanation:
h(x) × k(x)
= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL
= 2(- 6x² + 3x + 10x - 5)
= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2
= - 12x² + 26x - 10 → C
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
Write 3 expressions containing exponents so that each expression equals 81
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
What is the value of x in the equation 5 (4 x minus 10) + 10 x = 4 (2 x minus 3) + 2 (x minus 4)?
Answer:
x = 1.5
Step-by-step explanation:
5(4x-10)+10x=4(2x-3)+2(x-4)
Distribute(5)
20x-50+10x=4(2x-3)+2(x-4)
Distribute(4)
20x-50+10x=8x-12+2(x-4)
Distribute(2)
20x-50+10x=8x-12+2x-8
Combine like terms
30x-50=10x-20
Subtract(10x)
20x-50=-20
Add(50)
20x=30
Divide(20)
x = 1.5
Hope it helps <3
Answer:
x = 3/2Step-by-step explanation:
5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
Expand the terms
That's
20x - 50 + 10x = 8x - 12 + 2x - 8
Simplify
30x - 50 = 10x - 20
Group the constants at the right side of the equation
That's
30x - 10x = - 20 + 50
20x = 30
Divide both sides by 20
x = 3/2
Hope this helps you
10=12-x what would match this equation
Answer:
x=2
Step-by-step explanation:
12-10=2
Answer:
x=2
Step-by-step explanation:
10=12-x
Subtract 12 from each side
10-12 = 12-12-x
-2 =-x
Multiply by -1
2 = x
NEED HELP THANKLSSSS
Answer:
Side length: 3 cm.
Surface area: 54 cm squared.
Step-by-step explanation:
The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.
So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.
There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.
Hope this helps!
Ifx + iy = 1
1+i/
1-i
prove that, x² + y² = 1
HI MATE
A bicycle tire has a radius of 5 inches. To the nearest inch, how far does the tire travel when it makes 8 revolutions?
Answer:
251 inches
Step-by-step explanation:
c = 2πr
c = 2(3.14)(5) = 31.4
31.4 x 8 rev. = 251 inches
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Need help finding the length
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
Find three consecutive even integers such that the square of the third is 60 more that the square of the second
Answer:
-4,4,16
Step-by-step explanation:
They are all even integers.
-4^2=16
4^2=16
16^2=256
the square of the third,16 is 256 which is more than the square of the second,4=16
The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
Let the three even consecutive integers are 2n-2, 2n and 2n + 2.
According to the question,
So,
(2n + 2)² = (2n)² - 60
4n² + 4 + 8n = 4n² -60
8n = -64
n = -8
That means, the integers are -18, -16 and -14.
Therefore, the required even integers are -18, -16 and -14.
To learn more about the integers;
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24=3(n-5) solve for n
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
Does the mean represent the center of the data? A. The mean represents the center. B. The mean does not represent the center because it is the smallest data value. C. The mean does not represent the center because it is the largest data value. D. The mean does not represent the center because it is not a data value. E. There is no mean age.
Answer:
A. The mean represents the center.
A. The median represents the center.
B. The mode does not represent the center because it is the smallest data value.
Step-by-step explanation:
Mean
(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2
The mean 9.2 and it represents the center of data.
Median
By arranging the set of data, the median, the median is the center number
8,8,8,8,8,8,(9),9,9,10,11,12,12
The median is 9 and it represents the center of data.
Mode
The mode is the number that appears most in the set of data.
The number that appears most in the set of data is 8 and does not represent the set of data.
Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Given the following data set:
9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11
Let's find the mean, median, and mode.
Mean of the data set:
Mean = sum of all values / number of values
Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]
Mean = [tex]\frac{120}{13} = 9.2[/tex]
Median of the data set:
Order the data from the least to the greatest then find the middle value.
Thus:8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12
The middle value is 9.
The median = 9Mode of the data set:
The mode = the data value that appears most
8 appeared the most, therefore, the mode = 8
If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.
In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:
the mean is: 9.2the median is: 9the mode is: 8A. The mean does represents the center of the data set
Learn more here:
https://brainly.com/question/16882439
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
(25 points) PLEASE HELP, I gotta get this done or my mom will beat the hell out of me
Solve
x + y = 2
4y = -4x + 8
by elimination (not Gaussian!)
Thanks!
(also, please show work!)
Answer:
x=1
y=1
Step-by-step explanation:
Please look at the image below for solutions⬇️
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.
Point form
(x, 2-x)
What is the best way to remember the 6 trigonometric ratios?
Answer:
SOHCAHTOA
Step-by-step explanation:
Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.
Answer: SOHCAHTOA
Step-by-step explanation:
The pneumonic I learned is SOH-CAH-TOA. it says that Sin = opposite/hypotenuse. Cos = adjacent/hypotenuse. Tan = opposite/adjacent.
Hope it helps <3
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
find the values of x and y that make k ll j and m ll n
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]