Question 8
Which property justifies the fact that 5(x - 2) is equivalent to 5x - 10?
commutative
associative
O distributive
A sales manager collected data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. In the Microsoft Excel Online file below you will find a sample of data on years of experience of the salesperson and annual sales. Conduct a regression analysis to explore the relationship between these two variables and then answer the following questions.
Open spreadsheet
Compute b1 and b0 (to 1 decimal).
b1 =____ fill in the blank
b0 =____ fill in the blank
Complete the estimated regression equation (to 1 decimal).
y= ____ + ____x fill in the blank 5x
According to this model, what is the change in annual sales ($1000s) for every year of experience (to 1 decimal)?
____fill in the blank
Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
r2 =____ fill in the blank
What percentage of the variation in annual sales ($1000s) can be explained by the years of experience of the salesperson (to 1 decimal)?
fill in the blank ____ %
A new salesperson joins the team with 8 years of experience. What is the estimated annual sales ($1000s) for the new salesperson (to the nearest whole number)?
$____ fill in the blank
Salesperson Years of Experience Annual Sales ($1000s)
1 2 78
2 4 94
3 4 87
4 4 104
5 5 107
6 9 109
7 9 124
8 10 121
9 10 122
10 14 131
Answer:
(a) [tex]b_1 =3.4[/tex] and [tex]b_0 = 83.7[/tex]
(b) [tex]y=83.7+3.4 x[/tex]
(c) [tex]r^2 = 0.790[/tex]
(d) [tex]\% Variation = 79.0\%[/tex]
(e) The expected earnings is: $110,900
Step-by-step explanation:
The data for the 10 sales person is as follows:
[tex]\begin{array}{ccc}{Years\ of Experience} & {Annual\ Sales(\$ 1000)} & {Salesperson} & {1} & {1} & {85} & {2} & {3} & {97} & {3} & {3} & {95}& {4} & {5} & {97}& {5} & {7} & {105}& {6} & {8} & {106}& {7} & {10} & {122} & {8} & {10} & {120} & {9} & {12} & {113} & {10} & {12} & {134}\ \end{array}[/tex]
Required
Perform a regression analysis using Microsoft Excel
Note
I added two attachments to this solutionIn the first attachment, I highlighted the step to follow to perform regression analysis. At step 4, ensure that you fill in the input y range and the input x range. The input y range (in this question) is the column for sales person while the input x range is the annual sales Click ok, then Microsoft Excel will perform the analysis for you.
The question will be answered based on the result of the analysis performed by the application (See attachment 2)
See attachment 2 for the result of the analysis (I've highlighted the solution to each question on the attached file)
(a) b1 and b0
[tex]b_1 = 3.372767857[/tex]
[tex]b_1 \approx 3.4[/tex]
[tex]b_0 = 83.65625[/tex]
[tex]b_0 \approx 83.7[/tex]
(b) The estimated regression equation
The equation is of the form:
[tex]y =b_0 + b_1x[/tex]
Where:
[tex]b_1 =3.4[/tex]
[tex]b_0 =83.7[/tex]
So:
[tex]y=83.7+3.4 x[/tex]
(c) The coefficient of determination (r^2)
[tex]r^2 = 0.790361699[/tex]
[tex]r^2 \approx 0.790[/tex]
(d) Percentage of variation
To do this, we simply convert r^2 to percentage
[tex]\% Variation = r^2 * 100\%[/tex]
[tex]\% Variation = 0.790 * 100\%[/tex]
[tex]\% Variation = 79.0\%[/tex]
(e) Expected annual sales of a sales person with 8 years of experience.
Using the regression equation
[tex]y=83.7+3.4 x[/tex]
Where
[tex]x = 8[/tex] --- the years of experience.
So;
[tex]y = 83.7 + 3.4 * 8[/tex]
[tex]y = 83.7 + 27.2[/tex]
[tex]y = 110.9[/tex]
The expected earnings is: $110,900
Which statement describes ?
The series diverges because it has a sum of 4.
The series converges because it has a sum of 4.
The series diverges because it does not have a sum.
The series converges because it does not have a sum.
Answer: B
The series converges because it has a sum of 4.
Step-by-step explanation:
The convergence or divergence of a series depends on the sum of the series and its common ratio. The series converges because its sum is b
The series is given as:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
A geometric series is given as:
[tex]T_n = ar^{n-1}[/tex]
So, we rewrite the series as follows:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
Apply law of indices
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^{n-1} \times (\frac{2}{3})[/tex]
Rewrite
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 \times (\frac{2}{3})(\frac{2}{3})^{n-1}[/tex]
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
So, we have:
[tex]T_n = \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
Compare the above series to: [tex]T_n = ar^{n-1}[/tex]
[tex]a = \frac{4}{3}[/tex]
[tex]r = \frac{2}{3}[/tex]
The sum of the series to infinity is:
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
So:
[tex]S_{\infty} = \frac{4/3}{1 - 2/3}[/tex]
[tex]S_{\infty} = \frac{4/3}{1/3}[/tex]
[tex]S_{\infty} = 4[/tex]
i.e. [tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = 4[/tex]
Also:
The common ratio (r)
[tex]r = \frac{2}{3}[/tex]
[tex]r = \frac{2}{3}[/tex] [tex]< 1[/tex]
When common ratio is less than 1, then such series is convergent.
Hence, (b) is true because it has a sum of 4
Read more about series at:
https://brainly.com/question/10813422
PLEASE HELP FAST
What is the probability of rolling two dice and getting a sum that is a multiple of 5 or
rolling doubles (dice land on the same number)?
Answer:
1/3
Step-by-step explanation:
Look in the figure and circle all double rolls and all sums that equal 10.
See pic below. Then count them. There are 12.
12/36 = 1/3
debe tomar 4 fotos de una carrera. Cada vez que un corredor pasa a su lado, hay un 50% de probabilidad de que tome una foto de ese corredor. Además, para dos corredores cualesquiera, la probabilidad de que tome una foto de uno es independiente del otro. Una vez que obtenga 4 fotos, abandonará las instalaciones de la carrera y no intentará tomar más fotos. Si eres el sexto corredor en pasar al fotógrafo, entonces la probabilidad de que te tome una foto puede expresarse en la forma M / NM / N, donde MM y NN son números enteros positivos relativamente primos (es decir, su máximo común divisor es 1 ). Calcule M + NM + N.
Answer:
Ehhh waht ??im 10 jears old!
Step-by-step explanation:
Hahah
Find the function h(x) = f(x) - g(x) if f(x)=3^x and g(x) = 3^2x - 3^x
Step-by-step explanation:
h(x)=f(x)-g(x)h(x)=3^x-3^2x-3^xh(x)=3^x(1-3²-1)h(x)=3^x(-9)h(x)= -27^xhope it helps.
A national study, that revealed a normal distribution, revealed that the average time a student spends studying statistics on a weekend is 60 minutes. A random sample of 11 students in BU 203 were asked to record their statistic study time over a weekend. The sample revealed an average study time of 44.27 minutes with a standard deviation of 20.4. With an alpha of 5% State the null hypothesis (H0) and the alternate hypothesis (H1). Draw the distribution.
Answer:
Null hypothesis = H0 : μ = 60
Alternative hypothesis = H1 : μ < 60
Step-by-step explanation:
From the question given :
μ = 60 minutes
xbar = 44.27 minutes
s = 20.4 minutes
The alternative hypothesis is the claim ; which is to hypothesize that the average studying time is 44.27 (which is less than the population average studying time)
The null hypothesis is the initial truth and it is the opposite of the alternative hypothesis.
The hypothesis are :
H0 : μ = 60
H1 : μ < 60
Find the distance between the pair of points. E(-5, 4) and F(3,4)
Answer:
8
Step-by-step explanation:
you use distance formula
GIVING OUT BRAINLIEST ANSWER HELPPP ME QUICKKK PLSSS
Answer:
Number 2. Any circle can be mapped onto another circle by dilation then translation is FALSE
Step-by-step explanation:
CAN SOMEONE PLS DO TBJS U HAVE TO SHOW WORK BUT ITS EASG AND DOESNT NEED TO BE PERFECTT
Answer:
area? is that what u need? or perimeter
Step-by-step explanation:
I need the answer I just need DONT scam with a link
Answer:
==> C. , = 12x + 16x and 4(3x + 4x)
hope it helps
2 3/4 + 12 6/8 = answer
Answer:
15 1/2
Step-by-step explanation:
Answer:
15 1/2
Step-by-step explanation:
Write the equation of the circle with the given information.
Center: (-8, 0)
Diameter: 5
Answer:
(x + 8)² + y² = 6.25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 8, 0 ) and r = 5 ÷ 2 = 2.5 , then
(x - (- 8))² + (y - 0)² = 2.5² , that is
(x + 8)² + y² = 6.25
A high school administrator is interested in determining the relationship between high school students' final grades in geometry and chemistry. She randomly samples 400 students who took both classes and records their final scores (out of 100 points) and carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable, since the students take chemistry before geometry. The resulting data was used to produce the following output.
Simple linear regression results:
Dependent Variable: Geometry
Independent Variable: Chemistry
Geometry = 3.6276926 + 0.91857341*Chemistry
Sample size: 400
R2= 0.55808158
Estimate of error standard deviation: 9.417521
Which of the following is a reasonable interpretation of the slope of this simple linear regression?
a. The slope of this regression cannot be interpreted because 0 is not in the range of chemistry scores.
b. Getting high grades in chemistry lead students to achieve high grades in geometry.
c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score.
d. On average, a 1 percentage point difference in geometry score is associated with a 0.919 percentage point difference in chemistry score.
Answer: c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score
Step-by-step explanation:
Given that:
Slope value = 0.91857341
The dependent and independent variables are ;
Dependent Variable: Geometry
Independent Variable: Chemistry
Slope is the rate of change in the dependent variable per unit change in the independent variable.
Hence, from the information given, we can conclude that for every 1% change in chemistry score (independent variable), there is a corresponding approximately 0.919% change in geometry score (dependent variable).
From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.
Given :
She randomly samples 400 students who took both classes and records their final scores (out of 100 points). She carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable since the students take chemistry before geometry.Given the simple linear regression results that are:
The Dependent variable is Geometry.
The Independent variable is Chemistry.
Geometry = 3.6276926+0.91857341[tex]\times[/tex]Chemistry
Comparing the above equation with the slope-intercept form which is given by:
y = mx + c
Therefore, slope, m = 0.91857341.
It is also given that:
Sample size is 400
R2= 0.55808158
Estimate of error standard deviation: 9.417521
From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.
For more information, refer to the link given below:
https://brainly.com/question/12402189
Which one of the figures is the Pre-Image? Please help me no links!
Answer:
the one in black
Step-by-step explanation:
The coordinates of a rectangle, LMNO, are L(- 1,3), M(2,3), N(2, - 5), and 0(- 1,- 5).
a. What is the length and width of this rectangle?
b. What is the perimeter of the rectangle?
c. What is the area of the rectangle?
Answer:
length = 8; width = 3
perimeter = 22
area = 24
Step-by-step explanation:
L(- 1,3), M(2,3)
LM = |-1 - 2| = 3
M(2,3), N(2, - 5)
MN = |-5 - 3| = 8
length = 8; width = 3
perimeter = 2(L + W) = 2(8 + 3) = 22
area = LW = 8 × 3 = 24
5,8, 21, 17, 10, 11,5
What is the median of the set of numbers?
Answer:
10
Step-by-step explanation:
Rearrange in order, 5, 5, 8, 10, 11, 17, 21 and the median would be 10.
Do -16 and 16 have the same value
Answer:
No they do not
Step-by-step explanation:
16 is positive -16 is negative they have different values. Hope this helps!
Jesse makes a large wooden picture frame in the shape of a rectangle with a diagonal brace on the back, as shown in the diagram.
What is the length, in feet, of the diagonal brace that Jesse uses?
Answer Choices:
F. 5ft
G.15ft
H.60ft
J.7ft
Answer:5 ft
Step-by-step explanation: ( 36 x 36 ) + ( 48 x 48 ) = 3600 inches
Square root of 3600 is 60
Convert inches to feet: 60 / 12 = 5
what statement is not true about the absolute value of 6
Answer:
I can't answer this sorry dude and next time show us the picture so that we can understand
Rewrite in simplest terms: 0.1d – 0.5(8d – 10)
Answer:
...
Step-by-step explanation:
0.1d - 4d -5
Answer:
-3.9d-5
I believe this is the answer! Hope this helps!
The area between z = 1.74 and z = 1.25
Round your answer to three decimal places.
Answer:
The area between z = 1.74 and z = 1.25 is of 0.065.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
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.
The area between two values of Z is given by the subtraction of the pvalue of the larger value by the smaller.
The area between z = 1.74 and z = 1.25.
This is the pvalue of z = 1.74 subtracted by the pvalue of z = 1.25.
z = 1.74 has a pvalue of 0.959
z = 1.25 has a pvalue of 0.894
0.959 - 0.894 = 0.065
The area between z = 1.74 and z = 1.25 is of 0.065.
Solve the equation 40 = -10(y+0.3). what does the y equal
Answer:
y = -4.3
Step-by-step explanation:
40 = -10(y + 0.3) {Step 1: Use the distributive property to multiply -10 by y + 0.3}
40 = -10y + -10(0.3)
40 = -10y - 3 {Step 2: Add 3 to both sides.}
40 + 3 = -10y
43 = -10y {Step 3: Divide both sides by -10}
43/-10 = y
-4.3 = y
y equals -4.3.
Answer:
y = -4.3
Step-by-step explanation:
40 = -10(y + 0.3)
40 = -10y - 3
-3. -3
43 = -10y
Divide 43 by -10
y equal 4.3
Which is an equivalent way to express 3y
Answer:
3 f(x)
Step-by-step explanation:
this is very open-ended, (6y)/2 is equal to 3y
Undo the half of what was left amount. Multiply 2
Undo the spent $5 add $5
Undo the spent $8 Add $8
Answer:
the three numbers below are your answers. (in order)
Step-by-step explanation:
[tex]2*2=4\\4+5=9\\9+8=17[/tex]
Help please asap will mark brainliest !
Answer:
b = 29
Step-by-step explanation:
C x D = A x B
15(11x - 91) = 7(2x + 10)
165x - 1365 = 14x + 70
add 1365 to both sides of the equation:
165x = 14x + 1435
subtract 14x from both sides:
151x = 1435
divide both sides by 151:
x = 9.5
b = 2(9.5) + 10 = 29
Use technology or a z-score table to answer the question.
The number of baby carrots in a bag is normally distributed with a mean of 94 carrots and a standard deviation of 8.2 carrots.
Approximately what percent of the bags of baby carrots have between 90 and 100 carrots?
23.3%
31.2%
45.5%
76.73%
Answer:
46% is the percent of the bags of baby carrots that have between 90 and 100 carrots
Step-by-step explanation:
The baby carrot is normally distributed.
z = (x - µ)/σ
x is equal to number of baby carrots
µ = mean
σ = standard deviation
Substituting the given values, we get -
90 ≤ x ≤ 100
z = (90 - 94)/8.2 = - 0.49
For z value of -0.49, the probability is 0.31
For x = 100
z = (100 - 94)/8.2 = 0.73
For z value of 0.73, the probability is 0.77
P(90 ≤ x ≤ 100) = 0.77 - 0.31 = 0.46
The percent of the bags of baby carrots having carrots between 90 and 100 carrots is 0.46 × 100 = 46%
Find the volume for the regular pyramid.
V =
Answer:
What do you mean by that?
Estimate the sum of 8.43 + 8.12 + 7.98.
Answer:
we estimate it and get
the answer is 25.53
Fifty students were surveyed and asked if they played sports and if they had a job. The table summarizes their responses.
Of the students who play sports, what percent do not have a job?
Answer: 10%
Step-by-step explanation: The percentage of 50-5 is 10%