The regression line that forecasts home equity using the FICO credit score as the explanatory variable has the equation Y' = 1798X + 0.
Due to the fact that this linear regression model includes two parameters that need to be estimated from training data, it has two degrees of freedom. One additional column in the data (one additional input variable) would provide the model one extra degree of freedom.
An equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable, represents a linear regression line. A line's intercept (the value of y when x = 0) is equal to the slope of the line, which is b.
Hence we get the required answer.
Learn more about Regression line here:
brainly.com/question/25987747
#SPJ4
Determine the ditance from point P(-2, -1, 1) to the plane [x, y, z) = [4,-1, 6] t[1, 6, 3] [-2, 3, 1]. The Ditance Between a Point and Plane Formula can be ued ONLY to check your anwer. Pleae provide me with the full olution of thi problem
The distance of the given point P from the plane would be [tex]\frac{-1}{\sqrt{6}}, \frac{-5}{\sqrt{6}},and, \frac{2}{\sqrt{6}}.[/tex]
What is a plane?
A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is a two-dimensional equivalent of a point, a line, and a three-dimensional space.
The given point P is P(-2, -1, 1) and the plane coordinates are [4, -1, 6].
Then the distance will be
[tex]= \frac{-2.4+(-1*-1)+1.6}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{-1}{\sqrt{6} }[/tex]
Now the distance of a point P from the plane t[1, 6, 3]
[tex]= \frac{-2.1+(-1*6)+1.3}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{-5}{\sqrt{6} }[/tex]
Now the distance of a point P from the plane [-2, 3, 1]
[tex]= \frac{-2.-2+(-1*3)+1.1}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{2}{\sqrt{6} }[/tex]
hence, the distance would be [tex]\frac{-1}{\sqrt{6}}, \frac{-5}{\sqrt{6}},and, \frac{2}{\sqrt{6}}.[/tex]
To learn more about planes in 3-D geometry, visit:
https://brainly.com/question/2251564
#SPJ4
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the exponential function f(x) = 3ˣ is attached below and comparing the graphs with the options available, the answer is option D
Graph of Exponential FunctionAn exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.
In the given function
f(x) = 3)ˣ
Applying the values from the table of function, a graph can be drawn to represent the function.
we can use a graphing calculator to plot the graph while applying the values from the table of function
Comparing the graph plotted and the options given, the answer is option D
Kindly find the attached graph below
Learn more on graph of exponential function here;
https://brainly.com/question/20707489
#SPJ1
What is an example of a set that is closed under addition?.
The set of whole numbers is closed under addition.
What are sets?A set is the mathematical model for a collection of different things.
The addition of any two whole numbers always produces another whole number. Therefore, the set of whole numbers is closed under addition.
Hence, The set of whole numbers is closed under addition.
For more references on sets, click;
https://brainly.com/question/8053622
#SPJ1
[tex]2\frac{--80}{4} -14[/tex]
The value of the expression given as 2 - (80/4) - 14 when evaluated is -32
How to evaluate the expression?From the question, we have the following parameters that can be used in our computation:
2--80/4-14
To start with, we need to represent the expressions properly
This can be done with the use of brackets
So, we have the following representation
2 - (80/4) - 14
Solving further, we need to evaluate the expression in the bracket
This gives
2 - (80/4) - 14 = 2 - (20) - 14
Next, we remove the bracket
So, we have the following representation
2 - (80/4) - 14 = 2 - 20 - 14
Evaluate the difference
So, the expression becomes
2 - (80/4) - 14 = -18 - 14
Evaluate the last difference
So, the expression becomes
2 - (80/4) - 14 = -32
Hence, the solution is -32
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
Find all zeroes of the polynomial: 9x^3-36x^2+2x-8
x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given polynomial is 9x³-36x²+2x-8
We have to find roots or zeroes of polynomial.
Nine times of x cube minus thirty six x square plus two times of x minus eight.
(((9(x³)) - (2²3²x²)) + 2x) - 8 = 0
((3²x³ - (2²3²x²)) + 2x) - 8 = 0
9x³-36x²+2x-8 is not a perfect cube
9x³-36x²+2x-8
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x-8= 2(x-4)
Group 2: -36x²+9x³=9x²(x-4)
Add up the two groups :
(x-4) (9x²+2)
x=4
x=0.0000-0.4714i
x=0.0000+0.4714i
Hence x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8
To learn more on Polynomial click:
https://brainly.com/question/11536910
#SPJ1
Subtract 4 from any element's value that is greater than maxval. Ex: if maxval = 10, then datapoints = {2, 12, 9, 20} becomes {2, 8, 9, 16}.
Answer:
Step-by-step explanation:
for (i = 0; i < dataPoints.size(); ++i) {
if (dataPoints.at(i) > maxVal) {
dataPoints.at(i) = dataPoints.at(i) - 4;
}
}
A poster whose area is 180 square inches, has 1 inch margin at bottom and on sides 2 inch margin at the top. What are its dimensions for which printed area is maximized?
The dimensions for which the printed area is maximized are 16.432 × 10.954 in².
let the height of the poster = x inches
area of the poster = 180 in²
thus, its width is 180/x inches.
The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.
The sides have a margin of 1 inch, so the width of the printed area is:
180/x - 2
the area of printed area A is given by the formula of a rectangle,
A = height × width
A = (x-3)(180/x - 2)
A = 180 - 2x - 540/x + 6
the maximized area is when dA/dx = 0
dA/dx = - 2 - 540(- 1/x²) = 0
540/x² = 2
x = √270
hence height = √270 = 16.432 inches,
and width = 180/√270 = 10.954 inches.
know more about the maximized area here: https://brainly.com/question/28821169
#SPJ4
How many units are in a square?.
A unit square is a square with sides measuring 1 unit, while a square unit is a unit of measurement.
What are Square Units?
In geometry, a square unit can be defined as the metric unit used to measure area for example the area of this rectangle is measured in square units using unit squares.
Also, the square is an Imperial unit of area that is used in the construction industry, 1 square is equal to 100 square feet.
In the system of measurement, some commonly used square units can be square centimeter (cm²), square meter (m²), and square kilometer (km²).
Thus, a square unit is a unit of measurement where as a unit square is a square with sides measuring 1 unit.
To learn more about area refer here
https://brainly.com/question/25292087
#SPJ4
water leaks from a tank at a rate of 2 8t liters per hour, where t is the number of hours after 7 {\tiny{am}}. how much water is lost between 9 and 11 {\tiny{am}}?
The water that was lost between 9 and 11 am is 52 liters by using integration.
What is meant by integration?An integral in mathematics assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that come from merging infinitesimal data. The process of determining integrals is known as integration. Along with differentiation, integration is a fundamental, essential operation of calculus and is used to answer issues in mathematics and physics involving the area of an arbitrary form, the length of a curve, and the volume of a solid, among others.
The integrals listed below are definite integrals, which can be defined as the signed area of the plane region circumscribed by the graph of a given function between two points on the real line.
Rate of leaking R'(t)=2+8t
Here t is the number of hours.
Total water lost from 9 and 11 am
=[tex]\int\limits^8_2[/tex] (2+8t)dt
=(2t+(8t²/2))⁴₂
=(8+64)-(4+16)
=72-20
=52 liters.
The water that was lost between 9 and 11 am is 52 liters.
To know more about integration, visit:
https://brainly.com/question/18125359
#SPJ4
1, 5, 4, 7, 3, 7, 9, 2. if the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3. the correct answer is
The Correct answer is 27
Odd number are the numbers that are not multiple 2 and cannot be divided into two parts equally.
For examples: 3 , 5 , 7, 9,11 . . . . .
According to the question,
If the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3.
Sequence of the number is 1, 5, 4, 7, 3, 7, 9, 2
where 1 , 5 , 7 , 7 ,9 are odd numbers
The third odd number is 7 which is greater than 6
according to question we have to multiple 9 by 3
= 9 × 3
= 27
To know more Odd number here
https://brainly.com/question/10850080
#SPJ1
In a room there are 40 people. 26 of these are women, the rest are men. What percentage of the people are men.
Answer:
35%
Step-by-step explanation:
Find the number of men:
40-26= 14
Find the ratio of men out of the 40 people
14/40 = 0.35
0.35 * 100% = 35%
Which line is the graph of y = 2x - 1?
line a
line d
line c
line b
Answer: Line A Is the answer
Apply the distributive property to create an equivalent expression. 1/2(6e-3f-3/4)
Answer:
(1/2*6e)-(1/2*3f)-(1/2*3/4)
Step-by-step explanation:
[tex]\Large \boxed{\sf 3e-\frac{3}{2}f -\frac{3}{8} }\\\\\\\displaystyle \sf Applying\ the\ distributive\ property \\\\\\\frac{1}{2} \times 6e+\frac{1}{2} \times -3f +\frac{1}{2} \times \frac{-3}{4} \\\\\\ \frac{6e}{2}+\frac{-3f}{2} +\frac{-3}{2 \times 4} \\\\\\ 3e+\frac{-3f}{2} +\frac{-3}{8}[/tex]
What amount is 20% more than 1500?.
The amount 20% more than 1500 is 1800.
The amount 20% of 1500 is
=20/100 × 1500
=300
NOW,
The amount 20% more than 1500 is
=300 + 1500
=1800
Learn more about finding the percentages here;
https://brainly.com/question/24877689
#SPJ4
Ricardo measured his back yard. He said it was 93 feet long. How many yards is that?
By performing a change of units from feet to yards, we will see that the backyard measures 31 yards.
How many yards measure the backyard?We know that Ricardo measured his backyard and he found that it measured 93 feet, but we want to find this measure in yards, so we need to perform a change of units.
To do it, we will use the relation:
1 yard = 3 feet
Then we can write:
1 = (1 yard)/(3 feet).
Now we have the measure:
93 ft
And we can multiply it by (1 yard)/(3 feet), that is equal to 1, so it does not change the measure, only the units:
93 ft = 93ft*(1 yd/3ft) = 31 ft
The backyard measures 31 ft.
Learn more about changes of units:
https://brainly.com/question/9032119
#SPJ1
There are 7 children that are taking turns using the swing on a playground. How many different ways are there in which they each can use the swing where everyone gets exactly one turn? roscoe has 15 books on his summer reading list. He wants to choose 6 books to read in order from first to last. In how many ways can he do this? the student council has 15 students. They need to choose a president, vice president, secretary and treasurer for student council. In how many ways can the 4 different positions be appointed from the 15 students? thomas is creating a 7 digit passcode using the digits 0 through 9. How many 7 digit passcodes are possible if the numbers cannot be repeated?
The number of different ways for all 4 conditions is 5040 ways, 3603600 ways, 32760 ways, and 604800 ways respectively.
What are permutation and combination?
A permutation is an orderly arrangement of objects or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
First condition,
The number of ways to take turns for 7 children is:
= Permutation of 8 children
= 7!
= 5040 ways
Second condition,
The number of ways to select 6 from 15 and in order is computed as the number of permutations of 15 books taken 6 at a time
= 15*14*13*12*11*10
= 3603600 ways
Third condition,
The number of ways to choose 4 different positions from 15 students is:
= Number of permutation of 15 students taken 4 at a time
= 15*14*13*12
= 32760 ways
Last condition,
The numbers cannot be repeated here, the number of permutations of 10 digits taken 7 at a time is:
= 10*9*8*7*6*5*4
= 604800 ways
To learn more about permutation and combination
https://brainly.com/question/1216161
#SPJ4
The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club. Each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell. Which equation represents this situation?72 = 3x + 6 (6)
72 = 3x + 6
72 = 6x + 3
72 = 6x + 3 (6)
72 = 3x + 6 equation represents if each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell.
Define equation.In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated proposition that has been mathematically quantified. There are numerous possible equation types. To equate two expressions, we employ equations.
Given,
The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club.
Each pie was then cut into six pieces and sold.
There were a total of 72 pieces to sell.
Equation representing this equation is:
72 = 3x + 6
To learn more about equation, visit:
https://brainly.com/question/11153801
#SPJ4
What is the rule for multiplying by 6?.
Answer:
If you multiply 6 by an even number, it will end in the same digit. For example, 6 x 4 = 24, so 4 and the 4 in 24 are the same. The number in the tens place will be half the number in the ones place, so the 2 in 24 is half of 4
in 2019, stan rented an apartment to dani and received a security deposit of $350 that he planned to return to her at the end of the lease. in 2021, dani moved out and stan used the $350 to repair the damage she had caused. which of the following statements is correct?
The following statements are correct :
Property A(Stan):
Security Deposit is not part of Rental Income if it is returned at the end of lease period = $0
In cash basis, any amount received as rent will be taxable regardless if it is earned in that period or not = $1400
$15400
If your tenant pays any of your expenses, those payments are rental income. You may also deduct the expenses if they're considered deductible expenses = $0
Property B(Dani):
$18000
If security deposit is used for paying rent, then it is part of rental income = $1500
$1600
If your tenant pays any of your expenses, those payments are rental income. You may also deduct the expenses if they're considered deductible expenses = $0
To learn more about Rental Income click here:
brainly.com/question/19131406
#SPJ4
Laurie has a signed contract with I- Mobile where she will pay a $25 fee each month plus $2 per phone call.
Part A: Equation representing the relationship between cost (y) and number of calls (x) is 25 = y - 2x.
Part B: The number of phone calls in January is 15.
Part C: Total bill for March is $ 35.
Part D: Graph for the equation is attached below.
Give a brief account on algebraic equation.A statement that states the equality of two expressions formulated by applying an algebraic equation, an algebraic operation—addition, subtraction, multiplication, division, power, square root—to a set of variables. Examples are x³ + 1 and (y⁴x² + 2xy – y)/(x – 1) = 12.
Part A: Equation representing the relationship between cost (y) and number of calls (x).
y = 2x + 25
25 = y - 2x
Part B: For the number of phone calls in January
55 = 25 + 2x
30 = 2x
x = ³⁰/₂
x = 15
Part C: Total bill for March
y = 25 + 2(5)
y = 35
To know more about algebraic equation, visit:
https://brainly.com/question/953809
#SPJ1
what is the perimeter and area
The perimeter is 29' and the area is 30 square units
How to determine the perimeter and the areaThe perimeter
This is the sum of the side lengths
From the question, the side lengths are
Side lengths = 9', 4', 11' and 5'
When these side lengths are added, we have
Perimeter = 9 + 4 + 11 + 5
Evaluate the sum
Perimeter = 29
So, the perimeter is 29'
The area
This is calculated as
Area = 1/2 * Sum of parallel sides * Height
So, we have
Area = 1/2 * (9 + 11) * 3
Evaluate
Area = 30
So, the area is 30 square units
Read more about area and perimeter at
https://brainly.com/question/25292087
#SPJ1
The probability of an outcome that lies within 99.7% of the mean is a good indicator that it lies in which standard deviation?
A.There is a probability that the outcome is within 1 standard deviation of the mean.
B.There is a probability that the outcome is within 3 standard deviations of the mean.
C.Standard deviations are not reliable, so the probability cannot be determined.
D.There is a probability that the outcome is within 2 standard deviations of the mean.
The probability of an outcome that lies within 99.7% of the mean is a good indicator that it lies in which standard deviation is B. There is a probability that the outcome is within 3 standard deviations of the mean.
What is a probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
It should be noted that 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviation of the mean. 99.7% of the population is within 3 standard deviation of the mean
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
from a point along a straight road, the angle of elevation to the top of a hill is . from farther down the road, the angle of elevation to the top of the hill is . how high is the hill? round to the nearest foot.
From a point along a straight road, the angle of elevation to the top of a hill is 33°. A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. The hill is 165.87 ft high.
Check the file attached below for a pictorial understanding of the question
[tex]tan[/tex]θ[tex]= \frac{opposite}{adjacent}[/tex]
From ΔABC..........(1)
[tex]tan33 = \frac{y}{x}[/tex]
From ΔABD............(2)
[tex]tan20 = \frac{y}{x+200}[/tex]
[tex]y = (x+200)tan20 ........(2)[/tex]
[tex]Equating (1) and (2)[/tex]
[tex]xtan33[/tex] [tex]= (x+200)tan20[/tex]
[tex]xtan33 = xtan20 + 200tan20[/tex]
[tex]0.649x = 0.364x + 72.794[/tex]
[tex]0.649x-0.364x = 72.794\\0.285x = 72.794\\x = \frac{72.794}{0.285} \\x = 255.42ft[/tex]
Substitute the value of x into equation (1)
[tex]y = 255.42tan33[/tex]
[tex]y = 165.87 ft[/tex]
The angle of elevation is an angle this is formed between the horizontal line and the road of sight. If the line of sight is upward from the horizontal line, then the angle fashioned is a perspective of elevation. A smooth-to-recollect equation for finding change in elevation as a decimal is “rise over run,” which means the upward push (the trade-in vertical distance) divided via the run (the change in horizontal distance).
Elevations are probably organized for some of the motives, consisting of: As part of a survey of current buildings. To create a document of a construction. To discover and communicate indoor and outdoor design options. The elevation of an object is at its top above sea level. Altitude refers to the peak of an object above a given factor. Elevation refers to the peak of a place above the mean sea degree.
To learn more about the angle of elevation visit here:
brainly.com/question/11897796
#SPJ4
Complete Question:
From a point along a straight road, the angle of elevation to the top of a hill is 33°. A distance of 200 ft farther down the road, the angle of elevation to the top of the hill is 20°. How high is the hill?
ealth insurers are beginning to offer telemedicine services online that replace the common office visit. wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. wellpoint claims that users of its livehealth online service saved a significant amount of money on a typical visit. the data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by wellpoint. click on the datafile logo to reference the data. 92 34 40 105 83 55 56 49 40 76 48 96 93 74 73 78 93 100 53 82 assuming that the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit. if required, round your answers to two
The 95% confidence interval would be given by (60.554;81.446)
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population means that sits between an upper and lower interval is frequently stated as a percentage.
Here, we have
Given Data: 92 34 40 105 83 55 56 49 40 76 48 96 93 74 73 78 93 100 53 82
We can calculate the mean and the deviation from these data with the following formulas:
X = ∑ᵃ 1ⁿxₐn
s = √∑ᵃ = 1ⁿ(xₐ - X)²n -1
X = 71 represents the sample mean for the sample
s=22.35 represent the sample standard deviation
n=20 represents the sample size
The confidence interval for the mean is given by the following formula:
X ± tα/2 - √n...(1)
In order to calculate the critical value tα/2 we need to find first the degrees of freedom, given by:
df = n - 1 = 20 -1 = 19
Since the Confidence is 0.95 or 95%, the value of α = 0.05 and α/2 = 0.025
and we can use excel, a calculator, or a table to find the critical value. The excel command would be:
tα/2 = 2.09
Now we have everything in order to replace into formula (1):
71 - 2.09- 2.35√20 = 60.554
71 + 2.09- 2.35√20 = 81.446
Hence, the 95% confidence interval would be given by (60.554;81.446).
To learn more about the confidence interval from the given link
https://brainly.com/question/15712887
#SPJ4
Positive
Negative
No Correlation
Answer:
No Correlation
Step-by-step explanation:
The points are scattered randomly and there is no pattern so there is no correlation.
f(x) = 3x² + 6x - 5
g(x) = 4x³ - 5x² +6
Find (f + g)(x).
O A. (f+g)(x) = -4x³ + 8x² + 6x − 11
B. (f+g)(x) = 4x³ + 3x² + 11x + 1
O c. (f+g)(x) = 7x³ + x² + 1
O D. (f+g)(x) = 4x³ - 2x² + 6x +1
Can 5cm 9cm 3cm be sides of a triangle?.
Answer: It is not possible
Step-by-step explanation:
to have a triangle with sides 5 cm, 3 cm and 2 cm. Sum of any two sides of a triangle must be greater than the third side.
3 cm + 2 cm = 5 cm
it shows also that the barn will be used as part of the fencing on one side. find the largest area that can be enclosed if 88 feet of fencing material is available
The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².
Given, a barn has a perimeter of 88 feet.
Now, the perimeter of the rectangle i.e. Barn is 88 feet.
Perimeter = 2(l + b)
88 = 2(l + b)
l + b = 44
b = 44 - l
Now, area = l × b
Area = l × (44 - l)
Area = 44l - l²
On differentiating both the sides, we get
A' = 44 - 2l
On putting A' = 0
44 - 2l = 0
l = 22
Now, for l = 22 the area will be the largest.
if l = 22
then, 22 + b = 44
b = 22
So, the largest area will be 22×22 = 484
Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².
Learn more about Applications of Derivatives here https://brainly.com/question/25120629
#SPJ4
1. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.2-cm and a standard deviation of 2.3-cm. For shipment, 25 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm.
P(M < 124.5-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
2. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 168.5-cm and a standard deviation of 1.2-cm. For shipment, 24 steel rods are bundled together.
Find the probability that the average length of a randomly selected bundle of steel rods is between 168.3-cm and 169-cm.
P(168.3-cm < M < 169-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
1. The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
2. The probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.
P(M 169.3 cm 168.3 cm) = 0.7724
Given that,
In this question we have 2 question.
1. Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.
We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5-cm) =
We know that,
Mean =μ= 125.2
Standard deviation=σ=2.3
n=25
P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]
=P(z<-1.522)
Using the z-table,
=0.0603
Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.
P(M < 124.5) = 0.0603.
2. Steel rods are produced by a firm. Steel rod lengths have a mean of 168.5 cm and a standard deviation of 1.2 cm, and they are regularly distributed. 24 steel rods are packaged together for shipping.
We have to determine the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.
P(M 169.3 cm 168.3 cm) =
We know that,
Mean =μ= 168.5
Standard deviation=σ=1.2
n=24
P(168.3<M<169)= P[168.3-168.5/0.2449<(M-μ)/σ< 169-168.5/0.2449]
=P(-0.817<z<2.042)
=P(z<2.042)-P(z<-0.817)
Using the z-table,
=0.9794-0.2070
=0.7724
Therefore, the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.
P(M 169.3 cm 168.3 cm) = 0.7724
To learn more about probability visit: https://brainly.com/question/14125181
#SPJ4
the graphical solution to a linear programming problem can only be used when there are two part 2 a. objective functions. b. constraints. c. available resources. d. decision variables.
The correct option d. decision variables; is used to find the the graphical solution to a linear programming problem.
Define the term decision variables?An uncertain in an optimization method is a choice variable. It has a domain, that is an condensed representation of the entire set of the variable's potential values.
The types of decision variables are references to objects, whose precise nature is determined by the model's underlying optimizer.The quantities which that decision makers need to know are described by decision variables. They are the variables in a model for mathematical programming. Usually, we will use an optimization technique to find the best values for them.These are the unknowables that the LPP solution is supposed to approximate as an output. All linear programming issues seek to maximize as well as minimize any numerical value that represents revenue, expenditure, output volume, etc.Thus, a linear programming problem's graphical solution is found using decision variables.
To know more about the decision variables, here
https://brainly.com/question/18188900
#SPJ4
