From the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
How to know legitimate probability distribution?We should know that Probability is the chance of occurrence of an even (E) over a period of time.
A legitimate probability distribution must be that which adds up to 1 and cannot be negative.
Legitimate Distribution= P(a)+P(b)+P(c)+.....+P(n)
Where a,b,c and n are Probabilities of events.
From the given Parameters
(a) Rolling a die to record P(1) =0, P(2)=[tex]\frac{1}{6}[/tex], P(3)=[tex]\frac{1}{3}[/tex], P(4)=[tex]\frac{1}{3}[/tex], P(5)=[tex]\frac{1}{6}[/tex], P(6)=0
Add up the probabilities to get 1
⇒0+[tex]\frac{1}{6} +\frac{1}{3}+\frac{1}{3}+\frac{1}{6}+0[/tex]
⇒[tex]\frac{0+1+2+2+1+0}{6}[/tex]
P(E)=[tex]\frac{6}{6}=1[/tex]
This implies that the distribution is legitimate
(b) Choosing a college student at random,
Add up the probabilities to get 1
P(female full time)+P(male full time)+P(female part time)+P(male part time)
⇒0.56+0.44+0.24+0.17
=1.41
The probability of the distribution is not legitimate because it is greater than one.
(c) Deal a card from a shuffled deck.
Add up the probabilities to get 1
P(club)+P(diamond)+P(hearts)+P(spades)
[tex]\frac{12}{52} +\frac{12}{52}+\frac{12}{52}+\frac{52}{16}[/tex]
[tex]\frac{12+12+12+16}{52}[/tex][tex]\frac{52}{52}=1[/tex]
The distribution is legitimate because the sum of the probabilities is
equal to 1
In conclusion, from the various probabilities, (a) the distribution is legitimate (b) the distribution is not legitimate (c) the distribution is legitimate.
Learn more about legitimate distribution on https://brainly.com/question/16852397
#SPJ1
use a power series to approximate the definite integral, i, to six decimal places. 0.3 x4 1 x7 dx 0
The trapezoidal rule uses trapezoidal approximations to approximate the definite integral, whereas the midpoint rule uses rectangular regions to do so. By first approximating the original function with piecewise quadratic functions, Simpson's rule approximates the definite integral.
Since
"frac" (1-x) = (1-x)-1 = 1+x2+x3+x4+.... = "sum_n=0" infty" xn "hspace"
5mm for "left | x | 1"
How can a power-based integral be evaluated?
Power Rule for Integrals To apply this rule, simply add one to the exponent.The expression is then divided by the same number.The constant C is added in the final step. Now, we will solve some problems to determine the integrals of polynomials and root functions.
To learn more about definite integral here
https://brainly.com/question/14279102
#SPJ4
yolanda is planning a 778-mile trip to visit her daughter in maryland. she plans to average 50 miles per hour. at that speed, approximately how long will the trip take? express your answer to the nearest tenth of an hour.
a given sequence $r 1, r 2,\dots, r n$ of distinct real numbers can be put in ascending order by means of one or more 'bubble passes'. a bubble pass through a given sequence consists of comparing the second term with the first term and exchanging them if and only if the second term is smaller, then comparing the third term with the current second term and exchanging them if and only if the third term is smaller, and so on in order, through comparing the last term, $r n$, with its current predecessor and exchanging them if and only if the last term is smaller.the example below shows how the sequence 1, 9, 8, 7 is transformed into the sequence 1, 8, 7, 9 by one bubble pass. the numbers compared at each step are underlined.\begin{align*}\underline{1 \quad 9} \quad 8 \quad 7 \\1 \quad {}\underline{9 \quad 8} \quad 7 \\1 \quad 8 \quad \underline{9 \quad 7} \\1 \quad 8 \quad 7 \quad 9\end{align*}suppose that $n
The desired probability calculated from the given data is 931.
The first thirty-one numbers can be arranged in $31!$ different ways, and in $29!$ different ways so that the highest number is in the 31st position and the second-largest is in the 20th.
The result is $931$ since this gives us the desired probability of
$\frac{29!}{31!} = \frac{1}{31\cdot 30} = \frac{1}{930}$, so the answer is required answer is $\931$.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
To learn more about probability
https://brainly.com/question/11234923
#SPJ4.
why does a post-anova planned comparison use a pooled estimate of more groups than the number of groups whose means you are comparing?
In a post-anova planned comparison additional information increases the likelihood that the data may vary, leading to more degree of freedom.
Define the post-anova plan?The ANOVA test determines whether there is a general difference between the groups, but does not identify the precise groups that varied—only post hoc analyses do that.
Post hoc tests should only be conducted when you have demonstrated an overall statistically significant distinction in group averages since they are used to confirm where the differences between groups occurred (as statistically significant one-way ANOVA result). Similar to how one-way ANOVA was being used instead of numerous t-tests to control the find a different error rate (often alpha = 0.05), post hoc tests aim to do the same. A posteriori tests, or post hoc tests, are those that are carried out after the fact.Thus, the post-anova planned comparison makes use of a pooled estimate of data from more groups than just the number of studies whose means you intend comparing because more data increases the degree of freedom and the possibility that the data may change.
To know more about the post-anova plan, here
https://brainly.com/question/15084465
#SPJ4
A line with a slope of
4/7 passes through the points (h,10) and (–4,6). What is the value of h?
100 grams/day of substance x is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. substance x is undergoing in the nephron and would have a clearance value that is .(choose one)
100 grams/day of substance x is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. substance x is undergoing in the nephron net secretion and would have a clearance value that is greater than GFR
The formula for calculating clearance is Cx is given in terms of volume per time, where Ax is the quantity of x removed from the plasma, Px is the average plasma concentration, and Cx = Ax /Px.
Ax= 125 grams/day
and Px= 50 grams/day
Cx= 125/ 50
Cx= 2.5 grams/day
Therefore, the creatinine clearance overestimates GFR more severely in patients with a very low GFR than in those with higher GFR values. For a patient with a very low GFR, the secreted component is a relatively larger fraction of the total amount excreted.
Creatinine clearance remains the most popular method for routinely assessing patient GFR and the integrity of renal filtration, despite its low cost and convenience.
For more information on clearance kindly visit to
https://brainly.com/question/29461581
#SPJ4
Complete question :
Patient was experiencing respiratory acidosis (the increased hydrogen ion concentration was predominantly activating his peripheral chemoreceptors). 100 grams/day of substance X is filtered, 50 grams/day is reabsorbed, 75 grams/day is secreted and 125 grams/day is excreted. Substance X is undergoing ___________ in the nephron and would have a clearance value that is _________.(choose one)
A)net reabsorption, less than GFR
B)net secretion, greater than GFR
C)neither net reabsorption nor net secretion, equal to GFR
D)net reabsorption, greater than GFR
E) net secretion, less than GFR
A cla vote for their cla preident. Candidate
A
receive 21
21
vote, which i 60%
60
%
of the vote. What i the total number of tudent who voted?
There were 35 students that cast ballots in total.
How much is a percentage?
In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Frequently, it is denoted with the percent sign ("%")
We possess
60% of the vote, or 21 votes, are cast in favor of Candidate A.
The answer to the query is
Formulate the following given the conditions: 21 /60%
Use the same number to multiply the numerator and denominator: 210/6
Remove the connecting element: 35
Consequently, 35 students in all cast ballots.
From this point on, learn more about percentage.
https://brainly.com/question/24877689
#SPJ4
please answer asap (15 points)
only write down what I gotta put in the box and explanation
Answer:
b=-14
Step-by-step explanation:
slope intercept form is y=mx+b
m- slope
b- y intercept
So just fill in what we know
-2=2(6)+b
-2=12+b
-12 -12
-14=b
Hopes this helps please mark brainliest
how to graph
[tex]1 \frac{1}{3} [/tex]
and
[tex] \frac{2}{3} [/tex]
on a cartesian plane? please explain how
The point (1 and 1/3, 2/3) on the Cartesian plane is given by the image shown at the end of the answer.
How to graph the points on the Cartesian plane?All the points on the coordinate map have a x-coordinate and an y-coordinate, and the format of the point is given by the relation as follows:
(x,y).
The meaning of each coordinate is given as follows:
x-coordinate: horizontal position relative to the origin, that is, relative to x = 0.y-coordinate: vertical position relative to the origin, that is, relative to y = 0.The x-coordinate of the point in this problem is:
x = 1 and 1/3.
It is a mixed number, hence the decimal equivalent is of:
x = 1 + 1/3 = 1 + 0.33 = 1.33.
Meaning that the point is at an horizontal position that 1.33 units from the origin zero, that is, one point plus one third of the distance from one to two.
The y-coordinate is of:
y = 2/3.
Meaning that the vertical position of the point is 2/3 of the way from y = 0 to y = 1.
More can be learned about the coordinate map at brainly.com/question/27963537
#SPJ1
Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.
Margin of error for the given standard deviation is m = 3.77 , 4.21.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
Consider the given data, the sample of 84 announcements of upcoming engineering conferences were randomly selected. Here, sample mean = 3.94 days and sample standard deviation s = 1.28 days. The population standard deviation is unknown.
C.I . = 95% = 0.95
value of 0.95 in z-table = 1.96
m(margin of error ) = x - bar ±z*σ/√n
m = 3.94 ± 1.96*1.28/√84
m = 3.94±0.27
m = 3.77 , 4.21
Hence margin of error is m = 3.77 , 4.21
to know more about standard deviation click on the link below
brainly.com/question/475676
#SPJ4
59.303 x 10 to the second power
Since 10 to the power of 2 is 100, we multiply 59.303 by 100, meaning we can just push the decimals two places up with an answer of 5930.3
Hope this helps.
Answer:5930.3
Step-by-step explanation:
10^2=10x10
10x10x59.303=5930.3
You have solved equations containing square roots by squaring each side. You were
using the property that if a = b then a²-b². Show that the following statements are
NOT true for all real numbers.
a) if a² = b² then a = b
b) if a s b then a² sb²
These statements are not always true for all real numbers
What is a real number ?
A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.
a. If a² = b² and a = b is not always true because (-3)² = (3)² is true but
-3 = 3 is not true
Hence if a² = b² then a = b is not always true
b. if a< b then a²<b² is not always true
because -5<4 is true but (-5)² < (4)² is not true
Hence if a<b then a² < b² is not always true
To learn more about a real number from the given link
https://brainly.com/question/17201233
#SPJ1
A polygon has vertices at (-1, 3), (−1, 6), (2, 10), (5, 6), and (5, 3).
What is the area of the polygon? Enter your answer in the box.
The perimeter of the polygon is 22 units.
What is the area of the polygon?
The area of a polygon is defined as the area enclosed by the polygon's boundary. In other words, the region occupied by any polygon determines its area. In this lesson, we will learn how to calculate polygon area and the difference between polygon perimeter and area in detail.
we know that
the perimeter of a polygon is the sum of the length sides
in this problem, we have five vertices
so the polygon has five sides
Let,
A(-1, 3)
B(−1, 6)
C(2, 10)
D(5, 6)
E(5, 3).
the perimeter is equal to
P = AB + BC + CD + DE + AE
The formula to calculate the distance between two points is equal to
d = √(y₂ - y₁)² + (x₂ - x₁)²
The distance of AB:
A(-1, 3)
B(−1, 6)
d = √(6 - 3)² + (-1 - (-1))²
d = √(3)² + (0)²
d = 3
The distance of BC:
B(−1, 6)
C(2, 10)
d = √(10 - 6)² + (2 - (-1))²
d = √(4)² + (3)²
d = 5
The distance of CD:
C(2, 10)
D(5, 6)
d = √(6 - 10)² + (5 - 2)²
d = 5
The distance of DE:
D(5, 6)
E(5, 3).
d = √(3 - 6)² + (5 - 5)²
d = 3
The distance of AE:
A(-1, 3)
E(5, 3)
d = √(3 - 3)² + (5 - (-1))²
d = 6
Find the perimeter
the perimeter is equal to
P = AB + BC + CD + DE + AE
P = 3+5+5+3+6
P = 22 units.
Hence, the perimeter of the polygon is 22 units.
To learn more about the area of the polygon visit,
https://brainly.com/question/22640000
#SPJ1
can it be concluded at a 0.01 level of significance that there is a linear correlation between the two variables?
The p value is 0.0055 and it can be .concluded at a 0.01 level of significance that there is a linear correlation between the two variables
What is meant by correlation?In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although the term "correlation" can apply to any sort of link, in statistics it usually refers to the degree to which two variables are linearly related. The association between the height of parents and their kids, as illustrated in the so-called demand curve, is an example of a dependent phenomenon.
Dependent variable :Distance
Independent variable :Weight
Distance=10.336482+0.34383484 weight
Sample size=24
Correlation coefficient(R)=0.54872231
Estimation error of standard deviation=8.5738353
Parameter estimates:
Parameter Estimate Std.Err Alternative DF T-Stat P-value
Intercept 10.336482 9.7264272 ≠0 22 1.0627214 0.2994
Slope 0.34383484 0.11168494 ≠0 22 3.0786141 0.0055
From the above values in the table,
p-value=0.0055 which is less than 0.01.
So, the significant linear correlation exists between two variables.
To know more about correlation, visit:
https://brainly.com/question/28898177
#SPJ4
PLEASE HELP!!!
Identify all angle pairs of each type in the diagram.
corresponding angles:
alternate interior angles (2pairs):
alternate exterior angles:
same side interior angles:
The required angles are :
corresponding angles: ∠7=∠5
alternate interior angles: ∠4 = ∠2 and∠3 = ∠1
alternate exterior angles: ∠7 = ∠6
same side interior angles: ∠7 = ∠8
What do you understand by the terms ?Corresponding anglesalternate interior angles
alternate exterior angles
same side interior angles
Corresponding angles:
one that hold the same relative position as another angle somewhere in figure.
Alternate interior angles:
Alternate interior angles are the angles formed on the opposite sides of the transversal.
Alternate exterior angles:
Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Same side interior angles:
The theorem states that the same-side interior angles must be supplementary given the lines intersected by the transversal line are parallel.
corresponding angles:
∠7=∠5
alternate interior angles:
∠4 = ∠2
∠3 = ∠1
alternate exterior angles:
∠7 = ∠6
same side interior angles:
∠7 = ∠8
To learn more about geometry , visit:
https://brainly.com/question/28899589
#SPJ1
look at the 2 boxes and the 4 probability histograms below. each box has 2 probability histograms associated with it. one is the probability histogram for the sum of 2 draws made at random with replacement and the other is the probability histogram for the sum of 20 draws made at random with replacement from the box.
Explaining a bar graph
A bar graph graphically displays information. It uses bars that extend to various heights to symbolize value. Bar graphs can be created using any of the following: vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars (bars containing multiple types of information).
Two sketches are shown in Histogram I for Box A.
20 drawings from Box B are represented in Histogram II.
20 drawings from Box A are represented in Histogram III.
Two draws are shown in Histogram IV for Box B.
Learn more about bar graph
https://brainly.com/question/24741444
#SPJ4
define points $a(-3, 5)$, $b(-5, -3)$, $c(7, 9)$, and $d(1, 3)$. find the distance between the midpoint of $\overline{ab}$ and the midpoint of $\overline{cd}$.
The midpoint of A and B is (Xa , Yb) = (-4,1) and the midpoint of C and D is (Xc , Yd) = (4 , 6)
What is midpoint?
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places.A(-3,5) and B(-5, -3)
(Xa , Yb) = [(x₁ + x₂ / 2) , (y₁ + y₂ / 2)]
= [(-3 + (-5) / 2) , (5 +(-3) / 2)]
= (-8/2 , 2/2)
(Xa , Yb) = (-4,1)
Hence, the midpoint of A and B is (Xa , Yb) = (-4,1).
C(7,9) and D(1,3)
(Xc , Yd) = [(x₁ + x₂ / 2) , (y₁ + y₂ / 2)]
= [(7+1/2) , (9+3 / 2)]
= ( 8/2 , 12/2)
(Xc , Yd) = (4 , 6)
Hence, the midpoint of C and D is (Xc , Yd) = (4 , 6).
To know more about midpoint check the below link:
https://brainly.com/question/5566419
#SPJ4
the expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps: step 1: secant x over tangent x plus 1 over tangent x step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x step 4: 1 over sine x plus cosine x over sine x step 5: cosecant x plus cosine x over sine x step 6: cosecant x plus cotangent x which identity/formula was used to simplify from step 4 to step 5?
The identity used to simplify from step 4 to step 5 is the definition of the cosecant function: cosecant x = 1/sine x.
What is trigonometry?The connections between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is founded on the principles of right triangles, that are right angles. We can use trigonometry to calculate the lengths of the sides of a right triangle given the lengths of some or all of the other sides. It also enables us to determine the angle's size in a right triangle given its side tangent. In various disciplines, such as engineering, physics, and astronomy, trigonometry is utilised to solve issues involving triangles and the characteristics of circles. It is also used in navigation and surveying to estimate distances and angles between sites.
How to solve?
This identity allows us to rewrite the expression 1/sine x as cosecant x. Therefore, in step 4 we have 1/sine x + cosine x/sine x, and in step 5 we have cosecant x + cosine x/sine x = cosecant x + cotangent x.
To learn more about trigonometry, visit:
https://brainly.com/question/29060359
#SPJ4
Answer: Reciprocal Identity
Step-by-step explanation:
According to USA today, customers are not settling for automobiles straight off the production lines. As an ex. , those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMWs mini cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500.
A. Calculate a 95% confidence interval for the average cost of accessories on Mini Cooper.
B. Determine the margin of error in estimating the average cost of accessories on Mini Coopers.
C. What sample size would be required to reduce the margin of error by 50%?
The 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746
The margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The required sample size should be 34574400 to reduce the
margin of error by 50%
Sample size, n = 179
Sample mean, x = 5,000
Population standard deviation, σ = 1,500
Confidence level, 1-α=0.95
⇒ Level of significance, α = 0.05
From the z-table, the tabulated value is given by
[tex]Z_{\alpha /2}[/tex] / [tex]Z_{0.025}[/tex]
=1.95
95% confidence interval for the average cost of accessories on Mini Cooper is
5,000±1.96×(1,500/√179)
= (5,000 ± 219.7459)
=($4790.254, $5219.746)
Therefore the 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746.
Margin of error
= 1.96x(1,500/√179)
= 219.7459
Therefore, the margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The margin of error (E) is 0.50
⇒(0.50) √n=1.96(1500)
√n = 1.96(1500) /0.50
= n = (1.96(1500) /0.50)²
= n = (5880)²
= n = 34574400
Therefore, the required sample size should be 34574400 to reduce the
the margin of error by 50%
To learn more about probability and statistics,
https://brainly.com/question/14210034
#SPJ4
4. For all non-zero real numbers x and y such that x - y = xy. What is the value of (1/x)-(1/y)
Answer:
The value is -1-----------------------------
Simplify 1/x - 1/y1/x - 1/y = Common denominator is xyy/(xy) - x/(xy) = Bring to common denominator (y - x)/(xy) = Combine numerators- (x - y)/(xy) = Both numerator and denominator are same- 1 AnswerJustine started her own landscaping business. she charges $6 an hour for mowing lawns and $11 for pulling weeds. in september she mowed lawns for 13 hours and pulled weeds for 5 hours. how much money did she earn in september?
If she mowed lawns for 13 hours and pulled weeds for 5 hours, then she earn $133 in September
The charges for mowing lawns = $6 per hour
The charges for pulling weeds = $11 per hour
Total number of hours that she mowed the lawn = 13 hours
Total number of hours that she pulled weeds = 5 hours
Total amount that she earned in September = (The charges for mowing lawns × Total number of hours that she mowed the lawn) + (The charges for pulling weeds × Total number of hours that she pulled weeds)
Substitute the values in the equation
6 × 13 + 11 × 5
= 78 + 55
= $133
Hence, the total amount that she earned in September is $133
Learn more about equation here
brainly.com/question/14603452
#SPJ4
An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and height 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone.
(a) When the sand remaining in the upper cone has height of y inches, find its volume in terms of y
(b) When the sand in the lower cone has reached a height of h inches, find its volume in terms of h
(c) Assume the total volume of sand in the hourglass is 3π/4 cubic inches. Also, assume the height of the sand in the upper cone is decreasing at a rate of 14/100 inches per second. At the instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is increasing at what rate?
a) The volume is (π/27)y³
b) the volume is π -(π/27)(3 -h)³.
c) the rate at which the sand in the lower cone is increasing is 0.0116 inches per second
a) since we know The volume of a cone is: V = 1/3πr²h, for the problem here we have h = y and r = y/3, so the volume is : (1/3)π(y/3)²(y) = (π/27)y³
b) Now, we know The empty volume of the lower cone is the same as the volume of the upper cone with y=3, so V = (π/27)(3³) = π , as the sand height is h in the lower cone, so the height of the empty space is (3-h), the volume of the empty space is : (π/27)(3-h)³ and the volume will be the difference between that and the cone volume: π -(π/27)(3 -h)³. c) since the ratio of rates of change in height will be inversely proportional to the surface areas of the sand in each section of the cone, the ratio will be proportional to the square of the distance from the sand surface to the cone tip. For the height of the sand in the lower cone of 1 inch high, its volume is: π -(π/27)(3 -1)³ = π -(8π/27) = 19π/27, then the volume of the sand in the upper cone is: 3π/4 -19π/27 = 5π/108, the height of the sand in the upper cone is then
(π/27)h³ = π(5/108)
h³ = 5/4 ,h = ∛(5/4), the ratio of the surface areas in the two cones are The ratio of surface areas : (2 / ∛(5/4))², the rate of decrease is 4/100, rate of increase of sand in lower cone is (4/100)/((2 / ∛(5/4))²) =(∛12.5)/200 ≈ 0.0116
To know more about volume refer to the link https://brainly.com/question/1578538?referrer=searchResults.
#SPJ4
A freight train traveling along a certain route ue 12 unit of fuel per mile plu an additional 2. 2
unit of fuel per mile for each railcar on the train. Let N repreent the number of railcar on the train. What i an expreion for f (N), the total number
of unit of fuel ued per mile?
The total number of units of fuel used per mile is f(N) = 12 + 2.2N
What is a linear function?
A straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.
Let 'N' represent the number of railcars on the train.
Each railcar on the train adds 2.2 units of fuel per mile and then,
Total consumption for 'N' number of railcars = 2.2N units of fuel per mile.
The fixed amount of fuel consumption = 12 units of fuel per mile.
The expression for fuel consumption per mile is given by:
f(N) = 12 + 2.2N
Hence, the expression for f(N) is 12 + 2.2N.
To learn more about a linear function
https://brainly.com/question/29213643
#SPJ4
A confidence interval is made from a __________ to estimate the truth for a ______________.
For the given blank, a confidence interval is made from a range value to estimate the truth for a population parameters.
As given in the question,
Points required for a confidence interval are as follow:
To have information about the whole population,
Collect the sample data of the population.This is the interval or the range which gives the estimate of the whole population.Margin of error is very less.Method is useful in giving the result for long period of time.It gives population parameter at state level.Confidence interval = Sample mean ± Margin error.
Therefore, for the given blank, a confidence interval is made from a range value to estimate the truth for a population parameters.
Learn more about confidence interval here
brainly.com/question/24131141
#SPJ1
) find the number of ways to distribute 10 identical cards into 3 boxes, where each box has at least one card.
Numbers of ways to distribute 10 identical cards into 3 boxes is 36
Combination is is a way of selecting items from a collection where the order of selection does not matter.
Formula of combination:
Let a x-combination of a set is a subset of x distinct elements of S. If the set has n elements, the number of x-combinations is equal to the binomial coefficient.
ⁿCₓ = n(n-1)(n-2)(n-3). . . (n-x+1) / (x-1)(x-2)(x-3) . . . .(1)
which can be written as ⁿCₓ = n! / (n-x)! x! , when n > x
ⁿCₓ = 0 , when n < x
Where n = distinct object to choose from
C = Combination
x = spaces to fill
According to the question,
Number of identical cards : n =10
Number of box cards are being distributed : x = 3
Number of ways to distribute when no condition is given : ⁿ⁺ˣ⁻¹Cₓ₋₁
If we place one one card in each box then
Number of cards left with us = 10 - 3
= 7
Now, condition of at least one cards in each box is satisfied ,
Then total number of ways to distribute 7 cards into 3 = ⁷⁺³⁻¹C₃₋₁
=> ⁹C₂ = 9! / (9 - 2)! 2!
=> 9×8×7! / 7!2!
=> 9×8/2
=> 9×4
=>36 ways
To know more about Combination here
https://brainly.com/question/28065038
#SPJ4
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 7 kg weighs 63 N. Find the weight
of an object whose mass is 10 kg.
By using Unitary method, it can be calculated that
An object whose mass is 10 kg weighs 90 N
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method will be used
The weight of an object varies directly with the mass of the object.
An object whose mass is 7 kg weighs 63 N
An object whose mass is 1 kg weighs [tex]\frac{63}{7}[/tex] N
An object whose mass is 1 kg weighs 9 N
An object whose mass is 10 kg weighs [tex]9 \times 10[/tex] = 90 N
To learn more about unitary method, refer to the link -
https://brainly.com/question/24587372
#SPJ1
there are a large number of potential human errors. what are possible counter measures for inexperimence?
The countermeasures to avoid potential human errors are Visual aids & work instructions, education and/or discipline, work standardization and discipline and TPM and skill building etc.
Many major accidents, such as Texas City, Piper Alpha, and Chernobyl, were caused by potential human error. Companies must manage human failure as rigorously as they manage technical and engineering measures to avoid accidents and illness.
There are several countermeasures for amateur or beginner mistakes. Potential human errors can be avoided by some measures including training, skill development, work standardisation, visual aids, and work instructions. Every human being makes mistakes, whether they are professional or not.
Thus, Visual aids and work instructions, education and/or discipline, work standardisation and discipline, TPM and skill building, and other counter measures are used to avoid potential human errors.
To learn more about human errors refer here
https://brainly.com/question/19575648
#SPJ4
Which congruence theorem can be used to prove triangle ABC is congruent to triangle DEC?.
Because the corresponding sections of congruent triangles are congruent, you may use the Vertical Angles Congruence Theorem to demonstrate that ABC DEC. b. CAB CDE.
Which congruence theorem can be used to demonstrate that triangles ABC and DEF are congruent?Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.
The SAS Theorem is what?The side-angle-side (SAS) theorem is the first such theorem. The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.
Learn more about Congruency here:
brainly.com/question/7888063
#SPJ4
A company policy requires that, for every 60 employees, there must be 3 supervisors. If there are 264 supervisors at the company, how many employees does the company have?.
The company has 5280 employees and 264 supervisors as calculated using ratios.
The company has 3 supervisors for 60 employees.
Ratio of employees to supervisors = 60 : 3 = 20 : 1
So for 264 supervisors employees = 264 × 20 = 5280 employees.
Hence the company has 5280 employees.
An ordered pair of other integers, a fraction with the first number in the numerator and the second in the denominator, or the value this fraction denotes are all ways to conceptualize ratios.
Rational numbers, and occasionally natural numbers as well, are ratios of counts stated in terms of (non-zero) natural numbers. When two integers are compared with the same unit of measurement, which happens frequently, the ratio of the two integers is a dimensionless number.
A rate is created by multiplying two numbers with different unit measurements. Even though the values being compared are initially measured in separate units, ratios can still be unitless provided they relate quantities in the same dimension.
To learn more about employees visit:
https://brainly.com/question/11768194
#SPJ4
In Chicago, the temperature dropped from 21 degrees to -7 degrees over the course of 6 hours.
Identify a rational number that represents the average temperature change per hour.
The rational number that represents the average temperature change per hour is 28/6.
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
Given that, the temperature dropped from 21 degrees to -7 degrees over the course of 6 hours.
The change in temperature is:
21 - (-7)
= 21 + 7
= 28
The average temperature change per hour is:
28/6
Hence, the rational number that represents the average temperature change per hour is 28/6.
Learn more about rational numbers:
https://brainly.com/question/24398433
#SPJ1
