Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.
Answer:
0.07
Step-by-step explanation:
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
Answer:
[tex]\large \boxed{0.07}[/tex]
Step-by-step explanation:
The usual question is, "What is the probability of A, given B?"
They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"
We must first complete your frequency table by calculating the totals for each row and column.
The table shows that there are 30 students, two of whom drive to school.
[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]
Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.
Answer: D
Step-by-step explanation:
According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year
The initial population Po = 114000
Rate = 1.5% = 0.015
The declining population formula will be:
P = Po( 1 - R%)x^2
The decay formula
Since the population is decreasing, take away 0.015 from 1
1 - 0.015 = 0.985
Substitutes all the parameters into the formula
P(s) = 114000(0.985)x^2
P(s) = 114000× 0985x^2
The correct answer is written above.
Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.
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━━━━━━━☆☆━━━━━━━
▹ Answer
0.25 = 1/4 because 25/100 = 1/4
▹ Step-by-Step Explanation
0.25 to a fraction → 25/100
25/100 = 1/4
Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Please answer this correctly
Answer:
Option 2
Step-by-step explanation:
The average temperature in January is -1 degrees celsius. Last year, it was 1 degrees celsius higher than the average.
-1 + 1 = 0
Answer:
The second answer.
Step-by-step explanation:
The average temp. is -1C.
'was 1C warmer' = +1
-1+1=0
Which proportion would convert 18 ounces into pounds?
Answer:
16 ounces = 1 pound
Step-by-step explanation:
You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
co
Which graph represents the inequality?
-2
1-1
-12
1
1 2
NE
1
Y>-
2
2
А
++
1 -1
-12
ou
-2
od
1
NIE
1
B
1 2
2
2
---
Oto
-2
-1
1 2
-12
-
NIE
NI
12
D
-2
1 - 1
1
0
1
1 2
NIS
2
NI
Answer:
A
Step-by-step explanation:
Given the equality y > -½, it means the values of y is greater than -½.
The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .
Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.
Therefore, the graph that indicates the inequality y > ½ is A
Answer:
A
Step-by-step explanation:
find the value of k if x minus 2 is a factor of P of X that is X square + X + k
Answer:
k = -6
Step-by-step explanation:
hello
saying that (x-2) is a factor of [tex]x^2+x+k[/tex]
means that 2 is a zero of
[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]
and we can verify as
[tex](x^2+x-6)=(x-2)(x+3)[/tex]
so it is all good
hope this helps
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
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1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000
Answer:
See explanation
Step-by-step explanation:
To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:
A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].(a)Given the function: f(x)=100x+1000
The highest power of n is 1.
Therefore f(x) is O(x).
Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].
[tex](b) f(x)=100x^ 2 + 1000[/tex]
The highest power of n is 2.
Therefore the function is [tex]O(x^2)[/tex].
Answer:
i think its 2000
Step-by-step explanation:
A fair die is rolled repeatedly. Calculate to at least two decimal places:__________
a) the chance that the first 6 appears before the tenth roll
b) the chance that the third 6 appears on the tenth roll
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
d) the expected number of rolls until six 6's appear
e) the expected number of rolls until all six faces appear
Answer:
a. 0.34885
b. 0.04651
c. 0.02404
d. 36
e. 14.7, say 15 trials
Step-by-step explanation:
Q17070205
Note:
1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.
2. use R to find the probability values from the respective distributions.
a) the chance that the first 6 appears before the tenth roll
This means that a six appears exactly once between the first and the nineth roll.
Using binomial distribution, p=1/6, n=9, x=1
dbinom(1,9,1/6) = 0.34885
b) the chance that the third 6 appears on the tenth roll
This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.
Again, we have a binomial distribution of p=1/6, n=9, x=2
p1 = dbinom(2,9,1/6) = 0.27908
The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.
Thus the probability of both happening, by the multiplication rule, assuming independence
P(third on the tenth roll) = p1*p2 = 0.04651
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
Again, using binomial distribution, probability of 3-6's in the first 10 rolls,
p1 = dbinom(3,10,1/6) = 0.15504
Probability of 3-6's in the NEXT 10 rolls
p1 = dbinom(3,10,1/6) = 0.15504
Probability of both happening (multiplication rule, assuming both events are independent)
= p1 * p1 = 0.02404
d) the expected number of rolls until six 6's appear
Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6
= n(1-p)/p
Total number of rolls by adding n
= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36
e) the expected number of rolls until all six faces appear
P1 = 6/6 because the firs trial (roll) can be any face with probability 1
P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials
P3 = 6/4 ...
P4 = 6/3
P5 = 6/2
P6 = 6/1
So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials
For the triangle show, what are the values of x and y (urgent help needed)
we just have to use the Pythagoras theorem and then calculate the value of x and y.
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it.
The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pie.
A. 1,980
B. 1,788
C. 1,034
D. 1,884
Answer:
B. 1788
Step-by-step explanation:
The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by
length * height * width
The volume for current object is :
12 * 28 * 5
= 1788 cubic yards.
Answer: 1778
Step-by-step explanation:
because Ik I had the question
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Answer:
a) Mean = 0.125 inch
Standard deviation = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673
c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673
Step-by-step explanation:
Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)
Let the distribution of the width of the door be X₂ (μ₂, σ₂²)
The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂
when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with
Mean = Σλᵢμᵢ
λᵢ = coefficient of each disteibution in the manner that they are combined
μᵢ = Mean of each distribution
Combined variance = σ² = Σλᵢ²σᵢ²
λ₁ = 1, λ₂ = -1
μ₁ = 24 inches
μ₂ = 23 7/8 inches = 23.875 inches
σ₁² = (1/8)² = (1/64) = 0.015625
σ₂ ² = (1/16)² = (1/256) = 0.00390625
Combined mean = μ = 24 - 23.875 = 0.125 inch
Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125
Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)
This is a normal distribution problem
Mean = μ = 0.125 inch
Standard deviation = σ = 0.13975 inch
We first normalize/standardize 0.25 inch
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89
P(X > 0.25) = P(z > 0.89)
Checking the tables
P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673
c) Probability that the door does not fit in the casing
If X₂ > X₁, X < 0
P(X < 0)
We first normalize/standardize 0 inch
z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89
P(X < 0) = P(z < -0.89)
Checking the tables
P(X < 0) = P(z < -0.89) = 0.18673
Hope this Helps!!!
You spend 6,380.00 a year for rent. This is 22% of your income. What is your income?
Answer: 29,000.00
Step-by-step explanation:
Let the income=x. 22%=0.22.
So 6380/x=0.22
x=6380/0.22=29,000.00
Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Simplify the expression (5j+5) – (5j+5)
Answer:
0
Step-by-step explanation:
multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!
Answer:
0
Explanation:
step 1 - remove the parenthesis from the expression
(5j + 5) - (5j + 5)
5j + 5 - 5j - 5
step 2 - combine like terms
5j + 5 - 5j - 5
5j - 5j + 5 - 5
0 + 0
0
therefore, the simplified form of the given expression is 0.
Please help! V^2 = 25/81
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
Learn more about Equation here:
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The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
Answer:
161.6 cm²Step-by-step explanation:
Surface Area of the rectangular box = 2(LW+LH+WH)
L is the length of the box
W is the width of the box
H is the height of the box
let dL, dW and dH be the possible error in the dimensions L, W and H respectively.
Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm
The surface Area of the rectangular box using the differentials is expressed as shown;
S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]
Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;
S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}
S = 2{19.2+11.6+19.2+9.6+11.6+9.6}
S = 2(80.8)
S = 161.6 cm²
Hence, the surface area of the box is 161.6 cm²
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m