Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are Normally distributed with a mean of 6.5 inches and a standard deviation of 1.2 inches. According to the 68-95-99.7 rule, we expect 95% of head breadths to be:___________.
Answers
Answer:
"According to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
Step-by-step explanation:
According to the 68-95-99.7 rule, approximately:
68% (more precisely, 68.27%) of the data from the normal distribution lie one standard deviation, [tex] \\ \sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].95% (more precisely, 95.45%) of the data lie two standard deviations, [tex] \\ 2\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex], and finally,99.7 (or more precisely, 99.73%) of the data lie three standard deviations, [tex] \\ 3\sigma[/tex], above and below the population mean, [tex] \\ \mu[/tex].Then, if we have--from the question--that:
The random variable is head breadths.This variable follows a normal distribution.The population's mean for this distribution is [tex] \\ \mu = 6.5[/tex] inches.The population's standard deviation is [tex] \\ \sigma =1.2[/tex] inches.We have to remember that two parameters characterize a normal distribution: the population's mean and the population's standard deviation. So, mathematically, the distribution we have from question is [tex] \\ N(6.5, 1.2)[/tex].
For 95% (95.45%) of the head breadths, we expect that they are two standard deviations below and above the population's mean.
For solving this, we need to use the cumulative standard normal distribution (in case we need to find probabilities) and also use standardized values or z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score "tells us" the distance from the mean in standard deviations units. If the z-score is positive, it is above the mean. If it is negative, it is below the mean.
Since 95% (95.45%) of the head breadths are two standard deviations (above and below the mean), we have (using [1]):
[tex] \\ \pm2 = \frac{x - \mu}{\sigma}[/tex]
But we already know that [tex] \\ \mu=6.5[/tex] inches and [tex] \\ \sigma=1.2[/tex] inches.
Thus (without using units) for values above the population's mean:
[tex] \\ 2 = \frac{x - 6.5}{1.2}[/tex]
Solving the equation for x, we multiply by 1.2 at each side of [1] :
[tex] \\ 2 * 1.2 = \frac{x - 6.5}{1.2} * 1.2[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]
[tex] \\ 2 * 1.2 = (x - 6.5)*1[/tex]
[tex] \\ 2 * 1.2 = x - 6.5[/tex]
Adding 6.5 at each side of the previous equation:
[tex] \\ (2 * 1.2) + 6.5 = x - 6.5 + 6.5[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x + 0[/tex]
[tex] \\ (2 * 1.2) + 6.5 = x[/tex]
Therefore, the raw value, x, in the distribution that is two standard deviations above the population's mean is:
[tex] \\ x = (2 * 1.2) + 6.5[/tex]
[tex] \\ x = 2.4 + 6.5[/tex]
[tex] \\ x = 8.9[/tex] inches.
For two standard deviations below the mean, we proceed in the same way:
[tex] \\ -2 = \frac{x - 6.5}{1.2}[/tex]
[tex] \\ -2*1.2 = x - 6.5[/tex]
[tex] \\ (-2*1.2) + 6.5 = x[/tex]
[tex] \\ x = (-2*1.2) + 6.5[/tex]
[tex] \\ x = -2.4 + 6.5[/tex]
[tex] \\ x = 4.1[/tex] inches
Therefore, "according to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.
The graph below shows these values, and the shaded area represents 95% of the data, or, to be more precise, 95.45% (0.954499).
Related Questions
Use the quadratic formula to find both solutions to the quadratic equation given below. 2x^2+3x-5=0
Answers
Answer:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Step-by-step explanation:
We have the following equation given:
[tex] 2x^2 +3x -5=0[/tex]
And if we use the quadratic formula given by:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Answer:
B and C
Step-by-step explanation:
The sum of three numbers is 10. Two times the second number minus the first number is equal to 12. The first number minus the second number plus twice the third number equals 7. Find the numbers. Listed in order from smallest to largest, the numbers are , , and .
Answers
Answer:
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Step-by-step explanation:
Step(i):-
Given sum of the three numbers is 10
Let x , y , z be the three numbers is 10
x +y + z = 10 ...(i)
Given two times the second number minus the first number is equal to 12
2 × y - x = 12 ...(ii)
Given the first number minus the second number plus twice the third number equals 7
x + y + 2 z = 7 ...(iii)
Step(ii):-
Solving (i) and (iii) equations
x + y + z = 10 ...(i)
x + y + 2 z = 7 .. (iii)
- - - -
0 0 -z = 3
Now we know that z = -3 ...(a)
from (ii) equation
2 × y - x = 12 ...(ii)
x = 2 y -12 ...(b)
Step(iii):-
substitute equations (a) and (b) in equation (i)
x+y+z =10
2 y - 12 + y -3 =10
3 y -15 =10
3 y = 10 +15
3 y =25
[tex]y = \frac{25}{3}[/tex]
Substitute [tex]y = \frac{25}{3}[/tex] and z = -3 in equation(i) we will get
x+y+z =10
[tex]x + \frac{25}{3} -3 = 10[/tex]
[tex]x +\frac{25-9}{3} = 10[/tex]
[tex]x +\frac{16}{3} = 10[/tex]
[tex]x = 10 - \frac{16}{3}[/tex]
[tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]
Final answer :-
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Answer:
-2, 5, 7 on Edge.
Step-by-step explanation:
I got the Answer right.
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away. After several rows he figures the mean number of flights to be 57 with a standard deviation of 12. What is the probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor
Answers
Answer:
= 0.0041
Step-by-step explanation:
Given that:
A farmer was interest in determining how many grasshoppers were in his field. He knows that the distribution of grasshoppers may not be normally distributed in his field due to growing conditions. As he drives his tractor down each row he counts how many grasshoppers he sees flying away
mean number of flights to be 57
a standard deviation of 12
fewer flights on average in the next 40 rows
[tex]\mu = 57\\\\\sigma=12\\\\n=40[/tex]
so,
[tex]P(x<52)[/tex]
[tex]=P(\frac{x-\mu}{\sigma/\sqrt{n} } <\frac{52-57}{12/\sqrt{40} } )\\\\=P(z<\frac{-5\times6.325}{12} )\\\\=P(z<\frac{-31.625}{12})\\\\=P(z<-2.64)[/tex]
using z table
= 0.0041
The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor is 0.0041 and this can be determined by using the properties of probability.
Given :
The distribution of grasshoppers may not be normally distributed in his field due to growing conditions.The mean number of flights to be 57 with a standard deviation of 12.The probability of the farmer will count 52 or fewer flights on average in the next 40 rows down which he drives his tractor, can be determined by using the following calculations:
[tex]\rm P(x<52)=P\left (\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}<\dfrac{52-57}{\dfrac{12}{\sqrt{40} }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-5\times 6.325}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<\dfrac{-31.625}{12 }}\right)[/tex]
[tex]\rm P(x<52)=P\left (z<-2.64\right)[/tex]
Now, using z-table:
P(x < 52) = 0.0041
For more information, refer to the link given below:
https://brainly.com/question/21586810
A school needs 1,860 pencils for its students. The pencils are sold in boxes of 12. How many boxes does the school need to order?
Answers
Answer:
Step-by-step explanation:
155
The number of boxes required by the school to order is 155.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.
We need to find the school needs to requires boxes to order.
Total number of pencil = 1,860
Number of boxes = 12
Therefore, boxes needed = 1,860 / 12
= 155
Hence, the number of boxes required by the school to order is 155.
To learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ5
Find the exact solution of 3x^2+7=28
Answers
[tex]\text{Solve:}\\\\3x^2+7=28\\\\\text{Subtract 7 from both sides}\\\\3x^2=21\\\\\text{Divide both sides by 3}\\\\x^2=7\\\\\text{Square root both sides}\\\\\sqrt{x^2}=\sqrt7\\\\x=\pm\sqrt7\\\\\boxed{x=\sqrt7\,\,or\,\,x=-\sqrt7}[/tex]
Here It Is !!
More Otw
Answers
Answer:
3
Step-by-step explanation:
0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.
I need help
On these two
Answers
Answer:
10.
A. 10240
6.
B. 2^18 = 262144
Step-by-step explanation:
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards. A sample of 20 cards are selected from the lot without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least one defective card appears in the sample
Answers
Answer:
The probability that at least one defective card appears in the sample
P(D) = 0.9644 or 96.44%
Step-by-step explanation:
Given;
Total number of cards t = 140
Number of defective cards = 20
Number of non defective cards x = 140-20 = 120
The probability that at least one defective card = 1 - The probability that none none is defective
P(D) = 1 - P(N) ........1
For 20 selections; r = 20
-- 20 cards are selected from the lot without replacement for functional testing
The probability that none none is defective is;
P(N) = (xPr)/(tPr)
P(N) = (120P20)/(140P20)
P(N) = (120!/(120-20)!)/(140!/(140-20)!)
P(N) = (120!/100!)/(140!/120!) = 0.035618370821
P(N) = 0.0356
The probability that at least one defective card appears in the sample is;
P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644
P(D) = 0.9644 or 96.44%
Note: xPr = x permutation r
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 2 9 . There are 45 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be
Answers
Answer:
10 red marbles
Step-by-step explanation:
Total= 45 marbles
Probability of red= 2/9
Number of red= 45*2/9= 10
b) A man purchased 5 dozen of eggs at Rs 5 each. 10 eggs were broken and he
sold the remaining at Rs 5.70 each. Find
(ii) Profit or loss percent.
(i) his total profit or loss.
Answers
Answer:
Dear User,
Answer to your query is provided below
(i) Total Loss = Rs.15
(ii) Loss percent = 5%
Step-by-step explanation:
Eggs purchased = 5x12 = 60
Total Cost = 60x5 = Rs 300
Eggs Broken = 10
Eggs Broken cost = 10x5= Rs. 50
Eggs sold = 60-10 = 50
Egg Sale cost = 50x5.70 = Rs 285
(i) Total Loss = C.p. - S.p. = 300 - 285 = 15
(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%
Fifteen different Thursday evening programs reported that a commercial cost an average of $169,000 with a standard deviation of $81,000. What is the 95% confidence interval for the true mean
Answers
Answer:
The 95% confidence interval for the true mean is between $0 and $342,729
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
M = T*s = 2.1448*81000 = 173,729.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 169,000 - 173,729 = -4,... = $0(cannot be negative)
The upper end of the interval is the sample mean added to M. So it is 169,000 + 173,729 = $342,729
The 95% confidence interval for the true mean is between $0 and $342,729
The graph of Ax), shown below, resembles the graph of G(X) = x, but it has
been stretched and shifted. Which of the following could be the equation of
Fx)?
Answers
Answer:
sorry'but I don't know the answer
At the beginning of the season,jamie pays full price for a ticket to see the panthers,her favorite baseball team.
Answers
Corrected Question
At the beginning of the season, Jamie pays full price($49.64) for a ticket to see the panthers, her favorite baseball team. Ticket prices decrease $0.41 for every game the panthers lose this season. the panthers currently have 33 wins and 31 losses.
(a)Represent the total change in the cost of a ticket given their losses.
(b) What is the cost of a ticket for the next game they play?
Answer:
(a)$(49.64-0.41x)
(b)$36.93
Step-by-step explanation:
(a)Cost of a Full Ticket =$49.64
Let x be the number of losses
The ticket price reduces by $0.41 for every loss
Therefore:
Ticket Price after x losses =$(49.64-0.41x)
Therefore, total change in the cost of a ticket given their losses=$(49.64-0.41x)
(b)For this season the Panthers has suffered 31 losses.
Number of Losses, x=31
Therefore, cost of a ticket for the next game they play
= $(49.64-0.41*31)
=49.64-12.71
=$36.93
Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio): • Independent variable = ______________ • Condition A = ______________ • Condition B = ______________ • Dependent variable = _______________ • How do you know this DV is measured on a continuous scale? • How would you word the null hypothesis for your sample study? • How would you word the alternative hypothesis for your sample study? • What alpha level would you set to test your hypothesis? Why?
Answers
Answer:
Step-by-step explanation:
A possible study is to compare the prices of items in a two different online auction platform: the Dutch auction and the first-priced sealed auction.
Independent variable = the two types of auction
• Condition A = Dutch auction
• Condition B = First-price sealed auction
The Dependent variable in my case study is the prices for each pair of identical items I place in each auction using a known pair sample. The depends variable is measured in the continuous scale because prices are in numbers and these numbers vary continuously, it is not fixed.
The null hypothesis for my study would be: there is no difference in the prices of identical items in the two different auction.
The alternative hypothesis for my study would be: there is a difference in the prices of identical items in the two different auction.
I would set it to the 0.05 level of significance because this is the standard level of significance normally set in a study although this varies.
Write an integral for the area of the surface generated by revolving the curve y equals cosine (2 x )about the x-axis on negative StartFraction pi Over 5 EndFraction less than or equals x less than or equals StartFraction pi Over 5 EndFraction .
Answers
Answer:
The integral is
∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
x₁ = (-π/5)
x₂ = (π/5)
And the area of the surface generated by revolving = 9.71 square units
Step-by-step explanation:
When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by
A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
For this question,
y = cos 2x
x₁ = (-π/5)
x₂ = (π/5)
y' = -2 sin 2x
1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)
So, the Area of the surface of revolution is
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx
Substituting these variables
A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
Let 2 sin 2x = t
4 cos 2x dx = dt
2 Cos 2x dx = (dt/2)
dx = (1/2cos 2x)(dt/2)
Since t = 2 sin 2x
when x = (-π/5), t = 2 sin (-2π/5) = -1.90
when x = (π/5), t = 2 sin (2π/5) = 1.90
A
= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)
= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)
= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
But note that
∫ √(a² + x²) dx
= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c
where c is the constant of integration
So,
∫ √(1 + t²) dt
= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c
∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀
= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]
= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]
= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]
= [2.04 + 0.70] - [-2.04 - 1.4]
= 2.74 - [-3.44]
= 2.74 + 3.44
= 6.18
Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= (π/2) × 6.18
= 9.71 square units.
Hope this Helps!!!
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column 1 2nd Column 4 3rd Column negative 2 2nd Row 1st Column 3 2nd Column h 3rd Column negative 6 EndMatrix ]
Answers
Answer:
Step-by-step explanation:
Consider the augments matrix (the right most column is the extra vector).
[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]
By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix
[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]
Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.
Donte simplified the expression below. 4(1+3i) - (8-5i)
4 + 3i - 8 + 5i
-4 + 8i
What mistake did donte make?
Answers
Answer:
Donde didn't multiply 4(1+3i)
Answer: it’s A he did not apply distributive property yo
Step-by-step explanation:
What is the equation of the line that passes through (4, 2) ) and is parallel to 3x - 2y = - 6 ?
Answers
Answer:
[tex]y=\frac{3}{2} x-4[/tex]
Step-by-step explanation:
The graph I provided shows it passes thru (4,2) and that it is parallel
Answer:
y = 3/2x -4
Step-by-step explanation:
3x - 2y = - 6
First find the slope by putting it in slope intercept form
Subtract 3x from each side
-2y = -3x-6
Divide by -2
y = -3x/-2 -6/-2
y = 3/2x +3
The slope is 3/2
Parallel lines have the same slope
We have the slope 3/2 and a point (4,2)
y = mx+b where m is the slope and b is the y intercept
y =3/2x+b
Substitute the point into the equation
2 = 3/2(4) +b
2 = 6 +b
Subtract 6
2-6 = 6-6+b
-4 =b
y = 3/2x -4
Find the term that must be added to the equation x2−2x=3 to make it into a perfect square. A. 1 B. 4 C. -3 D. 2
Answers
Answer:
1
Step-by-step explanation:
x^2−2x=3
Take the coefficient of x
-2
Divide by 2
-2/2 =-1
Square it
(-1)^2 = 1
Add this to each side
What is 27 ÷ 4 rounded to the nearest tenth?
Answers
Answer:
6.8
Step-by-step explanation:
27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.
If 3 boxes of apples weigh 105 pounds, how much would 2 boxes of apples weigh?
Answers
Answer:
70 pounds
Step-by-step explanation:
3 boxes= 105 pounds
2boxes= x pounds
Cross Multiply
3*x=105 *2
3x=210
3x/3=210/3
x=70 pounds
Answer:
70
Step-by-step explanation:
105/3=35
35x2=70
So 70 is the answer
John leaves school to go home.his bus drives 6 kilometers north and then goes 7 kilometers west.how far is John's house from the school?
Answers
Answer:
John is 9.21 km form the school.
Step-by-step explanation:
John leaves school to go home. His bus drives 6 kilometres north and then goes 7 kilometres west. It is required to find John's distance from the school. It is equal to the shortest path covered or its displacement. So,
[tex]d=\sqrt{6^2+7^2} \\\\d=9.21\ km[/tex]
So, John is 9.21 km form the school.
determine whether the forces in the pair are pulling at right angles to each other for the values. a-3.4 and b=2.6, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth
Answers
Answer:
4.3 units
Step-by-step explanation:
In this question we use the Pythagorean Theorem which is shown below:
Data are given in the question
Right angle
a = 3.4
b = 2.6
These two are legs of the right triangle
Based on the above information
As we know that
Pythagorean Theorem is
[tex]a^2 + b^2 = c^2[/tex]
So,
[tex]= (3.4)^2 + (2.6)^2[/tex]
= 11.56 + 6.76
= 18.32
That means
[tex]c^2 = 18.56[/tex]
So, the c = 4.3 units
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation
Answers
Answer:
(x, y) → (4/5 x, 4/5 y)
Question:
The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:
A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?
A) (x, y) → (0.5 − x, 0.5 − y)
B) (x, y) → (x − 7, y − 7)
C) (x, y) → ( 5/4 x, 5/4 y)
D) (x, y) → (4/5 x, 4/5 y)
Step-by-step explanation:
To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.
Let's check the options out.
In option (A), the coordinates is subtracted from the constant (0.5).
In option (B), the constant (7) is subtracted from the coordinates.
In option (C), the coordinates are multiplied by constant (5/4).
But 5/4 = 1.25. This is greater than 1.
In option (D), the coordinates are multiplied by constant (4/5).
4/5 = 0.8
The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)
4/5 = 0.8
0.8 is less than 1
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Unit 2 Tutorials
Question 20
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For the arithmetic sequence beginning with the terms (-2,0,2,4,6,8...), What is the sum of the first
18 terms?
0 238
0 340
o 304
0 270
Sove and continue
Answers
Answer:
270
Step-by-step explanation:
For any arithmetic sequence
nth term is given by
nth term = a + (n-1)d
where a is first term,
d is common difference
d is given by nth term - (n-1)th term
sum of n terms given by
sum = n/2(2a + (n-1)d)
________________________________________________
Given arithmetic sequence
-2,0,2,4,6,8...
first term a = -2
lets take third term as nth term and second term as (n-1)th term to find common difference d.
d = 2 - 0 = 2
using a = -2 , d = 2, n = 18
thus, sum of first 18 terms = n/2(2a + (n-1)d)
=18/2( 2*(-2) + (18-1) 2)
=9 ( -4 + 34)
=9 ( 30) = 270
Thus, sum of first 18 terms is 270.
If a function f(x) is defined as 3x2 + x + 2, what is the value of Lim h-0 f(x+h)-f(x)/h? A. 3x + 1 B. 3x + 2 C. 6x + 1 D. 6x + 2
Answers
Answer:
[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]
[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]
And replacing we got:
[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]
And if we simplfy we got:
[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]
And replacing we got:
[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]
And the bet option would be:
C. 6x + 1
Step-by-step explanation:
We have the following function given:
[tex] f(x) = 3x^2 +x+2[/tex]
And we want to find this limit:
[tex] lim_{h \to 0} \frac{f(x+h) -f(x)}{h}[/tex]
We can begin finding:
[tex] f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2[/tex]
[tex]f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2[/tex]
And replacing we got:
[tex] lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}[/tex]
And if we simplfy we got:
[tex] lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h [/tex]
And replacing we got:
[tex]lim_{h \to 0} 6x + 1 +3h = 6x+1[/tex]
And the bet option would be:
C. 6x + 1
Answer:
6x+1
Step-by-step explanation:
Plato :)
I WILL GIVE BRAINLIEST ANSWER ASAP
Answers
Answer: B
Step-by-step explanation:
For this problem, to solve for x, you want to move all like terms to one side.
[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]
Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.
[tex]-\frac{1}{4} x=1[/tex]
x=-4
Answer:
[tex]x = - 4[/tex]
Second answer is correct
Step-by-step explanation:
[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]
hope this helps you
Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per gallon is added to the tank at 6 gal/min, and the resulting solution leaves at the same rate. Find the quantity Q(t) of salt in the tank at time t > 0.
Answers
Answer:
The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]
Where:
[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].
[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].
[tex]V[/tex] - Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]
[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]
This equation is solved as follows:
[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]
[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]
[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]
[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]
The initial concentration in the tank is:
[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]
[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]
Now, the integration constant is:
[tex]0.167 = 30 + C[/tex]
[tex]C = -29.833[/tex]
The solution of the differential equation is:
[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]
Now, the quantity of salt at time t is:
[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]
[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]
Where t is measured in minutes.
In the circle above, P is the center,What is the value, in degrees, of θ?
Answers
Answer:
45°
Step-by-step explanation:
There is a propiety that says "The measure of the inscribed angle is half that of the arc that the two sides cut out of the circle."
So the central angle is 90, the inscribed angle will be 90/2=45°
Scientists think that robots will play a crucial role in factories in the next several decades. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 507 cables. The cables were examined and there were 9 defectives. If human assemblers have a defect rate of 0.035 (3.5%), does this data support the hypothesis that the proportion of defectives is lower for robots than humans
Answers
Answer:
The data support the hypothesis that the proportion of defectives is lower for robots than humans.
Step-by-step explanation:
To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.
From the data given:
Total number of cables a robot assembled = 507
Defectives = 9
To get the defect rate = the number of defects divided by the total number of cables, multiplied by 100.
Defect rate = (9 / 507) x 100 = 0.01775 x 100
Defect rate for the robot = 1.775%
From the question, a robot was used and the defect rate after the calculation is 1.775%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745 defectives.
x / 507 = 3.5%
x (defectives) = 17.745
Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.
