Answer:
(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].
(b) Hence the relative error is 1.54%.
Step-by-step explanation:
Here the given are,
The Radius of the circle r = 26cm.
The maximum error in measurement dr = 0.2 cm.
Answer:
(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Step-by-step explanation:
radius, r = 26 cm
error = 0.2 cm
(a) The area of the disc is given by
[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]
Now
A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2
So, the area with error is given by
[tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) The relative error is
[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Please help with this function problem
Answer:
-2
-1
-2
Step-by-step explanation:
really ? this is a problem ? why ?
f(0) means the functional value for x = 0.
is x = 2 ? no.
so, automatically the other case applies, and f(0) = -2
f(2) means x=2
is x = 2 ? yes.
so that case applies, and f(2) = -1
f(5) means x=5
is x = 2 ? no.
so again, the case for x <> 2 applies, f(5) = -2
i don’t understand… but thank you if u do answer my question :))
Answer:
7/0
Step-by-step explanation:
This is because if a number is divided by 0 then there is no answer or it is undefined
Think of it like this,
You have 7 apples and wanted to give it to zero friends, is it possible?
Hope this helped :)
Answer:
Second option (7÷0)
Explanation:
Dividing by zero is considered undefined since you can't divide something by nothing. It's like saying you have a pizza and you want to divide it between 7 people but since you're dividing by zero, you're not splitting the pizza between anyone.
Find the probability of 3 success for the binomial experiment with 7 trial and the success probability of 0.3. Then find the mean and standard deviation. Write the formula substitute
the values.
Answer:
[tex]P(x=3)=0.2269[/tex]
Mean=2.1
Standard deviation=1.21
Step-by-step explanation:
We are given that
n=7
Probability of success, p=0.3
q=1-p=1-0.3=0.7
We have to find the probability of 3 success for the binomial experiment and find the mean and standard deviation.
Binomial distribution formula
[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]
Using the formula
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]P(x=3)=0.2269[/tex]
Now,
Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]
Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]
Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]
Standard deviation, [tex]\sigma=1.21[/tex]
Please help …………………….
9514 1404 393
Answer:
(-3, 3)
Step-by-step explanation:
The blanks are trying to lead you through the process of finding the point of interest.
__
The horizontal distance from T to S is 9 . (or -9, if you prefer)
The ratio you're trying to divide the line into is the ratio that goes in this blank:
Multiply the horizontal distance by 2/3 . (9×2/3 = 6)
Move 6 units left from point T.
The vertical distance from T to S is 6 .
Multiply the vertical distance by 2/3 . (6×2/3 = 4)
Move 4 units up from point T.
__
Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).
Please help.
Evaluate 6!
3,125
720
120
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{6!}\\\large\textsf{= 6}\times\large\textsf{5}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{6(5) = \bf 30}\\\large\textsf{= 30}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{30(4) = \bf 120}\\\large\textsf{= 120}\times\large\textsf{3}\times\large\textsf{2}\times\textsf{1}\\\large\textsf{120(3) = \bf 360}\\\large\textsf{= 360}\times\large\textsf{2}\times\large\textsf{1}[/tex]
[tex]\large\textsf{360(2) = \bf 720}\\\large\textsf{720}\times\large\textsf{1}\\\large\textsf{= \bf 720}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: \bf 720}\huge\textsf{ (option B)}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which quadratic function has minimum value at x = -b/2a?
O y=-3x2 + 5 X + 6
O y=x2 + 5 x + 6
O y=-x2 + 5x + 6
O y = -4 x2 + 5x + 6
Answer:
The choose (2)
y=x²+5x+6
Step-by-step explanation:
y=x²+5x+6 —> (–5/2 , –1/4)
y=-3x² + 5 X + 6 —> (5/6, 97/12)
y=-x² + 5x + 6 —> (5/2,49/4)
y = -4 x² + 5x + 6 —> (5/8 , 121/16)
If computers sell for $1160 per unit and hard drives sell for $ 102 per unit, the revenue from x computers and y hard drives can be represented by what expression? If computers sell for $ per unit and hard drives sell for $102 per unit, the revenue from x computers and y hard drives can be represented by
Y+10 like terms from expression 2
Answer:
y+10=2
y=-8
Step-by-step explanation:
y=2-10
y=-8
Claims from Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. Claims from Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. All claim amounts are independent of the other claims. Fifty claims occur in each group. Find the probability the total of the 100 claims exceeds 1,530,000.
Answer:
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Sum of normal variables:
When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.
Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.
This means that:
[tex]\mu_A = 10000*50 = 500000[/tex]
[tex]s_A = 1000\sqrt{50} = 7071[/tex]
Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.
This means that:
[tex]\mu_B = 20000*50 = 1000000[/tex]
[tex]s_B = 2000\sqrt{50} = 14142[/tex]
Distribution of the total of the 100 claims:
[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]
Find the probability the total of the 100 claims exceeds 1,530,000.
This is 1 subtracted by the p-value of Z when X = 1530000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]
[tex]Z = 1.9[/tex]
[tex]Z = 1.9[/tex] has a p-value of 0.9713
1 - 0.9713 = 0.0287
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. [Binomail Probability] Less than four twos
Answer:
0.5665 = 56.65% probability of less than four twos.
Step-by-step explanation:
For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 20 times
This means that [tex]n = 20[/tex]
One out of six sides is 2:
This means that [tex]p = \frac{1}{6} = 0.1667[/tex]
Probability of less than four twos:
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]
[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]
[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]
[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]
So
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]
0.5665 = 56.65% probability of less than four twos.
What proportion of the students scored at least 23 points on this test, rounded to five decimal places
This question is incomplete, the complete question is;
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.
What proportion of the students scored at least 23 points on this test, rounded to five decimal places?
Answer:
proportion of the students that scored at least 23 points on this test is 0.30850
Step-by-step explanation:
Given the data in the question;
mean μ = 22
standard deviation σ = 2
since test closely followed a Normal Distribution
let
Z = x-μ / σ { standard normal random variable ]
Now, proportion of the students that scored at least 23 points on this test.
P( x ≥ 23 ) = P( (x-μ / σ) ≥ ( 23-22 / 2 )
= P( Z ≥ 1/2 )
= P( Z ≥ 0.5 )
= 1 - P( Z < 0.5 )
Now, from z table
{ we have P( Z < 0.5 ) = 0.6915 }
= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850
P( x ≥ 23 ) = 0.30850
Therefore, proportion of the students that scored at least 23 points on this test is 0.30850
Two balls are picked at random from a box containing 5 red balls and 3 green balls. What is the probability that 1 red ball and 1 green ball are selected?
Answer:
Step-by-step explanation:
Answer:
3/8 x 5/8= 15/64
Step-by-step explanation:
solve above question
A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix packaging. The designers use the equation r=Vhπ⎯⎯⎯⎯⎯⎯√r=Vhπ to determine the radius of the can for a certain height hh and volume VV. The company decides they want the can to have a volume of 1280πcm31280πcm3. Find the radius of the can if the height is 16cm16cm. Keep your answers in simplified radical form.
Answer:
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Radius of the can:
The radius of the can is given by:
[tex]r^2 = \frac{V}{h\pi}[/tex]
In which V is the volume and h is the height.
In this question:
[tex]V = 1280\pi, h = 16[/tex]
Thus
[tex]r^2 = \frac{V}{h\pi}[/tex]
[tex]r^2 = \frac{1280\pi}{16\pi}[/tex]
[tex]r^2 = 80[/tex]
[tex]r = \sqrt{80}[/tex]
[tex]r = \sqrt{5*16}[/tex]
[tex]r = \sqrt{5}\sqrt{16}[/tex]
[tex]r = 4\sqrt{5}[/tex]
The radius of the can, in centimeters, is of [tex]4\sqrt{5}[/tex]
A. If x:y= 3:5, find = 4x + 5 : 6y -3
Answer:
17 : 27
Step-by-step explanation:
x=3
y=5
4(3)+5 : 6(5)-3
= 12+5 : 30-3
= 17 : 27
A new car costs $23000. The value decreases by 15% each year.(a) Write the exponential model to represent the cars value after t years. (b) To the nearest dollar, how much will the car be worth after 4 years?
Answer:
(a) 23000(1-15%)^t
(b) about 12006.14375
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
And with the values, we get the exponential model 23000(1-15%)^t
(b) From question (a) we already have the model and the time period given here is 4 years. So putting it in the formula we get,
23000(1-15%)^4
=23000(1-15/100)^4
=23000(0.85)^4
=23000x0.52200625
=12006.14375 (Ans)
lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies. She then had 3/7 of the container of sugar left. How much sugar was in the container at first
Answer:
At the beginning, there were 2,678.26 grams of sugar in the container.
Step-by-step explanation:
Since Lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies, and she then had 3/7 of the container of sugar left, to determine how much sugar was in the container at first, the following calculation must be performed:
880 + 1 / 10X = 3 / 7X
880 + 0.1X = 0.4285X
880 = 0.4285X - 0.1X
880 = 0.3285X
880 / 0.3285 = X
2,678.26 = X
Therefore, at the beginning there were 2,678.26 grams of sugar in the container.
The profit, in dollars, of selling n items is given by P(n) = 0.86n - 2800. Identify the slope and the y-intercept.
Answer: 0.86 and -2800 (choice A)
Explanation:
Think of the given equation as y = 0.86x - 2800
Then compare it to y = mx + b
We see that m = 0.86 is the slope and b = -2800 is the y intercept.
Answer:
Slope: 0.86 , Y-intercept:-2800
Step-by-step explanation:
Linear equations go by the form of y=mx + c
where m is the gradient(slope of the graph) and c is the y-intercept
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000
Answer:
The correct answer is "76.98%".
Step-by-step explanation:
According to the question,
⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]
[tex]=P(-1.2<z<1.2)[/tex]
[tex]=P(z<1.2)-P(z<-1.2)[/tex]
[tex]=0.8849-0.1151[/tex]
[tex]=0.7698[/tex]
or,
[tex]=76.98[/tex]%
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH
Answer:
[tex]|F'H'| = 2 * |FH|[/tex]
Step-by-step explanation:
Given
[tex]E = (0,1)[/tex] [tex]E' = (-1,2)[/tex]
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]G = (2,0)[/tex] [tex]G' =(3,0)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
[tex](x,y) = (1,0)[/tex] -- center
[tex]k = 2[/tex] --- scale factor
See comment for proper format of question
Required
Compare FH to F'H'
From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;
Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.
i.e.
[tex]|F'H'| = k * |FH|[/tex]
[tex]|F'H'| = 2 * |FH|[/tex]
To prove this;
Calculate distance of segments FH and F'H' using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Given that:
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
We have:
[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]
[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]
[tex]FH = \sqrt{1 + 1}[/tex]
[tex]FH = \sqrt{2}[/tex]
Similarly;
[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]
[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]
Distribute
[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]
[tex]F'H' = \sqrt{(2)^2*2}[/tex]
Split
[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]
[tex]F'H' = 2 *\sqrt{2}[/tex]
[tex]F'H' = 2\sqrt{2}[/tex]
Recall that:
[tex]|F'H'| = 2 * |FH|[/tex]
So, we have:
[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]
[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true
Hence, the dilation relationship between FH and F'H' is::
[tex]|F'H'| = 2 * |FH|[/tex]
Answer:NOTT !! A segment in the image has the same length as its corresponding segment in the pre-image.
Step-by-step explanation:
An absolute value function has
A. Curved lines that only increases and decreases.
B. Straight lines that do both increase ,decrease, or stay constant on the same graph
C.Straight line that do both increase and decrease on the same graph
D. Straight lines that only increase or decrease
E. Curved lines that do both increase and decrease on the same graph
Muhammad lives twice as far from the school as Hita. Together, the live a total of 12 km
from the school. How far away drom the school does each of them live?
Answer:
Muhammad lives 8 km away from the school.
Hita lives 4 km away from the school.
Step-by-step explanation:
First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.
21 × 6 ÷ 7 + 12 - 15
Answer:
15
Step-by-step explanation:
By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.
21*6 = 126
126/7 = 18
18 + 12 = 30
30 - 15 = 15
Answer:
15
Step-by-step explanation:
21 × 6 ÷ 7 + 12 - 15
= 126 ÷ 7 + 12 - 15
= 18 + 12 - 15
= 30 - 15
= 15
Need Help! ASAP!!! I gave a screen shot. Please someone give me the correct answer.
9514 1404 393
Answer:
x ∈ {-35, 0, 35}
Step-by-step explanation:
We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.
[tex]x+xy^2=250y\ \Rightarrow\ x=\dfrac{250y}{1+y^2}\\\\x-xy^2=-240y\ \Rightarrow\ x=\dfrac{-240y}{1-y^2}\\\\\dfrac{250y}{1+y^2}+\dfrac{240y}{1-y^2}=0\\\\\dfrac{25y(1-y^2)+24y(1+y^2)}{(1+y^2)(1-y^2)}=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=\dfrac{250(\pm 7)}{1+(\pm7)^2}=\pm35,\quad=\dfrac{250(0)}{1+0^2}=0\\\\\boxed{x\in\{-35,0,35\}}[/tex]
Use the graph of the function y=g(x) below to answer the questions.
Answer:
Step-by-step explanation:
g(5) = 2 > 0
:::::
g(x) = 0 for x = -2, 2, 4
:::::
g(x) < 0 for -3 ≤ x < -2
Samir estimates the value of Three-fifths times 16.1. Which estimate is reasonable?
3
9
12
15
Answer: 9
Step-by-step explanation:
[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]
Write the fraction 24/40 in its simplest form.
The product of 86 and the depth of the river
Answer:
Step-by-step explanation:
Are you trying to find a variable expression? the product of 86 means multiplication so 86*n or 86n. Other than that I dont understand the question.
If P(x) = 2x2 – 3x + 7 and Q(x) = 8 - x), find each function value.
15. P(-3)
16. Q(2)
17. P(4)
18. Q(-3)
Answer:
15. 52
16. 6
17. 59
18. 11
Step-by-step explanation:
Select the correct answer
The equation of a line is y= 15x-2 What are its slope and y-intercept?
A.slope = 15 and y-intercept=-2
B.slope = 15 and y-intercept = 2
C.slope = 2 and y-intercept=15
D.siope =-2 and y-intercept=15
RES
Answer:
A
Step-by-step explanation:
Slope = term that multiply x
y intercept = the number without a variable