Answer:
Sheridan Service reduce its debt $1,392, now its due is $1,200.
Step-by-step explanation:
Sheridan Service received a shipment on January 15, with an invoice dated January 14, terms 4/10 E.O.M.
Term written on the invoice means 4% discount if paid within 10 days or full amount is due for the payment at the End of the Month.
Invoice shipment having amount = $2,592
Partial payment of the invoice by check = $1,392
So amount due = 2,592 - 1,392 = $1,200
Sheridan Service reduce its debt $1,392, now its due is $1,200.
Which is an equation for the nth terms of the sequence 12,15,18,21
[tex]\bf 12~~,~~\stackrel{12+3}{15}~~,~~\stackrel{15+3}{18}~~,~~\stackrel{18+3}{21}~\hspace{10em}\stackrel{\textit{common difference}}{d=3} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=12\\ d=3 \end{cases} \\\\\\ a_n=12+(n-1)3\implies a_n=12+3n-3\implies a_n=3n+9[/tex]
Answer:
tₙ = 3(3 + n)
Step-by-step explanation:
Points to remember
nth term of an AP
tₙ = a + (n - 1)d
Where a - first term of AP
d - Common difference of AP
To find the nth term
The given series is,
12,15,18,21 .....
Here a = 12 and d = 15 - 12 = 3
tₙ = a + (n - 1)d
= 12 + (n - 1)3
=12 + 3n - 3
= 9 + 3n
= 3(3 + n)
Therefore tₙ = 3(3 + n)
Two boys can paint a fence in 5 hours. How many hours would it take 3 boys to paint the same fence? 3 (A) 2 (B) 3 (C) 31 3 2:3=X (D) 4 IS 2/3 3
Two boys working together can paint a fence in 5 hours with a work rate of 0.2 fences per hour. Adding one more boy increases this work rate to 0.3 fences per hour. This would allow them to complete the painting of the fence in approximately 3.3 hours.
Explanation:This problem can be solved using the concept of work rate. The work rate is defined as the amount of work done per unit time.
In this case, two boys can paint a fence in 5 hours. So, their combined work rate is 1 fence per 5 hours, or 0.2 fences per hour.
When we add another boy to the group, we increase the total work rate by 50% as now there are 3 boys. So, their combined work rate becomes 0.2 fences/hour + (0.2 fences/hour) * 50% = 0.3 fences/hour.
To find out how long it would take these three boys to paint the fence, we divide the total work (1 fence) by the total work rate (0.3). So, 1 fence divided by 0.3 fences/hour = approximately 3.3 hours. That's how long it would take three boys to paint the fence.
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1 -For what value of x is line a parallel to line b
2-For what value of x is line a parallel to line b
Answer:
1) x = 17, line a parallel to line b
2) x = 18, line a parallel to line b
Step-by-step explanation:
If line a parallel to line b then (10x - 40) + 50 = 180
Solve for x
10x - 40 + 50 = 180
Combine like terms
10x + 10 = 180
10x = 170
x = 17
x = 17, line a parallel to line b
-------------------------------------------------
If line a parallel to line b then 5x - 16 = 74
Solve for x
5x - 16 = 74
5x = 90
x = 18
x = 18, line a parallel to line b
The value of x which makes line a parallel to line b can be found by equating the slopes of the two lines and solving for x.
Explanation:In mathematics, two lines a and b are parallel if and only if their slopes are equal. When we are given the equations of the lines and are asked to find the value of x that make the lines parallel, we start by setting the slopes of the two lines equal to each other. Let's assume now that line a is represented by y = mx + b1 and line b by y = nx + b2. In order for line a to be parallel to line b, m must be equal to n. Therefore, you solve for x from the equation m=n.
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The concept of determining which reactant is limiting and which is in excess is akin to determining the number of sandwiches that can be made from a set number of ingredients. Assuming that a cheese sandwich consists of 2 slices of bread and 3 slices of cheese, determine the number of whole cheese sandwiches that can be prepared from 44 slices of bread and 75 slices of cheese.
Answer: There are 22 whole cheese sandwiches that can be prepared.
Step-by-step explanation:
Since we have given that
Number of slices of bread = 44
Number of slices of cheese = 75
According to question, a cheese sandwich consists of 2 slices of bread and 3 slices of cheese.
So, we need to find the number of whole cheese sandwiches that can be prepared.
Number of sandwich containing only slice of bread is given by
[tex]\dfrac{44}{2}=22[/tex]
Number of sandwich containing only slice of cheese is given by
[tex]\dfrac{75}{3}=25[/tex]
As we know that each sandwich should contain both slice of bread and slice of cheese.
So, Least of (22, 25) = 22
Hence, there are 22 whole cheese sandwiches that can be prepared.
The claim is that the IQ scores of statistics professors are normally distributed, with a mean greater than 135. A sample of 23 professors had a mean IQ score of 140 with a standard deviation of 13. Find the value of the test statistic.
Answer: 1.8446
Step-by-step explanation:
Given claim : [tex]\mu>\mu_0,\text{ where }\mu_0=135[/tex]
Sample size : [tex]n=23[/tex]
Sample mean : [tex]\overline{x}=140[/tex]
Standard deviation : [tex]\sigma = 13[/tex]
The test statistic for population mean is given by :-
[tex]z=\dfrac{x-\mu_0}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]\Rightarrow\ z=\dfrac{140-135}{\dfrac{13}{\sqrt{23}}}\\\\\Rightarrow\ z=1.84455058589\approx1.8446[/tex]
Hence, the value of test statistic = 1.8446
Suppose a man is 25 years old and would like to retire at age 60. ?Furthermore, he would like to have a retirement fund from which he can draw an income of ?$100,000 per yearlong dash?forever! How can he do? it? Assume a constant APR of 8?%.
He can have a retirement fund from which he can draw ?$100,000 per year by having ?$ ______ in his savings account when he retires.
Answer:
$1314.37
Step-by-step explanation:
We have to calculate final value i.e. balance to earn $100,000 annually from interest.
= [tex]\frac{100,000}{0.08}[/tex] = $1,250,000
Now, N = n × y = 12 × 25 = 300
I = 8% = APR = 0.08
PV = 0 = PMT = 0
FV = 1,250,000 = A
[tex]A=\frac{PMT\times [(1+\frac{apr}{n})^{ny}-1]}{\frac{apr}{n}}[/tex]
[tex]PMT=\frac{A\times (\frac{APR}{n})}{[(1+\frac{APR}{n})^{ny}-1]}[/tex]
[tex]PMT=\frac{1,250,000\times (\frac{0.08}{12})}{[(1+\frac{0.08}{12})^{12\times 25}-1]}[/tex]
[tex]PMT=\frac{1,250,000\times (0.006667)}{[(1+\frac{0.08}{12})^{12\times 25}-1]}[/tex]
[tex]PMT=\frac{1,250,000\times (0.006667)}{[(1+0.006667)^{300}-1]}[/tex]
[tex]PMT=\frac{\frac{25000}{3}}{[1.006667^{300}-1]}[/tex]
[tex]PMT=\frac{\frac{25000}{3}}{6.340176}[/tex]
Monthly payment (PMT) = $1314.369409 ≈ $1314.37
$1314.37 is required monthly payment in order to $100,000 interest.
Which complete bipartite graphs Km, are trees? (b) Let T be a full 8-ary tree with 201 vertices. (ii) How many internal vertices does T have? (iii) How many leaves does T have?
Answer:
the answer is a
Step-by-step explanation:
i just know
What is the scale factor of this dilation?
2/3
1 1/2
3
5
The scale factor of this dilation is 2/3.
It is required to find scale factor of this dilation.
What is the scale factor?Scale Factor is defined as the ratio of the size of the new image to the size of the old image.
In the figure showing 6 to 9 is 2/3 dilation and 10 to 15 is also a 2/3 dilation.
So, the scale factor of this dilation is 2/3.
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Option b is correct. The scale factor is [tex]1 \frac{1}{2}[/tex].
To determine the scale factor of the dilation from Triangle ABC to Triangle A'B'C', we need to compare the lengths of corresponding sides.
The side lengths of Triangle ABC are:
AB = 6BC = 10CA = 6The side lengths of Triangle A'B'C' are:
A'B' = 9B'C' = 15C'A' = 9The scale factor is calculated by dividing the lengths of the corresponding sides of the triangles. Let's use AB and A'B' for our calculation:
Scale Factor = A'B'/AB = 9/6 = 3/2 = 1 whole 1/2
Thus, the scale factor is [tex]1 \frac{1}{2}[/tex], which corresponds to option b.
Complete question:
What is the scale factor of this dilation? Triangle ABC to A'B'C'.
Triangle ABC with AB = 6, BC = 10, CA = 6
Triangle A'B'C' with A'B'= 9, B'C'= 15, C'A' =9
a. 2/3
b. [tex]1 \frac{1}{2}[/tex]
c. 3
d. 5
(1 point) The players on a soccer team wear shirts, with each player having one of the numbers 1, 2, ..., 11 on their backs. The set A contains players with even numbers on their shirts. The set B comprises players wearing an odd number less than 7. The set C contains the defenders, which are those wearing numbers less than 6. Select the correct set that corresponds to each of the following. Part a) A∩(B∪C) A. {1,2,3,4,5} B. ∅ C. {1,3,5} D. {2,4} E. {2} Part b) (A∩Bc)∪(B∩C)c A. {6,7,8,9,11} B. {2,4,6,7,8,9,10,11} C. {2,3,4,5,6,8,10} D. {1,2,3,4,5,6,8,10} E. {6,7,8,10,11}
This question involves operations on sets to identify specific members based on conditions. Part a) resolves to D. {2,4}, while part b) finds the solution to be B. {2,4,6,7,8,9,10,11}, highlighting the application of intersection, union, and complement operations in set theory.
Explanation:To solve these problems, we need to understand the operations on sets such as intersection (A∩B), union (A∪B), and the complement of a set (Bc). For part a), we identify set A as {2,4,6,8,10}, B as {1,3,5}, and C as {1,2,3,4,5}. A∩(B∪C) means we're looking for the intersection of A with the union of B and C. Since B∪C = {1,2,3,4,5}, intersecting this with A gives us D. {2,4} as the answer.
For part b), (A∩Bc)∪(B∩C)c means we're looking at elements in A but not in B, combined with elements not in both B and C. Since Bc = {6,7,8,9,10,11} and (B∩C)c = {6,7,8,9,10,11}, union these two gives us answer B. {2,4,6,7,8,9,10,11}, by including A∩Bc = {2,4,6,8,10} and excluding duplicates when union with (B∩C)c.
A weather forecasting website indicated that there was a 90% chance of rain in a certain region. Based on that report, which of the following is the most reasonable interpretation? Choose the correct answer below. A. 90% of the region will get rain today. B. There is a 0.90 probability that it will rain somewhere in the region at some point during the day. C. In the region, it will rain for 90% of the day. D. None of the above interpretations are reasonable.
Final answer:
The most B. reasonable interpretation of a 90% chance of rain is that there is a 0.90 probability that it will rain somewhere in the region.
Explanation:
The most reasonable interpretation of a 90% chance of rain, according to the given weather forecasting website, is option B: There is a 0.90 probability that it will rain somewhere in the region at some point during the day. This means that there is a high likelihood that rain will occur in the region, but it does not guarantee that every part of the region will experience rain. It indicates that out of 100 instances, rain is expected in approximately 90 of them.
It is important to note that options A, C, and D are not reasonable interpretations because option A assumes that 100% of the region will get rain, option C assumes that it will rain for 90% of the day, and option D states that none of the interpretations are reasonable, which is not accurate.
Final answer:
The most reasonable interpretation of a 90% chance of rain in a weather forecast is that there is a 0.90 probability of rainfall somewhere in the specified region at some point during the day.
Explanation:
When a weather forecast indicates a 90% chance of rain, it means there is a 0.90 probability that it will rain somewhere in the specified region at some point during the day. Therefore, the correct interpretation based on the given options is B. There is a 0.90 probability that it will rain somewhere in the region at some point during the day. Interpretation A, suggesting that 90% of the region will get rain, is not accurate because the percentage given in a forecast refers to probability, not an area's coverage. Interpretation C, suggesting it will rain for 90% of the day, is also incorrect because the percentage does not refer to the duration of rain but to the probability of occurrence. Statement D is incorrect because B provides a reasonable interpretation.
Camille Uses a 20 % Off Coupon When Buying a Sweater That Costs $ 47.99 .If, She Also pays 6 % Sales tax on the Purchase , How Many does She Paid For ????
Answer:
take 47.99 x .20 = 9.598
$9.60 off
then take 47.99 - 9.60 = $ 38.39
take 38.39 x .06 = 2.3034
$ 2.30 (tax)
add 38.39 + 2.30 = $40.69 or $40.70 is the final purchase price
(the two amounts depends on your choice answer or how it is rounded)
Step-by-step explanation:
Polygon ABCDE and polygon FGHIJ are similar. The area of polygon ABCDE is
40. What is the area of FGHIJ?
Answer: 640
Step-by-step explanation:
Since the two triangles are similar we can simply multiply the lesser triangle's area by a constant to get our answer.
Polygon FGHIJ is ABCDE with a scale change of 4
For the reason that we are dealing with area, we will multiply 40 by 4² in stead of just 4.
40 * 16 = 640
Answer:
B. 640
Step-by-step explanation:
got it right 2021
(a + 3)(a - 2)
hurry helpppp asapppp
(a+3)(a-2)
Multiply the two brackets together
a^2-2a+3a+3*-2
a^2+a-6
Answer is a^2+a-6
ANSWER
[tex]{a}^{2} + a - 6[/tex]
EXPLANATION
The given expression is
[tex](a + 3)(a - 2)[/tex]
We expand using the distributive property to obtain:
[tex]a(a - 2) + 3(a - 2)[/tex]
We multiply out the parenthesis to get:
[tex] {a}^{2} - 2a + 3a - 6[/tex]
Let us now simplify by combining the middle terms to obtain;
[tex]{a}^{2} + a - 6[/tex]
When are two distinct non vertical lines parallel
Answer:
Two lines are parallel when they share the same slope.
Step-by-step explanation:
Two lines are parallel when they share the same slope.
The slope-intercept form of the equation of a line is: y=mx + b, where 'm' is the slope and 'b' the y-intercept.
If two equations have the same value for 'm', then those lines are parallel, for example:
y = 3x + 8 (Red line)
y = 3x + 5 (Blue line)
y = 3x - 10 (Green line)
All the equations stated above are parallel, to show that, I'm attaching the graph of the equations :).
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 100 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.
Answer:
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is __-80___feet per second.
Step-by-step explanation:
The average change rate m is calculated using the following formula
[tex]m=\frac{f(t_2)-f(t_1)}{t_2-t_1}[/tex]
In this case [tex]f(t) = -16t^2 + 48t + 100[/tex], [tex]t_2 = 5\ s\ \ , t_1=3\ s[/tex]
Then
[tex]f(t_2) = f(5) =-16(5)^2 + 48(5) + 100[/tex]
[tex]f(t_2) = -60[/tex]
[tex]f(t_1) = f(3) =-16(3)^2 + 48(3) + 100[/tex]
[tex]f(t_1) = 100[/tex]
Finally
[tex]m=\frac{(-60)-100}{5-3}[/tex]
[tex]m=-80[/tex]
Please solve and show work.
Answer:
63.16 in approx.
Step-by-step explanation:
Let the shorter leg be S. Then the longer leg is L = 3S + 3.
The formula for the area of a triangle is A = (1/2)(base)(height). Here, that works out to A = 84 in^2 = (1/2)(S)(3S + 3).
Simplifying, we get 168 in^2 = S(3S + 3), or
3S^2 + 3S - 168 = 0, or
S^2 + S - 56 = 0. This factors as follows: (S - 8)(S + 7) = 0, so the positive root is S = 8. We discard the negative root.
Thus, the shorter leg length is 8 and the longer leg length is 3(8) + 3, or 27.
According to the Pythagorean Theorem, the hypotenuse length is given by
L^2 = 8^2 + 27^2, or
L^2 = 64 + 729 = 793.
L = hypotenuse length = √793, or approx. 28.2 in.
Then the perimeter of the triangle is 8 + 27 + 28.2 in, or approx. 63.16 in
What is the sign of 4.3 .(-3.2) .0 ? Is it positive or negative
Answer:
Zero
Step-by-step explanation:
We are given the following expression and we are to determine what is the sign of its product:
[tex] 4 . 3 . ( - 3 . 2 ) . 0 [/tex]
One of the three terms in the expression is positive while one is negative. So if we start multiplying the two terms from the left side. we will get a negative number.
But when we will multiply it with zero, the whole product will become zero as anything times zero is always zero. Therefore, answer will be zero.
Answer:
it is negative
Step-by-step explanation:
a positive times a negative is a negative.
(a + 8)(b + 3)
ab + 8a + 3b + 24
ab + 3a + 8b + 24
11ab
24ab
Answer:
ab + 3a + 8b + 24
Step-by-step explanation:
(a + 8)(b + 3)
a(b + 3) + 8(b + 3)
ab + 3a + 8b + 24
y 7 • y 9
Multiply or divide as indicated.
For this case we have the following expression:
[tex]y^ 7 * y^ 9 =[/tex]
By definition of multiplication of powers of the same base, we have to put the same base and add the exponents, that is:
[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]
So:
[tex]y ^ 7 * y ^ 9 = y ^{7 + 9} = y ^ {16}[/tex]
Answer:
[tex]y^{16}[/tex]
What is the solution of the equation 4^(x + 1) = 21? Round your answer to the nearest ten-thousandth.
For this case we must solve the following equation:
[tex]4 ^ {x + 1} = 21[/tex]
We find Neperian logarithm on both sides:
[tex]ln (4 ^ {x + 1}) = ln (21)[/tex]
According to the rules of Neperian logarithm we have:
[tex](x + 1) ln (4) = ln (21)[/tex]
We apply distributive property:
[tex]xln (4) + ln (4) = ln (21)[/tex]
We subtract ln (4) on both sides:
[tex]xln (4) = ln (21) -ln (4)[/tex]
We divide between ln (4) on both sides:
[tex]x = \frac {ln (21)} {ln (4)} - \frac {ln (4)} {ln (4)}\\x = \frac {ln (21)} {ln (4)} - 1\\x = 1,19615871[/tex]
Rounding:
[tex]x = 1.1962[/tex]
Answer:
x = 1.1962
Answer: [tex]x[/tex]≈[tex]1.196[/tex]
Step-by-step explanation:
Given the equation [tex]4^{(x + 1)} = 21[/tex] you need to solve for the variable "x".
Remember that according to the logarithm properties:
[tex]log_b(b)=1[/tex]
[tex]log(a)^n=nlog(a)[/tex]
Then, you can apply [tex]log_4[/tex] on both sides of the equation:
[tex]log_4(4)^{(x + 1)} = log_4(21)\\\\(x + 1)log_4(4) = log_4(21)\\\(x + 1) = log_4(21)[/tex]
Apply the Change of base formula:
[tex]log_b(x) = \frac{log_a( x)}{log_a(b)}[/tex]
Then you get:
[tex]x =\frac{log(21)}{log(4)}-1[/tex]
[tex]x[/tex]≈[tex]1.196[/tex]
Suppose that 45% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 55% regularly consume at least one of these two products. (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? (b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
Answer: a) 30% and b) 45%
Step-by-step explanation:
Since we have given that
Probability that adults regularly consume coffee P(C) = 45% = 0.45
Probability that adults regularly consume carbonated soda P(S) = 40% = 0.40
Probability that adults regularly consume atleast one of these two products P(C∪S) = 55% = 0.55
a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
As we know that
P(C∪S ) = P(C) +P(S)-P(C∩S)
[tex]0.55=0.45+0.40-P(C\cap S)\\\\0.55=0.85-P(C\cap S)\\\\0.55-0.85=-P(C\cap S)\\\\-0.30=-P(C\cap S)\\\\P(C\cap S)=0.30=30\%[/tex]
b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
P(C∪S)'=n(U)-P(C∪S)
[tex]\\P(C\cup S)'=100-55=45\%[/tex]
Hence, a) 30% and b) 45%
3.17 Scores on stats final. Below are final exam scores of 20 Introductory Statistics students. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 (a) The mean score is 77.7 points. with a standard deviation of 8.44 points. Use this information to determine if the scores approximately follow the 68-95-99.7% Rule. (b) Do these data appear to follow a normal distribution? Explain your reasoning using the graphs provided below.
Answer:
Yes they do.
And yes they do follow a normal distribution.
Percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have a data of final exam scores of 20 Introductory.
a) Range of 1 standard deviation:
(77.7 – 8.44, 77.7 + 8.44) [69.3, 86.1]
Range of 2 standard deviation:
(77.7 – 2(8.44), 77.7 + 2(8.44)) [60.8, 94.6]
Range of 3 standard deviation:
(77.7 – 3(8.44), 77.7 + 3(8.44)) [52.4, 103.0]
Number of data points lie within 1 standard deviation = 14
Percent of data points lie within 1 SD = (14/20)×100 = 70%
Number of data points lie within 2 SD = 19
Percent of data points lie within 1 SD = (19/20)×100 = 95%
Number of data points lie within 3 SD = 20
Percent of data points lie within 1 SD = (20/20)×100 = 100%
Because these percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed.
b)
Because the histogram in the graph is symmetric, and the normal probability plot reveals that the points are very close to a straight line, the data appears to follow a normal distribution.
Thus, percentages are close to 68-95-99.7%, we can declare that yes, the 68-95-99.7% rule is roughly followed and yes data appear to follow a normal distribution.
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Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per microliter. Find the value closest to the probability that a randomly selected woman has a red blood cell count above the normal range of 4.2 to 5.4 million cells per microliter. Round to four decimal places.
The likelihood of a randomly chosen woman having a red blood cell count higher than the typical range of 4.2 to 5.4 million cells per microliter, given that the counts are normally distributed with a mean of 4.577 and a standard deviation of 0.382 million cells, is approximately 0.0158 or 1.58% when expressed as a percentage.
Explanation:The subject matter here is the use of statistics to understand biological phenomena, specifically the distribution of red blood cell counts in women. The question asks for the probability that a randomly selected woman has a red blood cell count above the normal range of 4.2 to 5.4 million cells per microliter, given that the counts are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells.
Firstly, to answer this question, we must establish the z-scores for the boundaries of our range. The z-score formula is Z = (X - μ) / σ, where X is the value we are evaluating, μ is the mean, and σ is the standard deviation. The upper boundary of our range is 5.4 million cells, so to find the z-score for this we substitute into the formula: Z = (5.4 - 4.577) / 0.382, which gives us a Z-score of approximately 2.15.
However, we are interested in the probability of a woman having a count above the normal range, so we need the area of the curve beyond this z-score. You can find this probability using standard normal distribution tables or a calculator, which suggests that the probability of having a count above 5.4 is approximately 0.0158, or 1.58% when expressed as a percentage and rounded to four decimal places.
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Analyze the diagram below and complete the instructions that follow.
Find Sin
Sin is the measure of the opposite leg over the hypotenuse from the given angle:
opposite/hypotenuse
We must find the sin of Angle A, and in order to do so we must find the opposite leg and hypotenuse:
opposite leg/hypotenuse
8/10
Simplify:
8/10 = 4/5
Hence, the sin of <A is 4/5
For this case we have by definition, the sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle. Then, according to the figure we have:
[tex]Sin (A) = \frac {8} {10}[/tex]
Simplifying we have to:
[tex]Sin (A) = \frac {4} {5}[/tex]
Answer:
Option B
What is the value of x? In this figure
A:53
B:43
C:57
D:47
Answer:
should be 53 if im right
What are the solutions of the following system?
Answer:(-6,312), (6,312)
Step by Step explanation:
Solve the first equation for y.10x^2-y=48
y=-48+10x^2
Substitute the given value of y into the equation 2y=16x^2+482(-48+10x^2)=16x^2+48
Solve the equation for x.
x=-6
x=6
Substitute the given value of x into the equation y=-48+10(-6)^y=-48+10(-6)^2
y=-48+10×6^2
Solve the equation for yy=312
y=312
Find f if f ''(x) = 12x2 + 6x − 4, f(0) = 9, and f(1) = 1.
Answer:
f(x) = x^4 +x^3 -2x^2 -8x +9
Step-by-step explanation:
You know that the anitderivative of ax^b is ax^(b+1)/(b+1). The first antiderivative is ...
f'(x) = 4x^3 +3x^2 -4x +p . . . . . where p is some constant
The second antiderivative is ...
f(x) = x^4 +x^3 -2x^2 +px +q . . . . where q is also some constant
Then the constants can be found from ...
f(0) = q = 9
f(1) = 1 + 1 - 2 +p + 9 = 1
p = -8
The solution is ...
f(x) = x^4 +x^3 -2x^2 -8x +9
_____
The graphs verify the results. The second derivative is plotted against the given quadratic, and they are seen to overlap. The function values at x=0 and x=1 are the ones specified by the problem.
Final answer:
To find f(x) given f''(x) = 12x² + 6x − 4, one must integrate twice and use the initial conditions f(0) = 9 and f(1) = 1 to solve for the constants. The final function is f(x) = x⁴ + x³ - 2x² - 8x + 9.
Explanation:
The question asks to find the antiderivative f(x) given its second derivative f''(x) = 12x² + 6x − 4, and two initial conditions, f(0) = 9, and f(1) = 1. To solve for f(x), we first integrate the second derivative twice to get the original function.
Integrating f''(x), we get:
f'(x) = ∫( 12x² + 6x - 4)dx = 4x³ + 3x² - 4x + C
We then integrate f'(x) to find f(x):
f(x) = ∫(4x³ + 3x² - 4x + C)dx = x⁴ + x³ - 2x² + Cx + D
Using the initial conditions:
For f(0) = 9, we substitute x = 0 and determine D = 9.For f(1) = 1, we substitute x = 1: 1 + 1 - 2 + C + 9 = 1, solving for C gives us C = -8.Therefore, the original function is f(x) = x⁴ + x³ - 2x² - 8x + 9.
Three boxes contain red and green balls. Box 1 has 5 red balls* and 5 green balls*, Box 2 has 7 red balls* and 3 green balls* and Box 3 contains 6 red balls* and 4 green balls*. The respective probabilities of choosing a box are 1/4, 1/2, 1/4. What is the probability that the ball chosen is green?
Final answer:
The probability of choosing a green ball from the three boxes, given their individual selection probabilities and color distributions, is calculated using the law of total probability. The overall probability of selecting a green ball is found to be 29/80, or roughly 36.25%.
Explanation:
The question asks for the probability of choosing a green ball from three different boxes, given their individual probabilities of being chosen and the distribution of red and green balls in each box. To solve this, we employ the law of total probability which combines the probability of each event (selecting a box) with the conditional probability of finding a green ball within that selected box.
Box 1: Probability of green ball = 5 green balls / (5 red + 5 green) = 1/2
Box 2: Probability of green ball = 3 green balls / (7 red + 3 green) = 3/10
Box 3: Probability of green ball = 4 green balls / (6 red + 4 green) = 2/5
The overall probability is calculated as: P(Green) = P(Box 1) * P(Green|Box 1) + P(Box 2) * P(Green|Box 2) + P(Box 3) * P(Green|Box 3) = (1/4) * (1/2) + (1/2) * (3/10) + (1/4) * (2/5) = 1/8 + 3/20 + 1/10 = 29/80.
Therefore, the probability that the ball chosen is green is 29/80 or approximately 36.25%.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 5 4 1 ln(t) dt, n = 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule
I guess the "5" is supposed to represent the integral sign?
[tex]I=\displaystyle\int_1^4\ln t\,\mathrm dt[/tex]
With [tex]n=10[/tex] subintervals, we split up the domain of integration as
[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]
For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to
[tex]\ell_i=1+\dfrac{3(i-1)}{10}[/tex]
and right endpoints are given by
[tex]r_i=1+\dfrac{3i}{10}[/tex]
where [tex]1\le i\le10[/tex].
a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, [tex]\dfrac{4-1}{10}=\dfrac3{10}[/tex], and "bases" equal to the values of [tex]\ln t[/tex] at both endpoints of each subinterval. The area of the trapezoid over the [tex]i[/tex]-th subinterval is
[tex]\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)[/tex]
Then the integral is approximately
[tex]I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}[/tex]
b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of [tex]\ln t[/tex] at the average of the subinterval's endpoints, [tex]\dfrac{\ell_i+r_i}2[/tex]. The area of the rectangle over the [tex]i[/tex]-th subinterval is then
[tex]\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}[/tex]
so the integral is approximately
[tex]I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}[/tex]
c. For Simpson's rule, we find a quadratic interpolation of [tex]\ln t[/tex] over each subinterval given by
[tex]P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}[/tex]
where [tex]m_i[/tex] is the midpoint of the [tex]i[/tex]-th subinterval,
[tex]m_i=\dfrac{\ell_i+r_i}2[/tex]
Then the integral [tex]I[/tex] is equal to the sum of the integrals of each interpolation over the corresponding [tex]i[/tex]-th subinterval.
[tex]I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt[/tex]
It's easy to show that
[tex]\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)[/tex]
so that the value of the overall integral is approximately
[tex]I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}[/tex]
The question asks to approximate the given integral using three numerical methods: the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule. These methods use simple geometric shapes to estimate the area under the curve. Due to the complexity of the integral in question, assistance from computer software or a graphing calculator will likely be necessary.
Explanation:The question is about using numerical methods to approximate a given integral using three methods: the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule. All of these methods are used to approximate the definite integral of a function over an interval. They divide the interval into n subintervals and then use simple geometric shapes to approximate the area under the curve of the function.
To compute these, you would follow these steps: 1. For the Trapezoidal Rule, average the end points and multiply by the width of each interval. 2. For the Midpoint Rule, evaluate the function at the midpoint of each interval, multiply by the width of each interval. 3. For Simpson's Rule, apply the specific weighted average formula that gives more weight to the midpoint
Please note, however, that due to the complexity of the integral of ln(t), you would likely need to use computer software or a graphing calculator to perform these approximations. Please consult with your teacher for the best approach based on what resources are available to you.
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Use the Taylor series you just found for sinc(x) to find the Taylor series for f(x) = (integral from 0 to x) of sinc(t)dt based at 0. a.Give your answer using summation notation. b.Give the interval on which the series converges.
In this question (https://brainly.com/question/12792658) I derived the Taylor series for [tex]\mathrm{sinc}\,x[/tex] about [tex]x=0[/tex]:
[tex]\mathrm{sinc}\,x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}[/tex]
Then the Taylor series for
[tex]f(x)=\displaystyle\int_0^x\mathrm{sinc}\,t\,\mathrm dt[/tex]
is obtained by integrating the series above:
[tex]f(x)=\displaystyle\int\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}\,\mathrm dx=C+\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}[/tex]
We have [tex]f(0)=0[/tex], so [tex]C=0[/tex] and so
[tex]f(x)=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}[/tex]
which converges by the ratio test if the following limit is less than 1:
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+3}}{(2n+3)^2(2n+2)!}}{\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)^2(2n)!}{(2n+3)^2(2n+2)!}[/tex]
Like in the linked problem, the limit is 0 so the series for [tex]f(x)[/tex] converges everywhere.
The Taylor series for the function f(x) = ∫ sinc(t)dt based at 0 is derived from the Taylor series of sinc(x) by integrating it term by term, given in summation notation as ∑ (-1)ⁿ * xⁿ⁺¹ / (n+1)! for n=0 to n=∞. The series converges for all real numbers (-∞, ∞).
Explanation:In order to find the Taylor series for the function f(x) = ∫ sinc(t)dt based at 0, one can use the Taylor series for sinc(x) and integrate term by term. We know the Taylor series for sinc(x) is x - x³/3! + x⁵/5! - ..., so the Taylor series for f(x) can be written as x²/2 - x⁴/4*3! + x⁶/6*5! - ... . In summation notation, this is ∑ (-1)ⁿ * xⁿ⁺¹ / (n+1)! for n=0 to n=∞.
The Taylor series for any function converges to the function itself within a certain interval called the radius of convergence. For the Taylor series of sinc(x), due to the nature of sine being bounded between -1 and 1, the series will converge for all real numbers (-∞, ∞).
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