Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?
Step-by-step explanation:
Total catalysts = 10
Probability of 2 lower acidic catalysts = 2/10 = 1/5
Find the measure of a.
A. 60
B. 57
C. 40
D. 80
Answer:
Option (C)
Step-by-step explanation:
Since angle 'a' is the inscribed angle of the given triangle
Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.
x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]
By the tangent-chord theorem,
"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"
[tex]\frac{x}{2}[/tex] = 40°
Therefore, a = [tex]\frac{x}{2}[/tex] = 40°
Option (C) will be the answer.
Find secα, if sinα=−2/3 and 3π/2 <α<2π . Also the α=alpha symbol
Answer:
Step-by-step explanation:
Given sinα=−2/3, before we can get secα, we need to get the value of α first from sinα=−2/3.
[tex]sin \alpha = -2/3[/tex]
Taking the arcsin of both sides
[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]
Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;
α = 180°+41.8°
α = 221.8° which is between the range 270°<α<360°
secα = sec 221.8°
secα = 1/cos 221.8
secα = 1.34
v divided by 5 is equal to 60.
Answer:
[tex]\boxed{v=300}[/tex]
Step-by-step explanation:
Hey there!
To find v we’ll set up the following,
v ÷ 5 = 60
To get v by itself we’ll do
5*60 = 300
v = 300
Hope this helps :)
a=5,and 5+z=14,so a+z=14
Answer:
Z=9
Step-by-step explanation:
Insert A into A+Z=14
5+z=14
Subtract 5 on both sides, to find Z.
-5 -5
z=9
what does 7g equal in like a verbal form
Answer:
see below
Step-by-step explanation:
7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
Please answer this correctly without making mistakes
Answer:
Put 1/10 in the box.
Step-by-step explanation:
Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.
Best Regards!
Answer:
To Oakdale to Milford:
2/5 mi
Step-by-step explanation:
1/10 + 3/20 + 3/20
1/10 = 2/20
then;
2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20
8/20 = 2/5
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty.
Now, it look like there is some information missing in the answer. The whole problem should look like this:
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
She sold 24 copies of the cd each day.
Step-by-step explanation:
In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:
x= Number of copies sold.
So we can start setting our equation up. So we take the first part of the problem:
"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."
This can be translated as:
40-x
where this expression represents the number of copies left on the shelf by the end of monday.
"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."
so we represent it like this:
(40-x)+(40-x)
"In other words, she doubled the number that was left in the display."
so the previous expression can be simplified like this:
2(40-x)
"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."
so the expression now turns to:
2(40-x)-x this is the number of copies left by the end of tuesday.
"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."
this translates to:
3[2(40-x)-x]
This is the number of copies on the shelf by the begining of Wednesday.
"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."
this piece of information lets us finish writting our equation:
3[2(40-x)-x] -x = 0
since there were no copies left on the shelf, then the equation is equal to zero.
So now we proceed and solve the equation for x:
3[2(40-x)-x] -x = 0
We simplify it from the inside to the outside.
3[80-2x-x]-x=0
3[80-3x]-x = 0
we now distribute the 3 so we get:
240-9x-x=0
we combine like terms so we get:
240-10x=0
we move the 240 to the other side of the equation so we get:
-10x=-240
and divide both sides into -10 so we get:
x=24
so she sold 24 copies each day.
X = y + 12
How to solve for variable
Answer:
x-y=12
Step-by-step explanation:
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.
Answer:
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
Step-by-step explanation:
The summary of the given statistics is:
Population Mean = 26,500
Sample Mean = 30,150
Standard deviation = 10560
sample size = 24
The objective is to state the null hypothesis and the alternate hypothesis.
An hypothesis is a claim with insufficient information which tends to be challenged into further testing and experimentation in order to determine if such claim is significant or not.
The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.
The alternative hypothesis is the research hypothesis that the researcher is trying to prove.
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
The test statistic can be computed as follows:
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]
[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]
[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]
z = 1.6933
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis
In a frequency distribution of 290 scores, the mean is 99 and the median is 86. One would expect this distribution to be:
Answer:
positively skewed to the right
Step-by-step explanation:
The measure of the central tendency is a profound way to describe the mean, median and mode. The measure of central tendency indicates where the center of distribution tends to be. The measure of central tendency provide a validity and answers whether the scores are high or generally low.
In this measure,The mean is usually pulled to the tail. The skewed is determined by where the tail goes, to the right side , it is positively skewed and to the left side , it is known as negatively skewed distribution.
Given that:
In a frequency of distribution of 290 scores,
the mean = 99
the median = 86
One would expect this distribution to be; positively skewed to the right since the mean value is greater than the median value.
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. A straight line is shown and is marked with three angles. The first angle measures 50 degrees. The second angle measures 60 degrees. The third angle is labeled x. The line between the 40 degree angle and angle x extends below the straight line. The angle formed is labeled angle y. Write and solve an equation to determine the measure of angle y.
Step-by-step explanation:
sorry but u should provide with a diagram for better understanding of ur question
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
what number must be added to the sequence of 7,13 and 10 to get an average of 13
Answer:
22
Step-by-step explanation:
We can write an equation:
(7+13+10+x)/4=13
x represents the number that needs to be added to get an average of
(7+13+10+x)/4=13
(30+x)/4=13
30+x=52
x=22
The number is 22
Hope this helps! Have a wonderful day :)
What is the area of polygon EFGH?
Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]
Answer:
10.295Step-by-step explanation:
Using the value for calculating the confidence interval as given;
CI = xbar + Z*σ/√n
xbar is the mean = 37.14+42.86/2
xbar= 80/2
xbar = 40
Z is the z-score at the 90% confidence = 1.645
σ is the standard deviation
n is the sample size = 35
Given the confidence interval CI as [37.14, 42.86]
Using the maximum value of the confidence interval to get the value of the standard deviation, we will have;
42.86 = xbar + Z*σ/√n
42.86 = 40 + 1.645* σ/√35
42.86-40 = 1.645*σ/√35
2.86 = 1.645*σ/√35
2.86/1.645 = σ/√35
1.739 = σ/√35
1.739 = σ/5.92
σ= 1.739*5.92
σ = 10.295
Hence, the sample standard deviation of a pair of jeans is 10.295
Find the missing side or angle.
Round to the nearest tenth.
Answer:
b=2.7
Step-by-step explanation:
using sine rule,,,
Step-by-step explanation:
So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.
So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.
53 + 80 + A = 180
133 + A = 180
A = 47
Now that we have the angle of A, we can use the law of sines to fine the length of b.
b / sin(B) = a / sin(A)
b = sin(B) * a / sin(A)
b = sin(80) * 2 / sin(47)
b = 2.693
Now round that to the nearest tenth to get
b = 2.7
Cheers.
ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
Answer:
rose. is. 18/2=9 years old
Answer:
Stephanie is 18years old and she is twice older than her sister
so rosa is 18÷2(since stephanie is twice older than rosa
so rosa is 9 years old
Find the value of x. A: 15 B: 12 C: 10 D: 8
Answer:
[tex]\boxed{\sf C. \ 10}[/tex]
Step-by-step explanation:
[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]
[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]
[tex]NH \times HT = MH \times HY[/tex]
[tex](x+20) \times 8=12 \times 20[/tex]
[tex]\sf Expand \ brackets \ and \ multiply.[/tex]
[tex]8x+160=240[/tex]
[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]
[tex]8x+160-160=240-160[/tex]
[tex]8x=80[/tex]
[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]
[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]
[tex]x=10[/tex]
The value of x is 10.
We have a circle and inside it two chords MY and NT intersect at point H.
We have to find the value of x in the figure.
What is intersecting chord theorem?According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then
AO x OB = CO x OD
Applying the chord intersecting theorem to the figure in the question, we get -
MH x HY = NH x HT
12 x 20 = (x+20) x 8
240 = 8x + 160
8x = 80
x = 10
Hence the value of x is 10.
To solve more questions on Circles and chords, visit the link below -
https://brainly.com/question/15568573
#SPJ5
What value of x makes this equation true?
17 5 - 7 = -4
x=
y Su
What value of x makes this equation true? X/6-7=-4
Answer:
x=18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = 3
(x/ 6) * 6 = 3*6
x = 18
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
A box is filled with 8 blue cards, 6 red cards, and 6 yellow cards. A card is chosen at a random from the box. What is the probability that the card is not red ? Write your answer as a fraction.
Answer:
14/20 or .7 or 70%
Step-by-step explanation:
Total Number of cards: 20
Number of Red cards: 6
The leftover cards: 20 -6 = 14
The probability of not getting a red = 14/20
14/20 as a decimal = 14/20 = 70/100 = .7
14/20 as a percent = 14/20 = 70/100 = 70%
