Answer:
(3)(x+7)(x-1)
Step-by-step explanation:
3x^2+18x-21
Let's start by taking 3 out of the equation.
3(x^2+6x-7)
Now, when we factor, we need to find two numbers that add up to 6 and multiply to -7.
The numbers would be 7 and -1.
So the factored form of this would be:
(3)(x+7)(x-1)
Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)
Answer:
[tex]A=1500-1450e^{-\dfrac{t}{250}}[/tex]
Step-by-step explanation:
The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.
Volume = 500 gallons
Initial Amount of Salt, A(0)=50 pounds
Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min
[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}[/tex]
When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
Concentration c(t) of the salt in the tank at time t
Concentration, [tex]C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}[/tex]
[tex]R_{out}[/tex]=(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}[/tex]
Now, the rate of change of the amount of salt in the tank
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]
[tex]\dfrac{dA}{dt}=6-\dfrac{A}{250}[/tex]
We solve the resulting differential equation by separation of variables.
[tex]\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}[/tex]
Taking the integral of both sides
[tex]\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}[/tex]
Recall that when t=0, A(t)=50 (our initial condition)
[tex]50=1500+Ce^{-\frac{0}{250}}50=1500+Ce^{0}\\C=-1450\\$Therefore the amount of salt in the tank at any time t is:\\A=1500-1450e^{-\dfrac{t}{250}}[/tex]
A broth used to manufacture a pharmaceutical product has its sugar content, in mg/mL, measured several times on each of three successive days.
Day 1: 5.0, 4.8, 5.1, 5.1, 4.8, 5.1, 4.8, 4.8, 5.0, 5.2, 4.9, 4.9, 5.0
Day 2: 5.8, 4.7, 4.7, 4.9, 5.1, 4.9, 5.4, 5.3, 5.3, 4.8, 5.7, 5.1, 5.7
Day 3: 6.3, 4.7, 5.1, 5.9, 5.1, 5.9, 4.7, 6.0, 5.3, 4.9, 5.7, 5.3, 5.6
Can you conclude that the variability of the process is greater on the third day than on the second day?
Answer:
Yes
Step-by-step explanation:
To compare the variability of the measured sugar content for each day, we can estimate the standard deviation using the Range rule.
Standard Deviation =[tex]\dfrac{\text{Maximum Value-Minimum Value}}{4}[/tex]
Day 1
5.0, 4.8, 5.1, 5.1, 4.8, 5.1, 4.8, 4.8, 5.0, 5.2, 4.9, 4.9, 5.0
Maximum Value=5.2Minimum Value=4.8Standard Deviation =[tex]\dfrac{5.2-4.8}{4}[/tex]
=0.1
Day 2
5.8, 4.7, 4.7, 4.9, 5.1, 4.9, 5.4, 5.3, 5.3, 4.8, 5.7, 5.1, 5.7
Maximum Value=5.8Minimum Value=4.7Standard Deviation =[tex]\dfrac{5.8-4.7}{4}[/tex]
=0.275
Day 3
6.3, 4.7, 5.1, 5.9, 5.1, 5.9, 4.7, 6.0, 5.3, 4.9, 5.7, 5.3, 5.6
Maximum Value=6.3Minimum Value=4.7Standard Deviation =[tex]\dfrac{6.3-4.7}{4}[/tex]
=0.4
Since the estimated standard deviation of the third day is higher than that of the second day, the variability of the process is greater on the third day than on the second day.
What is the solution to the system of equations below?
x + 3y = 1
-3x - 3y = -15
Answer:
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
-2x = -14
x = 7
7 + 3y = 1
3y = -6
y = -2
(7, -2)
Answer:
x =7 , y= -2
Step-by-step explanation:
x + 3y = 1
-3x - 3y = -15
Add the equations together to eliminate y
x + 3y = 1
-3x - 3y = -15
-------------------------
-2x = -14
Divide by -2
-2x/-2 = -14/-2
x = 7
Now we can find y
x+3y = 1
7 + 3y = 1
Subtract 7 from each side
7+3y-7 = 1-7
3y = -6
Divide by 3
3y/3 = -6/3
y = -2
what do you think 40x40 is And tell me how you got your answer
Answer:
40*40 =1600
Step-by-step explanation:
Find the value of x round to the nearest tenth
Answer:
4.1 cm
Step-by-step explanation:
The segment marked x bisects the chord, so the triangle shown has legs x and 7.8, and hypotenuse 8.8.
The Pythagorean theorem can be used to find x:
8.8² = x² +7.8²
x² = 8.8² -7.8² = 77.44 -60.84 = 16.60
x = √16.6
x ≈ 4.1 . . . cm
How do you relate the points made by Professor Degraeve and the use of decision trees as a decision making tool?
In practice, do you feel that organizations focus more on outcomes or decisions?
Suggest at least one idea as to how an organization can make a cultural shift to focusing on the process associated with decision making as opposed to the outcomes.
Answer:
Organizations really focus more on early results, than on thinking carefully about the decisions they must make to achieve accurate and reliable results.
The diagram of the decision tree really helps to analyze all the possible associated variables that can contribute to a good result.
Step-by-step explanation:
We could think of an organization that has children's toys as its final product; At first this organization might think that it is best to make the most popular toys that are promoted by the advertising media, but making a decision diagram and really evaluating what is best at the moment and how this affects demand, it could be induced to look all the variables that could determine to what extent those "toys" to which the media advertise so much are so acceptable in the children's market; we could really be surprised.
Please help! Correct answr only, please! The following information matrices show the number of breakfasts & lunches sold at a little creek middle school on Monday and the prices of breakfast and lunch Which of the following best describes the element? A. Sixth graders paid a total of $60.50 for their breakfast meals on Monday. B. There are 22 sixth graders eating breakfast on Monday. C. Sixth graders paid a total of $508.50 for all their meals on Monday. D. Breakfast costs $2.75
Answer:
Hello There Again. The correct answer is D.
Explanation: Because it shows that you need to subtract 2.75 - 3.50 which that will be 75. So the correct answer will be D.
Hope It Helps! :)
Sixth graders paid a total of $508.50 for all their meals on Monday.
The answer ? What is it i want to kbow it get better in maths and studying so please give me the answer and thank you .
Answer:
6/8
Step-by-step explanation:
6/8
Please answer this correctly
Answer:
= 16 12/13 mm
Step-by-step explanation:
To find the perimeter, we add all the sides
P = 4 3 /13 +4 3/13+ 4 3 /13 +4 3/13
Adding the whole numbers
4+4+4+4 = 16
Adding the fractions
3/13+3/13+3/13+3/13 = 12/13
Putting this back together
= 16 12/13 mm
Can someone solve this??
Answer:
see below
Step-by-step explanation:
There are a few relevant relations involved:
an inscribed angle is half the measure of the arc it interceptsan arc has the same measure as the central angle that intercepts itthe angle exterior to a circle where secants meet is half the difference of the intercepted arcs (near and far)the angle interior to a circle where secants meet is half the sum of the intercepted arcsthe angle where tangents meet is the supplement of the (near) arc interceptedan exterior angle of a triangle is equal to the sum of the remote interior anglesthe angle between a tangent and a radius is 90°the angle sum theoremAB is a diameter, so arcs AB are 180°.
a) BC is the supplement to arc AC: 180° -140° = 40°
b) BG is the supplement to AG: 180° -64° -38° = 78°
c) ∠1 has the measure of BC: 40°
d) ∠2 is inscribed in a semicircle, so has measure 180°/2 = 90°
e) ∠3 is half the measure of arc AE: 64°/2 = 32°
f) ∠4 is half the sum of arcs AG and BC: ((64°+38°) +40°)/2 = 71°
g) ∠5 is half the difference of arcs AC and EG: (140° -38°)/2 = 51°
h) ∠6 is half the sum of arcs EAC and BG: ((140°+64°) +78°)/2 = 141°
i) ∠7 is the difference of exterior angle 4 and interior angle 1: 71° -40° = 31°
j) ∠8 is the measure of arc AC: 140°
k) ∠9 is the supplement to arc AC: 180° -140° = 40°
l) ∠10 is the complement of angle 7: 90° -31° = 59°
A pile of 23 coins consists of nickels and dimes. The total value
of the coins is $1.40. Find the number of each type of coin.
Answer:
5 dimes and 18 nickels
Step-by-step explanation:
5D + 18 N =
5 x 10 + 18 x 5 =
5 x.10 + 18 x 0.05=
.50 + .90=
$1.40
You need to arrange six of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you?
ways
(Type a whole number.)
Answer:
The first book can be chosen from ANY of the 6 books,
the second book can be chosen from the OTHER 5 books and continuing in this way, we get:
6 * 5 * 4 * 3 * 2 * 1 = 720 ways
Step-by-step explanation:
Jasmine found a wooden jewelry box shaped like a right rectangular prism. What is the volume of the jewelry box?
Answer:
The volume of the jewelry box will be given by,
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Step-by-step explanation:
It is provided that, Jasmine found a wooden jewelry box shaped like a right rectangular prism.
Consider the diagram below for the shape of a right rectangular prism.
The volume of a right rectangular prism is given by the formula:
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Here,
l = length of the rectangle
w = width of the rectangle
h = height of the rectangular prism
Thus, the volume of the jewelry box will be given by,
[tex]\text{Volume}=\text{l}\times \text{w}\times\text{h}[/tex]
Answer:
In the given problem, since it was stated that the dimension of the right rectangular prism is 8 by 6 by 14 cm. To solve the problem, you can use the formula for finding the volume. Therefore, the volume of the jewelry box is 672 cubic cm.
What is the value of sec(-45°)? there was no photo given or answer choices... sorry guys. thats why i asked on here lol
Answer:
It is about 1.41421356. (square root of 2)
Step-by-step explanation:
You can use a calculator to figure it out! Just enter the value (-45) and press the sec button! Hope this helps :)
sec (-45) = 1/ cos (-45) .
and cos (-45) = (sqrt 2)/2 is the answer to the question
What is the value of sec(-45°)? there was no photo given or answer choices... sorry guys. thats why i asked on here lol
A coal mine worker is 650 feet below the ground in a mine. Another coal mine worker is 7 feet above ground operating machinery.
Write an integer for the position of each worker relative to the ground.
Find the absolute value of each integer.
Which worker is farther from the ground surface?
Answer:
The first coal mine worker is 650 feet below, so they're -650 ft.
The second coal mine worker is 7 feet above, so they're +7 ft.
| -650 | = 650 ft
| 7 | = 7 ft
650 > 7, so the first worker is farther from the surface.
Which graph represents the solution for x2 + x - 12 > 0?
Answer:it’s c on edge, sorry i’m late but for anyone else who needs help it’s c !!
Step-by-step explanation:
Answer:
C. on edg2020
Step-by-step explanation:
Hope this helps!!! Have a great day!!! : )
how many pieces each 2 3/4 m long may be cut from a string 16 1/2 ?
Answer:
6
Step-by-step explanation:
2 3/4 = 2.75 & 16 1/2 = 16.5
No of pieces = 16.5/2.75 = 6
Answer:
6 pieces.
Step-by-step explanation:
16 1/2 / 2 3/4
= 33/2 / 11/4
= 33/2 * 4/11
= 132 / 22
= 6
What is the value of Y?
Answer:
Finding the y value is easy if you know the slope of the line and the x coordinate. Review the equation for the slope of a line. The equation for finding the slope is: m = [y1 - y2] / [x1 - x2]. If you know x, you can solve for y to find the y value for the slope of the line.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer B
cause a full triangle degrees is 180 degrees and u just have to remove:
180-40-30= 110 degrees
The department of public safety has an old memo stating that the number of accidents per week at a hazardous intersection varies according to a Normal distribution, with a mean of 2.2 and a standard deviation of 1.4. Department officials implemented a new safety plan, heavier police patrols and new signs, to see if they could reduce the average number of accidents at this intersection. They recorded the number of accidents per week for 52 weeks. They find that the average over that period was two accidents per week.
What is the PP‑value for the test of H0:????=2.2 against H????:????<2.2H0:μ=2.2 against Ha:μ<2.2 ?
A. 0.8485
B. 0.4443
C. 0.1515
Answer:
C. 0.1515
Step-by-step explanation:
The main objective here is to find the P-value for the test of [tex]H_0[/tex]
Given that ;
the mean value = 2.2
the standard deviation = 1.4
number of recorded accident per week = 52
The null hypothesis is : [tex]H_o: \mu =2[/tex]
The alternative hypothesis is : [tex]H_A = \mu < 2[/tex]
The Z- value can be calculated as:
[tex]z = \dfrac{x- \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]z = \dfrac{2- 2.2}{\dfrac{1.4 }{\sqrt{52}}}[/tex]
[tex]z = \dfrac{- 0.2}{\dfrac{1.4 }{7.211}}[/tex]
z = -1.03
From the normal distribution table for probability;
P(z< -1.03 ) = 0.1515
A fair die has just been rolled five times – giving scores of 1, 2, 3, 4, 5 in that order. How likely is it that the score on the next roll will be a 6?
A. no chance B. less than evens C. evens D. better than evens E. certain
Answer:
b. less than evens
Step-by-step explanation:
the probability that the next roll is 6 is
[tex] \frac{1}{6} [/tex]
B. less than evens should be the answer
If SinP + SinQ = 7/5 and angle P + angle Q = 90 degrees, without the use of a calculator, determine the value of Sin2P
Answer:
sin2P ≈ 1Step-by-step explanation:
Given SinP + SinQ = 7/5...1 and
∠P + ∠Q = 90°... 2
From compound angle; SinP +SinQ = [tex]2sin(\frac{P+Q}{2} )cos(\frac{P-Q}{2} )[/tex]... 3
Substituting equation 2 into 3 we will have;
SinP +SinQ = [tex]2sin(\frac{90}{2} )cos(\frac{P-Q}{2} )[/tex] = 7/5
[tex]2sin45^{0} cos\frac{P-Q}{2}=7/5[/tex]
since P = 90-Q from equation 1, then;
[tex]2sin45^{0} cos\frac{90-Q-Q}{2}=7/5\\2sin45^{0} cos\frac{90-2Q}{2}=7/5\\2(\frac{1}{\sqrt{2} } ) cos\frac{90-2Q}{2}=7/5\\cos\frac{90-2Q}{2} = 7/5* \frac{\sqrt{2} }{2} \\cos\frac{90-2Q}{2} = \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = cos^{-1} \frac{7\sqrt{2}}{10}\\\frac{90-2Q}{2} = 8.15\\90-2Q = 16.30\\2Q = 90-16.3\\2Q = 73.7\\Q = 36.85^{0} \\\\P = 90-36.85\\P = 53.15^{0}[/tex]
To get sin2P; Accoding to the trig identity;
Sin2P = 2SinPCosP
Sin2P = 2Sin53.15cos53.15
sin2P = 0.9598
sin2P ≈ 1
A coffeepot contains 1 1⁄2 quarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1⁄2 cups of coffee remain in the pot. How much coffee did Tonya pour into each cup? (cups and oz)
Answer:
2 cups
Step-by-step explanation:
to find the extra cup of coffee
[tex]3\frac{1}{2}-1\frac{1}{2}=\frac{7}{2}-\frac{3}{2}=\frac{4}{2}=2 cups[/tex]
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 17 in-state applicants results in a SAT scoring mean of 1046 with a standard deviation of 37. A random sample of 10 out-of-state applicants results in a SAT scoring mean of 1118 with a standard deviation of 50. Using this data, find the 90% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Answer:
Step-by-step explanation:
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean score of in-state applicants
x2 = sample mean score of out -of-state applicants
s1 = sample standard deviation for in-state applicants
s2 = sample standard deviation for out-of-state applicants
n1 = number of in-state applicants
n1 = number of out-of-state applicants
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (17 - 1) + (10 - 1) = 25
z = 1.708
x1 - x2 = 1046 - 1118 = - 72
Margin of error = z√(s1²/n1 + s2²/n2) = 1.708√(37²/17 + 50²/10) = 31.052239
Confidence interval is - 72 ± 31.052239
The number of houses being built each year is modeled by the growth equation, H(=350 20.12. How long will it take for the
number of new houses to reach 70,000? Round to the nearest whole number.
Answer:
H(24) = 70,000
Step-by-step explanation:
If the growth equation is
H(35020) = 12
Then we are told to find H(70,000)
35020 = 12
70,000 = x
35020x = 12 × 70,000
x = 12 × 70,000/35020
= 23.99
≈ 24.
H(24) = 70,000
what expression is equal to -4x²-36?
Answer:
−4(x^2+9)
Step-by-step explanation:
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200students in group 1 had a mean score of 24.5 with a standard deviation of 4.3, while the 200 students in group 2 had a mean score of 16.3 with a standard deviation of 3.1.Complete parts (a) and (b) below.(a) Determine the 90% confidence interval for the difference in scores, mu 1 minus mu 2.Interpret the interval. ( , ) (Round to three decimal places asneeded.)Interpret the interval. Choose the correct answer below.A.There is a 90% probability that the difference of the means is in the interval.B.The researchers are 90% confident that the difference of the means is in the interval.C.The researchers are 90% confident that the difference between randomly selected individuals will be in the interval.D.There is a 90% probability that the difference between randomly selected individuals will be in the interval.(b) What does this say about priming?A.Since the 90% confidence interval does not contain zero, the results suggest that priming does not have an effect on scores.B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.C.Since the 90% confidence interval contains zero, the results suggest that priming does have an effect on scores.D.Since the 90% confidence interval contains zero, the results suggest that priming does not have an effect on scores.
Answer:
Step-by-step explanation:
a) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
Where
x1 = sample mean of group 1
x2 = sample mean of group 2
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
For a 90% confidence interval, the z score is 1.645
From the information given,
x1 = 24.5
s1 = 4.3
n1 = 200
x2 = 16.3
s2 = 3.1
n2 = 200
x1 - x2 = 24.5 - 16.3 = 8.2
z√(s1²/n1 + s2²/n2) = 1.645√(4.3²/200 + 3.1²/200) = 1.645√0.1405
z = 0.62
Therefore, the 90% confidence interval is 8.2 ± 0.62
Interpretation:
B.The researchers are 90% confident that the difference of the means is in the interval.
b) B.Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 27 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.1 years and a sample variance of 36.0 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girlCalculate the t statistic. To do this, you first need to calculate the estimated standard error. The estimated standard error is SM______ . The t statistic is_________
Answer:
The estimated standard error is SM=1.1547 . The t statistic is 1.4722.
Step-by-step explanation:
We have to esimate the standard error and test statistic for a sample.
The sample has a size n=27.
The sample mean is M=17.7.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√36=6.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{27}}=1.1547[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.7-16}{1.1547}=\dfrac{1.7}{1.1547}=1.4722[/tex]
A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, TechnicsA switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules to answer the following questions:
a. In how many ways can one component of each type be selected?
b. In how many ways can components be selected if both the receiver and the compact disc player are to be Sony?
c. In how many ways can components be selected if none is to be Sony?
d. In how many ways can a selection be made if at least one Sony component is to be included?
e. If someone flips switches on the selection in a completely random fashion, what is the probability that the
system selected contains at least one Sony component?Exactly one Sony component?
Answer:
a) 240 ways
b) 12 ways
c) 108 ways
d) 132 ways
e) i) 0.55
ii) 0.4125
Step-by-step explanation:
Given the components:
Receiver, compound disk player, speakers, turntable.
Then a purcahser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood => 5 offers
Compact disc player: Onkyo, Pioneer, Sony, Technics => 4 offers
Speakers: Boston, Infinity, Polk => 3 offers
Turntable: Onkyo, Sony, Teac, Technics => 4 offers
a) The number of ways one component of each type can be selected =
[tex] \left(\begin{array}{ccc}5\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 5 * 4 * 3 * 4 = 240 ways [/tex]
b) If both the receiver and compact disk are to be sony.
In the receiver, the purchaser was offered 1 Sony, also in the CD(compact disk) player the purchaser was offered 1 Sony.
Thus, the number of ways components can be selected if both receiver and player are to be Sony is:
[tex] \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}4\\1\end{array}\right) [/tex]
[tex] = 1 * 1 * 3 * 4 = 12 ways [/tex]
c) If none is to be Sony.
Let's exclude Sony from each component.
Receiver has 1 sony = 5 - 1 = 4
CD player has 1 Sony = 4 - 1 = 3
Speakers had 0 sony = 3 - 0 = 3
Turntable has 1 sony = 4 - 1 = 3
Therefore, the number of ways can be selected if none is to be sony:
[tex] \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) [/tex]
[tex] = 4 * 3 * 3 * 3 = 108 ways [/tex]
d) If at least one sony is to be included.
Number of ways can a selection be made if at least one Sony component is to be included =
Total possible selections - possible selections without Sony
= 240 - 108
= 132 ways
e) If someone flips switches on the selection in a completely random fashion.
i) Probability of selecting at least one Sony component=
Possible selections with at least one sony / Total number of possible selections
[tex] \frac{132}{240} = 0.55 [/tex]
ii) Probability of selecting exactly one sony component =
Possible selections with exactly one sony / Total number of possible selections.
[tex] \frac{\left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) + \left(\begin{array}{ccc}4\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}3\\1\end{array}\right) \left(\begin{array}{ccc}1\\1\end{array}\right)}{240} [/tex]
[tex] = \frac{(1*3*3*3)+(4*1*3*3)+(4*3*3*1)}{240} [/tex]
[tex] \frac{27 + 36 + 36}{240} = \frac{99}{240} = 0.4125 [/tex]
Find the interval of converge to this series? Sum when n=1 and goes to infinity (x-2) ^n/ (n! .2^)
[tex] sum (x - 2)^{2} \ (ni.{2}^{n}) [/tex]
By the ratio test, the series converges if
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(x-2)^{n+1}}{(n+1)!2^{n+1}}}{\frac{(x-2)^n}{n!2^n}}\right|=|x-2|\lim_{n\to\infty}\frac{n!2^n}{(n+1)!2^{n+1}}[/tex]
[tex]=\displaystyle\frac{|x-2|}2\lim_{n\to\infty}\frac1{n+1}[/tex]
is less than 1. The limit itself is 0 < 1, so the series converges everywhere, i.e. on the entire real line [tex](-\infty,\infty)[/tex].
5/8x + 4 = 3/8x + 12
Answer:
x = 32
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5/8*x+4-(3/8*x+12)=0
Step by step solution :
Step 1 :
3
Simplify —
8
Equation at the end of step 1 :
5 3
((—•x)+4)-((—•x)+12) = 0
8 8
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
12 12 • 8
12 = —— = ——————
1 8
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3x + 12 • 8 3x + 96
——————————— = ———————
8 8
Equation at the end of step 2 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 3 :
5
Simplify —
8
Equation at the end of step 3 :
5 (3x + 96)
((— • x) + 4) - ————————— = 0
8 8
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 8 as the denominator :
4 4 • 8
4 = — = —————
1 8
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
5x + 4 • 8 5x + 32
—————————— = ———————
8 8
Equation at the end of step 4 :
(5x + 32) (3x + 96)
————————— - ————————— = 0
8 8
Step 5 :
Step 6 :
Pulling out like terms :
6.1 Pull out like factors :
3x + 96 = 3 • (x + 32)
Adding fractions which have a common denominator :
6.2 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(5x+32) - (3 • (x+32)) 2x - 64
—————————————————————— = ———————
8 8
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
2x - 64 = 2 • (x - 32)
Equation at the end of step 7 :
2 • (x - 32)
———————————— = 0
8
Step 8 :
When a fraction equals zero :
8.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2•(x-32)
———————— • 8 = 0 • 8
8
Now, on the left hand side, the 8 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2 • (x-32) = 0
Equations which are never true :
8.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
8.3 Solve : x-32 = 0
Add 32 to both sides of the equation :
x = 32
One solution was found :
x = 32
Step-by-step explanation:
