Answer:
(a) 25 degrees
(b) -11 degrees
(c) 38 degrees
Step-by-step explanation:
The temperature function is:
[tex]T(t) = -t^2+4t+34[/tex]
(a) The average value for a temperature is:
[tex]M=\frac{1}{b-a}* \int\limits^b_a {f(x)} \, dx[/tex]
In this particular case, the average temperature is:
[tex]M=\frac{1}{9-0}* \int\limits^9_0 {T(t)} \, dt \\M=\frac{1}{9}* \int\limits^9_0 {(-t^2+4t+34)} \, dt \\M=\frac{1}{9}* {(-\frac{t^3}{3}+2t^2+34t)}|_0^9\\M=\frac{1}{9}*( {(-\frac{9^3}{3}+2*(9^2)+34*9)-0)[/tex]
[tex]M=25[/tex]
The average temperature is 25 degrees.
(b) The expression is a parabola that is concave down, therefore there are no local minimums, which means that the minimum temperature will be at one of the extremities of the interval:
[tex]T(0) = -0^2+4*0+34=34\\T(9) = -9^2+9*4+34=-11[/tex]
The minimum temperature is -11 degrees.
(c) The maximum temperature will occur at the point for which the derivate of the temperature function is zero:
[tex]T(t) = -t^2+4t+34\\T'(t)=-2t+4=0\\2t=4\\t=2[/tex]
At t = 2, the temperature is:
[tex]T(2) = -2^2+4*2+34=38[/tex]
The maximum temperature is 38 degrees.
Solve for x in the equation X^2-16^x=0
Answer:
-1/2
Step-by-step explanation:
x^2- 16^x = 0x^2 = 16^xx^2 = 4^2xx = 4^xlogx = xlog41/x×logx = log4log(x^1/x) = log4x^(1/x) = 4At this point you can guess and try. And it seems that x = -1/2, lets check:
(-1/2)^(1 /-1/2)= (-1/2)^-2= 2^2= 4So, this is correct: x= -1/2
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for
itself since the time it takes to produce the product using the new machine is significantly less than the
production time using the old machine. To test the claim, independent random samples were taken from
both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your
Answer:
Step-by-step explanation:
We will develop a test to compare the mean of two population
Population 1.
population mean μ₀₁ = 25 ; Sample variance 27 ; and sample size n = 45
Population 2.
population mean μ₀₂ = 23 ; Sample variance 7,56; and sample size n = 36
As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)
Test Hypothesis
Null Hypothesis H₀ ⇒ μ₀₂ - μ₀₁ = 0
Alternative Hypothesis Hₐ ⇒ μ₀₂ - μ₀₁ < 0
We will use confidence of 90 %, therefore α = 10 % α = 0,1
α = 0,1
We get z score of z = 1,28 or z = - 1,28 ( left tail)
And compute z(s) = ( μ₀₂ - μ₀₁ ) /√ (s₁)²/n₁ + (s₂)²/n₂
z(s) = - 2 / √(729/45) + (57,15/36)
z(s) = - 2 / √16,2 + 1,59
z(s) = - 2 / 4,2178
z(s) = - 0,4742
As |z(s)| < |z(c)|
We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and α/2 = 0,05 in this case
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± z(0,05)√ (s₁)²/n₁ + (s₂)²/n₂ )
From z Table z ( 0,05 ) ⇒ z score z = 1,64
And √ (s₁)²/n₁ + (s₂)²/n₂ ) = √(729/45) + (57,15/36) = 4,2178
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± 1,64 *4,2178]
₀,₉CI ( μ₀₂ - μ₀₁) = ( - 8,917 ; 4,917 )
We can see that 0 is a possible value in the ₀,₉CI ( μ₀₂ - μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one we should not recomend to purchase the new machine
What is the measure of < x
Answer:
78
Step-by-step explanation:
The measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.
x = 31 + 47
x = 78
determine both the lower and upper limits of a 90% z-confidence interval for µ , the mean score for all students in the school district who are enrolled in gifted and talented programs.
Answer:
CI = ( μ - 1,64 * σ /√n ; μ + 1,64 * σ /√n )
Step-by-step explanation:
We assume Normal Distribution
For Confidence Interval, CI = 90 % and α = 10 %
α = 0,1 and α/2 = 0,05
So we will look for z score reciprocate to these values, at the two tails of the bell
z(α/2) = 1,64 at th right tail and -1,64 at the left
CI = ( μ ± 1,64 * σ /√n )
CI = ( μ - 1,64 * σ /√n ; μ + 1,64 * σ /√n )
Families USA, a monthly magazine that discusses issues related to health and health costs, survey 19 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,800. The standard deviation of the sample was $1095.
A. Based on the sample information, develop a 99% confidence interval for the population mean yearly premium
B. How large a sample is needed to find the population mean within $225 at 90% confidence? (Round up your answer to the next whole number.)
Answer:
a
$10,151 [tex]< \mu <[/tex] $11448.12
b
[tex]n = 158[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 19
The sample mean is [tex]\= x =[/tex]$10,800
The standard deviation is [tex]\sigma =[/tex]$1095
The population mean is [tex]\mu =[/tex]$225
Given that the confidence level is 99% the level of significance is mathematically represented as
[tex]\alpha = 100 -99[/tex]
[tex]\alpha = 1[/tex]%
=> [tex]\alpha = 0.01[/tex]
Now the critical values of [tex]\alpha = Z_{\frac{\alpha }{2} }[/tex] is obtained from the normal distribution table as
[tex]Z_{\frac{0.01}{2} } = 2.58[/tex]
The reason we are obtaining values for [tex]\frac{\alpha }{2}[/tex] is because [tex]\alpha[/tex] is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while [tex]\frac{\alpha }{2}[/tex] is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Now the margin of error is obtained as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58* \frac{1095 }{\sqrt{19} }[/tex]
[tex]MOE = 648.12[/tex]
The 99% confidence interval for the population mean yearly premium is mathematically represented as
[tex]\= x -MOE < \mu < \= x +MOE[/tex]
substituting values
[tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]
[tex]10800 -648.12 < \mu < 10800 + 648.12[/tex]
$10,151 [tex]< \mu <[/tex] $11448.12
The largest sample needed is mathematically evaluated as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{\mu} ][/tex]
substituting values
[tex]n = [ \frac{ 2.58 * 1095}{225} ]^2[/tex]
[tex]n = 158[/tex]
Penny's parents gave her $50 to spend on new video games. Used games are $7 and new games are $12. 1. What is the system of inequalities that represent this situation? 2. What is the maximum amount of used games that she could buy? 3. What is the minimum amount of new games that she could buy? 4. What are two possible combinations of used and new games she can purchase?
The correct answers are Part 1: 7x + 12y 50, x,y 0; Part 2: 7; Part 3: 0: Part 4: 2 old and 3 new video games.
Step-by-step explanation:
Penny's parents gave her $50 to buy new video games.
Price of used games are $7 and new games are $12.
Let Penny buy x number of old video games and y number of new video games.
Part 1:
Total price she spent on buying the video games are 7x + 12y.
This amount should be less than or equal to the amount of money she possess. therefore 7x + 12y 50, x, y 0.
Part 2:
Maximum number of used game she can buy can be given when she spends all her money just on used games. Therefore y = 0. This implies x .
Thus the maximum number of used game she can buy is 7 where she does not buy any new game and has $1 left with her after the purchase.
Part 3:
Minimum number of new games that Penny can buy is zero. She can not buy any new games and spent all her money purchasing old games.
Part 4:
The possible combination in which she can purchase both the video games is 2 old games and 3 new games.
hope this helps
Your birthday was in June and your rich Aunt Edna, who had been acting a little weird lately, gave you a check for $25,000 to help you celebrate. You opened a checking account with this money by making a DEPOSIT on June 16th and proceeded to have the time of your life!
The first thing you did was move out of your parent’s house and into a high-rise apartment near downtown. On June 25th, you wrote CHECK #101 to the Trumble Tower for $1800 which included a $600 deposit. You wanted your “new” flat to be really cool, so you decided to decorate it with style and taste. You bought a home theater system and television at Best Buy using your Mastercard. At Rooms-To-Go, you purchased a living room set and bedroom set using your VISA card. You used your DEBIT card on July 4th for a $129.45 purchase at Macy’s. You invited all your friends over the following Saturday night for pizza and drinks and paid for it with your Mastercard.
On July 8th you realized that you needed some food and supplies for a day at the beach. First you went to Starbucks for breakfast using your DEBIT card to pay the $12.83 bill. You stopped at Walmart and bought $132.56 in food and supplies using your DEBIT card. At Kroger’s you used your DEBIT card to purchase $52.23 of groceries and your VISA card to buy gas. You also stopped by the ATM machine at your bank to withdraw $100 for the day at the beach.
On July 15th, you filled out a DEPOSIT slip for your paycheck of $250 since you forgot to sign up for direct deposit. After driving to and from the beach, you realized you needed a new car! You decided to go car shopping on July 16th since you did not have to work that day. At Best Friend Ford, you found the perfect car for $12,498.99! You wrote CHECK #102 for the car. Since you got a new car, you decided that you needed to look good while driving it so you went shopping on July 19th. You purchased clothing at H&M and Abercrombie & Fitch using your Mastercard.
Since you had been driving around in a new car wearing new clothes, your friends decided that they wanted to be paid the money that you owed them. Paul Smith accepted the $20 CHECK #103 you wrote him on July 21st. Linda Boltman and Max Badger wanted cash immediately so you went to the nearest gas station with an ATM and withdrew $80 in cash to pay them on July 23rd. Your bank charged you an ATM service FEE of $2.50 for the withdrawl.
At the end of the month, the bills started to arrive. You forgot to set up online banking with your checking account so you had to write checks. You paid the utility company Greenhouse Energy with CHECK #104 for $155.87 on July 25th, paid AllConnect with CHECK #105 for $150 for TV, internet, and phone on July 27th, paid Mastercard with CHECK #106 for $1518.23 on August 3rd, and paid VISA with CHECK #107 for $1994.02 on August 5th. You wrote a DEPOSIT slip on August 1st for your $250 paycheck and got $30 cash back with the deposit.
THE END
Check Register Codes
ATM – ATM WithdrawalDEB – Debit CardDEP – Deposit
FEE – Checking Account Fee### (check number) – Check
2
Answer:
Dang shes rich, but what is the question?
Step-by-step explanation:
A survey of 181 registered voters in one state reveals that 112 of them favor approval of a bill before the legislature. Construct a 98% confidence interval for the true proportion of all voters in the state who favor approval of the bill. Give your answers as decimals, rounded to 3 places after the decimal point (if necessary). 98% confidence interval for p: ( , )
Answer:
Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is ( 0.541 , 0.683)
Step-by-step explanation:
The sample proportion is = p = 112/181 = 0.61878= 0.612
q = 1-p = 1- 0.612= 0.388
The degree of confidence is 98 % so z₀.₀₂₅= 1.96 taking α = 5 at 95 %
The interval X~± 0.98 is a random variable because X does not have a particular value but takes different values in different samples.
In repeated samples of size 16 from a normal distribution with standard deviation 2 the interval X~± 0.98 will contain true unknown value of mean about 95 percent of the time .
p ± z ( base alpha by 2) √pq/n
Substituting the values
0.612 ± 1.96√0.612*0.388/181
Multiplying p and q
= 0.612 ± 1.96 √0.237456/181
Solving the square root
=0.612 ± 1.96( 0.03622)
Multiplying value of z with the value of square root
=0.612 ± 0.07099
Adding or subtracting will give 0.683, 0.541
Hence the approximate 98% confidence interval for the voters in favor of the approval of the bill is ( 0.541 , 0.683)
The amount of flow through a solenoid valve in an automobile's pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Four different levels (low, fair, moderate, and high) of each factor were chosen, and a single observation on flow was made for each combination of levels.A) The resulting data set consisted of how many observations?
B) Is this an enumerative or analytic study? Explain.
Answer:
A) 64 observations
B) analytic study
Step-by-step explanation:
Given:
There are 3 number of factors i.e. armature length, spring load, and bobbin depth.
There are 4 levels i.e. low, fair, moderate, and high
There is a single i.e. 1 observation on flow made for each combination of levels.
A)
To find:
Number of observations.
There are 4 levels so these 4 levels are to be considered for each factor.
Number of observations = 4.4.4 = 64
For example if we represent low fair moderate and high as L,F,M,H
and factors armature length, spring load, and bobbin depth as a,s,b
Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]
So resulting data set has 64 observations.
B)
This is analytic study.
The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.
The cost of plastering the 4 walls of a room which is 4m high and breadth one third of its length is Rs. 640 at the rate of Rs. 5/m². What will be the cost of carpeting its floor at the rate of Rs. 250/m².
Answer:
Rs. 32,000
Step-by-step explanation:
height = 4m
let length = x m
breadth = x/3 m
Area of the 4 walls = 2(length × height) + 2(breadth × height)
Area = 2(4×x) + 2(4 × x/3) = 8x + (8x)/3
Area = (32x)/3 m²
1 m² = Rs. 5
The cost for an area that is (32x)/3 m²= (32x)/3 × 5 Rs.
The cost of plastering 4 walls at Rs.5 per m² = 640
(32x)/3 × 5 = 640
(160x)/3 = 640
x = length = 12
Area = (32x)/3 m² = (32×12)/3 = 128m²
The cost of carpeting its floor at the rate of Rs. 250/m²:
= 128m² × Rs. 250/m² = 32,000
The cost of carpeting its floor at the rate of Rs. 250/m² = Rs. 32,000
What is the slope of the line passing through the points (6,7) and (1,5)
Answer:
2/5
Step-by-step explanation:
(7-5)/(6-1)
Simplify 3/4(1/2x-12)+4/5
Answer:
3x/8 - 41/5
Step-by-step explanation:
Simplify each term.
3x/8 − 9+4/5
To write −9 as a fraction with a common denominator, multiply by 5/5
3x/8−9 x 5/5 + 4/5
Combine −9 and 5/5
Combine the numerators over the common denominator.
3x/8 + −41/5
Move the negative in front of the fraction
3x/8 - 41/5
Hope this helps you
I have a couple more questions and I don’t have time to answer them all lol, my science class starts in 15 minutes.
Answer:
[tex]\boxed{x = 7}[/tex]
Step-by-step explanation:
75 = 11x-2 (Corresponding angles are equal)
11x -2 = 75
Adding 2 to both sides
11x = 75+2
11x = 77
Dividing both sides by 11
x = 7
Answer:
[tex]\left[\begin{array}{ccc}\\x = 7\\\end{array}\right][/tex]
Step-by-step explanation:
Well to find x we can set up the following equation,
11x - 2 = 75
So we have to single out x.
+2 to both sides
11x = 77
Divide 11 by both sides
x = 7
Thus,
x = 7.
Hope this helps :)
Veda solves the following system of linear equations by elimination. What is the value of x in the solution of the system
of equations?
6+4x-2y=0
-3-7y=10x
Answer:
work shown and pictured
Answer:
x= -1 y = 1
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
1. Identify the focus and the directrix for 36(y+9) = (x - 5)^2 2. Identify the focus and the directrix for 20(x-8) = (y + 3)^2
Problem 1
Focus: (5, 0)
Directrix: y = -18
------------------
Explanation:
The given equation can be written as 4*9(y-(-9)) = (x-5)^2
Then compare this to the form 4p(y-k) = (x-h)^2
We see that p = 9. This is the focal distance. It is the distance from the vertex to the focus along the axis of symmetry. The vertex here is (h,k) = (5,-9)
We'll start at the vertex (5,-9) and move upward 9 units to get to (5,0) which is where the focus is situated. Why did we move up? Because the original equation can be written into the form y = a(x-h)^2 + k, and it turns out that a = 1/36 in this case, which is a positive value. When 'a' is positive, the focus is above the vertex (to allow the parabola to open upward)
The directrix is the horizontal line perpendicular to the axis of symmetry. We will start at (5,-9) and move 9 units down (opposite direction as before) to arrive at y = -18 as the directrix. Note how the point (5,-18) is on this horizontal line.
================================================
Problem 2
Focus: (13,-3)
Directrix: x = 3
------------------
Explanation:
We'll use a similar idea as in problem 1. However, this time the parabola opens to the right (rather than up) because we are squaring the y term this time.
20(x-8) = (y+3)^2 is the same as 4*5(x-8) = (y-(-3))^2
It is in the form 4p(x-h) = (y-k)^2
vertex = (h,k) = (8,-3)
focal length = p = 5
Start at the vertex and move 5 units to the right to arrive at (13,-3). This is the location of the focus.
Go back to the focus and move 5 units to the left to arrive at (3,-3). Then draw a vertical line through this point to generate the directrix line x = 3
It is a well-known fact that Dr. Barnes rides a skateboard, sometimes even on campus. Suppose that Dr. Barnes selects a skateboard by first picking one of two skateboard shops at random and selecting a skateboard from that shop at random. The first shop contains two "rad" skateboards and three "gnarly" skateboards, and the second shop contains four "rad" skateboards and one "gnarly" skateboard. What is the probability that Dr. Barnes picked a skateboard from the first shop if he has selected a "gnarly" skateboard?
Answer:
75%.
Step-by-step explanation:
In total, there are 3 gnarly boards in the first shop and 1 gnarly board in the second. We know that he has selected one gnarly board out of the 3 + 1 = 4 existing boards.
The probability the board came from the first shop is 3 / 4 = 0.75 = 75%.
Hope this helps!
Probability of landing on even # on a spinner; probability of rolling an odd # on a die
Answer:
Spinner: 50%
Die: 50%
Step-by-step explanation:
Well for the spinner it depends on the amount of numbers it has,
in this case we’ll use 6.
So The probability of landing on the even numbers in a 6 numbered spinner.
2, 4, 6
3/6
50%
Your average die has 6 sides so the odd numbers are,
1, 3, 5
3/6
50%
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.
16 sin4x
16sin4x = _____
Answer:
[tex]6-8cos2x+2cos4x[/tex]
Step-by-step explanation:
We are given that
[tex]16sin^4 x[/tex]
We can write the given expression as
[tex]16(sin^2x \times sin^2 x)[/tex]
[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]
By using the formula
[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]
[tex]4(1-cos2x)^2[/tex]
[tex]4(1-2cos2x+cos^2(2x)[/tex]
Using the identity
[tex](a-b)^2=a^2+b^2-2ab[/tex]
[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]
[tex]4-8cos2x+2+2cos4x[/tex]
[tex]6-8cos2x+2cos4x[/tex]
This is required expression.
M angle D=? What is the degree of the angle?
Answer:
80°Step-by-step explanation:
In ACB and ECD
AC =~ CE [ Given ]
BC =~ CD [ Given ]
<ACD =~ <ECD [ Vertical angles ]
Hence, ∆ ACB =~ ECD by SAS congruency of triangles.
Then, <B = <D
In ∆ABC , sum of all three angles must be 180°
<A + <B + <C = 180°
plug the values
[tex] 30 + < d \: + 70 = 180[/tex]
Add the numbers
[tex]100 + < d = 180[/tex]
Move constant to R.H.S and change it's sign
[tex] < d = 180 - 110[/tex]
Subtract the numbers
[tex] < d = 80[/tex] °
Hope this helps..
Best regards!!
10 points + brainliest = 15 points!
Answer:
(2x^2+1)(4x+3)
Step-by-step explanation:
8x^3 + 6x^2 + 4x+3
Split into two groups
8x^3 + 6x^2 + 4x+3
Factor out 2x^2 from the first group and 1 from the second group
2x^2( 4x+3) +1( 4x+3)
Factor out (4x+3) from each group
(4x+3) (2x^2+1)
Rearranging the order
(2x^2+1)(4x+3)
Answer:
(2x²+1)(4x+3)
Step-by-step explanation:
8x³ + 6x² + 4x +3= regroup as follows(8x³ + 4x) + (6x²+3) =4x(2x²+1) + 3(2x²+1)=(2x²+1)(4x+3)Correct choice is the second one
Solve x is less than or equal to 0 and x is greater than or equal to -4
Answer:
x = {-3, -2, -1, 0}
Step-by-step explanation:
x ≤ 0
x > -4
then
x {-3, -2, -1, 0}
Give me the correct format of report writing plzzz (subject English) help plz
Step-by-step explanation:
Hi, there!!..
The format of report writing are given in points;
Title (reflects of report as its main function and it should be clear, brief, specific and weighty.)After title you have to right place and date.and start your body,
Background information about the report. (it should be clear and have reasons)Purpose (the report should have purpose)Actions or, sequences of happening should be clearly written. Characters mentioned should be written properly.and write conclusion,
Observation (it should be clear, factual and objectives).You may add comments on it.
Hope it helps....
letry. 14 Chapter 9: Chapter 9 rest Chapter Test
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height of the roof.
Round your answer to the nearest tenth.
15 ft
h
8 ft
17 ft
Answer:
h = 7.1 cm
Step-by-step explanation:
To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:
[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]
Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:
[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]
So the area of the triangle is:
[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]
[tex]S = 60\ cm^2[/tex]
Now, to find the height, we can use the following equation for the area of the triangle:
[tex]S = base * height/2[/tex]
The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:
[tex]60 = 17 * h/2[/tex]
[tex]h = 120/17[/tex]
[tex]h = 7.06\ cm[/tex]
Rounding to the nearest tenth, we have h = 7.1 cm
Answer:
7.1 cm
Step-by-step explanation:
:D
Integrate the following: ∫84 [tex]dx[/tex]
A. 42x
B. 84x
C. 84x + C
D. 42x + C
Answer:
Choice C. [tex]84\, x + C[/tex].
Step-by-step explanation:
Consider the power rule for integration. Let [tex]n[/tex] be a real number that is not equal to [tex](-1)[/tex]. The power rule for integration states that:
[tex]\displaystyle \int x^{n}\, d x = \frac{1}{n + 1}\, x^{n+ 1} + C[/tex],
How could this rule apply to this question, since there's apparently no [tex]x[/tex] (or its powers) in the integrand? Keep in mind that [tex]x^{0} = 1[/tex] for all real (and particularly non-zero) values of [tex]x[/tex]. In other words, the integrand [tex]84[/tex] is equal to [tex]84\, x^0[/tex]. The integral becomes:
[tex]\displaystyle \int 84\, x^{0}\, dx[/tex].
The constant can be moved outside the integral sign. Therefore:
[tex]\displaystyle \int 84\, x^{0}\, dx= 84 \int x^{0}\, dx[/tex].
Now that resembles the power rule. In particular, [tex]n = 0[/tex], such that [tex]n + 1 = 1[/tex]. By the power rule:
[tex]\begin{aligned}84 \int x^{0}\, dx = 84\, \left(\frac{1}{1}\, x^{1} + C\right) = 84\, x + 84\, C\end{aligned}[/tex].
The non-zero constant in front of [tex]C[/tex] can be ignored (where [tex]C[/tex] represents the constant of integration.) Therefore:
[tex]\displaystyle \int 84\, dx = 84\, x + C[/tex].
If a is a constant then it's inetgration is
[tex]\boxed{\sf \displaystyel\int adx=ax+C}[/tex]
Here 84 is constant[tex]\\ \rm\Rrightarrow \displaystyle\int 84dx[/tex]
[tex]\\ \rm\Rrightarrow 84x+C[/tex]
Option C
A standard dice is tossed twice. What is the probability of obtaining exactly one 5? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
There are a couple of ways to look at this.
1) If you make a matrix of all possibilities, you find there are 36 possible outcomes from the roll of a die twice. (That is the same number as for rolling two dice once.) Of those 36 outcomes, 10 are outcomes in which a 5 shows exactly once: (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5).
The probability of obtaining exactly one 5 is 10/36 = 5/18.
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2) As listed above, there are two ways to get exactly one 5 in two rolls:
(5 on the first, non-5 on the second) or (non-5 on the first, 5 on the second)
When the rolls are independent, as we assume here, the probability of a certain sequence is the product of the probabilities of the events in that sequence.
P(5, non-5) = (1/6)(5/6) = 5/36
P(non-5, 5) = (5/6)(1/6) = 5/36
The probability of obtaining either event is the sum of their individual probabilities:
P({5, 5'} or {5', 5}) = 5/36 +5/36 = 10/36 = 5/18
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The probability of obtaining exactly one 5 in two rolls of a die is 5/18.
Answer:
S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:
(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)
And then the probability would be:
[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]
Step-by-step explanation:
For this case w ehave the following sample space:
S= (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For this case the size of the sample space is 36 now we count the number of pairs with exactly one 5 and we have:
(1,5), (2,5), (3,5), (4,5), (6,5), (5,6), (5,4), (5,3), (5,2), (5,1)
And then the probability would be:
[tex] p=\frac{10}{36}= \frac{5}{18}[/tex]
a(b + c) = a × b + a × c where a, b, and c are real numbers
use the distributive property to simplify the expression
8(3 + 4) = 24 + ?
Answer:
32
Step-by-step explanation:
8(3 + 4) = 24 + ?
8(3)+8(4)= 24 + ?
24+32= 24 + ?
24-24+32=?
32=?
Answer:
? = 32
Step-by-step explanation:
Let's assume a = 8 , b = 3 , c = 4
[tex] \sf \: So :- \: \: a(b + c) = 8(3 + 4)[/tex]
[tex]8 \times 3 + 8 \times 4[/tex]
[tex]24 + 32[/tex]
Hence, The required value of ? = 32 .
Write these numbers in standard form 906000000
Answer:
9.06×10 to the power of 8(8 is superscript above 10)
Answer:
9.06 x 10^8
Step-by-step explanation:
906000000 = 9.06 x 10^8
8 decimal places in
Which expression is equivalent to 0.83¯ ?
Answer:
Hello There!!
Step-by-step explanation:
Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...
A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: Ŷ = 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If we want to test for the significance of the regression model, the critical value of F at the 5% level of significance is a. 3.29. b. 3.24. c. 3.68. d. 4.54.
Answer: C. 3.68
Step-by-step explanation:
Given that;
Sample size n = 18
degree of freedom for numerator k = 2
degree of freedom for denominator = n - k - 1 = (18-2-1) = 15
level of significance = 5% = 5/100 = 0.05
From the table values,
the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68
Therefore option C. 3.68 is the correct answer