For this case we propose a system of equations:
x: Variable representing the anticipated tickets
y: Variable representing the same day tickets
So:
[tex]x + y = 45\\25x + 35y = 1375[/tex]
We clear x from the first equation:
[tex]x = 45-y[/tex]
We substitute in the second equation:
[tex]25 (45-y) + 35y = 1375\\1125-25y + 35y = 1375\\10y = 1375-1125\\10y = 250\\y = 25[/tex]
We look for the value of x:
[tex]x = 45-25\\x = 20[/tex]
Thus, 20 of anticipated type and 25 of same day type were sold.
Answer:
20 of anticipated type and 25 of same day type were sold.
Answer: 20 advance tickets and 25 same-day tickets.
Step-by-step explanation:
Set up a system of equations.
Let be "a" the number of advance tickets and "s" the number of same-day tickets.
Then:
[tex]\left \{ {{25a+35s=1375} \atop {a+s=45}} \right.[/tex]
You can use the Elimination method. Multiply the second equation by -25, then add both equations and solve for "s":
[tex]\left \{ {{25a+35s=1,375} \atop {-25a-25s=-1,125}} \right.\\.............................\\10s=250\\\\s=\frac{250}{10}\\\\s=25[/tex]
Substitute [tex]s=25[/tex] into an original equation and solve for "a":
[tex]a+(25)=45\\\\a=45-25\\\\a=20[/tex]
A town's January high temperatures average 36degreesF with a standard deviation of 8degrees, while in July the mean high temperature is 72degrees and the standard deviation is 9degrees. In which month is it more unusual to have a day with a high temperature of 57degrees? Explain.
Answer: July
Step-by-step explanation:
Formula of z score :
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
Given: The mean high temperature in January = [tex]\mu_1=36^{\circ} F[/tex]
Standard deviation : [tex]\sigma_1=8^{\circ}F[/tex]
For X = [tex]57^{\circ}F[/tex]
[tex]z=\dfrac{57-36}{8}=2.625[/tex]
The mean high temperature in July = [tex]\mu_1=72^{\circ} F[/tex]
Standard deviation : [tex]\sigma_1=9^{\circ}F[/tex]
[tex]z=\dfrac{57-72}{8}=-1.875[/tex]
⇒ 57° F is about 2.6 standard deviations above the mean of January high temperatures, and 57° F is about 1.9 standard deviations below the mean of July’s high temperatures.
A general rule says that z-scores lower than -1.96 or higher than 1.96 are considered unusual .
Hence, the 57˚F is more unusual in January.
Final answer:
A high temperature of 57 degrees is more unusual in January than in July, as it is 2.625 standard deviations above the January mean, compared to 1.667 standard deviations below the July mean.
Explanation:
To determine in which month it is more unusual to have a high temperature of 57 degrees Fahrenheit, we can calculate the z-score for each month. The z-score tells us how many standard deviations away from the mean a particular value is.
For January, the z-score is calculated as follows:
Z = (57 - 36) / 8 = 21 / 8 = 2.625
This means that a temperature of 57 degrees in January is 2.625 standard deviations above the January mean.
For July, the z-score is calculated as follows:
Z = (57 - 72) / 9 = -15 / 9 = -1.667
This means that a temperature of 57 degrees in July is 1.667 standard deviations below the July mean.
Since the absolute value of the January z-score (2.625) is higher than the absolute value of the July z-score (-1.667), a high temperature of 57 degrees is more unusual in January than in July.
evaluate the logarithmic expression.
Answer:
Step-by-step explanation:
I'm making the assumption you are looking for a graph of y=log_3(x)
So 3^0=1 which means log_3(1)=0 graph (1,0)
3^1=3 which means log_3(3)=1 graph (3,1)
3^2=9 which means log_3(9)=2 graph (9,2)
3^3=27 which means log_3(27)=3 graph (27,3)
Can you find a graph that fits these points?
what is 6% sales tax on $4929.00
Answer: $5,224.74
Step-by-step explanation:
You need to calculate the 6% of $4,929.00.
Convert the percentage to decimal form:
[tex]\frac{6}{100}=0.06[/tex]
Now multiply $4,929.00 by 0.06:
[tex](\$4,929.00)(0.06)=\$295.74[/tex] (This is the 6% of $4,929.00)
Finally, you need to add $295.74 to $4,929.00. Then you get:
[tex]\$4,929.00+\$295.74=\$5,224.74[/tex]
Therefore, the 6% sales tax on $4,929.00 is: $5,224.74
A furniture manufacturer sells three types of products: chairs, tables, and beds. Chairs constitute 35% of the company's sales, tables constitute 55% of the sales, and beds constitute the rest. Of the company's chairs, 5% are defective and have to be returned to the shop for minor repairs, whereas the percentage of such defective items for tables and beds are 12% and 8% respectively. A quality control manager just inspected an item and the item was not defective. What is the probability that this item was a table? Round your result to 2 significant places after the decimal (For example, 0.86732 should be entered as 0.87).
Answer:
53.27
Step-by-step explanation:
To begin, we want to figure out what percent of products are defective and non defective, and of which type, so we can figure out probabilities. So, we start with that 5% of chairs are defective. We know that 35% of product sales are chairs, so 5% of 35% is 35%*0.05 (a percent can be divided by 100 to convert to decimals)= 1.75%. For tables, 12% of 55 is 55*0.12=6.6 percent. For beds, we first must figure out what percent of sales are beds. For this, we must take our total (100%) and subtract everything that is not beds, which is tables and chairs. This, 100-35-55=10, which is our percent of beds. Then, 8% of that is 0.8%. So, we know that the probability that an item is defective is 0.8+6.6+1.75=9.15%. The item pulled was not defective, so we want to figure out the probability of that, which would be the total-defective=100-9.15=90.85%. We then need to figure out which of that 90.85 is divided by tables, as we want to figure out what the probability of a table is. We know that 12% of tables are defective, so 100-12=88% are not. 88% of 55% is 55*0.88=48.4, so there is a 48.4% chance that if you picked out anything, it would be a non defective table. However, we are only picking things out from nondefective items, or the 90.85%. We know that 48.4 is 48.4% of 100, but we want to figure out what percent 48.4 is of 90.85. To find this, we do (48.4/90.85) * 100, which is 53.27 rounded. Feel free to ask further questions!
Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
Answer:
p = 0.718 and n = 20
Step-by-step explanation:
p is the probability of success and n is the number of trials.
Here, p = 0.718 and n = 20.
Answer:
There is a 29.50% probability of winning more than 15 times.
Step-by-step explanation:
For each time you play the arcade game, there are only two possible outcomes. Either you win, or you lose. This means that we can solve this problem using the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem we have that:
The probability of winning a game is 0.718. So [tex]p = 0.718[/tex].
The game is going to be played 20 times, so [tex]n = 20[/tex].
If you play the arcade game 20 times, we want to know the probability of winning more than 15 times.
This is
[tex]P(X > 15) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.2950[/tex].
There is a 29.50% probability of winning more than 15 times.
It took 2 men 5 hours to build an airstrip. Working at the same rate, how many additional men could have been hired in order for the job to have taken 1/hour less? (A) Two (B) Three (C) Four (D) Six
The problem is to calculate the number of additional men needed to build an airstrip in less time given two men already took five hours. The additional man required is one after solving the equation, but this is not an option provided, indicating a potential error in the question.
Explanation:The question involves calculating the number of additional men required to build an airstrip in less time. If it took 2 men 5 hours to build an airstrip, we can say they have a combined work rate of 1 airstrip per 5 hours, or (1/5) airstrip per hour. To finish the job in 4 hours, which is 1 hour less than the original time, we would need a work rate of 1 airstrip per 4 hours.
So, if we let the number of additional men be X, we can set up the equation as follows:
(2 + X) men × 4 hours = 2 men × 5 hours(2 + X) × 4 = 102 + X = 10 / 4X = 2.5 - 2X = 0.5Since we cannot hire half a person, we round up to the nearest whole number. Hence, one additional man would be sufficient to complete the work in 1 hour less time. However, none of the options given (A) Two, (B) Three, (C) Four, or (D) Six, are correct. Therefore, the answer is not provided in the given options and this represents a possible error in the question itself.
Papa John wants to know if he should rename an old favorite pizza for his restaurant. He gives 60 patrons a pepperoni pizza and asks them to rate both the names ‘pepperoni deluxe’ and ‘venti extra cheesy pepperoni on toasted pan bread with tomato zest pesto’. He takes the ratings and wants to perform a statistical test. What would be the best statistical test to be used?
Answer:
gragh
Step-by-step explanation:
its one of the few ways to analyze data and compare it to find the best choice
According to the research, 43% of homes sold in a certain month and year were purchased by first-time buyers. A random sample of 165 people who just purchased homes is selected. Complete parts a through e below. what is the probabilty that less than 75 of them are first time buyers
Answer Do it
Step-by-step explanation 165 divided by 100 =x times 43
when two dice are rolled, what is the probability the two numbers will have a sum of 10
A. 1/10
B.1/18
C.1/12
D.1/3
Answer:
The correct answer is option C. 1/12
Step-by-step explanation:
It is given that, two dies are rolled.
The outcomes of tossing two dies are,
(1,1), (1,2), (1,3), (1,4), (15), (1,6)
----- -------- ------ ------ ----- ----
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Number of possible outcomes = 36
To find the probability
The possible outcomes are getting sum 10 which are,
(4,6), (5, 5) and (6,4)
Number of possible outcomes = 3
Therefore probability of getting sum 10 = 3/36 = 1/12
The correct answer is option C. 1/12
#5 Points possible: 3. Total attempts: 5
Using your calculator, find the range and standard deviation, round to two decimals places:
The table below gives the number of hours spent watching TV last week by a sample of 24 children.
76
57
89
73
88
42
31
46
80
42
38
57
49
50
89
36
69
82
27
88
39
89
95
18
Range =
Standard Deviation =
Answer:
honesty you cant realy use a calculator because you need to meadian mode and range them first
Step-by-step explanation:
Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of its contents defective, while shipment II has 5% of its contents defective. It is equally likely an employee will go to either bin and select a component randomly. Use Bayes' Rule to find the probability that a defective component came from shipment II.
The probability that a defective component came from shipment II is:
[tex]0.7143\ or\ 71.43\%[/tex]
Step-by-step explanation:Let A denote the event that the defective component was from shipment I
Also, P(A)=2%=0.02
and B denote the event that the defective component was from shipment II.
i.e. P(B)=5%=0.05
Also, P(shipment I is chosen)=1/2=0.5
and P(shipment II is chosen)=1/2=0.5
The probability that a defective component came from shipment II is calculated by Baye's rule as follows:
[tex]=\dfrac{\dfrac{1}{2}\times 0.05}{\dfrac{1}{2}\times 0.02+\dfrac{1}{2}\times 0.05}}\\\\\\=\dfrac{0.05}{0.07}\\\\=\dfrac{5}{7}\\\\=0.7143\ or\ 71.43\%[/tex]
Hence, the answer is:
[tex]0.7143\ or\ 71.43\%[/tex]
By applying Bayes' Rule, we can compute the probability that a defective component came from shipment II as approximately 71.4%.
Explanation:Given that there are two shipments of components both containing defective parts, we can apply the Bayes' Rule to answer your question.
Let's assume that D is the event that a component is defective and I and II are events that the component came from shipment I and shipment II respectively. Since the defective component can come from either shipment with equal probability, P(I) = P(II) = 0.5. Also, it's given that the component is defective, so P(D) = 1.
The probability that a component from shipment I is defective, P(D/I), is 2% or 0.02 and from shipment II is 5% or 0.05. We want to find the probability that a defective component came from shipment II, or P(II/D).
To do this, we use Bayes' Rule: P(II/D) = [P(D/II) * P(II)] / P(D).
Substituting the values in, we get: P(II/D) = [0.05 * 0.5] / [0.5 * (0.02 + 0.05)] = 0.0625 / 0.035 = ~0.714. So the probability that a defective component came from shipment II is approximately 0.714 or 71.4%.
Learn more about Bayes' Rule here:https://brainly.com/question/33971056
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force of 400 N stretches a spring 2 m. A mass of 50 kg is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion?
Answer:
x = -5 sin (2t)
Step-by-step explanation:
k is the spring stiffness. The unstretched length of the spring is L.
When the mass is added, the spring stretches to an equilibrium position of L+s, where mg = ks. When the mass is displaced a distance x (where x is positive if the displacement is down and negative if it's up), the spring is stretched a total distance s + x.
There are two forces on the mass: weight and force from the spring. Sum of the forces in the downward direction:
∑F = ma
mg − k(s + x) = ma
mg − ks − kx = ma
Since mg = ks:
-kx = ma
Acceleration is second derivative of position, so:
-kx = m d²x/dt²
Let's find k:
F = kx
400 = 2k
k = 200
We know that m = 50. Substituting:
-200x = 50 d²x/dt²
-4x = d²x/dt²
d²x/dt² + 4x = 0
This is a linear second order differential equation of the form:
x" + ω² x = 0
The solution to this is:
x = A cos (ωt) + B sin (ωt)
Here, ω² = 4, so ω = 2.
x = A cos (2t) + B sin (2t)
We're given initial conditions that x(0) = 0 and x'(0) = -10 (remember that down is positive and up is negative).
Finding x'(t):
x' = -2A sin (2t) + 2B cos (2t)
Plugging in the initial conditions:
0 = A
-10 = 2B
Therefore:
x = -5 sin (2t)
Four different prime numbers, each less than 20, are multiplied together. What is greatest possible result?
a. 21,879
b. 28,728
c. 40,755
d. 46,189
e. 49,172
Please show me how I can solve this!!
Answer:
46,189
Step-by-step explanation:
The prime numbers that are less than 20 are :
1,2,3,5,7,11,13,17,19
to get the greatest value, we multiply the four numbers with the largest values i.e
11 x 13 x 17 x 19 = 46,189
The greatest possible product of four different prime numbers each less than 20 is found by multiplying the four largest primes in that range: 19, 17, 13, and 11, which equals 46,189.
Explanation:To find the greatest possible product of four different prime numbers each less than 20, we should choose the four largest prime numbers in that range. The largest primes less than 20 are 19, 17, 13, and 11. Multiplying these together gives us:
19 \times 17 \times 13 \times 11 = 46,189.
Thus, the greatest possible result when multiplying four different prime numbers, each less than 20, is 46,189, which matches option 'd'.
What is the future value of $510 per year for 8 years compounded annually at 9 percent?
The future value of $510 per year for 8 years compounded annually at 9 percent is $1,016.21.
What is the future value?The investment's future value refers to the compounded value of the present cash flows in the future, using an interest rate.
The future value can be determined using the future value table or formula.
We can also determine the future value using an online finance calculator as below.
Data and Calculations:N (# of periods) = 8 years
I/Y (Interest per year) = 9%
PV (Present Value) = $510
PMT (Periodic Payment) = $0
Results:
FV = $1,016.21 ($510 + $506.21)
Total Interest = $506.21
Thus, the future value of $510 per year for 8 years compounded annually at 9 percent is $1,016.21.
Learn more about future values at brainly.com/question/12890404
7(x - 2) = 3(x + 4)
Solve the following equation. Then enter your answer in the space provided using mixed number format.
Answer:
In mixed number format: 6 1/2
Step-by-step explanation:
To solve the following equation: 7(x - 2) = 3(x + 4), first we need to apply the distributive property:
7(x - 2) = 3(x + 4) → 7x -14 = 3x + 12
Solving for 'x' → 4x = 26 → x = 6.5
→ In mixed number format: 6 1/2
For this case we must solve the following equation:
[tex]7 (x-2) = 3 (x + 4)[/tex]
Applying distributive property to the terms within the parenthesis we have:
[tex]7x-14 = 3x + 12[/tex]
We subtract 3x on both sides of the equation:
[tex]7x-3x-14 = 12\\4x-14 = 12[/tex]
Adding 14 to both sides of the equation:
[tex]4x = 12 + 14\\4x = 26[/tex]
Dividing between 4 on both sides of the equation:
[tex]x = \frac {26} {4} = \frac {13} {2}[/tex]
ANswer:
[tex]x = \frac {13} {2}\\x = 6 \frac {1} {2}[/tex]
What is the simplest form of
Answer:
The simplest form of [tex]\sqrt[3]{27a^{3}b^{7}}[/tex] is
3ab²(∛b)
Step-by-step explanation:
The given term is:
[tex]\sqrt[3]{27a^{3}b^{7}}[/tex]
To convert it into its simplest form, we will apply simple mathematical rules to simplify the power of individual terms.
[tex]\sqrt[3]{27a^{3}b^{7}}\\= \sqrt[3]{3^{3} a^{3}b^{7}}\\= \sqrt[3]{3^{3}a^{3}b^{6}b}\\= 3^{3/3} a^{3/3}b^{6/3}b^{1/3}}\\= 3ab^{2}(\sqrt[3]{b})[/tex]
While simplifying the term, we basically took the cube root of individual terms. The powers cancelled out cube root for some terms. In the end, we were left with the simplest form of the expression.
Part A: Solve −np − 80 < 60 for n. Show your work. (4 points)
Part B: Solve 2a − 5d = 30 for d. Show your work. (6 points)
Answer:
Part A ⇒ n>-140/p and p≠0
Part B. ⇒ d=-30-2a/5
Step-by-step explanation:
Part A. -np-80<60
First, add by 80 both sides of equation.
-np-80+80<60+80
Simplify.
60+80=140
-np<140
Then, multiply by -1 both sides of equation.
(-np)(-1)>140(-1)
Simplify.
np>-140
Divide by p both sides of equation.
np/p>-140/p; p≠0
Simplify to find the answer.
n>-140/p; p≠0 is the correct answer from part a.
___________________________________
Part B. 2a-5d=30
First add by 2a from both sides of equation.
2a-5d+2a=30+2a
Then, simplify.
-5d=30-2a
Divide by -5 from both sides of equation.
-5d/-5=30/-5-2a/5
Simplify, to find the answer.
d=-30-2a/5 is the correct answer from part b.
Part A:
For this case we have the following inequality:
[tex]-np-80 <60[/tex]
We add 80 to both sides of the inequality:
[tex]-np <60+80\\-np <140[/tex]
Dividing between -p on both sides, having to change the inequality sign:
[tex]n> - \frac {140} {p}[/tex]
Part B:
For this case we have the following equation:
[tex]2a-5d = 30[/tex]
Subtracting 2a on both sides:
[tex]-5d = 30-2a[/tex]
Dividing between -5 on both sides:
[tex]d = \frac {30-2a} {- 5}\\d = \frac {-30+2a} {5}\\d = - \frac {30} {5} +\frac {2a} {5}\\d = -6+ \frac {2a} {5}[/tex]
Answer:
[tex]n> - \frac {140} {p}\\d = -6+\frac {2a} {5}[/tex]
Question Help For the month of MarchMarch in a certain city, 5757% of the days are cloudycloudy. Also in the month of MarchMarch in the same city, 5555% of the days are cloudycloudy and foggyfoggy. What is the probability that a randomly selected day in MarchMarch will be foggyfoggy if it is cloudycloudy?
Answer: There is probability of 96.4% that a day in March will be foggy if it is a cloudy.
Step-by-step explanation:
Since we have given that
Probability of the days in March are cloudy = 57%
Probability of the cloudy days in March are foggy = 55%
Let A be the event of cloudy days in March.
Let B be the event of foggy days in March.
So, here,
P(A) = 0.57
P(A∩B) = 0.55
We need to find the probability that days are foggy given that it is cloudy.
We would use "Conditional probability":
[tex]P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.55}{0.57}=0.964=96.4\%[/tex]
Hence, There is probability of 96.4% that a day in March will be foggy if it is a cloudy.
What is the domain of the function y = ^3 sqrt x ??
Answer:
-∞ < x < ∞
Explanation:
x³ is the inverse of ∛x and x³ has range of all real numbers and is one to one function, so its inverse will have domain of all real numbers.
Answer:
Option 1 negative (-) infinity < X < infinity
Step-by-step explanation:
A box contains 1 plain pencil and 4 pens. A second box contains 5 color pencils and 5 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
Write your answer as a fraction in simplest form.
1 pencil and 4 pens = 5 total
Picking the pencil would be 1/5 ( 1 pencil out of 5 total items)
5 color pencils + 5 crayons = 10 total items.
Picking a color pencil would be 5/10 which reduces to 1/2
To find the probability of both happening, multiply them together:
1/5 x 1/2 = 1/10
The probability is 1/10
If a dart was thrown randomly at the dart board shown below, what is the probability that it would land between the outer circle and the middle circle? The radius of the bulls eye is 2 cm, the radius of the middle circle is 8 cm, and the radius of the outer circle is 14 cm
A.68%
B.67%
C.14%
D.75%
Answer: B) 67%
Step-by-step explanation:
Find the Area of the Bullseye and Middle ring
A = π r²
A (inside) = π(8)² = 64π
Find the Area of the entire Target
A (target) = π (14)² = 196π
Find the Area of the Outer ring
A (outer ring) = A (target) - A(inside)
= 196 π - 64π
= 132 π
The last step is to find the probability of landing on the outer ring:
[tex]P=\dfrac{success (area\ of\ outer\ ring)}{total\ possible\ outcomes(area\ of\ target)}=\dfrac{132\pi}{196\pi}=0.673=\large\boxed{67\%}[/tex]
Answer:
67%
Step-by-step explanation:
A motorboat travels 180 km in 3 hours going upstream and 504 in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answer:
Speed of boat x = 84 km/hr
Speed of current = 12 km/hr
Step-by-step explanation:
Let 'x' be the speed of boat and 'y' be the speed of still water
Upstream speed = x - y and
Downstream speed = x + y
It is given that, A motorboat travels 180 km in 3 hours going upstream and 504 in 6 hours going downstream
Upstream speed = x - y = 180/3 = 60 km/hr
Downstream speed = x + y = 504/6 = 84 km/hr
To find the value of x and y
x + y = 84 ----(1)
x - y = 60 ----(2)
(1) + (2) ⇒
x + y = 84 ----(1)
x - y = 60 ----(2)
2x + 0 = 144
x = 144/2 = 72
x + y = 84
y = 84 - 72 = 12
Therefore speed of boat x = 84 km/hr
Speed of current = 12 km/hr
Suppose we wanted to differentiate the function h(x)= (5 - 2 x^6)^3 +1/(5 - 2 x^6) using the chain rule, writing the function h (x) as the composite function h(x)= f(g(x)). Identify the functions f (x) and g (x). f (x) = g (x) = Calculate the derivatives of these two functions f '(x) = g '(x) = Now calculate the derivative of h (x) using the chain rule
[tex]h(x)=(5-2x^6)^3+\dfrac1{5-2x^6}[/tex]
Let [tex]g(x)=5-2x^6[/tex] and [tex]f(x)=x^3+\dfrac1x[/tex]. Then [tex]h(x)=f(g(x))[/tex].
Set [tex]u=5-2x^6[/tex]. By the chain rule,
[tex]\dfrac{\mathrm dh}{\mathrm dx}=\dfrac{\mathrm dh}{\mathrm du}\cdot\dfrac{\mathrm du}{\mathrm dx}[/tex]
Since [tex]h(u)=u^3+\dfrac1u[/tex] and [tex]u(x)=5-2x^6[/tex], we have
[tex]\dfrac{\mathrm dh}{\mathrm du}=3u^2-\dfrac1{u^2}[/tex]
[tex]\dfrac{\mathrm du}{\mathrm dx}=-12x^5[/tex]
Then
[tex]\dfrac{\mathrm dh}{\mathrm dx}=\left(3u^2-\dfrac1{u^2}\right)(-12x^5)=\boxed{-12x^5\left(3(5-2x^6)^2-\dfrac1{(5-2x^6)^2}\right)}[/tex]
which we could rewrite slightly as
[tex]\dfrac{\mathrm dh}{\mathrm dx}=-\dfrac{12x^5(3(5-2x^6)^4-1)}{(5-2x^6)^2}[/tex]
To differentiate the given function using the chain rule, we need to identify the functions f(x) and g(x), then calculate their derivatives. Once we have the derivatives, we can apply the chain rule to find the derivative of the composite function h(x).
Explanation:Chain Rule
To differentiate the function h(x) = (5 - 2x^6)³ + 1/(5 - 2x^6) using the chain rule, we can write it as the composite function h(x) = f(g(x)).
Let's identify the functions f(x) and g(x):
f(x) = x³, g(x) = (5 - 2x^6)
Next, let's calculate the derivatives of f(x) and g(x):
f'(x) = 3x², g'(x) = -12x^5
Finally, we can apply the chain rule to differentiate h(x):
h'(x) = f'(g(x)) * g'(x) = (3(5 - 2x^6)²) * (-12x^5)
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In a clinical trial of a cholesterol drug, 374 subjects were given a placebo, and 21% of them developed headaches. For such randomly selected groups of 374 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches. The value of n is __________. (Do not round.) The value of p is __________. (Type an integer or a decimal. Do not round.) The value of q is __________. (Type an integer or a decimal. Do not round.)
Answer: The value of n is 374. The value of p is 0.21. The value of q is 0.79.
Step-by-step explanation:
Given : In a clinical trial of a cholesterol drug, 374 subjects were given a placebo, and 21% of them developed headaches.
∴ Sample size : [tex]n=374[/tex]
The probability that cholesterol drug developed headaches :[tex]p=0.21[/tex]
Then , the probability that cholesterol drug did not develop headaches :[tex]q=1-p=1-0.21=0.79[/tex]
Hence, The value of n is 374.
The value of p is 0.21.
The value of q is 0.79.
Graph the solution set of the system of inequalities or indicate that the system has no solution.
y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1
Answer:
the graph is shown below
Step-by-step explanation:
The solution region is that quadruply-shaded area above the line y=-2 and to the left of the line x=1. It is further bounded above by the line y = -1/2x +3.5.
How many collections of six positive, odd integers have a sum of 18? Note that 1 + 1 + 1 + 3 + 3 + 9 and 9 + 1 + 3 + 1 + 3 + 1 are considered to be the same collection.
Answer:
11
Step-by-step explanation:
Suitable software can generate these collections. They are ...
{13,1,1,1,1,1}, {11,3,1,1,1,1}, {9,5,1,1,1,1}, {9,3,3,1,1,1},
{7,7,1,1,1,1}, {7,5,3,1,1,1}, {7,3,3,3,1,1}, {5,5,5,1,1,1},
{5,5,3,3,1,1}, {5,3,3,3,3,1}, {3,3,3,3,3,3}}
The number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]
[tex]\[2(k_1 + k_2 + k_3 + k_4 + k_5 + k_6) + 6 = 18\]\[k_1 + k_2 + k_3 + k_4 + k_5 + k_6 = 6\][/tex]
Here are the possible combinations of non-negative integers (up to permutations) that sum to 6:
[tex]1. \( (6, 0, 0, 0, 0, 0) \)2. \( (5, 1, 0, 0, 0, 0) \)3. \( (4, 2, 0, 0, 0, 0) \)4. \( (4, 1, 1, 0, 0, 0) \)5. \( (3, 3, 0, 0, 0, 0) \)6. \( (3, 2, 1, 0, 0, 0) \)7. \( (3, 1, 1, 1, 0, 0) \)8. \( (2, 2, 2, 0, 0, 0) \)9. \( (2, 2, 1, 1, 0, 0) \)10. \( (2, 1, 1, 1, 1, 0) \)11. \( (1, 1, 1, 1, 1, 1) \)[/tex]
Now let's map these back to the odd integers using [tex]\(a_i = 2k_i + 1\):[/tex]
[tex]1. \( (13, 1, 1, 1, 1, 1) \)2. \( (11, 3, 1, 1, 1, 1) \)3. \( (9, 5, 1, 1, 1, 1) \)4. \( (9, 3, 3, 1, 1, 1) \)5. \( (7, 7, 1, 1, 1, 1) \)6. \( (7, 5, 3, 1, 1, 1) \)7. \( (7, 3, 3, 3, 1, 1) \)8. \( (5, 5, 5, 1, 1, 1) \)9. \( (5, 5, 3, 3, 1, 1) \)10. \( (5, 3, 3, 3, 3, 1) \)11. \( (3, 3, 3, 3, 3, 3) \)[/tex]
These are all distinct collections (up to permutations) of positive odd integers that sum to 18.
Thus, the number of distinct collections of six positive odd integers that sum to 18 is indeed:[tex]\[\boxed{11}\][/tex]
The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose we select a sample of 40 tires and use a simulator to determine the tread life. What is the likelihood of finding that the sample mean is between 59,050 and 60,950?
Answer: 0.8664
Step-by-step explanation:
Given : Mean : [tex]\mu = 60,000\text{ miles}[/tex]
Standard deviation : [tex]\sigma = 4,000\text{ miles}[/tex]
Sample size : [tex]n=40[/tex]
The formula to calculate the z-score :-
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x= 59,050
[tex]z=\dfrac{59050-60000}{\dfrac{4000}{\sqrt{40}}}\approx-1.50[/tex]
For x= 60,950
[tex]z=\dfrac{60950-60000}{\dfrac{4000}{\sqrt{40}}}\approx1.50[/tex]
The P-value : [tex]P(-1.5<z<1.5)=P(z<1.5)-P(z<-1.5)[/tex]
[tex]=0.9331927-0.0668072=0.8663855\approx0.8664[/tex]
Hence, the likelihood of finding that the sample mean is between 59,050 and 60,950=0.8664
The likelihood of finding that the sample mean is between 59,050 and 60,950 miles, according to the given normal distribution, is approximately 86.64%.
Explanation:To solve this problem, we consider that the population mean is 60,000 and the standard deviation is 4,000. If we choose a sample of 40 tires, the standard deviation of the sample mean (standard error) is the standard deviation divided by the square root of the sample size (σ/√n).
This gives us 4,000/√40 = 633. The z-scores for the lower and upper bounds of our interval (59,050 and 60,950) are calculated by subtracting the population mean from these values, and dividing by the standard error. For 59,050: (59,050 - 60,000)/633 = -1.5 and for 60,950: (60,950 - 60,000)/633 = 1.5.
Using standard normal distribution tables, we know that the probability associated with a z-value of 1.5 is 0.9332. Since the normal distribution is symmetric, the probability associated with -1.5 is also 0.9332. Therefore, the probability that the sample mean lies between 59,050 and 60,950 is 0.9332 - (1 - 0.9332) = 0.8664 or approximately 86.64%.
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Can I get these solved so I will have the points to mark them on a graph?
Y = -2X + 2
X + 3Y = -4
Answer:
points on the first line: (0, 2), (1, 0)points on the second line: (-4, 0), (-7, 1)Step-by-step explanation:
For equations like these, where the coefficient of one of the variables is 1, it is convenient to choose values for the other variable. Values of 0 and 1 are usually easy to work with.
In the first equation, ...
for x=0, y = 2 . . . . . . . . . point (0, 2)
for x=1, y = -2+2 = 0 . . . point (1, 0)
In the second equation, ...
for y=0, x = -4 . . . . . . . . . point (-4, 0)
for y=1, x +3 = -4, so x = -7 . . . . point (-7, 1)
Line m is parallel to line n. The measure of angle 3 is 86. What is the
measure of angle 5?
OA) 86
OB) 104°
OC) 94°
OD) 75
(Kinda hard to read sorry)
Answer:
C.94
Step-by-step explanation:
The alternate interior angle of angle c is angle 6. So from there you just subtract the 84 from the 180 to get the 94 degrees.
Lines a and b are parallel. Line c is perpendicular to both line a and line b. Which statement about lines a, b, and c is NOT true?
Line a and line b have the same slope.
The sum of the slopes of line b and line c is 0.
The product of the slopes of line c and line b is −1.
The product of the slopes of line a and line c is −1.
m + (-1/m) ≠ 0
⇒ The sum of the slopes of line b and line c is 0.
⇒ False ⇒ NOT true
Answer:
The sum of the slopes of line b and line c is 0.
Step-by-step explanation:
Remember that the product of the slopes of two parallel lines is -1, so in order to be -1 you have to multiply M*-1/m=-1 so since to add them up you would do it like this m+(-1/m) taht wouldn´t get as result 0, so that would be the option that is not correct, remember that parallel lines have the same slope, so that also eliminates all of the other options.