Answer:
r55
Step-by-step explanation:
all this energy came from the fission of 235U, which releases 200 MeV per fission event. Assume that all fission energy is converted into electrical energy. Part A How ma
Desmond wants to sell his car that he paid $8,000 for 2 years ago. The car depreciated, or decreased in value, at a constant rate each month over a 2-year period. If x represents the monthly depreciation amount, which expression shows how much Desmond can sell his car for today? \
8,000 + 24x
8,000 - 24x
8,000 + 2x
8,000 - 2x
Answer:
8,000-24x
Step-by-step explanation:
Let
y ----> depreciated value of the car
x---> rate of depreciation
t ----> the time in months
we know that
The linear equation that represent this situation is
y=8,000-xt
For
t=2 years=2*12=24 months
substitute
y=8,,000-x(24)
y=8,000-24x
Find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28. Round your answer to four decimal places, if necessary.
Answer:
The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
Step-by-step explanation:
We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.
The standard normal table represents the area under the curve.
[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex] .....(1)
According to the standard normal table, we get
[tex]P(z<-2.94)=0.0016[/tex]
[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]
Substitute these values in equation (1).
[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]
Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 is 0.9903 square units.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be
The standard normal table represents the area under the curve.
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1
According to the standard normal table, we have
[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]
Substitute these values in equation 1, we have
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]
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Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $450 for the coverage they need. Their insurance company offers a discount of 6 percent if they install dead-bolt locks on all exterior doors. The couple can also receive a discount of 2 percent if they install smoke detectors on each floor. They have contacted a locksmith who will provide and install dead-bolt locks on the two exterior doors for $50 each. At the local hardware store, smoke detectors cost $7 each, and the new house has two floors. Dave and Ellen can install them themselves. a. What discount will Dave and Ellen receive if they install the dead-bolt locks? Annual discount for deadbolts b. What discount will Dave and Ellen receive if they install smoke detectors? Annual discount for smoke detectors
Dave and Ellen could annually save $27 by installing dead-bolts and $9 by installing smoke detectors. This amounts to a significant discount on their homeowner's insurance premium.
Explanation:Dave and Ellen's annual homeowner's insurance premium is $450. If they install dead-bolts on all the exterior doors, they would receive a 6 percent discount, while smoke detector installations would fetch them a 2 percent discount. Let's calculate these discounts:
A. Dead-bolts discount: 6 percent of $450 translates to $(450*(6/100)) which equals $27.
B. Smoke detectors discount: 2 percent of $450would be $(450*(2/100)) that equals $9.
To summarize, the couple could annualy save $27 by installing dead-bolts and $9 by installing smoke detectors, which is a substantial reduction on the insurance premium.
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Dave and Ellen can save $27 annually by installing dead-bolt locks and $9 annually by installing smoke detectors. Total savings from both installations would be $36 annually.
Let's break down the problem step by step to calculate the discounts that Dave and Ellen will receive if they install dead-bolt locks and smoke detectors.
Part (a): Discount for Dead-Bolt Locks
1. Annual premium: $450
2. Discount for dead-bolt locks: 6%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the dead-bolt locks:
Discount amount for dead-bolt locks = 450 × [tex]\frac{6}{100} \][/tex]
Discount amount for dead-bolt locks = 450 × 0.06
Discount amount for dead-bolt locks = 27
Thus, Dave and Ellen will receive an annual discount of $27 if they install dead-bolt locks on all exterior doors.
Part (b): Discount for Smoke Detectors
1. Annual premium: $450
2. Discount for smoke detectors: 2%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the smoke detectors:
Discount amount for smoke detectors} = 450 × [tex]\frac{2}{100}[/tex]
Discount amount for smoke detectors} = 450 × 0.02
Discount amount for smoke detectors} = 9
Thus, Dave and Ellen will receive an annual discount of $9 if they install smoke detectors on each floor of their house.
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 65%
pure fruit juice?
Answer:
First type of fruit drinks: 48 pints
Second type of fruit drinks: 32 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
[tex]A + B = 80[/tex]
Then the total amount of pure fruit juice in the mixture will be:
[tex]0.55A + 0.8B = 0.65 * 80[/tex]
[tex]0.55A + 0.8B = 52[/tex]
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
[tex]-0.8A -0.8B = -0.8*80[/tex]
[tex]-0.8A -0.8B = -64[/tex]
[tex]-0.8A -0.8B = -64[/tex]
+
[tex]0.55A + 0.8B = 52[/tex]
--------------------------------------
[tex]-0.25A = -12[/tex]
[tex]A = \frac{-12}{-0.25}[/tex]
[tex]A = 48\ pints[/tex]
We substitute the value of A into one of the two equations and solve for B.
[tex]48 + B = 80[/tex]
[tex]B = 32\ pints[/tex]
To create an 80-pint batch of 65% pure fruit juice, the Royal Fruit Company needs to solve two equations representing the volume and percent mixture of the two juices. These equations can be solved simultaneously to find the required volumes of each juice.
Explanation:The subject of this question falls under Mathematics, particularly dealing with proportions and algebra. Given that the first type of juice is 55% pure fruit and the second type is 80% pure fruit, we can define our variables: let's denote X as the volume of the first type of drink and Y as the volume of the second one. We know that the total volume is 80 pints, so we have our first equation: X + Y = 80. The second equation derives from the percentage of fruit juice: 0.55X + 0.80Y = 0.65*80.
Now we can solve these two equations to find the volumes of X and Y. The solution to these equations will provide us with the volume needed from each of the two types of juice to achieve a 65% pure fruit juice drink.
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Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Final answer:
Lester Hollar can assess the impact of the fitness program on absenteeism by conducting a paired samples t-test at a 0.05 significance level. If the p-value is less than 0.05, the program effectively reduced absences; otherwise, there is insufficient evidence to conclude its effectiveness.
Explanation:
Evaluating the Exercise Program’s Impact on Employee Absenteeism
Lester Hollar wishes to assess if the company’s fitness program led to a decline in employee absences. With a sample of eight participants, he analyzed absenteeism before and after the program’s implementation. To determine if absences have decreased, a hypothesis test at the 0.05 significance level (alpha) is conducted.
To evaluate the change in absences, two sets of absenteeism data are compared using a statistical test, such as the paired samples t-test. This test examines if the mean difference in absences before and after the program is statistically significant. If the p-value obtained from the test is less than the significance level of 0.05, the null hypothesis (no change in absences) would be rejected, suggesting that the exercise program was effective in reducing absences.
If Lester Hollar finds a p-value greater than 0.05, he would not reject the null hypothesis, indicating that there isn’t sufficient evidence to conclude the program's impact. It’s also important to estimate the p-value precisely as it gives a measure of the strength of evidence against the null hypothesis. However, without the specific data, we cannot calculate the p-value or make a definitive conclusion here.
A probability experiment is conducted in which the sample space of the experiment is S={7,8,9,10,11,12,13,14,15,16,17,18}, event F={7,8,9,10,11,12}, and event G={11,12,13,14}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
Answer:
F or G = {7,8,9,10,11,12,13,14}
n(F or G) = 8
n(S) = 12
By counting the no. of outcome
P(F or G) = n(F or G) / n(S)
P(F or G) = 8 /12
P(F or G) = 2/3
By using the general addition rule
P(F or G) = P(F) + P(G) - P(F and G)
= 6/12 + 4/12 - 2/12
= 2/3
Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?
Answer:
Function which represents the product of these two numbers is:
(23+x)(28+2x)
Step-by-step explanation:
The first number is the sum of 23 and x
i.e. First number=23+x
The second number is 18 less than two times the first number.
i.e. Second number=2(23+x)-18
= 46+2x-18
= 28+2x
Product of the two numbers=(23+x)(28+2x)
Hence, function which represents the product of these two numbers is:
(23+x)(28+2x)
The window shown is the shape of a semicircle with a radius of 6 feet. The distance from F to E is 3 feet and the measure of = 45°. Find the area of the glass in region BCIH, rounded to the nearest square foot.
Answer:
The area of the glass in region BCIH is 11 to the nearest feet²
Step-by-step explanation:
* Lets explain the figure
- The window is a semicircle with center G and radius 6 feet
- There is a small semicircle with center G and radius GF
∵ GE is 6 feet and EF is 3 feet
∵ GE = GF + FE
∴ 6 = GF + 3 ⇒ subtract 3 from both sides
∴ 3 = GF
∴ The radius of the small semicircle is 3 feet
∵ m∠BGC = 45°
- The area of sector BGC is part of the area of the semicircle
∵ The area of semi-circle is 1/2 π r²
∵ The measure of the central angle of the semicircle is 180°
∵ The measure of the central angle of the sector BGC is 45°
∴ The sector = 45°/180° = 1/4 of the semi-circle
∴ The area of the sector is 1/4 the area of the semicircle
∵ The area of the semicircle = 1/2 π r²
∵ r = 6 feet
∴ The area of the semicircle = 1/2 π (6)² = 1/2 π (36) = 18 π feet²
∴ Area of the sector = 1/4 (18 π) = 4.5 π feet²
- The small sector HGI has the same central angle of the sector BGC
∴ The area of the sector HGI is 1/4 The area of the small semicircle
∵ The area of the small semicircle = 1/2 π r²
∵ r = 3 feet
∴ The area of the small semicircle = 1/2 π (3)² = 1/2 π (9) = 4.5 π feet²
∴ Area of the sector HGI= 1/4 (4.5 π) = 1.125 π feet²
- The area of the glass in region BCIH is the difference between the
area of sector BGC and the area of the sector HGI
∴ The area of the glass in region BCIH = 4.5 π - 1.125 π ≅ 11 feet²
Answer:
11 feet to the nearest square foot.
Step-by-step explanation:
The area of sector BCG
= 45/180 * 1/2 π r^2
= 1/4 * 1/2 π r^2
= 1/8 * π * 6^2
= 4.5 π ft^2.
The radius of the inner semicircle is 6 - 3 = 3 feet.
The area of sector HIG = 1/4 * 1/2 π 3^2
= 1.125 π ft^2.
So the area of BCIH
= area of BCG - area HIG
= 4.5 π - 1.125 π
= 3.375 π
= 10.6 square feet.
2. An investment company pays 9% compounded semiannually. You want to have $8,000 in the future. How much should you deposit now to have that money 5 years from now?
Answer:
$5151.42
Step-by-step explanation:
The formula you need is
[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]
where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings per year, and t is time in years. The info we have is
A(t) = 8000
P = ?
r = .09
t = 5
Filling in we have
[tex]8000=P(1+\frac{.09}{2})^{(2)(5)}[/tex]
Simplifying a bit and we have[tex]8000=P(1+.045)^{10}[/tex]
Now we will add inside the parenthesis and raise 1.045 to the 10th power to get
8000 = P(1.552969422)
Divide away the 155... on both sides to solve for P.
P = $5151.42
Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches. The ratio is (Type an integer or a simplified fraction)
Answer: The ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
Step-by-step explanation:
Since we have given that
Radius of first sphere = 5 inches
Radius of second sphere = 10 inches
We need to find the ratio of volume of first sphere to volume of second sphere:
As we know the formula for "Volume of sphere ":
[tex]Volume=\dfrac{4}{3}\pi r^3[/tex]
So, it becomes,
Ratio of first volume to second volume is given by
[tex]\dfrac{4}{3}\pi (5)^3:\dfrac{4}{3}\pi (10)^3\\\\=5^3:10^3\\\\=125:1000\\\\=1:8[/tex]
Hence, the ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
The ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches is 1/8.
Explanation:To find the ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Let's calculate the volumes of the two spheres:
For the sphere with a radius of 5 inches:
V1 = (4/3)π(5)³ = (4/3)π(125) = 500π inches³
For the sphere with a radius of 10 inches:
V2 = (4/3)π(10)³ = (4/3)π(1000) = 4000π inches³
Therefore, the ratio of the two volumes is:
R = V1/V2 = (500π)/(4000π) = 1/8
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The average annual salary for employees in a store is $50,000. It is given that the population standard deviation is $4,000. Suppose that a random sample of 70 employees will be selected from the population.What is the value of the standard error of the average annual salary? Round your answer to the nearest integer.
Answer: 478
Step-by-step explanation:
The formula to calculate the standard error of the population mean is given by :-
[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\sigma[/tex] is the standard deviation and 'n' is the sample size.
Given: Mean : [tex]\mu=$\50,000[/tex]
Standard deviation : [tex]\sigma= $\4,000[/tex]
Sample size : [tex]n=70[/tex]
Now, the value of the standard error of the average annual salary is given by :-
[tex]S.E.=\dfrac{50000}{\sqrt{70}}=478.091443734\approx478[/tex]
Hence, the standard error of the average annual salary = 478
The value of the standard error of the average annual salary is calculated using the formula SE = population standard deviation / [tex]\sqrt{sample size}[/tex] ,which for a population standard deviation of $4,000 and a sample size of 70 employees, comes out to approximately $478.
To calculate the standard error of the average annual salary, you'd use the formula for the standard error of the mean when you know the population standard deviation: SE = σ /[tex]\sqrt{n}[/tex], where σ is the population standard deviation and n is the sample size.
In this case, the population standard deviation σ is $4,000, and the sample size n is 70 employees. Using the formula, we get SE = 4000 / [tex]\sqrt{70}[/tex], which will give us the standard error of the average annual salary.
Performing the calculation: SE = 4000 / [tex]\sqrt{70}[/tex] ≈ 4000 / 8.367 = 478.29, which when rounded to the nearest integer is $478. Therefore, the value of the standard error of the average annual salary is approximately $478.
Create a question with this scenario you could ask that could be answered only by graphing or using logarithm.
David estimated he had about 20 fish in his pond. A year later, there were about 1.5 times as many fish. The year after that, the number of fish increased by a factor of 1.5 again. The number of fish is modeled by f(x)=20(1.5)^x.
Answer:
After how many years is the fish population 100?
x=3.97 years
Step-by-step explanation:
The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation
[tex]f (x) = 20 (1.5) ^ x[/tex]
Where x represents the number of years elapsed f(x) represents the amount of fish.
Given this situation, the following question could be posed
After how many years is the fish population 100?
So we do [tex]f (x) = 100[/tex] and solve for the variable x
[tex]100 = 20 (1.5) ^ x\\\\\frac{100}{20} = (1.5)^x\\\\ 5= (1.5)^x\\\\log_{1.5}(5) = log_{1.5}(1.5)^x\\\\log_{1.5}(5) = x\\\\x =log_{1.5}(5)\\\\x=3.97\ years[/tex]
Observe the solution in the attached graph
A survey asked 816 college freshmen whether they had been to a movie or eaten in a restaurant during the past week. The following information was obtained: 385 freshmen had been to neither a movie nor a restaurant, and 268 had been to a movie. If 96 of those who had been to a movie had not been to a restaurant, how many of the surveyed freshmen had been to the following?
Answer:
the answer is 90
Step-by-step explanation:
296-96=90
32a³b²
_____
8ab²
Simplify the following expression.
Answer:
[tex]4a^{2}[/tex]
Step-by-step explanation:
We need to simplify the following expression:
[tex]y=\frac{32a^{3}b^{2}}{8ab^{2}}[/tex]
We know that: [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]. Applying this rule, we have that:
[tex]y = \frac{32a^{3}b^{2}}{8ab^{2}} = 4a^{3-1}b^{2-2} = 4a^{2}[/tex]
Then, the solution is: [tex]4a^{2}[/tex]
Klassen Toy Company, Inc., assembles two parts (parts 1 and 2): Part 1 is first processed at workstation A for 10 minutes per unit and then processed at workstation B for 20 minutes per unit. Part 2 is simultaneously processed at workstation C for 30 minutes per unit. Work stations B and C feed the parts to an assembler at workstation D, where the two parts are assembled. The time at workstation D is 15 minutes. a) The bottleneck of this process is workstation D , at 4 minutes per unit (enter your response as a whole number).
Answer:
The bottleneck of this process is Workstation C, at 30 minutes per unit.
Step-by-step explanation:
The throughput of each workstation is ...
A: 6 per hourB: 3 per hourC: 2 per hourD: 4 per hourSince each process must be executed once per finished product, the bottleneck is the station with the lowest throughput. It is clearly Workstation C.
The bottleneck of this process is workstation D, where the time per unit is 15 minutes.
Explanation:The bottleneck of this process is workstation D, where the time per unit is 15 minutes. This means that workstation D takes the longest time to complete one unit compared to other workstations. The bottleneck determines the maximum output rate of the entire process, as the other workstations cannot work faster than the slowest one.
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At the local pet store, zebra fish cost $1.80 each and neon tetras cost $2.00each. Of Sameer bought 14 is for a total cost of $26.80, not including tax, how many of each type of fish did he buy?
the center of a circle represent by the equation (x+9)^2+(y-6)^2=10^2 is___. options.... (-9,6), (-6,9), (6,-9) ,(9,-6)
Answer:
(-9, 6)
Step-by-step explanation:
It's all about pattern matching.
A circle centered at (h, k) with radius r has the equation ...
(x -h)^2 + (y -k)^2 = r^2
Comparing this pattern to the equation you have, you can see that ...
h = -9k = 6r = 10Then the center is (h, k) = (-9, 6).
Answer:
(-9, 6)
Step-by-step explanation:
i took the test
The total annual spending by tourists in a resort city is $450 million. Approximately 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on. Write the geometric series that gives the total amount of spending generated by the $450 million and find the sum of the series.
Answer:
G.P. is, 450, 360, 288, 230.4,......
The sum is 2250.
Step-by-step explanation:
Given,
The first total spending in the resort city = $ 450 million,
Also, 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on.
Thus, there is a G.P. that represents the given situation,
450, 360, 288, 230.4,......
Which is an infinite geometric series having first term, a = 450,
Common ratio, r = 0.8,
Hence, the sum of the series,
[tex]S_n=\frac{a}{1-r}[/tex]
[tex]=\frac{450}{1-0.8}[/tex]
[tex]=\frac{450}{0.2}[/tex]
[tex]=2250[/tex]
(CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20.1 ounces and a standard deviation of 0.3 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces? 0.553 0.748 0.252 0.447
Final answer:
To find the probability of the mean weight of 25 randomly selected ice cream cartons being greater than 20.06 ounces, we can use the Central Limit Theorem. By calculating the standard error, finding the z-score, and using a z-table or calculator, we can determine the probability.
Explanation:
To find the probability that the mean weight of 25 randomly selected ice cream cartons is greater than 20.06 ounces, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution will be approximately normal, as long as the sample size is large enough.
First, we need to find the standard error of the mean (SE). The formula for SE is SE = standard deviation / √(sample size). In this case, the standard deviation is 0.3 ounces and the sample size is 25. So, SE = 0.3 / √25 = 0.06 ounces.
Next, we calculate the z-score, which measures how many standard deviations the mean is from the population mean. The formula for z-score is z = (sample mean - population mean) / standard error. In this case, the sample mean is 20.06 ounces, the population mean is 20.1 ounces, and the standard error is 0.06 ounces. So, z = (20.06 - 20.1) / 0.06 = -0.67.
We can use a z-table or a calculator to find the probability associated with the z-score. From the table or calculator, we find that the probability of getting a z-score greater than -0.67 is approximately 0.748. Therefore, the probability that the mean weight of the 25 ice cream cartons is greater than 20.06 ounces is approximately 0.748.
a ball is shot straight upward. with it's height, in feet, after t seconds given by the function f(t)=-16t^2+192t. Find the average velocity of the ball from t=1 to t=6
ANSWER
[tex]80 {ms}^{ - 1} [/tex]
EXPLANATION
The average velocity of the ball is the rateof displacement over the total time.
The height of the ball, in feet, after t seconds is given by the function:
[tex]f(t)=-16t^2+192t[/tex]
At time t=1, the height of the ball is
[tex]f(1)=-16(1)^2+192(1)[/tex]
[tex]f(1)=-16+192 = 176ft[/tex]
At time t=6, the height of the ball is
[tex]f(6)=-16(6)^2+192(6)[/tex]
[tex]f(6)=-16(36)+192(6)[/tex]
[tex]f(6)=-576+1152 = 576[/tex]
The average velocity
[tex] = \frac{f(6) - f(1)}{6 - 1} [/tex]
[tex]= \frac{576- 176}{6 - 1} [/tex]
[tex]= \frac{400}{5} [/tex]
[tex] = 80 {ms}^{ - 1} [/tex]
Find the area under the curve y =f( x) on [a,b] given f(x)=tan(3x) where a=0 b=pi/12
Answer:
The area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.
Step-by-step explanation:
The given function is
[tex]f(x)=\tan(3x)[/tex]
where a=0 and b=pi/12.
The area under the curve y=f(x) on [a,b] is defined as
[tex]Area=\int_{a}^{b}f(x)dx[/tex]
[tex]Area=\int_{0}^{\frac{\pi}{12}}\tan (3x)dx[/tex]
[tex]Area=\int_{0}^{\frac{\pi}{12}}\frac{\sin (3x)}{\cos (3x)}dx[/tex]
Substitute cos (3x)=t, so
[tex]-3\sin (3x)dx=dt[/tex]
[tex]\sin (3x)dx=-\frac{1}{3}dt[/tex]
[tex]a=\cos (3(0))=1[/tex]
[tex]b=\cos (3(\frac{\pi}{12}))=\frac{1}{\sqrt{2}}[/tex]
[tex]Area=-\frac{1}{3}\int_{1}^{\frac{1}{\sqrt{2}}}\frac{1}{t}dt[/tex]
[tex]Area=-\frac{1}{3}[\ln t]_{1}^{\frac{1}{\sqrt{2}}[/tex]
[tex]Area=-\frac{1}{3}(\ln \frac{1}{\sqrt{2}}-\ln (1))[/tex]
[tex]Area=-\frac{1}{3}(\ln 1-\ln \sqrt{2}-0)[/tex]
[tex]Area=-\frac{1}{3}(-\ln 2^{\frac{1}{2}})[/tex]
[tex]Area=-\frac{1}{3}(-\frac{1}{2}\ln 2)[/tex]
[tex]Area=-\frac{1}{6}\ln 2[/tex]
Therefore the area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.
An ellipse has vertices at (0, #17) and foci at (0, ±15). Write the equation of the ellipse in standard form. Graph the ellipse.
ANSWER
[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]
See attachment for the graph
EXPLANATION
The standard equation of the vertical ellipse with center at the origin is given by
[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]
where
[tex] {a}^{2} \: > \: {b}^{2} [/tex]
The ellipse has its vertices at (0,±17).
This implies that:a=±17 or a²=289
The foci are located at (0,±15).
This implies that:c=±15 or c²=225
We use the following relation to find the value of b²
[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]
[tex] \implies \: 289 - {b}^{2} = 225[/tex]
[tex] - {b}^{2} = 225 - 289[/tex]
[tex] - {b}^{2} = - 64[/tex]
[tex] {b}^{2} = 64[/tex]
We substitute into the formula for the standard equation to get:
[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]
Please. Answer Fast! Use composition to determine if G(x) or H(x) is the inverse of F(x) for the
domain x ≥ 2.
will mark brainliest
Answer:
A. H(x) is an inverse of F(x)
Step-by-step explanation:
The given functions are:
[tex]F(x)=\sqrt{x-2}[/tex]
[tex]G(x)=(x-2)^2[/tex]
[tex]H(x)=x^2+2[/tex]
We compose F(x) and G(x) to get:
[tex](F\circ G)(x)=F(G(x))[/tex]
[tex](F\circ G)(x)=F((x-2)^2)[/tex]
[tex](F\circ G)(x)=\sqrt{(x-2)^2-2}[/tex]
[tex](F\circ G)(x)=\sqrt{x^2-4x+4-2}[/tex]
[tex](F\circ G)(x)=\sqrt{x^2-4x+2}[/tex]
[tex](F\circ G)(x)\ne x[/tex]
Hence G(x) is not an inverse of F(x).
We now compose H(x) and G(x).
[tex](F\circ H)(x)=F(H(x))[/tex]
[tex](F\circ H)(x)=F(x^2+2)[/tex]
[tex](F\circ H)(x)=\sqrt{x^2+2-2}[/tex]
We simplify to get:
[tex](F\circ H)(x)=\sqrt{x^2}[/tex]
[tex](F\circ H)(x)=x[/tex]
Since [tex](F\circ H)(x)=x[/tex], H(x) is an inverse of F(x)
An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the investment is $29220. How much
did he invest at each amount? Use the six-step method.
He invested $_____at 7% and ____at 8%.
Answer:
$70,000 at 7%$304,000 at 8%Step-by-step explanation:
Given:
Total interest earned on two investments is $29,220.
An amount is invested at 7%.
$24,000 more than 4 times that amount is invested at 8%.
Find:
The amount invested at each rate.
Solution:
Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.
Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...
interest on 7% account + interest on 8% account = total interest
0.07x + 0.08(24000+4x) = 29220
0.39x + 1920 = 29220 . . . . . . . . . . . simplify
0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920
x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x
24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%
He invested $70,000 at 7% and $304,000 at 8%.
Check
The answer must satisfy ...
7% interest + 8% interest = 29,220
0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required
_____
Comment on 6-step method
We have tried to hit the highlights. Your steps appear to be ...
Identify the given information (Given)Identify the question you are asked to answer (Find)Identify the useless information in the problem statement (is none)Decide on a strategy. Make a model or drawing. (model equation shown)Solve and show work (Solution)Explain why the answer makes sense (Check)A quality control inspector has drawn a sample of 1414 light bulbs from a recent production lot. If the number of defective bulbs is 22 or more, the lot fails inspection. Suppose 20%20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
Answer: 0.8021
Step-by-step explanation:
The given problem is a binomial distribution problem, where
[tex]n=14,\ p=0.2, q=1-0.2=0.8[/tex]
The formula of binomial distribution is :-
[tex]P(X=r)=^{n}C_{r}p^{r}q^{n-r}[/tex]
The probability that the lot will fail inspection is given by :_
[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\[/tex]
[tex]=1-(^{14}C_{0}(0.2)^{0}(0.8)^{14-0}+^{14}C_{1}(0.2)^{1}(0.8)^{14-1})\\\\=1-((1)(0.8)^{14}+(14)(0.2)(0.8)^{13})\\\\=0.802087907\approx0.8021[/tex]
Hence, the required probability = 0.4365
According to a study, 86% of K-12 schools or districts in a country use digital content such as ebooks, audiobooks, and digital textbooks. Of these 86%, 11 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is nothing.
Answer: Our required probability is 47.3%.
Step-by-step explanation:
Since we have given that
Probability of schools or district in a country use digital content = 86% = 0.86
Probability of schools or district uses digital content as a part of their curriculum out of 86% = [tex]\dfrac{11}{20}[/tex]
So, Probability that a selected school or district uses digital content and uses it as a part of their curriculum is given by
[tex]\dfrac{86}{100}\times \dfrac{11}{20}\\\\=0.86\times 0.55\\\\=0.473\\\\=47.3\%[/tex]
Hence, our required probability is 47.3%.
The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3% and this can be determined by using the given data.
Given :
According to a study, 86% of K-12 schools or districts in a country use digital content such as ebooks, audiobooks, and digital textbooks.Of these 86%, 11 out of 20 use digital content as part of their curriculum.The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is given by:
[tex]=\dfrac{11}{20}\times \dfrac{86}{100}[/tex]
Now, multiply 11 by 86 and also multiply 20 by 100 in the above expression.
[tex]=\dfrac{11\times 86}{20\times 100}[/tex]
SImplify the above expression.
[tex]=\dfrac{946}{2000}[/tex]
= 0.473
So, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3%.
For more information, refer to the link given below:
https://brainly.com/question/21586810
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to: = > (a) -a x + 4x12 4x1x38x231; (b) 3-33 + 4xrj224x3122a3= 1; (c) 4a7 2x1 2x1X36x2a3 = 1. 2. Solve the following systems of differential equations using the matrix exponential technique 3x 4 (a) x(0) = 5, y(0) = 1; 4x-3y 3.x y(0) = 9, y(0) = 3; -2x 6x2y
Answer:
678
Step-by-step explanation:
How many millimeters are in 4.3 centimeters? How many centimeters are in 57 millimeters? Approximately how many centimeters are in an inch?
Answer:
a) 43
b) 5.7
c) 2.54
Step-by-step explanation:
The metric system is so easy to work with, everything is in base of 10, and all measures use a prefix. Here, we're talking about length, with the main measure being the meter.
1 m = 100 centimeters (centi- = 1/100)
1 m = 1000 millimeters (milli- = 1/1000)
So, for each centimeter, you have 10 millimeters.
a) How many millimeters are in 4.3 centimeters?
1 cm = 10 mm as shown above, so 4.3 cm = 43 mm
b) How many centimeters are in 57 millimeters?
10 mm = 1 cm so, 57 mm = 5.7 cm
c) Approximately how many centimeters are in an inch?
There are approximately 2.54 cm in an inch. No real calculation to make here, it's just a unit conversion between systems, done following a known reference table.
you begin playing a new game called hooville. You are King of Hooville, a city of owls that is located in the treetops near Fords of Beruna. In order to know how much food to produce each year, you must predict the population of Hooville. History shows that the population growth rate of Hooville is 3.5%. The current population of owls is 80,000. Using the monetary growth formula that you used in the Uncle Harold problem, write a new function for the population of hooville. (let n=1.) PLEASE HELP. I HAVE NO IDEA WHAT IM DOING!!
Answer:
Part 1) [tex]y=80,000(1.035)^{x}[/tex]
Part 2) The table in the attached figure
Part 3) The graph in the attached figure
Step-by-step explanation:
Part 1) Find the population function
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
y ----> is the population
x ----> the time in years
a is the initial value (a=80,000 people)
b is the base (b=100%+3.5%=103.5%=1.035)
substitute
[tex]y=80,000(1.035)^{x}[/tex]
Part 2) Construct the table
For x=0 years
substitute in the function equation
[tex]y=80,000(1.035)^{0}=80,000\ people[/tex]
For x=10 years
substitute in the function equation
[tex]y=80,000(1.035)^{10}=112.848\ people[/tex]
For x=20 years
substitute in the function equation
[tex]y=80,000(1.035)^{20}=159,183\ people[/tex]
For x=40 years
substitute in the function equation
[tex]y=80,000(1.035)^{40}=316,741\ people[/tex]
For x=50 years
substitute in the function equation
[tex]y=80,000(1.035)^{50}=446,794\ people[/tex]
For x=75 years
substitute in the function equation
[tex]y=80,000(1.035)^{75}=1,055,884\ people[/tex]
For x=100 years
substitute in the function equation
[tex]y=80,000(1.035)^{100}=2,495,313\ people[/tex]
Part 3) The graph in the attached figure
An experimenter has prepared a drug dosage level that she claims will induce sleep for 80% of people suffering from insomnia. After examining the dosage, we feel that her claims regarding the effectiveness of the dosage are inflated. In an attempt to disprove her claim, we administer her prescribed dosage to 20 insomniacs and we observe Y , the number for whom the drug dose induces sleep. We wish to test the hypothesis H0 : p = .8 versus the alternative, Ha : p < .8. Assume that the rejection region {y ≤ 12} is used.
Answer:
cool
Step-by-step explanation: