Answer:
y = x^4 - 2x^2 + 3
y' = 4x^3 - 4x
y'' = 12x^2 - 4
To find local minimum and local maximum, we find solution of y' = 0
=> 4x^3 - 4x = 0
<=>4x(x - 1)(x + 1) = 0
<=> x = 0,
substitute into y => y(0) = 0 - 0 + 3 = 3 => A(0, 3)
substitute into y'' => y''(0) = 0 - 4 = -4 < 0 => A(0, 3) is a maximal
<=> x = 1,
substitute into y => y(1) = 1 - 2 + 3 = 2 => B(1, 2)
substitute into y'' => y''(1) = 12 - 4 = 8 > 0 => B(1, 2) is a minimal
<=> x = -1,
substitute into y => y(-1) = 1 - 2 + 3 = 2 => C(-1, 2)
substitute into y'' => y''(-1) = 12 - 4 = 8 > 0 => C(-1, 2) is a minimal
Hope this helps!
:)
Factor 64b-16c to identify the equivalent expressions. *
Answer:
The factored form of this would be 16(4b - c)
Step-by-step explanation:
In order to find this, look for the greatest common factor of 16 and 64. You can do this by listing out their factors. Once this is done and we identify 16 as the GCF, we can then put that on the outside of the parenthesis and divide all the terms inside by that number.
Suppose a classroom teacher wants to measure whether offering candy as a reward will increase the number of times that a student raises his/her hand to answer a question in class. A study yields the following data.Row C1 C21 9 122 7 83 15 144 10 115 8 7If column 1 is the number of times that a student raised their hand to answer a question before the candy reward was implemented, and column 2 is the number of times that the same students raised their hands to answer questions after the candy reward was implemented, which of the following is the appropriate inference method to analyze these data?A) Inference for regressionB) Two independent samples C) Matched pairs
Answer:
C) Matched pairs
Step-by-step explanation:
Matched samples (also called matched pairs, paired samples or dependent samples) is a type of sampling that involves pairing participants that share every characteristic except for the one under study. The paired participants could be same individuals studied at different time such as:
The study of same participants before and after an interference. The study of the same participants at two different interference.What is the value of the y in te equation y-13=57
Answer:
Y=70
Step-by-step explanation:To find Y add 57 + 13. To check your answer do 70-13=57.
a box contains 5 green pencils and 7 yellow pencils. two pencils are chosen at random from the box without replacement. what is the probability they are different colors
Answer:
A box contains 5 green pencils and 7 yellow pencils.
Two pencils are chosen at random from the box without replacement.
=> There are two cases:
1st pick green & 2nd pick yellow: P = 5/12 x 7/11 = 0.265
1st pick yellow & 2nd pick green: P = 7/12 x 5/11 = 0.265
Add up both cases, the probability they are different colors:
P = 0.265 + 0.265 = 0. 53
Hope this helps!
:)
What is the fourth term in the binomial expansion of (2x – y) 7?
Answer:
[tex] (7C4) (2x)^4 (-y)^{7-4}[/tex]
And replacing we got:
[tex] 35 (2^4) x^4 (-y)^{-3}[/tex]
And then the final term would be:
[tex] -560 x^4 y^3[/tex]
Step-by-step explanation:
For this case we have the following expression:
[tex] (2x-y)^7[/tex]
And we can use the binomial theorem given by:
[tex] (x+y)^n =\sum_{k=0}^n (nCk) x^k y^{n-k}[/tex]
And for this case we want to find the fourth term and using the formula we have:
[tex] (7C4) (2x)^4 (-y)^{7-4}[/tex]
And replacing we got:
[tex] 35 (2^4) x^4 (-y)^{-3}[/tex]
And then the final term would be:
[tex] -560 x^4 y^3[/tex]
An isosceles triangle has a base whose length is 14 centimeters and whose base angle each measure 68
Answer:
I guess you want to find the lenght of the sides and the other angle, so let's do that:
We know that the base has a length of 14 cm.
The two base angles are 68°
First, we can find the other angle knowing that the sum of all interior angles of a triangle must add up to 180°.
2*68° + X = 180°
X = 180° - 2*68° = 44°
Now let's find the length of the sides (that is the same for both sides, as we have an isosceles triangle.
For this we can draw a line for the middle of the base that goes through the top vertex, creating in this way a triangle rectangle.
We know that one of the cathetus will have half of the length of the base, this is 7cm.
the adjacent angle to this cathetus is 68°, now we want to find the hypotenuse of this triangle, we can use the relation:
Cos(A) = adjacent cathetus/hypotenuse:
Cos(68°) = 7cm/H
H = 7cm/cos(68) = 18.7cm
this hypotenuse is equal to the side length of our isosceles triangle, so now we have it fully determined.
what is Evaluate
120 + 5
Answer:
24
Step-by-step explanation:
1: Divide 120 by 5 = 24
Answer: 24
Hope this helps.
Dan drives 140 miles on Monday and 125 km on Tuesday. How many km did he drive in total?
Answer:
365.308 km
Explanation:
If you convert 140 miles into kilometers you get 225.308 km. Then you just have to add 140 and 225.308 together to get your answer. Hope this helped.
Payton cut out two shapes, as shown, that she will later put together to resemble a house.
Answer:
21 Square Units
Step-by-step explanation:
edge 2020
Solve this equation: -72 + 12 - 2.x = 23 + 13.2
Answer:
x =-48.1
Step-by-step explanation:
-72 + 12 - 2.x = 23 + 13.2
Combine like terms
-60 -2x = 36.2
Add 60 to each side
-2x -60+60 = 36.2+60
-2x = 96.2
divide by -2
-2x/-2 = 96.2/-2
x =-48.1
Answer:
[tex] = - 48.1[/tex]
Step-by-step explanation:
[tex] - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is the difference between a low and a high variability
Answer:
Step-by-step explanation:
Variability refers to how spread out a group of data is. Data sets with similar values are said to have little variability, while data sets that have values that are spread out have high variability.
Factor the polynomial below.
4x^2-16
A.
4(x - 2)2
B.
4(x + 2)(x - 2)
C.
4(2 + x)(2 - x)
D.
4(2 - x)2
Answer:
The answer is: B. 4(x+2)(x-2)
Step-by-step explanation:
Just had this on a test, got it right!
samuel earns 3$ an hour less than jack. in 6 hours samuel earns 72$. which equation can be used to find x, the amount, in dollars, jack earns in an hour
Answer:
(x - 3) * 6 = 72
jack earns $ 15 an hour and samuel $12 an hour
Step-by-step explanation:
we know that samuel earns 3 dollars less than jack, let's say that "x" is what jack earns, in addition to this we know that samuel earns a total of 72 dollars in 6 hours, therefore we have to:
(x - 3) * 6 = 72
this would be the equation to determine x, we solve it:
6 * x - 18 = 72
6 * x = 72 + 18
x = 90/6
x = 15
which means that jack earns $ 15 an hour and samuel $12 an hour
100 PTS PLEASE HELP IM BEGGING YOUU
Answer:
3√5 thats the answer i glad yo me helping you
A basketball player has made 60% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight's game he does the following. a) Misses for the first time on his sixth attempt b) Makes his first basket on his fifth shot c) Makes his first basket on one of his first 3 shots a) The probability that in tonight's game the basketball player misses for the first time on his sixth attempt is
Answer:
a) The probability that in tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.
b) The probability that in tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.
c) The probability that in tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.
Step-by-step explanation:
For each shot, there are only two possible outcomes. Either the player makes it, or he does not. The probability of making a shot is independent of other shots. So we use the binomial probability distribution to solve this question.
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 combinations 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.
A basketball player has made 60% of his foul shots during the season.
This means that [tex]p = 0.6[/tex]
a) Misses for the first time on his sixth attempt
Makes the first five, which is P(X = 5) when n = 5.
Misses the sixth, with probability = 1-0.6 = 0.4.
So
[tex]p = 0.4P(X = 5)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]p = 0.4P(X = 5) = 0.4*(C_{5,5}.(0.6)^{5}.(0.4)^{0}) = 0.0311[/tex]
The probability that in tonight's game the basketball player misses for the first time on his sixth attempt is 0.0311 = 3.11%.
b) Makes his first basket on his fifth shot
Misses the first four, which is P(X = 0) when n = 4.
Makes the fifth, with a probability of 0.6.
So
So
[tex]p = 0.6P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]p = 0.6P(X = 0) = 0.6*(C_{4,0}.(0.6)^{0}.(0.4)^{4}) = 0.0154[/tex]
The probability that in tonight's game the basketball player makes his first basket on his fifth shot is 0.0154 = 1.54%.
c) Makes his first basket on one of his first 3 shots
Either he makes his first basket on one of his first 3 shots, or he misses all of them. The sum of these probabilities is decimal 1.
Misses the first three:
P(X = 0) when n = 3. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.6)^{0}.(0.4)^{3} = 0.064[/tex]
Makes on one of his first three:
1 - 0.064 = 0.936
The probability that in tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936 = 93.6%.
Answer:
Step-by-step explanation:
The probability that the basket player made a foul shot is 60% which is 0.60
Then the probability of good shot is 1 - 0.60 = 0.40
P = 0.40
a) the probability that the basket player misses for the first time on his sixth attempt is
P (first time on his sixth attempt) = (1 - P)⁵ (P)
= (1 - 0.4)⁵(0.4)
= (0.6)⁵(0.4)
= 0.07776 * 0.4
= 0.031104
≅ 0.0311
The probability that the basketball player misses for the first time on his sixth attempt is 0.0311
b) P(first basket on his fifth shot) = (1 - P)³ (P)
= (1 - 0.4)⁴(0.4)
= (0.60)⁴(0.4)
= 0.0518
c) The probability of making his first basket in first shot is 0.6
and the probability of making his first basket in second shot is
0.6 * 0.4 = 0.24
the probability of making his first basket in third shot is
0.6 * 0.4² = 0.096
So, the probability that the player makes his first basket on one of his first 3 shots is
= 0.6 + 0.24 + 0.096
= 0.936
Thus, the probability that in tonight's game the basketball player makes his first basket on one of his first 3 shots is 0.936
Marc and Michelle are married and earned salaries this year of $64,000 and $12,000, respectively. In addition to their salaries, they received interest of $350 from municipal bonds and $500 from corporate bonds. Marc contributed $2,500 to an individual retirement account, and Marc paid alimony to a prior spouse in the amount of $1,500. Marc and Michelle have a 10-year-old son, Matthew, who lived with them throughout the entire year. Thus, Marc and Michelle are allowed to claim a $2,000 child tax credit for Matthew. Marc and Michelle paid $6,000 of expenditures that qualify as itemized deductions and they had a total of $3,500 in federal income taxes withheld from their paychecks during the course of the year. What is Marc and Michelle's adjusted gross income?
Answer:
The total amount of deductions Marc and Michelle are going to get is $24750.
The taxable income of Marc and Michelle is $47750.
Further Explanation:
Income Tax: It is the additional charge on an individual’s income which he/she needs to pay to the government. The taxable income is calculated by adding all the incomes and deducting all the deductions which an individual can claim on his/her income.
Compute the total amount of deductions available for Marc and Michelle:
Total Deduction Available
= Higher of Standard Deduction for MJF and Itemized Deduction + Personal and Dependency Exemptions
= Higher of $12600 and $6000 + $12150 ($4050×3)
= $12600 + $12150
=$24750.
Therefore, the total deductions available to Marc and Michelle are $24750.
Gross Income of Marc and Michelle
= Salary of Marc + Salary of Michelle + Interest Earned on Corporate Bonds
= $64000 + $12000 + 500
= $76500.
Total Taxable Income of Marc and Michelle
= Gross Income – Qualified Moving Expenses – Alimony Paid – Total Deductions
= $76500 - $2500 - $1500 - $$24750
= $47750.
Therefore, the total taxable income of Marc and Michelle is $47750.
Learn More:
1. Learn more about the tax on the profit from selling the fixed assets
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2. Learn more about the personal tax
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3. Learn more about the role of money
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Answer details:
Grade: Senior School
Subject: Taxation
Chapter: Income Tax
Keywords: Taxable income, Marc and Michelle, Deductions, salary income, earned, corporate bond interest, interest on municipal bond, standard deductions, US tax brackets.
happy to help ya :)
multiply -x^2(x^2+5x-8)
Answer:
[tex]-x^4-5x^3+8x^2[/tex]
Step-by-step explanation:
[tex]\left(-x^2\right)x^2+\left(-x^2\right)\cdot \:5x+\left(-x^2\right)\left(-8\right)\\-x^2x^2-5x^2x+8x^2\\-x^4-5x^3+8x^2[/tex]
Answer: −x4−5x3+8x2
Step-by-step explanation:
Without graphing, determine the number of solutions of the system. State whether the system is consistent or inconsistent. If the system is consistent, state whether the equations are dependent or independent.
Answer: I cant see the picture right. So im sorry i could not help :(
Step-by-step explanation: IM SOOO SORRY D:
Find the volume of a right circular cone that has a height of 11.7m and a base with a circumference of 9 m.
Answer: Approximately 25.1 m^3
Step-by-step explanation:
The volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. We know the height, but we don't know the radius. Fortunately, we are given the circumference of the base circle.
[tex]C=2\pi r[/tex]
[tex]9=2\pi r[/tex]
[tex]r=\frac{9}{2\pi}[/tex]
Now that we have the r, we can plug it into the volume equation.
[tex]V=\pi r^2\frac{h}{3}[/tex]
[tex]V=\pi (\frac{9}{2\pi } )^2 (\frac{11.7}{3} )[/tex]
After you plug this into the calculator, you get approximately 25.1 m^3.
The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7 comma 539 hours. The population standard deviation is 840 hours. A random sample of 49 light bulbs indicates a sample mean life of 7 comma 359 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7 comma 539 hours question mark b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach?
Answer:
a) Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539
b) [tex]t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5[/tex]
The degrees of freedom are given by:
[tex]df=n-1=49-1=48[/tex]
The p value is given by:
[tex]p_v =P(t_{(48)}<-1.5)=0.07[/tex]
c) [tex]7359-2.01\frac{840}{\sqrt{49}}=7117.8[/tex]
[tex]7359+2.01\frac{840}{\sqrt{49}}=7600.2[/tex]
d) For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval
Step-by-step explanation:
Part a and b
Data given
[tex]\bar X=7359[/tex] represent the sample mean
[tex]\sigma=840[/tex] represent the population standard deviation
[tex]n=49[/tex] sample size
[tex]\mu_o =7539[/tex] represent the value to test
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the mean life is different from 7539 hours, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 7539[/tex]
Alternative hypothesis:[tex]\mu < 7539[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5[/tex]
The degrees of freedom are given by:
[tex]df=n-1=49-1=48[/tex]
The p value is given by:
[tex]p_v =P(t_{(48)}<-1.5)=0.07[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539
Part c
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We can find the critical value using the confidence level given of 95% and using the t distribution with 48 degrees of freedom we got [tex]t_{\alpha/2}=\pm 2.01[/tex]
Now we have everything in order to replace into formula (1):
[tex]7359-2.01\frac{840}{\sqrt{49}}=7117.8[/tex]
[tex]7359+2.01\frac{840}{\sqrt{49}}=7600.2[/tex]
Part d
For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval
In addition to rent, people who live in apartments often have to pay for what?
O A Homeowner's insurance
O B. Property taxes
O c. Utility bills
O D. Repairs to the apartment
Answer:
C
Step-by-step explanation:
When my parents rented a house, they had to pay utility (gas, water, bill) because it really just depends on how much we pay. Homeowner's insurance is not necessary since you don't own the house, property taxes are paid by the leaser, and repairs are usually covered by your security deposit or down payment.
Answer:
Utility bills
Step-by-step explanation:
No homeowners insurance because you are the renter
No property taxes because you don't own the property
Repairs are the responsibility of the landlord
Rewrite the equation by completing the square x^2+2x-3=0
Answer:
( x+1)^2 = 4
Step-by-step explanation:
x^2+2x-3=0
Add 3 to each side
x^2 +2x = 3
Take the coefficient of x
2
Divide by 2
2/2 =1
Square it
1^2 =1
Add to each side
x^2 +2x = 3
x^2 + 2x+1 = 3+1
( x+1)^2 = 4
Take the square root of each side
x+1 = ±2
Subtract 1 from each side
x+1-1 = -1 ±2
x = -1+2 x = -1-2
x =1 x = -3
Which detail supports the author's point that our senses lack precision?
"Some people boast of having a sixth sense..."
"Among our five senses, sight is the most special to us."
"Our .. eyes have no trouble spotting a lone match... across a darkened auditorium."
"Increase it (a sound's volume] by a factor of 2 and you will barely notice."
Answer:
"Some people boast of having a sixth sense..."
Step-by-step explanation:
The author of these statements emphasised that our senses lack precision with the statement - "Some people boast of having a sixth sense..."
This implies that no one of the five senses (smell, touch, taste, hearing, and sight) is being used for an action. Rather an intuitive sixth sense is being used. So the five senses lack precision.
The other options emphasise various senses:
- "Among our five senses, sight is the most special to us." Emphasises sight.is precise
- "Our .. eyes have no trouble spotting a lone match... across a darkened auditorium." Implies sight is precise
- "Increase it (a sound's volume] by a factor of 2 and you will barely notice." Implies precision of hearing. An increase by a factor of 2 is imperceptible
After several years of working, Katy has savings of $100,000. If she invests that $100,000 in a savings fund that adds 5% each year, about how much will her savings account have after 20 years? Ignore compounding and taxes, and assume Katy puts no additional money into savings.
Answer
$200,000
Step-by-step explanation:
She invested $100,000
5% of $100,000 is $5,000.
After 20 years, (5,000 X 20 years) = $100,000
Starting balance of $100,000 + $100,000 = $200,000
The total amount in 20% with simple interest for over 20 years will be $200,00.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year, the principal amount in simple interest remains constant.
As per the given,
Principle amount P =$100000
Rate of interest R = 5%
Time period T = 20 years
Total amount = Principal amount + interest
Total amount = P + PRT/100
Total amount = 100000 + (100000 x 5 x 20)/100
Total amount = $200,000
Hence "The total amount in 20% with simple interest for over 20 years will be $200,00".
For more about simple interests
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In the formula for the surface Area of a pyramid, whar do the letters of the formula mean?
Answer:
The formula for surface area of a pyramid is A=B*P*I
Step-by-step explanation:
Where B= Area of the base
P=Perimeter of the base
I=Slant height.
Right triangle EFG has its right angle at F, EG=6, and FG=4. What is the value of Cos(G)?
Answer:
cos(G)= 0.66667
Then value of angle G is
= 48.12°
Step-by-step explanation:
Right triangle EFG has its right angle at F.
EG=6, and FG=4.
What is the value of Cos(G)?
The value of cos(g)
= adjacent/hypotenuse
Where FG = adjacent
EG = hypotenuse
.cos(G) = 4/6
cos(G)= 0.66667
G = 48.12°
a bus drives 66km/h at an average of 24 km/h how long does the journey take?
Answer:
2 hours and 45 minutes
Step-by-step explanation:
speed=distance/time
given speed=24kmph
distance=66km
time=distance/speed
66/24
Two students were asked to use estimation strategies to find
a reasonable solution to this question:
A market sells blueberries for $3 per pint. The first day, the
market sold a total of $35 worth of blueberries. The second
day, the market sold a total of $47 worth of blueberries. And
the third day, the market sold a total of $57 worth of
blueberries. Estimate how many pints the market sold over
the three days
Answer:
15.45 pints on average
46.34 pints total
Step-by-step explanation:
To find out on average how many pints he sold in those 3 days, we must first calculate how many pints per day, knowing that $ 3 is a pint.
So,
first day
3/35 = 11.67
second day:
47/3 = 15.67
third day:
57/3 = 19
then the average would be:
(11.67 + 15.67 + 19) / 3 = 15.45
That is to say that on average 15.45 pints were sold in those 3 days
Or what is equal to having sold in those 3 days 46.34 pints
What does this mean?
Answer:
The correct answer is A
Using the numbers shown each line on the graph represents 0.1
R is 2 lines above 33.0, so R would be 33.2
The answer is A.
What’s the value of x?
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