(not a or not b) implies c <==> not (not a or not b) or c
so negating gives
not [(not a or not b) implies c] <==> not[ not (not a or not b) or c]
which we can simplify somewhat to
not (not (not a or not b)) and not c
(not a or not b) and not c
(not a and not c) or (not b and not c)
not (a or c) or not (b or c)
not ((a or c) and (b or c))
not ((a and b) or c)
Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
Y=2x-8 and intercept at (-4,-1)
Answer:
y=2x+7
Step-by-step explanation:
y=2x-8
2 is the gradient.
-4 is x
-1 is y
-1=2(-4)+c
-1=-8+c
-1+8=c
c=7
therefore,
y=2x+7
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
Answer:
Probability[Number of people from church] = 0.26 (Approx.)
Step-by-step explanation:
Given:
Total number of adult in survey = 1,033
Missing information:
Number of people from church = 269
Find:
Probability[Number of people from church]
Computation:
Probability of an event = Number of favourable outcomes / Number of total outcomes
Probability[Number of people from church] = Number of people from church / Total number of adult in survey
Probability[Number of people from church] = 269 / 1,033
Probability[Number of people from church] = 0.2604
Probability[Number of people from church] = 0.26 (Approx.)
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis: y=x6, y=1 about y=6.
Answer:
mehoimehoihoi
Step-by-step explanation:
A trucking company buys 25,275 gallons of gasoline. The federal excise tax is $0.195 per gallon. Find the amount of excise tax due. (Round your answer to the nearest cent if necessary)
Answer: 5,055
Step-by-step explanation
multiply the amount of gallons purchased by tax and round up
$4928.625 is the answer.
An Excise tax is an indirect tax, usually paid by the manufacturer or retailer of the product. then passes along in the price of the product to the consumer.
Amount of gasoline = 25,375 gallons.
The Excise tax = $0-195/gallon.
The amount of Excise tax dece = 25.875 X $0.195
= $4928.625
Se the amount of Excise tax due for 25975 gallons of gasoline is $ 4928.625
what is Excise tax?Excise tax is generally a tax levied on the sale of a particular good or service or for a particular purpose. State excise taxes are usually levied on the sale of gasoline, air tickets, heavy trucks, road tractors, tanning beds, tires, cigarettes, and other goods and services.
Excise can be used to charge prices for externalities or to discourage the consumption of goods by others. They can also be used as royalties to generate income from people who use certain government services. Income should be used to maintain those government services.
Learn more about excise tax here:https://brainly.com/question/2871942
#SPJ2
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir
bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
ОА.
3.25x + 13.50 S 40
OB.
3.25x + 13.50 240
Oc.
13.50x +3.25 S 40
OD.
13.50x +3.25 2 40
Answer:
A. 3.25x + 13.50 ≤ 40
The number of bracelets is x. It's a variable.
The 13.50 is a constant.
The total needs to be less than or equal to 40 because that's all the money he has.
Answer:
3.25x + 13.50 ≤ 40
Step-by-step explanation:
For this problem, you have to directly make the equation. Using the givens, it shows that he has only 40 dollars, and wants to buy only one hat for 13. 50. He wants to buy his friends braclets 3.25, but since you dont know how many friends its for, you will leave it as x.
There is only 40 dollars so you will use: ≤
The answer will be:
3.25x + 13.50 ≤ 40
Hope this helps.
We have 9 pens, of which 5 are green ink, 3 are red ink, and 1 is black. If we put the pens in a line, how many arrangements are possible
Answer:
504 arrangements are possible
Step-by-step explanation:
Arrangements of n elements:
The number of arrangements of n elements is given by:
[tex]A_{n} = n![/tex]
Arrangements of n elements, divided into groups:
The number of arrangements of n elements, divided into groups of [tex]n_1, n_2,...,n_n[/tex] elements is given by:
[tex]A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]
In this case:
9 pens, into groups of 5, 3 and 1. So
[tex]A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504[/tex]
504 arrangements are possible
Cho hàm số f(x, y) = ln(x
2 + y
2
).
a) Tính f
′
x
, f′
y
;
b) Tính f
′
x
(2; 1), f′
y
(2; 1).
Answer:
Sorry, I can't understand in which language you have written......
Step-by-step explanation:
So if you tell me the question in English then I can answer
Find the value of x (please)
9514 1404 393
Answer:
(a) 21
Step-by-step explanation:
The product of the lengths to the near and far circle intercepts are the same for the two lines. For the tangent, the near and far intercepts are the same point, so we have ...
(36)(36) = (27)(27+x)
48 = 27+x . . . . . . . . . . divide by 27
x = 21 . . . . . . . . subtract 27
what are all the factos of 36
Hi there!
»»————- ★ ————-««
I believe your answer is:
{1, 2, 3, 4, 6, 9, 12, 18, 36}
»»————- ★ ————-««
Here’s why:
A factor is a whole number that is multiplied by another to have a product have another number.
⸻⸻⸻⸻
The Factors Are:
1 (1 * 36 = 36)2 (2 * 18 = 36)3 (3 * 12 = 36)4 (4 * 9 = 36)6 (6 * 6 = 36) 9 (9 * 4 = 36)12 (12 * 3 = 36)18 (18 * 2 = 36)36 (36 * 1 = 36)⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, 7) (6, -33) (10, -105)
HELP PLZ
Answer:
[tex]y= -x^{2} -2x+15[/tex]
Step-by-step explanation:
[tex]y= -x^{2} -2x+15[/tex]
38. The ______ is also not convenient to use because the process of working for it produces large numbers due to squaring. 39. The ______ is the most reliable measure of variability. 40. The lesser the variability, the ______ is the mean.
Answer:
This Question Is From The Novel Of The Fantastic Mr.Fox
Q. Boggis , Bunce and Bean are Offering a reward for Mr.Fox , They are tired of Losing Chickens Geese and Cider , Create a Description And Drawing of Mr.Fox to allow him to be captured , use the word bank....
________________________________
Swift | Slay | Ginger | Rough | Fast
Thief. | Clever | Fur | Tail | Wife | Night
Cunning | Bushy | wiry | bush | Den | trick
________________________________
six options. Each of these six options leads to a menu with four options. For each of these four options, three more options are available. For each of these three options, another three options are presented. If a person calls the 800 number for assistance, how many total options are possible
Answer:
Hence the total number of possible options available to a person who calls the 800 number is 216.
Step-by-step explanation:
Given that the caller 10 800 telephone system has six options. For each of these four options, three more options are available. For each of these three options, another three options are presented.
Hence the total number of possible options available to a person who calls the 800 number = [tex]6 \times 4 \times 3 \times 3 = 216[/tex].
The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 120 and standard deviation of 18 . Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. a. Around what percentage of adults in the USA have stage 2 high blood pressure
Answer:
The percentage of adults in the USA have stage 2 high blood pressure=98.679%
Step-by-step explanation:
We are given that
Mean, [tex]\mu=120[/tex]
Standard deviation, [tex]\sigma=18[/tex]
We have to find percentage of adults in the USA have stage 2 high blood pressure.
[tex]P(x\geq 160)=P(Z\geq \frac{160-120}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq \frac{40}{18})[/tex]
[tex]P(x\geq 160)=P(Z\geq 2.22)[/tex]
[tex]P(x\geq 160)=1-P(Z\leq 2.22[/tex]
[tex]P(x\geq 160)=0.98679[/tex]
[tex]P(x\geq 160)=98.679[/tex]%
Hence, the percentage of adults in the USA have stage 2 high blood pressure=98.679%
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 528 hours. Round your answer to four decimal places.
Answer:
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours.
This means that [tex]\sigma = 15, \mu = 520[/tex]
Find the probability of a bulb lasting for at most 528 hours.
This is the p-value of Z when X = 528. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{528 - 520}{15}[/tex]
[tex]Z = 0.533[/tex]
[tex]Z = 0.533[/tex] has a p-value of 0.7031
0.7031 = 70.31% probability of a bulb lasting for at most 528 hours.
Please help me there’s a image above.
Answer:
4,-1 that is the answer so
Melanie has D dimes and Q quarters. She has no less than $4 worth of coins altogether. Write this situation as an inequality.
Step-by-step explanation:
D(.10) + Q(.25) = 4
I think
Answer:
D(.10) + Q(.25) = 4
Step-by-step explanation:
heeeeeeeeeeeeelp meee
Answer: i need the formula and i got you.
Step-by-step explanation:
Which among the following numbers could be the probability of an event? 1,1.4,-0.54,.32,.02,0
In other words, choices B and C are the non-answers while everything else is an answer.
==============================================================
Explanation:
Let p represent the probability of an event. The value of p must be between 0 and 1, inclusive of both endpoints. Symbolically, we can write [tex]0 \le p \le 1[/tex]
In other words, p = 0 is the smallest it can get and p = 1 is the largest it can get, or it could be anything in between.
The probability p = 0 means that the event will never happen, or there's 0% of it happening. The probability p = 1 means there's 100% certainty the event will happen.
Something like p = 1.4 is not possible as this indicates it's over 100%. So that rules out choice B. Choice C is also ruled out because we can't have negative probabilities.
Find the values of the sine, cosine, and tangent for ZA C A 36ft B
24ft
Find the values of the sine, cosine, and tangent for ∠A
a. sin A = [tex]\frac{\sqrt{13} }{2}[/tex], cos A = [tex]\frac{\sqrt{13} }{3}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
b. sin A = [tex]3\frac{\sqrt{13} }{13}[/tex], cos A = [tex]2\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{3}{2}[/tex]
c. sin A = [tex]\frac{\sqrt{13} }{3}[/tex], cos A = [tex]\frac{\sqrt{13} }{2}[/tex], tan A = [tex]\frac{3}{2}[/tex]
d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Answer:d. sin A = [tex]2\frac{\sqrt{13} }{13}[/tex], cos A = [tex]3\frac{\sqrt{13} }{13}[/tex], tan A = [tex]\frac{2 }{3}[/tex]
Step-by-step explanation:The triangle for the question has been attached to this response.
As shown in the triangle;
AC = 36ft
BC = 24ft
ACB = 90°
To calculate the values of the sine, cosine, and tangent of ∠A;
i. First calculate the value of the missing side AB.
Using Pythagoras' theorem;
⇒ (AB)² = (AC)² + (BC)²
Substitute the values of AC and BC
⇒ (AB)² = (36)² + (24)²
Solve for AB
⇒ (AB)² = 1296 + 576
⇒ (AB)² = 1872
⇒ AB = [tex]\sqrt{1872}[/tex]
⇒ AB = [tex]12\sqrt{13}[/tex] ft
From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of [tex]12\sqrt{13}[/tex] ft (43.27ft).
ii. Calculate the sine of ∠A (i.e sin A)
The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e
sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex] -------------(i)
In this case,
Ф = A
opposite = 24ft (This is the opposite side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (i) as follows;
sin A = [tex]\frac{24}{12\sqrt{13} }[/tex]
sin A = [tex]\frac{2}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
sin A = [tex]\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
sin A = [tex]\frac{2\sqrt{13} }{13}[/tex]
iii. Calculate the cosine of ∠A (i.e cos A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e
cos Ф = [tex]\frac{adjacent}{hypotenuse}[/tex] -------------(ii)
In this case,
Ф = A
adjacent = 36ft (This is the adjecent side to angle A)
hypotenuse = [tex]12\sqrt{13}[/tex] ft (This is the longest side of the triangle)
Substitute these values into equation (ii) as follows;
cos A = [tex]\frac{36}{12\sqrt{13} }[/tex]
cos A = [tex]\frac{3}{\sqrt{13}}[/tex]
Rationalize the result by multiplying both the numerator and denominator by [tex]\sqrt{13}[/tex]
cos A = [tex]\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }[/tex]
cos A = [tex]\frac{3\sqrt{13} }{13}[/tex]
iii. Calculate the tangent of ∠A (i.e tan A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e
tan Ф = [tex]\frac{opposite}{adjacent}[/tex] -------------(iii)
In this case,
Ф = A
opposite = 24 ft (This is the opposite side to angle A)
adjacent = 36 ft (This is the adjacent side to angle A)
Substitute these values into equation (iii) as follows;
tan A = [tex]\frac{24}{36}[/tex]
tan A = [tex]\frac{2}{3}[/tex]
What is the segment
Parallel lines
is this right please answer ill mark!!
Answer:
yeah u r correct..Step-by-step explanation:
hope it helps.stay safe healthy and happy......Answer:
yes
Step-by-step explanation:
cos=adjacent over hypotenouse
If 128x is a perfect square number what is the least value of x
Please answer the question fast
Answer:
in a square all sides are equal so x has to equal
128
Hope This Helps!!!
The time for a professor to grade a student’s homework in statistics is normally distributed with a mean of 13.3 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
Answer:
0.96784
Step-by-step explanation:
17-13.3/2
=1.85
p(x<1.85)
=0.96784
The probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
Mean [tex]\mu[/tex]=13.3 minutes
Standard deviation[tex]\sigma[/tex]=2 minutes
What is a z-score?The value of the z-score tells you how many standard deviations you are away from the mean.
So, the z-score of the above data
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{17-13.3}{2}[/tex]
[tex]z=1.85[/tex]
From the standard normal table, the p-value corresponding to z=1.85
Or, p(x<1.85)=0.9678 or 96.78%
Hence, the probability that randomly selected homework will require less than 17 minutes to grade is 0.9678.
To get more about the z-score visit:
https://brainly.com/question/25638875
Which parabola opens upward?
y = 2x – 4x^2 – 5
y = 4 – 2x^2 –5x
y = 2 + 4x – 5x^2
y = –5x + 4x^2 + 2
Answer:
D) y = –5x + 4x^2 + 2
Step-by-step explanation:
You can tell by the first number being positive or negative. To check use Desmo graphing calculator and enter your equation for next time.
Which graph shows the solution to the system of linear inequalities?
y>2/3x+3
y ≤ -1/3x+2
Answer:
Graph 2 which has both solid and dashed line
Step-by-step explanation:
Given the linear inequalities :
y>2/3x+3 - - - (1)
y ≤ -1/3x+2 - - - (2)
One quick observation that can be made from the two graphs is the type of line used to plot the two linear inequalities;
Inequalities that uses either the < or > sign are plotted using a dashed line while inequalities with makes use of ≤ or ≥ are plotted using the solid line. Therefore we can conclude that the graph which uses both the solid line and the dashed line to represent the linear inequality conditions is the correct choice.
Not sure what to pick
Answer:
option d is correct answer
Answer:
Step-by-step explanation:
D looks good
[tex]3x+7=12-2x;1[/tex]
Step-by-step explanation:
[tex]3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1[/tex]
performance task number 2.
answer it correctly and I will mark brainliest.:)
Answer:
I cant see the whole image
Step-by-step explanation:
please show it.
