Quy tắc suy luận nào là cơ sở của suy diễn sau: "Biết rằng: 2 đường thẳng d và d' song song hoặc cắt nhau. Ta đã có d không song song với d'. Vậy d cắt d'
Select one:
a. Luật loại trừ
b. Luật rút gọn
c. Luật phản chứng
d. Luật tách rời
Answer: a
Step-by-step explanation:
An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.
Which inequality describes all times t for which the object is traveling toward the right?
the function is given, and it's value is where the object is ("how far to the right").
so as long as it rises (going more right), this will be apply.
in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.
for the first 1.25 seconds the object goes to the left, and after that always to the right.
since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.
x(t) = 2t² – 5t – 18
x'(t) = 4t -5
x'(t) = 0
0 = 4t -5
5 = 4t
1.25 = t
plugging it into the second derivative
x''(t) = 4
x''(1.25) = 4
it's positive, so at t=1.25 there is a low point
(of course the second derivative is constant anyways.)
the object is traveling toward the right
the object is traveling toward the rightfor t > 1.25
The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
An object travels along the x-axis so that its position after t seconds is given by:
x(t) = 2t² – 5t – 18
x'(t) = 4t - 5
x'(t) = 0
4t -5 = 0
t = 5/4 = 1.25 seconds
x''(t) = 4
x''(1.25) = 4
x''(1.25) > 0
At t = 1.25 the object travels at a low point.
Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
Learn more about the inequality here:
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Solve (2x – 1)2 = 9. Question 11 options: A) x = 2, –1 B) x = 2, 1 C) x = –2, –1 D) x = –2, 1
Answer:
(2x – 1)2 = 9
4x-2=9
4x=9+2
4x=11
x=11/4
x=2.75
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
Because the P-value is ____ than the significance level 0.05, there ____ sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α= 0.05.
Do the results suggest that imported lemons cause carfatalities?
a. The results suggest that an increase in imported lemons causes car fatality rates to remain the same.
b. The results do not suggest any cause-effect relationship between the two variables.
c. The results suggest that imported lemons cause car fatalities.
d. The results suggest that an increase in imported lemons causes in an increase in car fatality rates.
Answer:
H0 : correlation is equal to 0
H1 : correlation is not equal to 0 ;
Pvalue < α ;
There is sufficient evidence
r = 0.945 ;
Pvalue = 0.01524
Step-by-step explanation:
Given the data :
Lemon_Imports_(x) Crash_Fatality_Rate_(y)
230 15.8
264 15.6
359 15.5
482 15.3
531 14.9
Using technology :
The regression equation obtained is :
y = 16.3363-0.002455X
Where, slope = - 0.002455 ; Intercept = 16.3363
The Correlation Coefficient, r = 0.945
H0 : correlation is equal to 0
H1 : correlation is not equal to 0 ;
The test statistic, T:
T = r / √(1 - r²) / (n - 2)
n = 5 ;
T = 0.945 / √(1 - 0.945²) / (5 - 2)
T = 0.945 / 0.1888341
T = 5.00439
The Pvalue = 0.01524
Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.
How many ways are there to choose three distinct integers between 1 and 20 inclusive such that the numbers form an arithmetic sequence?
*please try to answer by tomorrow/
Answer:
probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)
=194/285 or 0.6807.
Step-by-step explanation:
The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.
The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.
Hence
|E'| = C(14,3)
= 14×13×12/3!.
Therefore probability P(E')
= |E'|/|S|
= (14×13×12)/(20×19×18)
= (14×13×2)/(20×19×3)
=(7×13)/(5×19×3)
= 91/285.
Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.
If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Round to two decimal places if necessary.
volume= a^2 * h
area= a^2+4ah
take the second equation, solve for h
4ah=1100-a^2
h=1100/4a -1/4 a now put that expression in volume equation for h.
YOu now have a volume expression as function of a.
take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.
Cited from jiskha
please help me with geometry
Answer:
x = 5Step-by-step explanation:
triangol BCD = triangle BDA
so
3x - 1 = 34 - 2x
5x = 35
x = 35 : 5
x = 5Answer:
x = 7
Step-by-step explanation:
BD is an angle bisector , so
∠ ABD = ∠ DBC , that is
3x - 1 = 34 - 2x ( add 2x to both sides )
5x - 1 = 34 ( add 1 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
Convert the following equation
into standard form.
y = 7 - 7x
[?]x + y = []
Answer:
[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]
Answer:
7x + y = 7
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = 7 - 7x ( add 7x to both sides )
7x + y = 7 ← in standard form
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it.
[infinity]
â« e^-1.3x dx
1
Show that Reſiz) = -Im(z)
Step-by-step explanation:
[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]
plez halppp mehh ;-;
Answer:
False
True
True
Step-by-step explanation:
Angle 1 cannot be equal to angle 4. Even by just viewing one can see that they can't be equal.
Angle 1 and 2 when combined give a 90 degree angle going from a to c.
Angle 3 and 4 form a 180 degree angle.
HOPE THIS HELPED
Given: AABC, AC = 5
m C = 90°
m A= 22°
Find: Perimeter of AABC
A
C
B
9514 1404 393
Answer:
perimeter ≈ 12.4 units
Step-by-step explanation:
The side adjacent to the angle is given. The relationships useful for the other two sides are ...
Tan = Opposite/Adjacent
Cos = Adjacent/Hypotenuse
From these, we have ...
opposite = 5·tan(22°) ≈ 2.02
hypotenuse = 5/cos(22°) ≈ 5.39
Then the perimeter is ...
P = a + b + c = 2.02 + 5 + 5.39 = 12.41
The perimeter of ∆ABC is about 12.4 units.
Find the slope of the line passing through the points (9, 1) and (9,-4).
Answer:
slope is undefined
Step-by-step explanation:
(9, 1 ) and (9, - 4 )
Since the x- coordinates of the 2 points are 9, then the line is vertical and parallel to the y- axis with slope being undefined.
Slope is the change in y over the change in x.
Slope = (-4 - 1) / (9 -9) = -5/0 you cannot divide by 0,so the slope is undefined. This means it is a vertical line
a certain number plus two is five find the number
x=3
Step-by-step explanation:
x+2=5
x=5-2
x=3
3. Find the least common denominator for the group of denominators using the method of prime numbers. 45, 75, 63
We have to find LCM
3 | 45,75,63
3 | 15,25,21
5 | 5,25,7
5 | 1,5,7
7 | 1,1,7
LCM=3×3×5×5×7=1575
The least common denominator for the group of denominators using the method of prime numbers is 1575.
What is least common multiple?LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers. A factor is one of the numbers that multiplies by a whole number to get that number.
For the given situation,
The numbers are 45, 75, 63
Prime factors of 45 = [tex]3,3,5[/tex]
Prime factors of 75 = [tex]3,5,5[/tex]
Prime factors of 63 = [tex]3,3,7[/tex]
Then the LCM can be found by, first take the common factors then multiple the remaining factors as,
⇒ [tex](3)(3)(5)(5)(7)[/tex]
⇒ [tex]1575[/tex]
Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.
Learn more about least common multiple here
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Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-12x^2+2160x-59000 To maximize the monthly rental profit, how many units should be rented out? units What is the maximum monthly profit realizable?
Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
An urn contains 12 balls, five of which are red. Selection of a red ball is desired and is therefore considered to be a success. If three balls are selected, what is the expected value of the distribution of the number of selected red balls
The expected value of the distribution of the number of selected red balls is 0.795.
What is the expected value?The expected value of the distribution is the mean or average of the possible outcomes.
There are 12 balls in an urn, five of which are crimson. The selection of a red ball is desired and hence considered a success.
In this case, the possible outcomes are 0, 1, 2, or 3 red balls.
To calculate the expected value, we need to find the probability of each outcome and multiply it by the value of the outcome.
The probability of selecting 0 red balls is :
[tex]$\frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$[/tex].
The probability of selecting 1 red ball is :
[tex]$3 \cdot \frac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + 3 \cdot \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{315}{660}$[/tex].
The probability of selecting 2 red balls is
[tex]:$\dfrac{5}{12} \cdot \frac{7}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{5}{11} \cdot \frac{6}{10} + \frac{7}{12} \cdot \frac{6}{11} \cdot \frac{5}{10} = \frac{105}{660}$.[/tex]
The probability of selecting 3 red balls is
[tex]$\dfrac{5}{12} \cdot \frac{4}{11} \cdot \frac{3}{10} = \frac{15}{660}$[/tex]
The expected value is then :
[tex]$0 \cdot \frac{105}{660} + 1 \cdot \frac{315}{660} + 2 \cdot \frac{105}{660} + 3 \cdot \frac{15}{660} = \frac{525}{660} = \frac{175}{220} \approx \boxed{0.795}$[/tex]
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Please help !!! Plzzzz
Explanation:
Because we have a midsegment, this means that it is half as long as the side it's parallel to. You can think of "mid" as "middle" and that could lead to "halfway" to remember to take half.
So z = 14/2 = 7
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
Given the parent graph h(x) = x, what happens when it is changed to h(x + 9)?
Answer:
If the parent graph is h(x) = x, then h(x+9) would actually be shifting the graph 9 units to the LEFT.
Let me know if this helps!
Can someone please help me solve the equation?
Answer:
(0,0) is the x and y intercept of the function
Step-by-step explanation:
The parabola touches the x and y axis at 0
The x intercept is (0,0) and the y intercept is (0,0)
Answer:
(0, 0) is the x and y intercepts
Step-by-step explanation:
intercepts are where the curve of the equation contacts an axis
The equation is y = x²
fernando charges a flat fee of 4.50 plus 2.00 per mile for his taxi service, when he got to the airport the cab fare was 12.50 how many miles was the trip to the airport
the trip to the airport was 6.25 miles.
Please Help me! I will mark brainliest for correct answer!!!
Answer:
y=2/3x+1
Step-by-step explanation:
Identify the terminal point for a 45° angle in a unit circle.
O A (231)
O B.
O c.
V2 72
Answer:
D
Step-by-step explanation:
x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.
Answer:
0.8997 = 89.97% probability of a bulb lasting for at most 622 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.
Mean of 590 hours, standard deviation of 25 hours.
This means that [tex]\mu = 590, \sigma = 25[/tex]
Find the probability of a bulb lasting for at most 622 hours.
This is the p-value of Z when X = 622.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{622 - 590}{25}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997.
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
A 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:
∣
0
1
2
3
4
5
6
∣
0
6
8
8
8
0
2
6
6
7
8
1
2
6
6
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
00
10
20
30
40
50
60
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
0
0
0
0
1
0
0
6
2
2
8
6
6
8
6
6
8
7
0
0
8
0
Key:
2
∣
0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards
The surface area of a cylinder?
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
