Answer:
0.62
Step-by-step explanation:
Probability of rain = 34% = 0.34
Probability of wind = 38% = 0.38
Probability of wind and rain = 10% = 0.1
P(wind U rain) = p(wind) + p(rain) - p(both)
= 0.34 + 0.38 -1
= 0.62
The probability that it would be rainy or sunny in any given day in April is 62%
Change $35,000 per year to dollars per hours
the total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m +5. After a policy change, five more dollars are added on and then the total reimbursement amount is multiplied by 1.25 describe how to transform the graph of f. what is the total reimbursement for a trip of 95 miles?
Answer:
The slope becomes 0.5625 and y intercept becomes 12.5.
$65.9375
Step-by-step explanation:
Given that
the total reimbursement function in terms of [tex]m[/tex] miles:
[tex]f(x) = 0.45m +5[/tex]
After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.
To find:
How to transform the graph of f.
Total reimbursement for a trip of 95 miles?
Solution:
[tex]f(x) = 0.45m +5[/tex] can also be written as:
[tex]y = 0.45m +5[/tex]
It is nothing but slope intercept form, comparing with [tex]Y = M X+ C[/tex]
M is the slope and C is the y intercept.
Slope of the graph is 0.45.
Y intercept is 5.
After change in the function, first of all add $5.
[tex]0.45m + 5+5 = 0.45m+10[/tex]
Now, multiply with 1.25
Resulting function becomes:
[tex]f(x) =1.25\times (0.45m+10)\\\Rightarrow f(x) =0.5625m+12.5[/tex]
Kindly refer to the attached image for the graph of the two functions.
Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.
To find the reimbursement for a trip of 95 miles:
Put m = 95
[tex]f(95) =0.5625\times 95+12.5 = \bold{\$65.9375 }[/tex]
In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed.
Answer:
we accept the alternate hypothesis that
there is a difference between the rate of medical malpractice lawsuits that go to trial and the rate of such lawsuits that are dropped or dismissed.
Step-by-step explanation:
We first write out our null and alternate hypothesis.
H0: no difference
H1: there is difference
n = 1228
P = 856
X = n-p
= 372
Z = ((x+0.5)-1228/2) divided by √1228/2
= 372.5 - 614/17.52
= -13.784
|Z|= 13.784
The decision is to reject the null hypothesis and accept the alternate because there is evidence that dismissed lawsuit if bigger than 0.5. so there is difference between lawsuits that go to trial and lawsuits that are dismissed
Clara is growing her hair out and wants it to be no longer than 15 cm but more than 11 cm. Her hair is 7 cm right now and grows at a rate of 0.25 cm per week. The compound inequality 11 < 7 + 0.25t ≤ 15 models the scenario. How long will it take Clara to grow out her hair to the desired length? It will take Clara more than weeks and up to and including weeks to grow out her hair.
Answer:
It will take Clara more than
16
weeks and up to and including
32
weeks to grow out her hair.
Answer:
It will take Clara more than 16 weeks and up to and including 32 weeks to grow out her hair.
Step-by-step explanation:
The area of a rectangular piece of land J is 220 square metres.Its width is 12.5.what is the perimeter of the land ?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ {60.2 \: m}}}}}}[/tex]
Step-by-step explanation:
Given,
Area of rectangular piece of land ( l ) = 220 m²
Width ( w ) = 12.5 m
Finding length of the rectangular piece of land
[tex] \boxed{ \sf{area \: of \: rectangle = l \times w}}[/tex]
plug the values
⇒[tex] \sf{220 = l \times 12.5}[/tex]
Swap the sides of the equation
⇒[tex] \sf{12.5 \: l = 220}[/tex]
Divide both sides of the equation by 12.5
⇒[tex] \sf{ \frac{12.5 \: l}{12.5} = \frac{220}{12.5} }[/tex]
Calculate
⇒[tex] \sf{l = 17.6 \: m}[/tex]
Length of rectangular piece of land ( l )= 17.6 m
Finding perimeter of rectangular piece of land
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]
plug the values of length and breadth
⇒[tex] \sf{2(17.6 + 12.5) }[/tex]
Add the numbers
⇒[tex] \sf{2 \times 30.1}[/tex]
Multiply the numbers
⇒[tex] \sf{60.2 \: m}[/tex]
Therefore, Perimeter of rectangular piece of land is 60.2 m
Hope I helped!
Best regards!!
is 6 a solution of 2x+7=3x
Answer:
No
Step-by-step explanation:
because the answer is 7
2x + 7 = 3x
2x + 7 - 7 = 3x - 7
2x = 3x - 7
2x - 3x = 3x - 7 - 3x
-x = -7
x = 7
heplfdjnhkmxdjnhkml,;.
Answer:
d
Step-by-step explanation:
im pretty sure the right answer would be 12 and 21 just doesn't look right
simplify 2⁰+5¹+4³/7
Your question has been heard loud and clear.
2^0= 1
5^1= 5
4^3=64
2^0+5^1+4^3/7= 1+5+64/7 = 6+64/7= 15.14
So , 2^0+5^1+4^3/7 = 15.14
Thank you
The revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x2 + 2x – 80. The cost, in dollars, of producing the video game systems can be modeled by 5x2 – x + 100, where x is the number of video game systems sold. If profit is the difference between the revenue and the cost, what expression represents the profit?
Answer: 3x-180
Step-by-step explanation:
Given: Expression for Revenue = [tex]5x^2 + 2x - 80[/tex]
Expression for Cost = [tex]5x^2- x + 100[/tex]
If profit is the difference between the revenue and the cost then the expression for profit will be:
Profit = Revenue - cost
[tex]=5x^2 + 2x - 80-(5x^2- x + 100)\\\\=5x^2 + 2x - 80-5x^2+x-100\ \ [\text{Multiply ' - ' sign inside the bracket}]\\\\=2x+x-80-100\\\\=3x-180[/tex]
Hence, the expression represents the profit is 3x-180 .
Answer:
its 3x-180 and for the seond one its $2,820
Step-by-step explanation:
got it right on edge
The common ratio in a geometric series is 0.50.50, point, 5 and the first term is 256.
Find the sum of the first 6 terms in the series.
Answer:
504
Step-by-step explanation:
I think the correct question is like:The common ratio in a geometric series is 0.50 ( point 5) and the first term is 256.
Find the sum of the first 6 terms in the series.
If it's right, then
Sₙ = (a₁ × (1 - rⁿ)) / (1 - r)
S₆ = (256 × ( 1 - 0.5⁶)) / (1 - 0.5)
= (256 × 0.984375) / 0.5
= 504
hope it will help :)
solve the system of equations below
5x+2y=9
2×-3y=15
Answer:
The solution is (3, -3)
Step-by-step explanation:
5x + 2y = 9
2x - 3y = 15
Use elimination by addition/subtraction. Multiply the first equation by 3 and the second by 2, obtaining:
15x + 6y = 27
4x - 6y = 30
----------------------
19x = 57
This yields x = 3.
Substituting 3 for x into 5x + 2y = 9, we get 5(3) + 2y = 9, or
15 + 2y = 9, or
2y = -6
This yields y = -3.
The solution is (3, -3)
PRACTICE ANOTHER Calculate the standard deviation σ of X for the probability distribution. (Round your answer to two decimal places.) σ = (No Response) 1.00
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma = 1.17[/tex]
Step-by-step explanation:
From the question we are told that
The data is
x 1 2 3 4
P(X = x) 0.2 0.2 0.2 0.4
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \sum x^2 P(x) - (\sum x P(x))^2 }[/tex]
Here [tex]x^2 = 1^2 \ \ 2^2 \ \ 3 ^2 \ \ 4^2[/tex]
=> [tex]x^2 = 1 \ \ 4 \ \ 9\ 16 \[/tex]
[tex]\sum x^2 * P(x) = (1 * 0.2) + (4 * 0.2 ) + (9 * 0.2 ) + (16 * 0.2 )[/tex]
[tex]\sum x^2 * P(x) = 9.4[/tex]
[tex]\sum x P(x) = (1 *0.2) + (2*0.2) + (3 * 0.2) + (4 * 0.2)[/tex]
[tex]\sum x P(x) = 2.8[/tex]
So
[tex]\sigma = \sqrt{ 9.2 - (2.8)^2 }[/tex]
[tex]\sigma = 1.17[/tex]
1/64, 1/16, 1/4, 1... What is the pattern and next term???
Answer:
[tex]\huge\boxed{\text{next term}=4}\\\boxed{f(n)=4^{n-4}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{64},\ \dfrac{1}{16},\ \dfrac{1}{4},\ 1,\ ...[/tex]
It's the geometric sequence where
[tex]a_1=\dfrac{1}{64},\ q=4[/tex]
[tex]\dfrac{1}{16}=\dfrac{1}{64}\cdot4\\\\\dfrac{1}{4}=\dfrac{1}{16}\cdot4\\\\1=\dfrac{1}{4}\cdot4\\\\1\cdot4=4\to\text{next term}[/tex]
[tex]f(n)=\dfrac{1}{64}\cdot4^{n-1}=\dfrac{1}{4^3}\cdot4^{n-1}=\dfrac{4^{n-1}}{4^3}\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\f(n)=4^{n-1-3}=4^{n-4}[/tex]
Need help I don’t understand
Answer:
Complementary angles add up to 90 degrees, or a right angle.
In this case, it would be (c) AEF and FED, AEG and CEG
Step-by-step explanation:
Please help I dont understand
Answer:
X+Y=8W^2-7W+7
Step-by-step explanation:
HEY,... HERES YOUR ANSWER ! I HOPE I HELPED! BRAINLIEST WOULD BE APPRECIATED :)
THE QUESTION-->
X=7W^2+4W-6
Y=W^2-11W+13
X+Y=?
THE EXPLANATION-->
SO LETS JUST ADD BOTH EQUATIONS!
SO...
X+Y=7W^2+4W-6+W^2-11W+13
SIMPLIFY LIKE TERMS..
7W^2+W^2+4W-11W-6+13
SIMPLIFY EVEN FURTHER..
X+Y=8W^2-7W+7
THE ANSWER-->
X+Y=8W^2-7W+7
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period.2 5 10 124 4 5 1711 8 9 812 21 6 87 13 18 3(a) Develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24.Class Frequency0-4 5-9 10-14 15-19 20-24 Total (b) Develop a relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places.Class Relative Frequency0-4 5-9 10-14 15-19 20-24 Total (c) Develop a cumulative frequency distribution using the classes in part (a).(c) Develop a cumulative frequency distribution using the classesClass Cumulative Frequency0-4 5-9 10-14 15-19 20-24 (d) Develop a cumulative relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places.Class Cumulative Relative Frequency0-4 5-9 10-14 15-19 20-24 (e) What proportion of customers needing an oil change wait 9 minutes or less?%
Answer:
Kindly check explanation
Step-by-step explanation:
Waiting times collected over a one month period:
2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3
A)
Class(x) - - frequency(f)
0-4 - - - - - 4
5-9 - - - - - - 8
10-14 - - - - - 5
15-19 - - - - - 2
20-24 - - - - 1
B)
Class(x) - - frequency(f)- - relative frequency(rf)
0-4 - - - - - 4 - - - - - - - - - - 4/20 = 0.20
5-9 - - - - - - 8 - - - - - - - - - - 8/20 = 0.40
10-14 - - - - - 5 - - - - - - - - - - 5/20 = 0.25
15-19 - - - - - 2 - - - - - - - - - - 2/20 = 0.10
20-24 - - - - 1 - - - - - - - - - - - 1/20 = 0.05
C)
Class(x) - - frequency(f) - - cumulative frequency
0-4 - - - - - 4 - - - - - - - - - - - 4
5-9 - - - - - - 8 - - - - - - - - - - - 12
10-14 - - - - - 5 - - - - - - - - - - - 17
15-19 - - - - - 2 - - - - - - - - - - - 19
20-24 - - - - 1 - - - - - - - - - - - - 20
D)
Class(x) - - f - - cf - - - - rf - - - - - - crf
0-4 - - - - 4 - -- 4 - - - 0.20 - - - 0.20
5-9 - - - - - 8 - - 12 - - - 0.40 - - - 0.60
10-14 - - - 5 - - -17 - - - 0.25 - - - 0.85
15-19 - - - 2 - - - 19 - - - 0.10 - - - 0.95
20-24 - - 1 - - - 20 - - 0.05 - - - 1.00
crf - cumulative relative frequency
rf - relative frequency
cf - cumulative frequency
E) 0.6 (from the cumulative relative frequency column)
9 minutes or less :
Frequency = 12, total frequency = 20
12 / 20 = 0.6
The frequency distribution of the given data and frequency table for them would be presented as mentioned below.
Frequency Distribution
Given that,
Data
2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3
a). The use of classes to create a frequency distribution through classes would be as follows:
Class(X) frequency(f)
0-4 4
5-9 8
10-14 5
15-19 2
20-24 1
b). The relative frequency distribution would be as follows:
Class(X) frequency(f) relative frequency(rf)
0-4 4 4/20 = 0.20
5-9 8 8/20 = 0.40
10-14 5 5/20 = 0.25
15-19 2 2/20 = 0.10
20-24 1 1/20 = 0.05
c). The cumulative frequency distribution would be as follows:
Class(X) frequency(f) cumulative frequency(cf)
0-4 4 4
5-9 8 12
10-14 5 17
15-19 2 19
20-24 1 21
d). The cumulative frequency distribution employing classes in part a would be as follows:
Class(X) (f) (cf) rf crf
Frequency Cumulative Relative Cumulative Relative
Frequency Frequency Frequency
0-4 4 4 0.20 0.20
5-9 8 12 0.40 0.60
10-14 5 17 0.25 0.85
15-19 2 19 0.10 0.95
20-24 1 21 0.05 1
e). The proportion of customers requiring an oil change wait 9 minutes would be:
Frequency [tex]= 12[/tex]
Total Frequency [tex]= 20[/tex]
The Proportion of customers requiring an oil change wait 9 minutes or less
[tex]= 12/20\\= 0.6[/tex]
Learn more about "Frequency Distribution" here:
brainly.com/question/7523130
If 12 babies made up 0.1% of the babies born each day – how many in total were born each day?
Answer:
120 babies
Step-by-step explanation:
Divide 12 by 0.1:
12/0.1
= 120
So, 120 babies were born each day.
Determine whether Y=-x+6 x+y=20 is parallel, perpendicular or neither
Answer:
Parallel
Step-by-step explanation:
-x+6 slope:-1
X+y=20 slope -1
Hence the answer is parallel
Write the rational number 0.3 in the form ab , where a and b are integers.
Answer:
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
Step-by-step explanation:
Given
[tex]Number = 0.3[/tex]
Required
Represent as [tex]\frac{a}{b}[/tex]
Let [tex]\frac{a}{b} = 0.3[/tex]
This can be further written as
[tex]\frac{a}{b} = \frac{0.3}{1}[/tex]
Multiply the numerator and denominator by 10
[tex]\frac{a}{b} = \frac{0.3 * 10}{1 * 10}[/tex]
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
Since 3 and 10 are both integers, then
[tex]\frac{a}{b} = \frac{3}{10}[/tex]
A right triangle has the following vertices. Find the area of the triangle.
(7,-3), (4,-3), (4,9)
(A.) 18 square units
(B.) 36 square units
(C.) 27.4 square units
(D.) √153 square units
Answer:
B. 36 square unitsStep-by-step explanation:
Ara of a triangle = 1/2 * base * height.
Before we find the area, we must look for all the sides of the triangle by taking the difference between any two points.
Given D = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinates P(7,-3), Q(4,-3), R(4,9)
For the coordinates P(7,-3), Q(4,-3)
Given PQ = √(4-7)²+(-3+3)²
PQ = √(-3)²+0
PQ = √9
PQ = 3
For coordinates P(7,-3), R(4,9)
Given PR = √(4-7)²+(9+3)²
PR = √(-3)²+12²
PR = √9+144
PR = √153
For coordinates Q(4,-3), R(4,9)
Given QR = √(4-4)²+(9+3)²
QR = √(0)²+12²
QR = √0+144
QR = 12
Since it is a rright angled triangle, the base of the triamgle will be QR and the height will be PQ since the longest side is PR
Area of the triangle = 1/2 * PQ*QR
Area of the triangle = 1/2 * 12*6
Area of the triangle = 6*6
Area of the triangle = 36 square units
What percent of 290 is 120?
Round your answer to the tenths place.
__________________ percent
Answer:
41.4%
Step-by-step explanation:
120/290 = x/100
290x = 120 * 100
x = 41.3793...
What is the slope of the line that passes through the points (-3, -3)(−3,−3) and (-9, 5) ?(−9,5)? Write your answer in simplest form.
Answer:
Slope= -4/3
Step-by-step explanation:
The points are (−3,−3) and (-9, 5)
Slope= gradient between the two points
Slope= (y2-y1)/(x2-x1)
Where y2= 5
Y1= -3
X2= -9
X1= -3
Slope= (y2-y1)/(x2-x1)
Slope= (5-(-3))/(-9-(-3))
Slope= (5+3)/(-9+3)
Slope= 8/-6
Slope= -4/3
A newsletter publisher believes that above 41A% of their readers own a personal computer. Is there sufficient evidence at the 0.100.10 level to substantiate the publisher's claim?
Complete Question
A newsletter publisher believes that above 41% of their readers own a personal computer. Is there sufficient evidence at the 0.10 level to substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario.
Answer:
The null hypothesis is [tex]H_o : p \le 0.411[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.41[/tex]
Step-by-step explanation:
From the question we are told that
The proportion is [tex]p = 0.41[/tex]
Generally the null hypothesis is [tex]H_o : p \le 0.411[/tex]
The above condition represents the null hypothesis because it contains and equality in its condition
The alternative hypothesis is [tex]H_a : \mu > 0.41[/tex]
Which expression is equivalent to the following complex fraction?
StartFraction 3 Over x minus 1 EndFraction minus 4 divided by 2 minus StartFraction 2 Over x minus 1 EndFraction
StartFraction 2 (x minus 2) Over negative 4 x + 7 EndFraction
StartFraction negative 4 x + 7 Over 2 (x minus 2) EndFraction
StartFraction negative 4 x + 7 Over 2 (x squared minus 2) EndFraction
StartFraction 2 (x squared minus 2) Over (negative 4 x + 7) EndFraction
Answer:
[tex]\dfrac{-4x+7}{2(x-2)}[/tex]
Step-by-step explanation:
Write the terms of numerator and denominator using a common denominator.
[tex]\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\left(\dfrac{3-4(x-1)}{x-1}\right)}{\left(\dfrac{2(x-1)-2}{x-1}\right)}}=\boxed{\dfrac{-4x+7}{2(x-2)}}[/tex]
Answer: It's B on Edge 1843
Step-by-step explanation:
Don't listen to the guys in the comments they have peanuts for brains
What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday. B: Laura met with her academic advisor on campus at 11:00 AM last Friday. A and B are mutually exclusive. A and B are complementary. A and B are not mutually exclusive. If B is true, A is trus
Solve for x 5x2-4x=6
Answer:
That would equal 36
Step-by-step explanation:
i added them up
Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often, sometimes, and seldom. Below are the results of the one-way ANOVA. Source of Variation SS df MS F Between groups 1,959.79 3 653.26 21.16* Within groups (error) 3,148.61 102 30.86 Total 5,108.41 105 (a) What are the values for N and k
Answer:
K = 4 ; N = 106
Step-by-step explanation:
Given the following :
Source of VARIATION - SS - df - - MS - - - - - F
Between groups - 1,959.79 - 3 - - 653.26 - 21.16*
Error - - - - - - - - 3,148.61 - - - - 102 - - 30.86
Total - - - - - - - - - - - 5,108.41 - 105
The degree of freedom between group (treatment) (DFT) is obtained using the formula ;
K - 1, where k = number of groups observed
DFT = K - 1 ; From the ANOVA table, DFT = 3
3 = K - 1
3 + 1 = K
K = 4
To obtain sample size (N) :
Degree of freedom of Error (DFE) is the difference between the sample size and the number of groups observed.
DFE = N - K ; From. The table DFE = 102 ; K = 4
102 = N - 4
102 + 4 = N
N = 106
Zoom In
In Exercises 1-4, use the figure shown. Find the length of each segment.
U
-6-5-4-3-2-1
0
1
2 3
4 5
6 7
8
1. RS =
2. RT =
3. ST
4. RU=
oooo
For Exercises 5-7, use the figure shown.
5. What is PQ?
6. What is QR?
7. What is PR?
Points A, B, C, and D on the figure below are collinear. Use the figure for
Exercises 8 and 9
A
3x
4x
13
8. If AC = 24, what is AB?
9. If BC = 15, what is BD?
Use the figure shown for Exercises 10-13.
10. What is m_PTR?
11. What is m_PTQ?
12. What is m2QTS?
13. Understand Luis said that m2 QTR = 80
Explain Luis's error
Answer/Step-by-step Explanation:
When calculating the length of a segment on a number line, the absolute value of the difference between one point on the numberline, and another point is what we're looking for.
1. Length of RS = |-5 - (-2)| = |-5 + 2| = |-3|
RS = 3
2. Length of RT = |-5 - 2| = |-7|
RS = 7
3. Length of ST = |-2 - 2| = |-4|
ST = 4
4. Length of RU = |-5 - 8| = |-13|
RU = 13
5. Given that the following coordinates:
P = 3
Q = 8
R = 14
5. PQ = |3 - 8| = |-5| = 5
6. QR = |8 - 14| = |-6| = 6
7. PR = |3 - 14| = |-11| = 11
Given that points A, B, C, and D are collinear, and AB = x, BC = 3x, CD = 4x - 13
8. If AC = 24,
BC can be calculated as follows:
AB + BC = AC
[tex] x + 3x = 24 [/tex]
Solve for x
[tex] 4x = 24 [/tex]
Divide both sides by 4
[tex] x = 6 [/tex]
Thus,, BC = 3x = 3(6) = 18
BC = 18
9. If BC = 15, BD can be calculated as follows:
Find the value of x first
BC = 3x
15 = 3x
Divide both sides by 3
5 = x
x = 5.
BD = [tex] 3x + (4x - 13) [/tex]
Plug in the value of x
BD = [tex] 3(5) + (4(5) - 13) = 15 + (20 - 13) [/tex]
BD = [tex] 15 + 7 = 22 [/tex]
BD = 22
10. m<PTR = 80° (taking the reading at the top from 0°)
11. m<PTQ = 45°
12. m<QTS = 128 - 45 = 83°
13. Luis read m<QTR wrongly, what he measured was the whole of <PTR.
According to the angle addition theorem, m<QTR = 80 - 45 = 35°.
For each of the following vector fields
F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potentialfunction f (that is, ∇f = F) with f(0,0)=0. If it is not conservative, type N.
A. F(x,y)=(−16x+2y)i+(2x+10y) j f(x,y)= _____
B. F(x,y)=−8yi−7xj f(x,y)=_____
C. F(x,y)=(−8sin y)i+(4y−8xcosy)j f(x,y)=_____
(A)
[tex]\dfrac{\partial f}{\partial x}=-16x+2y[/tex]
[tex]\implies f(x,y)=-8x^2+2xy+g(y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=10y[/tex]
[tex]\implies g(y)=5y^2+C[/tex]
[tex]\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}[/tex]
(B)
[tex]\dfrac{\partial f}{\partial x}=-8y[/tex]
[tex]\implies f(x,y)=-8xy+g(y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x[/tex]
[tex]\implies \dfrac{\mathrm dg}{\mathrm dy}=x[/tex]
But we assume [tex]g(y)[/tex] is a function of [tex]y[/tex] alone, so there is not potential function here.
(C)
[tex]\dfrac{\partial f}{\partial x}=-8\sin y[/tex]
[tex]\implies f(x,y)=-8x\sin y+g(x,y)[/tex]
[tex]\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy}=4y[/tex]
[tex]\implies g(y)=2y^2+C[/tex]
[tex]\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}[/tex]
For (A) and (C), we have [tex]f(0,0)=0[/tex], which makes [tex]C=0[/tex] for both.
witch number produces a rational number when multipled by 0.25
Answer:
1
Step-by-step explanation:
.25 is already a rational number as it equals 25/100 and 1/4 simplified