Answer:
731 miles
Step-by-step explanation:
To solve this, we can set up a proportion.
Let's name the number of miles he travels in 17 hours x for now.
8/344=17/x
Simplify 8/344
2/86=17/x
Cross multiply
86*17=2*x
2x=1462
Divide both sides by 2.
x=731
He would travel 731 miles in 17 hours.
Answer:
731 miles
Step-by-step explanation:
Proportions:
344 miles ⇒ 8 hours
W miles ⇒ 17 hours
W = 344*17/8
W = 731
2. A map of a park has a scale of 1 inch to 1,000 feet. Another map of the same park has
a scale of 1 inch to 500 feet. Which map is larger? Explain or show your reasoning.
1
rade 7 Unit 1
esson 10
CC BY Open Up Resources. Adaptations CC BY IM.
Answer:
The map that has a scale of 1 inch to 500 feet must be larger in size
Step-by-step explanation:
Since both maps represent the ame park area, the map that show more detail using 1 inch for every 500 feet, must be larger in size. notice that in order to represent 1000 feet this map needs to use 2 inches, while the other one uses only 1 inch of paper.
a Find the amount compounded annually on Rs 25,000 for 2 years if the rates of
interest for two years ore 10 % and 12 % respectively,
Answer:
Rs 30800
Step-by-step explanation:
The formula for compound interest is
A = P[1 + (r/100)]^t, where
A = amount of compounded interest
P = principal amount
r = interest rate
Applying this to our question, we have
A = 25000 [1 + (10/100)] [1 + (12/100)]
A = 25000 (1 + 0.1) (1 + 0.12)
A = 25000 * 1.1 * 1.12
A = 25000 * 1.232
A = 30800
The amount of time adults spend watching television is closely monitored by firms becayse this helps to determine advertising pricing for commercials. Compete parts (a) through (d).
a) Do you think the variable "weekly time spent watching television" would be normally distributed? Yes or No.
If not, what shape would you expect the variable to have? Skewed Left, Skewed Right, Uniform or Symmetric?
b) According to a certain survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for "time spent watching TV on a weekday" is 1.93 hours. If a random sample of 40 adults is obtained, describe the sampling distribution of x-bar, the mean amount of time spent watching TV on a weekday.
Mean =
A) 2.35
B) 1.89
C) 2.25
SD = (round to six decimal places as needed)
c) Determine the probability that a random sample of 40 adults results in a mean time watching television on a weekday of between 2 and 3 hours.
The probability is ____ .
d) One consequence of the popularity of the Internet is that it is thought to reduce TV watching. Suppose that a random sample of 35 people who consider themselves avid Internet users results in a mean time of 1.89 hours watching TV on a weekday. Determine the likelihood of obtaining a sample mean of 1.89 hours or less from a population who mean is presumed to be 2.35 hours.
The likelihood is ____ .
Based on the result obtained, do Internet users watch less TV? Yes or No.
Answer:
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
Step-by-step explanation:
a)The variable "weekly time spent watching television" is normally distributed and is skewed right.
b) Mean = x` 2.35 hours
Standard deviation = s/√n = 1.93/√40=1.93/6.3245553= 0.3051598
c) P(2<X<3) = P (2-2.35/ 0.3051598< Z< 3 -2.35/ 0.3051598)
= P ( -1.14694 < Z <2.13003)
= 0.3729 + 0.4830
=0.8559
So the probability is 0.8559
(0.8559 we check the value of 2.13 from the normal distribution tables and add with the value of 1.14 to get the in between value -1.14694 < Z <2.13003)
d) Here n = 35 , s= 1.93 , mean = 2.35 and x= 1.89
So Putting the values
P (X ≤ 1.89) = P (Z ≤ 1.89- 2.35/ 1.93 / √35)
= P ( Z ≤ -0.238341/ 5.9160797)
= P ( Z ≤ -0.04028)
= 0.5 - 0.0159
= 0.4841
Similarly again subtracting from 0.5 the value from normal distribution table to get less than or equal to value.
Yes based on the result 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5
The mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes 0.4841 internet users watch less TV.
It is given that the amount of time adults spend watching television is closely monitored by firms because this helps to determine advertising pricing for commercials.
It is required to find the standard deviation and probability.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We know the formula for standard error:
[tex]\rm SE = \frac{s}{\sqrt{n} }[/tex]
Where 's' is the standard error
and n is the sample size.
In the question the value of s = 1.93 hours
and sample size n = 40
[tex]\rm SE = \frac{1.93}{\sqrt{40} }\\[/tex]
SE = 0.3051597
For the probability between 2 and 3 hours.
= P(2<X<3)
[tex]\\\rm =P(\frac{2-x)}{s} < Z < \frac{3-x)}{s})\\\\\rm = P(\frac{(2-2.35)}{0.3051598} < Z < \frac{(3-x)}{0.3051598})\\\\[/tex] (because the mean value x is 2.35)
=P(-1.14694 <Z < 2.13003)
=0.3729+ 0.4830 ( values get from Z table for -1.14 and 2.13 )
=0.8559
For P(X≤1.89)
[tex]\rm P(Z\leq \frac{(x'-x)}{\frac{s}{\sqrt[]{n} } } )\\\\\rm P(Z\leq \frac{(1.89-2.35)}{\frac{1.89}{\sqrt[]{35} } } )[/tex]
= P(Z ≤ -0.04028)
= 0.5 - 0.0159
=0.4841
Based on the result of 0.4841 the internet users watch less TV because the mean would be placed at 0.5 and it is less than 0.5.
Thus, the mean value is 2.35, SD is 1.93 with an SD error of 0.3051597 and the probability is 0.8559, and yes internet users watch less TV.
Learn more about the standard deviation here:
https://brainly.com/question/12402189
Subtract (x^2+3x-4) -(4x-2x^2-3)
Answer:
3 x^2 - x + -1
Step-by-step explanation:
Simplify the following:
-(4 x - 2 x^2 - 3) + x^2 + 3 x - 4
Factor -1 out of -2 x^2 + 4 x - 3:
--(2 x^2 - 4 x + 3) + x^2 + 3 x - 4
(-1)^2 = 1:
2 x^2 - 4 x + 3 + x^2 + 3 x - 4
Grouping like terms, 2 x^2 + x^2 + 3 x - 4 x - 4 + 3 = (x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3):
(x^2 + 2 x^2) + (3 x - 4 x) + (-4 + 3)
x^2 + 2 x^2 = 3 x^2:
3 x^2 + (3 x - 4 x) + (-4 + 3)
3 x - 4 x = -x:
3 x^2 + -x + (-4 + 3)
3 - 4 = -1:
Answer: 3 x^2 - x + -1
how many numbers are there from 75 to 586 that are divisible by 12 and 30
Answer:
8
Step-by-step explanation:
Numbers divisible by 12 and 30:
12= 2*630= 5*6LCM(12,30) = 2*5*6= 60So, numbers should be divisible by 60
To find the greatest one divide 586 by 60 and take whole part of quotient, which is 9, so there are 9 multiples of 60 smaller than 586.
Excluding 60 which is less than 75.
So required number is 9 - 1 = 8.
HELPP !! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answer:
w=5000+0.7s
Step-by-step explanation:
please give 5 star I need it
There are two routes Lucas can take to walk to school. Route A is 2 and StartFraction 1 over 8 EndFraction miles and is StartFraction 3 over 8 EndFraction mile longer than route B. The equation b + StartFraction 3 over 8 EndFraction = 2 and StartFraction 1 over 8 EndFraction can be used to represent this situation, where b is the length of route B. How many miles will Lucas walk if he takes route B?
Answer:
1 3/4
Step-by-step explanation:
i took this quiz its the correct answer...
Answer:
B. ! 3/4 miles
Step-by-step explanation:
I got it right on edge.
A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.11.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Required:
Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period.
Answer:
The probability is [tex]P(X < 3) = P(X \le 3-1 = 2 ) = 0.8074[/tex]
Step-by-step explanation:
From the question we are told that
The probability of a tornado is [tex]p = 0.11[/tex]
The sample size is [tex]n = 14[/tex]
Since the number of tornadoes in any calendar year is independent of the number of tornadoes in any other calendar year and there can be only outcome so we can evaluate probability using binomial distribution.
The probability of a tornado not occurring is mathematically evaluated
[tex]q = 1 - p[/tex]
=> [tex]q = 1 - 0.11[/tex]
=> [tex]q = 0.89[/tex]
The probability that there are fewer than 3 tornadoes in a 14-year period is mathematically represented as
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = \left n } \atop {}} \right. C_2 * p ^2 q^{n- 2 } + \left n } \atop {}} \right. C_1 * p ^1 q^{n- 1 } + \left n } \atop {}} \right. C_0 * p ^r q^{n- 0 }[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = \left 14 } \atop {}} \right. C_2 * (0.11) ^2 (0.89)^{14- 2 } + \left 14 } \atop {}} \right. C_1 * (0.11) ^1 (0.89)^{14- 1 } + \left 14 } \atop {}} \right. C_0 * (0.11) ^0 (0.89)^{14- 0 }[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = 91 * 0.0121*0.247 + 14 * 0.11*0.2198 + 1 * 1 * 0.197[/tex]
[tex]P(X < 3) = P(X \le 3-1 = 2 ) = 0.8074[/tex]
Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.
r=12/3--10 Cosθ
Answer:
a) 10/3
b) hyperbola
c) x = ± 6/5
Step-by-step explanation:
a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
[tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
Given the conic equation: [tex]r=\frac{12}{3-10cos\theta}[/tex]
We have to make it to be in the form [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]:
[tex]r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }[/tex]
Comparing with [tex]r=\frac{ep}{1\pm e*cos\theta}[/tex]
e = 10/3 = 3.3333, p = 6/5
b) since the eccentricity = 3.33 > 1, it is a hyperbola
c) The equation of the directrix is x = ±p = ± 6/5
what is the volume of the box below ?5cm,8cm,10cm
Answer: Hi!
To find the volume of a box (or cube), you multiply length times width times height.
In this case, you have all of the measurements, so all we have to do is multiply them together!
5cm * 8cm * 10cm = 400
So, the volume of this box is 400cm^3!
Hope this helps!
Let f(x) = x2 - 4x and g(x) = 2x – 3. Find f(g(4))
Answer:
[tex]f(g(4)) = 5[/tex]Step-by-step explanation:
f(x) = x² - 4x
g(x) = 2x – 3
To find f(g(4)) we must first find f(g(x))
To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)
That's
[tex]f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12[/tex]We have
[tex]f(g(x)) = {4x}^{2} - 20x + 21[/tex]Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4
We have
[tex]f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80[/tex]We have the final answer as
[tex]f(g(4)) = 5[/tex]Hope this helps you
Answer:
Answer:
f(g(4)) = 5f(g(4))=5
Step-by-step explanation:
f(x) = x² - 4x
g(x) = 2x – 3
To find f(g(4)) we must first find f(g(x))
To find f(g(x)) substitute g(x) into f(x) that's for every x in f(x) replace it with g (x)
That's
\begin{lgathered}f(g(x)) = ({2x - 3})^{2} - 4(2x - 3) \\ = 4x^{2} - 12x + 9 - 8x + 12 \\ = 4 {x}^{2} - 12x - 8x + 9 + 12\end{lgathered}
f(g(x))=(2x−3)
2
−4(2x−3)
=4x
2
−12x+9−8x+12
=4x
2
−12x−8x+9+12
We have
f(g(x)) = {4x}^{2} - 20x + 21f(g(x))=4x
2
−20x+21
Now to find f(g(4)) substitute the value of x that's 4 into f(g(x)) that's replace every x in f(g(x)) by 4
We have
\begin{lgathered}f(g(4)) = 4( {4})^{2} - 20(4) + 21 \\ = 4(16) - 80 + 21 \\ = 64 - 80 + 21 \\ = 85 - 80\end{lgathered}
f(g(4))=4(4)
2
−20(4)+21
=4(16)−80+21
=64−80+21
=85−80
We have the final answer as
f(g(4)) = 5f(g(4))=5
Hope this helps you
about 60000 acres of wetlands are lost each year in the United States. what integer represents the change in wetlands after 4 years?
Answer:
240 000
Step-by-step explanation:
Change in wetlands each year: 60 000 acres
Change in wetlands after 4 years:
60 000 x 4 = 240 000 (acres)
Rearrange the equation so w is the independent variable.
u-5= -4(w - 1)
Answer:
w = ((u-5)/-4) + 1
Step-by-step explanation:
To make w an independent variable, it must be by itself, so we have
u - 5 = -4(w-1)
We divide both sides by -4
(u-5)/-4 = -4(w-1)/-4
(u-5)/-4 = w-1
Now we add 1 to both sides,
(u-5)/-4+1 = w-1+1
((u-5)/-4) + 1 = w
w = ((u-5)/-4) + 1
Answer:
u = -4w + 9.
Step-by-step explanation:
If w is the independent variable, it will be the variable you are changing.
u - 5 = -4(w - 1)
u - 5 = -4w + 4
u = -4w + 9.
Hope this helps!
#12 will mark as brainliest
Answer:
-i
Step-by-step explanation:
[tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] * [tex]\sqrt{-1}[/tex] = -i
Solve for m.
0 = -12 + m
Answer:
[tex]\huge \boxed{m=12}[/tex]
Step-by-step explanation:
[tex]m+-12=0[/tex]
[tex]\sf Add \ 12 \ to \ both \ sides.[/tex]
[tex]m+-12+12=0+12[/tex]
[tex]m=12[/tex]
Solve the following (^ this sign symbolizes the power) 7). 4^2 8). 7^2 9). 6^4 10). 1^2 11) 5^3 12) 1^3
Answer:
7. 4^2 = 6
8. 7^2 = 49
9. 6^4 =1296
10. 1^2 = 1
11. 5^3 =125
12. 1^3 =1
Step-by-step explanation:
If a=mg-kv2/m,find,correct to the nearest whole number the value of v when a=2.8,m=12,g=9.8 and k=8/3
Answer:
v = 23
Step-by-step explanation:
Formatting the question gives;
a = mg - kv² / m
Make v subject of the formula as follows;
(i) Multiply both sides by m
ma = m²g - kv²
(ii) Collect like terms
kv² = m²g - ma
(iii) Divide through by k
v² = (m²g - ma) / k
(iv) Take the square root of both sides
v = √ [(m²g - ma) / k] --------------(ii)
From the question:
a = 2.8
m = 12
g = 9.8
k = 8/3
Substitute these values into equation (i) as follows;
v = √ [(12²(9.8) - 12(2.8)) / (8/3)]
v = √ [(1411.2 - 33.6) / (8/3)]
v = √ [1377.6 / (8/3)]
v = √ [1377.6 x (3/8)]
v = √ [1377.6 x 3 / 8)]
v = √ [516.6]
v = 22.73
v = 23 [to the nearest whole number]
Therefore v = 23 to the nearest whole number
Express as a trinomal (2x-9) (3x+4)
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]\begin{aligned} (2x-9)(3x+4)=\ &2(3x+4)\\&-9(3x+4)\\\\ =\ & 6x+8\\&-27x-36\\\\=\ &(6-27)x+8-36\\\\=\ &-21x-28\end{aligned}[/tex]
Thank you.
a pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S. NEED TO TURN IT IN TODAY
Equation for the monthly wage will be → W = 0.07S + 5000
Given in the question,
Monthly salary of the sales-person = $5000Commission = 7% of total salesLet the total sales of a month = $S
Therefore, commission on this sale = 7% of $S
= $0.07S
Salary of the month = $5000
Total earnings (W) of the sales person = $(0.07S + 5000)
Therefore, equation for the monthly wage will be,
W = 0.07S + 5000
Learn more,
https://brainly.com/question/25362379
Part 2: Use congruency theorems to prove congruency
Answer: see proof below
Step-by-step explanation:
Statement Reason
1. YO = NZ 1. Given
2. OZ = OZ 2. Reflexive Property
3. YO + OZ = YZ 3. Segment Addition Property
NZ + OZ = NO
4. YO + OZ = NZ + OZ 4. Addition Property
5. YZ = NO 5. Substitution
6. ∠M ≅ ∠X 6. Given
7. ∠N ≅ ∠Y 7. Given
8. ΔMNO ≅ ΔXYZ 8. AAS Congruency Theorem
Step-by-step explanation:
Hope it helps u please mark it as brainlist
POINTS!!!!!!
If an object is dropped from a height of h meters and it’s the ground in t seconds, then t = *square root* h/4.9. Suppose that an object is dropped from the top of a building that is 290.57 meters tall. How long does it take to hit the ground?
Round your answer to the nearest tenth....
?????? Seconds
Please state how many seconds first...
Answer:
7.7 seconds
Step-by-step explanation:
Put the given height into the formula and do the arithmetic.
t = √(290.57/4.9) = √59.3 ≈ 7.7 . . . seconds
The object will take 7.7 seconds to hit the ground.
Suppose a team of doctors wanted to study the effect of different types of exercise on reducing body fat percentage in adult men. The 57 participants in the study consist of men between the ages of 40 and 49 with body fat percentages ranging from 32%â34%. The participants were each randomly assigned to one of four exercise regimens.Ten were instructed to complete 45 min of aerobic exercise four times a week.Eleven were instructed to complete 45 min of anaerobic exercise four times a week.Nine were instructed to complete 45 min of aerobic exercise twice a week and 45 minutes of anaerobic exercise twice a week.Nine were instructed not to exercise at all.All participants were asked to adhere to their assigned exercise regimens for eight weeks. Additionally, to control for the effect of diet on weight loss, the doctors provided the participants with all meals for the duration of the study. After eight weeks, the doctors recorded the change in body fat percentage for each of the participants.The doctors plan to use the change in body fat percentage data in a one-way ANOVA F?test. They calculate the mean square between as MSbetween=11.632991 and the mean square within as MSwithin=1.261143. Assume that the requirements for a one-way ANOVA F?test have been met for this study.Choose all of the correct facts about the F statistic for the doctors' ANOVA test.A. The F statistic increases as the differences among the sample means for the exercise groups increase.B. The F statistic is 0.1084.C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.D. The F statistic indicates which exercise treatment groups, if any, are significantly different from each other.E. The F statistic has 4 degrees of freedom in the numerator and 38 degrees of freedom in the denominator.F. The F statistic is 9.2242.
Answer:
A. The F statistic increases as the differences among the sample means for the exercise groups increase.
C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.
F. The F statistic is 9.2242.
Step-by-step explanation:
Given that
Observations Samples Total
40-49 10 11 9 9 39
The degrees of freedom is given by
For numerator= k-1 = 4-1=3
For denominator= n-k= 39-4= 35
F statistic is given by
F= MS between/ MS within
=11.632991 / 1.261143 = 9.2242
Where
Mean Square Between = MS between = 11.632991
Mean Square Within = MS within = 1.261143
Hence the correct choices are A, C and F
A. The F statistic increases as the differences among the sample means for the exercise groups increase.
C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.
F. The F statistic is 9.2242.
Suppose we have
Mean Square Between = MS between = 18.632991
Mean Square Within = MS within = 1.261143
Then F statistic would be = 14.77468 > 9.2242
which tells that The F statistic increases as the differences among the sample means for the exercise groups increase.
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z2)j + (z + x2)k, C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
Answer:
[tex]\mathbf{\int_C F*dr= -125}[/tex]
Step-by-step explanation:
Given that:
[tex]F(x,y,z) = ( x+ y^2) i + (y +z ^2) j+(z + x^2)k[/tex] , where C is the triangle with vertices (5, 0, 0), (0, 5, 0), and (0, 0, 5).
The objective is to use Stokes' Theorem to evaluate CF. dr
Stokes Theorem : [tex]\int_c F .dr = \iint _s \ curl \ F. dS[/tex]
To estimate curl F , we need to find the partial derivatives:
So;
[tex]P = x+y^2[/tex]
partial derivative is:
[tex]\dfrac{\partial P }{\partial y }= 2y[/tex]
[tex]\dfrac{\partial P }{\partial z }= 0[/tex]
[tex]Q = y + z^2[/tex]
partial derivative is:
[tex]\dfrac{\partial Q }{\partial x }= 0[/tex]
[tex]\dfrac{\partial Q }{\partial z }= 2z[/tex]
[tex]R = z +x^2[/tex]
partial derivative is:
[tex]\dfrac{\partial R }{\partial x }= 2x[/tex]
[tex]\dfrac{\partial R }{\partial y }= 0[/tex]
These resulted into
curl F = (0 - 2z)i + ( 0 -2x) j + ( 0 - 2y) k
= ( -2z, -2x, -2y )
The normal vector and the equation of the plane can be expressed as follows:
If a = (0,5,0 - ( 5,0,0)
a = ( -5,5,0 )
Also ,
b = (0, 0,5) - (5,0,0)
b = (-5. 0,5)
However,
[tex]a \times b = \begin {vmatrix} \begin{array} {ccc} i &j&k \\-5&5&0 \\-5&0&5 \\ \end {array} \end {vmatrix}[/tex]
a × b = (25 - 0)i - (-25-0)j+ (0+25)k
a × b = 25i +25j +25k
∴ the normal vector can be n = (1,1,1)
If we assume x to be x = (x,y,z)
and [tex]x_0 = (5,0,0)[/tex]
Then
[tex]n*(x-x_0) =0[/tex]
[tex](1,1,1)*(x-5,y-0,z-0) =0[/tex]
[tex]x-5+y+z =0[/tex]
collecting like terms
x +y +z = 5
now, it is vivid that from the equation , the plane of the normal vector =(1,1,1)
Similarly, x+y+z = 5 is the projection of surface on the xy - plane such that the line x +y = 5
Thus; the domain D = {(x,y) | 0 ≤ x ≤ 5, 0 ≤ y ≤ 5 - x}
To evaluate the line integral using Stokes' Theorem
[tex]\iint_S \ curl \ F .dS= \iint _S (-2z,-2y,-2x) *(1,1,1) \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2z-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -2(5-x-y)-2y-2x \ dS[/tex]
[tex]\iint_S \ curl \ F .dS= \iint _S -(10) \ dS[/tex]
[tex]\int_C F*dr= \int ^5_0 \ \int ^{5-x}_0 -10 \ dy \ dx[/tex]
[tex]\int_C F*dr= -10 \int^5_0 (5-x) \ dx[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 5x - \dfrac{x^2}{2} \end {bmatrix}^5_0[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} 25 - \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\int_C F*dr= -10 \begin {bmatrix} \dfrac{25}{2} \end {bmatrix}[/tex]
[tex]\mathbf{\int_C F*dr= -125}[/tex]
Teresa has completed 57 deliveries so far this week. She needs to make 60 deliveries for the week. What percentage of her deliveries has Teresa completed?
Step-by-step explanation:
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6 Hundreds 3 Tens 17 Ones in Standard Form
Answer:
the answer is647
Step-by-step explanation:
600+30+17
Answer:
647
Step-by-step explanation:
600
+ 30
17
_____
647
The vector is first dilated by a factor of 2.5 and then rotated by radians. If the resulting vector is , then a =_____ and b = ____.
Answer:
a = 10
b = 2.5
Step-by-step explanation:
The given vector is
<-1, 4>
Let [tex]\vec A[/tex] represents <-1, 4>.
First, the dilation is done by a factor of 2.5.
If the dilation of a vector <[tex]x_1[/tex], [tex]x_2[/tex]> is done by a factor k:
Then the resulting vector becomes:
[tex]<kx_1, kx_2>[/tex]
The resulting [tex]\vec B[/tex] as per above explanation:
[tex]<2.5\times -1, 2.5\times 4> \Rightarrow \vec B \bold{<-2.5, 10 > }[/tex]
Now, it is given that the vector is rotated by [tex]\frac{\pi}{2}[/tex] or [tex]90^\circ[/tex].
The steps to find the resulting vector after the rotation of [tex]\frac{\pi}{2}[/tex] or [tex]90^\circ[/tex], we can use the simple method:
Step 1: Multiply the [tex]x[/tex] value with -1.
i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).
Step 2: Swap the values of [tex]x[/tex] and [tex]y[/tex].
So, the resulting vector is:
<10, 2.5>
In other form, we can represent the above vector as:
[tex]\left[\begin{array}{c}10&2.5\end{array}\right][/tex]
Comparing with [tex]\left[\begin{array}{c}a&b\end{array}\right][/tex]
a = 10
b = 2.5
Answer:
The correct answer is -10 and -2.5
Step-by-step explanation:
Plato
write the remainder when [x ^2 -1] is divided by (x-1)
(9x + 1) -(-7x2 + 4x + 10)
Answer:
= 7x² + 5x - 9
Step-by-step explanation:
(9x + 1) - (-7x² + 4x + 10)
= 9x + 1 - ( -7x² + 4x + 10)
= 9x + 1 + 7x² - 4x - 10
= 7x² + 5x - 9
The sum of the present ages of lily and Chris is 36. In 4 years time, the sum of their ages will equal twice Lily’s present age? How old are they now?
Answer:
If the present age is x, then age n years later/hence = x + n. If the present age is x, then age n years ago = x – n. The ages in a ratio a: b will be ax and bx. If the current age is y, then 1/n of the age is y/n.
hat are the two decisions that you can make from performing a hypothesis test? What are the two decisions that you can make from performing a hypothesis test? Select all that apply. A. make a type II error B. make a type I error C. reject the alternative hypothesis D. fail to reject the alternative hypothesis E. reject the null hypothesis F. accept the null hypothesis G. accept the alternative hypothesis H. fail to reject the null hypothesis
Answer:
One is :
C. reject the alternative hypothesis
F. accept the null hypothesis
The other is :
E. reject the null hypothesis
G. accept the alternative hypothesis
Another type of decision is when we
D. fail to reject the alternative hypothesis
E. reject the null hypothesis
and
H. fail to reject the null hypothesis
C. reject the alternative hypothesis
Step-by-step explanation:
There are two types of decisions that we can make .
One is :
C. reject the alternative hypothesis
F. accept the null hypothesis
The other is :
E. reject the null hypothesis
G. accept the alternative hypothesis
Another type of decision is when we
D. fail to reject the alternative hypothesis
E. reject the null hypothesis
and
H. fail to reject the null hypothesis
C. reject the alternative hypothesis
It is clear from the above that when we reject one hypothesis we accept the other hypothesis.
or
When we fail to reject one hypothesis we reject the other hypothesis.