By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be
[tex]\displaystyle \iint_{\partial R}\mathbf F\cdot\,\mathrm d\mathbf S = \iiint_R\mathrm{div}(\mathbf F)\,\mathrm dx\,\mathrm dy\,\mathrm dz \\\\ = \int_0^1\int_0^3\int_0^1\frac{\partial(2x^2)}{\partial x} + \frac{\partial(5y^2)}{\partial y} + \frac{\partial(3z^2)}{\partial z} \,\mathrm dx\,\mathrm dy\,\mathrm dz \\\\ = \int_0^1\int_0^3\int_0^1 (4x+10y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz = \boxed{60}[/tex]
In this exercise we have to calculate the flux by the divergent theorem:
[tex]\int\limits\int\limits_R\, ds = 60[/tex]
By the divergence theorem, the flux of F across the boundary of a region, ∂R, is equal to the integral of div(F ) over the region itself, R. In this case, the flux would be:
[tex]\int\limits\int\limits_R {F} \, ds= \int\limits \int\limits \int\limits_R {div(F)} \, dxdydz\\=\int\limits^1_0 \int\limits^3_0 \int\limits^1_0 {(4x+10y+6z)} \, dx dy dz= 60[/tex]
See more about vectorial calculus at : brainly.com/question/6960786
If angle DFG ~ angle RPQ, the value of x=_____
Answer:
[tex] x = 6.25 [/tex]
Step-by-step explanation:
Given that ∆DFG ~ ∆RPQ, therefore, [tex] \frac{DF}{PR} = \frac{DG}{QR} = \frac{FG}{QP} [/tex] (similarity theorem).
DF = 10
PR = 8
DG = 5
QR = 4
QP = 5
FG = x
[tex] \frac{10}{8} = \frac{5}{4} = \frac{x}{5} [/tex]
Using [tex] \frac{5}{4} = \frac{x}{5} [/tex] , solve for x
cross multiply:
[tex] 4*x = 5*5 [/tex]
[tex] 4x = 25 [/tex]
[tex] x = \frac{25}{4} [/tex]
[tex] x = 6.25 [/tex]
What is the best estimate of the number corresponding to A?
A
1
2
3
4
0 2.6
0 2.4
0 2.2
2.3
Answer:
2.6
Step-by-step explanation:
Let us assume that the unit of measurement is centimetre (cm)
To obtain the value of A, do the following:
From the diagram above, we can say that the scale is 5 cm to 1 unit since there are 5 lines before a number.
Next, we shall determine the value of 1 cm.
5 cm = 1 unit
Therefore,
1 cm = 1/5 = 0.2 unit
This means that 1 small line is equivalent to 0.2 unit.
Now we shall determine A as follow:
A is exactly 3 lines (3 cm) after number 2.
1 cm = 0.2 unit
3 cm = 3 x 0.2 = 0.6 unit
Now, add 0.6 to 2 to obtain the value of A.
A = 2 + 0.6
A = 2.6
Therefore, A correspond to 2.6
Directions: Round $45.58 to the nearest dollar.
$None of these
$46.60
$45.60
$45
$45
Answer:
none of these unless one of the 45s are 46
Step-by-step explanation:
nearest dollar means no cents so $46.60 and $45.60 are out
58 is over 50 so the two 45s go away
the only option left is none of these or 46 if you accidentally put 45 instead of 46
Under what circumstances can a very small treatment effect be statistically significant? Explain your response.
a) if the sample size big and the sample variance is small
b) if the sample size and the sample variance are both big
c) if the sample size is small and the sample variance is big
d) if the sample size and the sample variance are both small
Answer:
The correct answer is:
if the sample size big and the sample variance is small (a)
Step-by-step explanation:
The sample size of a study is the group of subjects that are selected from the general population and is considered an accurate representation of the population. With a large sample size, the likelihood of type I and type II errors occurring reduces. Increasing sample size allows the researcher to increase the significance level of the finding because it increases accuracy in coverage of the universal set, hence the effect accurately mirrors what goes on in the whole group. However, smaller sample size, on the other hand, does not accurately mirror the whole larger group.
The sample variance is the difference between the observed value and the true(actual). It is a measure of deviation or variability between the results and the true value. A smaller variance means increase closeness to the true value hence increase in accuracy and statistical significance.
Therefore, when the treatment effect is small but the sample size is large and variance is small, then the result is statistically significant.
Rachel just purchased a homeowners insurance policy for her new home that costs $0.43 per $100. Her home is worth $387,500. What is Rachel’s annual homeowners insurance premium? a. $1,666.25 b. $2,208.75 c. $8,802.33 d. $9,011.63 Please select the best answer from the choices provided
Answer:
The answer is A.
Do you need an explanation?
387,500 /100 = 3,875
3,875 * 0.43 = 1,666.25
I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!
Plewse help me idk how to do it (20 points)!!
The explicit formula for a straight line is written as y = Mx + b, where m is the slope and b is the y intercept.
The y intercept is the y value of where the line crosses the x axis. On the above picture the line crosses the x axis at -2, so the y intercept is -2
Use 2 points in the line for the slope:
Slope = change in y over the change in x:
(0,-2) (6,0)
Slope = (0- -2) / (6-0) = 2/6 = 1/3
Answer: y = 1/3x-2
(7-10x)/5 simplify express on integers and fractions
Answer:
-2x + 7/5
Step-by-step explanation:
(7-10x)/5
= [tex]\frac{-10x}{5}[/tex] + [tex]\frac{7}{5}[/tex]
= -2x + 7/5
A company sells x units of an item each day at the rate of Rs. 50. The cost of manufacturing each unit of an item is Rs. 36.50 and the dristributor demands a charge of Rs. 3.50 per unit. If the daily overhead charge is Rs. 2600, find the profit function. Also find the profit if 360 units of an item are produced and sold daily?
Answer:
Y(x) = 10x - 2600
Profit= RS. 1000
Step-by-step explanation:
Amount sold per item=RS. 50.
Cost of manufacturing= RS. 36.5
Distributor charges= Rs 3.5
Daily over head charge= RS.2600
Profit function Y (x)
Y (x) =x(50) -36.5(x) -3.5(x)-2600
Y(x) = (50-36.5-3.5)x-2600
Y(x) = 10x - 2600
If x= 360
Profit Y = 10(360) - 2600
Profit Y = 3600-2600
Profit = 1000
Profit= RS. 1000
The 7th grade had a book drive. They donated 2/3 of the books to the st James school. Then donated 1/4 of the remaining books to widener. If they had 16 books left after donating to the 2 schools, how many books did they collect in the book drive?
Answer: 192 books
Step-by-step explanation:
2/3 + 1/4 = 11/12
16 remaining books = 1/12
16 x 11 = 176
176 + 16=192
Answer:
ksdljfdacnkjdsfhbjfjkn
Step-by-step explanation:
Peter mixes 4 1/3 cups of orange juice, 2 1/3 cups of ginger ale, and 6 1/2 cups of strawberry lemonade to make some punch. What is
the total number of cups of punch that Peter makes?
Answer:
13 1/6 cups.
Step-by-step explanation:
4 1/3 + 2 1/3 + 6 1/2
= 4 + 2 + 6 + 1/3 + 1/3 + 1/2
= 12 + 2/6 + 2/6 + 3/6
= 12 + 7/6
= 12 + 1 1/6
= 13 1/6.
Answer:
13 1/6
Step-by-step explanation:
3/4x=21 Can you please assist?
Answer:
x =28
Step-by-step explanation:
Divide the numbers
Combine multiplied terms into a single fraction
Eliminate fraction denominators
Simplify
Divide both sides of the equation by the same term
Write this statement in your own words: ∃x ∈ ℕ, y ∈ ℤ|x² = y² Rewrite this using the appropriate mathematical notation: Even numbers are in the set of integers.
Answer:
See below.
Step-by-step explanation:
1)
So we have:
[tex]\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2[/tex]
This can be interpreted as:
"There exists a natural number x and an integer y such that x² is equal to y²."
2)
So we want even numbers are in the set of integers.
[tex]\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}[/tex]
This is interpreted as:
"The set of even numbers (2n such that n is an integer) is in the set of integers"
4.
Oscar Hammerstein's Island, an amusement park, plans a TV ad campaign. It will
run 30-second ads for the next 20 days on a daytime show. Hammerstein's will
also run 30-second ads for the next 5 days during a prime-time show. A 30-second
daytime ad costs $6,200, a 30-second prime-time ad costs $165,000. What is the
total ad campaign cost?
Answer:
Hey there!
30-second ads for 20 days on a day time show.
6200(20)=124000
30-second ads for 5 days on a prime time show.
165000(5)=825000
124000+825000=949000 dollars.
Let me know if this helps :)
A manufacturer has been selling 1000 flat-screen TVs a week at $400 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of TVs sold will increase by 100 per week.
(a) Find the demand function (price p as a function of units sold x).
(b) How large a rebate should the company offer the buyer in order to maximize its revenue?
(c) If its weekly cost function is C(x) = 73,000 + 110x, how should the manufacturer set the size of the rebate in order to maximize its profit?
Answer:
Explained below.
Step-by-step explanation:
(a)
It is provided that the price function for 1000 TVs is,
p (1000) = 400.
Also provided that if rebate of $10 is given then sale increases by 100 per week.
Let x be the number of unit sold per week then (x − 1000) is the increase in the number of units sold.
Then the price function is:
[tex]p(x)=400-\frac{1}{10}(x-1000)[/tex]
[tex]=400-\frac{x}{10}+100\\\\=500-\frac{x}{10}[/tex]
Thus, the demand function is, [tex]p(x)=500-\frac{x}{10}[/tex].
(b)
The revenue function is:
[tex]R(x)=x\cdot p(x)[/tex]
[tex]=x[500-\frac{x}{10}]\\\\=500x-\frac{x^{2}}{10}[/tex]
Maximize the revenue as follows:
[tex]\frac{d}{dx}(R(x))=0[/tex]
[tex]\frac{d}{dx}[500x-\frac{x^{2}}{10}]=0[/tex]
[tex]500-\frac{x}{5}=0[/tex]
[tex]\frac{x}{5}=500[/tex]
[tex]x=2500[/tex]
Observe that R'(x) > 0 for 0 ≤ x < 2500 and R'(x) < 0 for x > 2500. Hence, first derivative test will lead to the conclusion that maximum occurs at x = 2500.
Compute the value p (2500) as follows:
[tex]p(2500)=500-\frac{2500}{10}=500-250=250[/tex]
Then the rebate to maximize the revenue should be: $400 - $250 = $150.
(c)
The weekly cost function is,
[tex]C(x) = 73000 + 110x[/tex]
Compute the profit function as follows:
[tex]P(x)=R(x)-C(x)[/tex]
[tex]=500x-\frac{x^{2}}{10}- 73000 - 110x\\\\=390x-\frac{x^{2}}{10}- 73000[/tex]
Compute the marginal profit as follows:
[tex]\text{Marginal profit}=P'(x)\\=\frac{d}{dx}P(x)\\=\frac{d}{dx}[390x-\frac{x^{2}}{10}- 73000]\\=390-\frac{x}{5}[/tex]
Compute the value of x for P'(x) = 0 as follows:
[tex]P'(x)=0\\\\390-\frac{x}{5}=0\\\\x=390\times 5\\\\x=1950[/tex]
Observe that P'(x) > 0 for 0 ≤ x < 1950 and P'(x) < 0 for x > 1950. Hence, first
derivative test will lead to the conclusion that maximum occurs at x = 1950.
Compute the value p (1950) as follows:
[tex]p(1950)=500-\frac{1950}{10}=500-195=305[/tex]
Then the rebate to maximize the profit should be: $400 - $305 = $95.
The net of a square pyramid is shown
below. What is the surface area of the
pyramid?
A 100 cm2
B 136 cm2
C 172 cm2
D 192 cm2
Answer:
Option (D)
Step-by-step explanation:
Surface area of a square pyramid is determined from the formula,
Surface area = Area of the square base + 4(Area of one lateral triangular side)
Area of the base = (Side)²
= 8²
= 64 cm²
Area of one lateral triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(8)(8)[/tex]
= 32 cm²
Therefore, surface area of the square pyramid = 64 + 4(32)
= 64 + 128
= 192 cm²
Therefore, Option (D) will be the correct option.
PLEASE HELP! URGENT! Exponential function f is being represented by the table (photo attached) the function “g” is an exponential function passing through the points of (0, 15) , (2, 0). Which of the statements below correctly compared the behavior of these two functions on the interval (0, 2) ??
Answer:
C) Both functions are decreasing and both are positive on the interval (0;2)
Step-by-step explanation:
As known the exponent function has no minimum and has no maximum.
Otherwise exponent function can be only or increasing or decreasing for all x.
That means that in case y(x2)>y(x1) and if x2>x1- function is increasing.
That means that in case y(x2)<y(x1) and if x2>x1- function is decreasing.
Lets check what is going on with the function f(x)
If x1=0 f(x1)=24
If x2=2 f(x2)=0
So x2>x1 however f(x2)<f(x1)=> function is decreasing
Similarly g(x)
If x1=0 g(x1)=15
If x2=2 g(x2)=0
So x2>x1 however g(x2)<g(x1) => function is decreasing
So bothfunctions are decreasing.
Because f(x) is decreasing the function meaning with argument x1=0 has max in the interval x∈(0;2) And function meaning has the minimum if argument x2=2. So the function F(x) in interval (0;2) is changing from 24 to 0 => is positive on the interval (0,2)
The same is with g(x) . g(x) gonna be positive on the interval (0;2)
Write each statement as a decimal to two decimal places.
$6.00 to 95 cents =
3 hours to 35 minutes =
42 inches to 2 feet =
(Hint: there are 12 inches in 1 foot.)
Answer:
Step-by-step explanation:
To convert the statement to decimals, we need to use the following conversion rate.
Since $1 = 100cents
Writing $6.00 to 95 cents as a decimal, we need to writw both units in the same units.
$6.00 to 95 cents = 600cents to 95 cents
= 600cents:95cents
= 600cents/95cents
= 6.32 (to 2dp)
For 3 hours to 35 minutes
SI=ince 1 hour = 60minutes
3 hours to 35 minutes = (3*60)minutes to 35 minutes
= 180minutes : 35 minutes
= 180minutes/35 minutes
= 5.14 (to 2dp)
For 42 inches to 2 feet
Given 12inches = 1 foot
42 inches to 2 feet = 42inches to (2*12)inches
= 42inches to (24)inches
= 42inches : 24 inches
= 42inches/24 inches
= 1.75 (to 2dp)
V2y + 3 = 11
3. What is the value of y in this equation?
O A. y = 32
OB. y = 64
O C. y = 14
OD. y = 16
Answer:
v2y +3=11
V2y=11- 3
V2y=8
2y=8²
2y=64
y=64÷2
y=32 Answer
mg+rg=2H, solve for g
Answer:
[tex]g=\frac{2\,H}{m+r}[/tex]
Step-by-step explanation:
Starting with :
m g + r g = 2 H
extract "g" as a common factor on the left of the equal sign:
g (m + r) = 2 H
Now, in order to solve for "g" , divide both sides of the equal sign by the binomial (m + r):
g = (2 H )/(m + r)
[tex]g=\frac{2\,H}{m+r}[/tex]
To which subset(s) of real numbers does the number 4 belong? 1. Irrational numbers 2. Integers 3. Whole numbers 4. Natural numbers 5. Rational numbers
Answer:
whole number
hope it helps
Solve the following proportion for x.
X/11 = 7/17
Round your answer to the nearest tenth.
X = ??
Answer:
77/17 = 4.52941Nearest tenth = 4.5Step-by-step explanation:
[tex]\frac{x}{11}=\frac{7}{17}\\\\\mathrm{Multiply\:both\:sides\:by\:}11\\\\\frac{11x}{11}=\frac{7\cdot \:11}{17}\\\\\mathrm{Simplify\:}\frac{11x}{11}:\quad x\\\\\mathrm{Simplify\:}\frac{7\cdot \:11}{17}:\quad \frac{77}{17}\\\\x=\frac{77}{17}[/tex]
If x/5+6 =-14, then x=
Answer:
(5+6)14 = x
11×14 = x
154 =x
Answer:
x = -100
Step-by-step explanation:
x/5+6 =-14
Subtract 6 from each side
x/5+6 -6 = -14-6
x/5 = -20
Multiply each side by 5
x/5*5 = -20*5
x = -100
If a and b are two digits, then the following fraction
(ab0+ab0ab)÷(ab) -1 is equal to.
A.21 B. 1010
C. 110
D. 111
E. 1110
Answer:
B. 1010
Step-by-step explanation:
Simplify:
(ab0+ab0ab) ÷ (ab) - 1Note that:
ab = 10a +bab0 = 10* (10a + b) = 10abab0ab = 1000ab + ab = 1001 abTherefore:
(ab0+ab0ab) ÷ (ab) - 1 =(10ab + 1001ab) ÷ (ab) - 1 =(1011ab) ÷ (ab) - 1 = 1011 - 1= 1010Correct choice is B.1010
Travel
324 miles on 18 gallons of gas
Answer:
324 miles divided by 18 gallons = 18 miles per gallon (mpg)
Therefore, 41 gallons x 18 mpg = 738
Step-by-step explanation:
1.008÷0.8
show work
Answer:
1.26
Step-by-step explanation:
1.008 divided by o.8 =1.26
Answer:
1.26, Dude get a calculator
Step-by-step explanation:
0 1. 2 6 0
8 1 0. 0 8 0
− 0 Listen. Its hard to do long division ona computer.
1 0
− 8
2 0
− 1 6
4 8
− 4 8
0 0
− 0
0
Sandra has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and
the amount of money with her is Rs 75, then find the number of Re 1 and Rs 2 coins
I hope this helps you. Plz mark me as the brainliest.
HELP PLS! THANK YOU SO MUCH! Consider the quadratic equation 3x^2-6=2x. (a) What is the value of the discriminant? (b) What does the discriminant of the quadratic equation tell about the solutions to 3x^2-6=2x
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant Δ = b² - 4ac informs us about the nature of the roots.
• If b² - 4ac > 0 then 2 real and distinct roots ( solutions )
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then roots are not real
Given
3x² - 6 = 2x ( subtract 2x from both sides )
3x² - 2x - 6 = 0 ← in standard form
with a = 3, b = - 2, c = - 6 , thus
b² - 4ac = (- 2)² - ( 4 × 3 × - 6) = 4 - (- 72) = 4 + 72 = 76
Since b² - 4ac > 0 then the solution is 2 real and distinct roots
Below are some data examining whether reading the textbook for this course is related to class enjoyment.
Time Reading Textbook 1 2 3 4 5 6 1 2 3 5
Class Enjoyment 20 24 35 46 67 80 12 34 34 78
Note: Text Reading Time: 1 = does not read – 6 = only book I have ever read. Class Enjoyment: 1-100 scale.
Calculate the slope
a) 14.50
b) 13.36
c) 19.00
d) 12.43
Answer:
13.36
Step-by-step explanation:
I will first create a table
X. Y. XY. X²
1. 20. 20. 1
2. 24. 48. 4
3. 35. 105. 9
4. 46. 184. 16
5. 67. 335. 25
6. 80. 480. 36
1. 12. 12. 1
2. 34. 68. 4
3. 34. 102. 9
5. 78. 430. 25
ΣX = 32
ΣY = 430
ΣXY = 1744
ΣX² = 130
n = 10
The formula for regression line is given as :
Y = a + bX
a = intercept
b = slope
The question requires us to find b which is the slope.
b = nΣXY-ΣXΣY/nΣX²-(ΣX)²
= 10x1744-32x430/10x130-(32)²
= 17440-13760/1300-1024
= 3680/276
= 13.36
b = 13.36
Paulina’s father pays her $20 per month for doing chores. In April, she makes a deal with him. Rather than paying her $20, he can pay her 1¢ on the first day of the month, 2¢ on the second, 4¢ on the third, and continue each day by doubling the amount he paid on the previous day. Use the properties of exponents to write expressions for the first 5 days of the month. The, explain if Paulina will make more or less than $20 per month using this pattern.
Answer:
Step-by-step explanation:
This is a geometric sequence with first element 1 and common ratio 2:
a(n) = 1*2^(n - 1)
Thus, a(1) = 1
a(2) = 2^(2 - 1) = 2
a(3) = 2^(3 - 1) = 4
a(4) = 2 ^( 4 - 1) = 2^ 3 = 8
a(5) = 2^(5 -1) = 2^ 4 = 16
One month is approximately 30 days. Therefore,
a(30) = 2^ (30 - 1) = 2^29 = 536870912
Using this pattern, Paulina will "make" $536870.12 vs $20 via Paulina's father's plan.
what is 24,159 -3,168 =
Answer:
20991
Step-by-step explanation: