Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
Consider the following two questions designed to assess quantitative literacy: a. What is 15% of 1000? b. A store is offering a 1596 off sale on all TVs. The most popular television is normally priced at $1000. How much money would a customer save on the television during this sale? Suppose the first question is asked of 200 randomly selected college students, with 165 answering correctly; the second one is asked of a different random sample of 200 college students, resulting in 142 correct responses. Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context. (Use p1 for the true proportion students who answered the question without context correctly and p2 for the true proportion of students who answered the question with context correctly.) Carry out a test of hypotheses at significance level 0.05 to decide if the true proportion of correct responses to the question without context exceeds that for the one with context.
Answer:
The calculated value of z= 2.7225 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
Step-by-step explanation:
a: 15 % of 1000= 150
b. 15.96 % of $ 1000= $ 159.6
The customer would pay = $ 1000- $ 159.6= $ 840.4 and save $ 159.6
Formulate the hypotheses as
H0: p1= p2 true proportion of correct responses to the question without context is equal that for the one with context.
Ha : p1≠ p2
We choose the significance level ∝= 0.05
The critical value for two tailed test at alpha=0.05 is ± 1.96
The test statistic is
Z = p1-p2/ √pq (1/n1+ 1/n2)
p1= true proportion students who answered the question without context correctly = 165/200=0.825
p2= true proportion of students who answered the question with context correctly = 142/200= 0.71
p = an estimate of the common rate on the assumption that the two proportions are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.825) + 200 (0.71) / 400
p= 165+ 142/400= 307 /400 =0.7675
now q = 1-p= 1- 0.7675= 0.2325
Thus
z= 0.825- 0.71/ √0.7675*0.2325( 1/200 + 1/200)
z= 0.115/√ 0.17844( 2/200)
z= 0.115/0.04224
z= 2.7225
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level, true proportion of correct responses to the question without context exceeds that for the one with context.
PLEASE it's easy - "collecting like terms" It's algebra
Answer: The equation is correct.
Step-by-step explanation:
from the expression,
5x + 3( y + 4x² + 3x ) + 2( y - x² ) = 14x + 10x² + 5y
Open brackets with 3 and 2
5x + 3y + 12x² + 9x + 2y - 2x²
Now collect like terms
5x + 9x + 12x² - 2x² + 3y + 2y
14x + 10x² + 5y = 14x + 10x² + 5y (Q.E.D)
TH equation is correct
Area of a triangle
A/12 = 12/12bh
solve for b
Step-by-step explanation:
I hope this works for ya.
solve the following equations for x (3x-6)=18
Answer:
x = 8
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other side.
3x - 6 = 18
Add 6 to both sides
3x = 24
Divide both sides by 3
x = 8
The answer is 8
Hope this helps!
Answer:
x=8
Step-by-step explanation:
(3x-6)=18
Add 6 to each side
(3x-6+6)=18+6
3x= 24
Divide by 3
3x/3 = 24/3
x = 8
What are the factors of 60 ???
Answer:
Factors are 1,2,3,4,5,6,10,12,15,20,30,60
Step-by-step explanation:
Hope this helps
Factors refers to those numbers which muntiplied that no.here, numbers that muntiply 60 are 1,2,3,4,5,6,10,12,15,20,30,60.
thus these numbers are factors of 60.
a team's stadium has a capacity of 86,047. The fan base is notorious for selling out of tickets every game. If every game sells out this year, how many tickets are sold in their 12 game regular season play?
Answer:
1,032,564 tickets
Step-by-step explanation:
Find how many tickets they sell in total by multiplying the capacity of the stadium by the number of games in the season:
86,047(12)
= 1,032,564
So, if every game sells out, 1,032,564 tickets will be sold.
Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]
Answer:
y=3x
Step-by-step explanation:
-6/-2=3, -3/-1=3, 3/1=3. 6/2=3
Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the right ΔABD,
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]
BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]
= [tex]\frac{21}{2}[/tex]
Now by applying Cosine rule in the right ΔBDC,
Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]
x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]
x = [tex]\frac{21\sqrt{2}}{2}[/tex]
Therefore, Option (D) is the correct option.
6th grade math. :) help me please
Answer:
8 3/4
Step-by-step explanation:
The decimal 3.5 as an improper fraction is 35/10.
Answer:
[tex]8\frac{3}{4}[/tex]
Step-by-step explanation:
To write as a mixed number means that you will have a whole number and a fraction together. To find the mixed fraction version, see how many times the denominator (bottom) fits into the numerator (top) evenly.
4, 8, 12, 16, 20, 24, 28, 32, 36
1 2 3 4 5 6 7 8 9
4 can go into 35 '8' times without being greater than the numerator. 8 is the whole number. Now subtract the original numerator by the product of 4 and 8, which is 32:
[tex]35-32=3[/tex]
3 is the new numerator. Keep the same denominator. Insert all values:
[tex]\frac{35}{4}=8\frac{3}{4}[/tex]
:Done
the mass of 2bags of beans and
3 bags of salt is 410kgs
if the mass of 3bags of beans and
2bags of salt is 390kg find the
mass of each item.
Answer:
70kg- weight of the bag of beans, 90 kg- weight of the bag of salt
Step-by-step explanation:
Suppose the mass of a bag of beans - x kg, the mass of a bag of salt - y kg
The mass 2 bags of beans 2x, The mass 3 bags of salt 3y
2x+3y= 410
The mass of 3 bags of beans 3x, for 2 bags of salt it is 2y
3x+2y=390
We have system of equations (the equations are simultaneous)
2x+3y=410
3x+2y=390
2x= 410-3y
x=205-1.5y
3* (205-1.5y)+2y=390
615-4.5y+2y=390
2.5y= 225
y=90- the mass of the bag of salt
x= 205 - 1.5*90= 205-135= 70- the mass of the bags of beans
I need help with this math problem please (3x+2)(5x-7)
Answer:
Hey there!
Using the foil method: (3x+2)(5x-7)
15x^2+10x-21x-14
15x^2-11x-14
Let me know if this helps :)
Theresa bought 2 pineapples for $6. She be wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part A
Using the diagram, find the constant of proportionality in terms of dollars per pineapple.
Answer:
$3 per pineapple
Step-by-step explanation:
Hey there!
If 2 pineapples are $6,
6 / 2 = 3
So 1 pineapple is $3.
Hope this helps :)
Answer:
3 dollars for 1 pineapple
Step-by-step explanation:
well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.
You are planning to attend college next year. The total cost of tuition and textbooks is $10,000. If you go to school, your room and board will cost you $5,000. If you did not go to school, however, you would live at home, and your total room and board would only be $1,000. Additionally, if you did not go to college, you would work a job making $20,000 for the year.
1. In terms of room and board alone, what would be opportunity cost of attending college. Be sure to explain your answer
2. What are the explicit costs of attending school? How much should be included for room and board?
3. What would be the implicit cost of attending college next year?
4. What would be the total opportunity cost of attending college next year?
Opportunity Cost of attending college, in terms of room and board is $4000 . Explicit Cost, Implicit Cost of attending college is $14000, $20000. Total Opportunity Cost of attending college is $34000
1. Opportunity Cost is the cost of next best alternate foregone, as in value of sacrifice made, while choosing an alternative.
Money foregone to attend college, in room & board = room & board cost with college - room & board cost without college = 5000 - 1000 = 40002. Explicit Cost is the actual out of pocket cash expenses outflow, done for choosing an option. Eg : Cash expenditures
In this case, cash expenses for attending college = 140003. Implicit Cost is the implied estimated cost of self supplied factors of production, like value of self labour & self owned land etc.
In this case : Value of self labour, sacrificed for attending college, ie the salary which could have earned by doing job meanwhile = 200004. Total opportunity cost of attending college = Explicit Cost + Implicit Cost = 14000 + 20000 = 34000
To learn more, refer https://brainly.com/question/12121515?referrer=searchResults
Which is the solution to the inequality?
2 3/5 <b-8/15
Answer:
3 2/15 <b
Step-by-step explanation:
2 3/5 <b-8/15
Add 8/ 15 to each side
2 3/5 + 8/ 15 <b-8/15 + 8/15
2 3/5 + 8 /15 <b
Get a common denominator
2 3/5 *3/3 + 8/15
2 9/15 + 8/15 < b
2 17/15 < b
2 + 15/15 + 2 /15 < b
3 2/15 <b
Answer:
B > 3 2/15
Step-by-step explanation:
How much can 1/2 go into 25
Answer:
50
Step-by-step explanation:
please mark me as brainliest
Answer:
50
Step-by-step explanation:
Hi there!
Determining how much 1/2 can go into 25 is the same as solving for 25÷1/2:
[tex]25\div\frac{1}{2}[/tex]
Dividing by a fraction is the same as multiplying its reciprocal:
[tex]=25\times\frac{2}{1}\\=25\times2\\=50[/tex]
I hope this helps!
Please help! I’ll mark you as brainliest if correct.
Answer:
160 liters of 25%, 20 liters of 40%, 60 liters of 60%
Step-by-step explanation:
x + y + z = 240
0.25x + 0.4y + 0.6z = 0.35*240 = 84
z = 3y
x = 160
y = 20
z = 60
One more than three times a number is the same as four less than double a number
Answer:
3x + 1 = 2x - 4. x = -5
Step-by-step explanation:
In the figure above, point O is the center of the circle,
line segment BC is tangent to the circle at point B,
point A lies on the circle, and point O lies on line
segment AC. If the circumference of the circle is 50,
what is the length of minor arc AB ?
Answer:
16.67 or 16 2/3
Step-by-step explanation:
so, as BC is a tangent, it means the angle OBC is 90 degrees.
therefore, the angle BOC is 180 - 90 - 30 = 60 degrees.
that means the angle AOB is 180 - 60 = 120 degrees.
the triangle ABO must be an isosceles triangle, as the sides are both the radius of the circle. so, both remaining angles are the same : half of 180 - 120 = 60 = 30 degrees.
and so, we know that ABC is an isosceles triangle, because both "side angles" are equal = 30 degrees.
so, AB = BC.
and we know the circumference of the circle (50) and can calculate the radius
50 = 2×pi×r
25 = pi×r
r = 25/pi ≈ 7.96
now we have multiple ways to calculate AB.
AB = BC = tan(60) × r
or
AB = sqrt(r² + r² - 2×r×r×cos(120))
or ...
the first one might be easiest.
AB = tan(60) × 7.96 ≈ 13.78
oh, I just recognized, we need the arc AB (not the straight line).
even easier.
50 is the full "arc" of the circle for all 360 degrees.
but we only need the part of the angle AOB = 120 degrees.
so, this is then only the 120/360 part of the full circle circumference.
ABarc = 50 × 120/360 = 50 / 3 ≈ 16.67 or 16 2/3
Eliminate the parameter for the following set of parametric equations: x= t + 6 y= 3t – 1
Answer:
Solution : Option A
Step-by-step explanation:
What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.
( 1 ) x = t + 6, t = x - 6
( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )
y = 3x - 18 - 1 ( Combine like terms )
y = 3x - 19
As you can see our result will be option a, y = 3x - 19.
What is the value of X? HELP
with no further informations, just go by looking at it.
it's 90°, all other options are too far off
The value of y varies directly with x . Find the value of k when y 33.6 and x = 4.2
Answer:
k=8
Step-by-step explanation:
Since y and x are in direct proportions, the equation is
y= kx, where k is a constant.
when y= 33.6, x=4.2,
33.6= k(4.2)
k= 33.6 ÷4.2
k=8
Answer:
k=8
Step-by-step explanation:
Which equation is represented by the graph?
Answer:
I don't knowledge bro sorry
Compare the line passing through the points (–2, –9) and (4, 6) to the line given by the equation y = 25x – 4.
A. They have the same slope.
B. They have the same x-intercept.
C. The two lines are perpendicular.
D. They have the same y-intercept.
Answer:
D. They have the same y-intercep
Step-by-step explanation:
Before the comparison will be efficient, let's determine the equation of the two points and the x intercept .
(–2, –9) and (4, 6)
Gradient= (6--9)/(4--2)
Gradient= (6+9)/(4+2)
Gradient= 15/6
Gradient= 5/2
Choosing (–2, –9)
The equation of the line
(Y+9)= 5/2(x+2)
2(y+9)= 5(x+2)
2y +18 = 5x +10
2y =5x -8
Y= 5/2x -4
Choosing (4, 6)
The equation of line
(Y-6)= 5/2(x-4)
2(y-6) = 5(x-4)
2y -12 = 5x -20
2y = 5x-8
Y= 5/2x -4
From the above solution it's clear that the only thing the both equation have in common to the given equation is -4 which is the y intercept
Given the function h(t) = 2t to the power of 2 + 9 evaluate h(5)
9514 1404 393
Answer:
59
Step-by-step explanation:
Put 5 where t is and do the arithmetic.
[tex]h(t)=2t^2+9\\\\h(5)=2\cdot5^2+9=2\cdot25+9\\\\\boxed{h(5)=59}[/tex]
Please help me
(3 more coming soon so if you want points you can do those too when they come out
Answer:
The choose D. 15/16
Step-by-step explanation:
[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]
I hope I helped you^_^
Simplify 6m^2-5m-3+3m+4+9m^2
Answer: 15m²-2m+1
Step-by-step explanation:
To simplify, you want to combine like terms.
15m²-2m+1
Answer:
[tex]\huge\boxed{15m^2-2m+1}[/tex]
Step-by-step explanation:
[tex]6m^2-5m-3+3m+4+9m^2\\\\\text{combine like terms}\\\\=(6m^2+9m^2)+(-5m+3m)+(-3+4)\\\\=(6+9)m^2+(-5+3)m+1\\\\=15m^2-2m+1[/tex]
Urgent!!! Please simplify
Answer:
The answer is
3x² - 2x³Step-by-step explanation:
First factor (x+1)² out of the expression
That's
[tex] \frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) }{ ({x + 1})^{2} } [/tex]
Reduce the expression by (x + 1)²
We have
[tex]6 \cos( \frac{\pi}{3} ) \times {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) [/tex]
Using trigonometric values table
[tex] \cos( \frac{\pi}{3} ) = \frac{1}{2} [/tex]
[tex] \sin( \frac{\pi}{2} ) = 1[/tex]
So we have
[tex]6 \times \frac{1}{2} \times {x}^{2} - {x}^{3} \times 2 \times 1[/tex]
Simplify
We have the final answer as
[tex] {3x}^{2} - 2 {x}^{3} [/tex]
Hope this helps you
Find the value of x.
Is 1.45 times 10 to the -7 power a scientific notation
Answer:
Yes.
It is 1.45 x 10^-7 or 0.000000145
Hope it helps!
Answer:
It is 1.45 x 10^-7 or 0.000000145
Step-by-step explanation:
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!