Answer:
16.65 cm³
Step-by-step explanation:
Given that :
the diameter of the closed tin can = 12 cm
the height of the closed tin can = 11 cm
The thickness of the closed tin can = 0.04 cm
The main task required to be carried out is to use differentials to estimate the amount of tin in a closed tin can.
We all know that the volume of a tin can = [tex]\pi r ^ 2 h[/tex]
The differential of the volume is :
[tex]dV = \dfrac{\partial V}{\partial r}dr + \dfrac{\partial V}{\partial h} dh \ ----- \ (1)[/tex]
Differentiating V with respect to r; we have:
[tex]\dfrac{\partial V}{\partial r}= 2 \pi rh[/tex]
Differentiating V with respect to h ; we have:
[tex]\dfrac{\partial V}{\partial h} = \pi r^2[/tex]
Hence; the estimate of the amount of tin in a closed tin can is:
= [tex]2 \pi rh \ dr+ \pi r ^2 \ dh[/tex]
= [tex]\pi r(2h \ dr+ r \ dh)[/tex]
= [tex]\pi *6 (2 * 11 * 0.04 + 0.04 * 0.08)[/tex]
where;
dr = increase in radius = 0.04cm (since thickness of the radius = 0.04 cm)
dh = increase in the height = 0.04 + 0.04 = 0.08
= 16.65 cm³
Hence; the amount of tin in a closed tin can is = 16.65 cm³
Combine the like terms to create an equivalent expression: -12 - 6p - (-2)
Answer:
-6p -10
Step-by-step explanation:
-12 - 6p - (-2)
Subtracting a negative is like adding
-12 - 6p + (2)
Combine like terms
-6p -12+2
-6p -10
Answer:
-6p=10
Step-by-step explanation:
-12 - 6p - (-2) to combine like expression
-12-6p+2
-6p-10 to create equivalent expression an equal sign is used
-6p=10
Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 4 (x over 2) = 2
Answer:
The solution is x = 32.
Step-by-step explanation:
To solve the logarithmic equation [tex]\log _4\left(\frac{x}{2}\right)=2[/tex] you must:
Use the logarithmic definition [tex]\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c[/tex].
[tex]\log _4\left(\frac{x}{2}\right)=2\quad \Rightarrow \quad \frac{x}{2}=4^2[/tex]
Multiply both sides by 2
[tex]\frac{x}{2}\cdot \:2=4^2\cdot \:2[/tex]
Simplify
[tex]x=32[/tex]
6.1.3
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Answer:
The requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
Step-by-step explanation:
A normal-distribution is an accurate symmetric-distribution of experimental data-values.
If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.
If X [tex]\sim[/tex] N (µ, σ²), then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Thus, the requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
In the study of a nonlinear spring with periodic forcing, the equation y prime prime plus ky plus ry cubedy′′+ky+ry3equals=Upper A cosine omega tAcosωt arises. Let kequals=44, requals=33, Aequals=77, and omegaωequals=88. Find the first three nonzero terms in the Taylor polynomial approximation to the solution with initial values y(0)equals=0, y prime (0 )y′(0)equals=1.
Answer:
[tex]\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}[/tex]
Step-by-step explanation:
THe interpretation of the given question is as follows:
y'' + ky + ry³ = A cos ωt
Let k = 4, r = 3, A = 7 and ω = 8
The objective is to find the first three non zero terms in the Taylor polynomial approximation to the solution with initial values y(0) = 0 ; y' (0) = 1
SO;
y'' + ky " ry³ = A cos ωt
where;
k = 4, r = 3, A = 7 and ω = 8
y(0) = 0 ; y' (0) = 1
y'' + 4y + 3y³ = 7 cos 8t
y'' = - 4y - 3y³ + 7 cos 8t ---- (1)
∴
y'' (0) = -4y(0) - 3y³(0) + 7 cos (0)
y'' (0) = - 4 × 0 - 3 × 0 + 7
y'' (0) = 7
Differentiating equation (1) with respect to t ; we have:
y''' = - 4y' - 9y² × y¹ - 56 sin 8t
y''' (0) = -4y'(0) - 9y²(0)× y¹ (0) - 56 sin (0)
y''' (0) = - 4 × 1 - 9 × 0 × 1 - 56 × 0
y''' (0) = - 4
Thus; we have :
y(0) = 0 ; y'(0) = 1 ; y'' (0) = 7 ; y'''(0) = -4
Therefore; the Taylor polynomial approximation to the first three nonzero terms is :
[tex]y(t) = y(0) + y'(0) t + y''(0) \dfrac{t^2}{2!} + y'''(0) \dfrac{t^3}{3!}+...[/tex]
[tex]y(t) = 0 + t + 7 \dfrac{t^2}{2!} + \dfrac{-4}{3!} {t^3}+ ...[/tex]
[tex]\mathbf{y(t) = t + \dfrac{7}{2}t^2 - \dfrac{2}{3}t^3+ ...}[/tex]
Assume that the probability of a driver getting into an accident is 4.2%, the
average cost of an accident is $13,547.92, and the overhead cost for an
insurance company per insured driver is $130. What should this driver's
insurance premium be?
A. $699.01
B. $56.90
C. $569.01
O D. $186.90
Answer:
A. $699.01
Step-by-step explanation:
130 = x − (0.042) (13547.92)
x = 699.01
Please answer this correctly
Answer:
1/64
Step-by-step explanation:
The probability of landing on a 7 is 1/8.
The probability of landing on a 2 is 1/8.
[tex]1/8 \times 1/8[/tex]
[tex]= 1/64[/tex]
1/64
The probability of landing on a 7 is 1/8.
The probability of landing on a 2 is 1/8.
1/8 \times 1/81/8×1/8
= 1/64=1/64
Which property of equality was used to solve this equation?
Answer:
Division property of equality
Step-by-step explanation:
They are dividing both sides.
When the factors of a trinomial are (x + p) and (x + 9) then the constant term
of the trinomial is:
Answer:
9p
Step-by-step explanation:
(x + p)(x + 9) =
= x^2 + 9x + px + 9p
= x^2 + (9 + p)x + 9p
The constant term is 9p.
A ladder is placed 3.5 feet away from the base of a tree. If the ladder forms a 53° angle with the ground, how many feet up the tree will the ladder reach? Write only the number rounded to the nearest tenth of a foot.
Answer:
The ladder will reach 4.6 ft up the tree.
Step-by-step explanation:
When we draw out our triangle, we should see that we are given the horizontal leg and are trying to find the vertical leg. We use tan∅ to help solve:
tan53° = x/3.5
3.5tan53° = x
x = 4.64466
name the triangle with the following sides 5cm 5cm 6.4cm angles 80 and 50
Answer:
isoceles triangle
Step-by-step explanation:
All of these attributes fit an isoceles acute triangle. An isoceles triangle needs 2 equal sides (which this description names) and 2 equal angles 80, 50, and 50.
Answer:
The answer is acute isosceles triangle
Step-by-step explanation:
look at the right triangle ABC
Answer: A) Justification 1
Step-by-step explanation:
The student did not match the angles correctly.
∠ABC = 90° and ∠BCD = 60° so they cannot state that the angles are congruent. The other statement on that line is wrong also, but is irrelevant since there is already an error in that line.
Which of these shows equivalent fractions?
а
=
4.
8
=
AN
alw
10
2 - 3
3. 6
Answer:A
Step-by-step explanation:
a. 2(3y - 2x) = 6y - 4x or rewritten as -4x + 6y
4x + 6y - 8 x
= 4x - 8x + 6y
= -4x + 6y
what is the value of x in the equation 1/2x - 2/3 y = 30, when y = 15
Answer:
Step-by-step explanation:
1/2x - 2/3 × 15 = 30
1/2x - 10 = 30
1/2x = 30 + 10
1/2x = 40
x = 40 × 2
x = 80
hope this helps
plz mark it bas brainliest!!!!!!!!!
Which of the following is a key property of the absolute value parent function?
A. It has a slope of 1 on the left half.
B. It is U-shaped
C. It is in quadrants I and ll
D. Its vertex is not at the origin
Answer:
the absolute-value parent function has a slope of 1 on the right half.
I hope this will work fine for you.
Comment if you need more explanation
ThX
Step-by-step explanation:
Please help with how to find the area of the shape with work
Answer: 10 squares.
Step-by-step explanation:
We can do it with integrals.
If we take the bottom vertex as the point (0,0), the top right vertex as the point (0,4) and the left vertex as the point (5, 6)
then the area of the triangle is the area enclosed by two lines between the values x = 0 and x = 5.
the two lines are:
the bottom is the one that passes through (0,0) and (5,6)
f(x) = y = s*x (because it passes through the point (0,0))
and the slope is s = 6/5.
so f(x) = y = (6/5)*x.
The top line is the one that passes through (0,4) and (5,6)
the y-intercept is b = 4, and the slope is:
s = (6 - 4)/(5 - 0) = 2/5.
g(x) = y = (2/5)*x + 4.
Now, the area enclosed for the triangle is equal to:
[tex]\int\limits^5_0 {g(x) - f(x)} \, dx[/tex]
this is equal to:
[tex]\int\limits^5_0 {(2/5)x + 4 - (6/5)x} \, dx = \int\limits^5_0 {-(4/5)*x + 4} \, dx[/tex]
= (1/2)(-4/5)*(5)^2 + 4*5 - 0 = 10
The area is 10 squares
Find the measure of the indicated angle to the nearest degree. Thanks.
Answer:
34
Step-by-step explanation:
uts obtuse angle
Answer:
16°
Step-by-step explanation:
Let x° be the missing angle:
cos x° = 53/55
cos x° = 0.963
using a calculator:
cos^(-1) (0.963) = 15.63 ≈ 16
A certain three-cylinder combination lock has 65 numbers on it. To open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a three-number lock combination has been effected. Repetitions are allowed, and any of the 65 numbers can be used at each step to form the combination. What is the probability of guessing a lock combination on the first try?
Answer:
1/275,625 ≈ 3.641×10^-6
Step-by-step explanation:
There are 65×65×65 = 274,625 possible combinations. The probability of guessing the correct one is 1/275,625 ≈ 3.641×10^-6.
Which one is cheaper and why
A bag of 4 litre milk for $3.99, or a carton of 1 litre milk for $1.99
Hey there! :)
Answer:
The bag is cheaper because one litre is roughly $1.00, compared to the carton which is $1.99 for one litre.
Step-by-step explanation:
Given:
Bag of 4 litre milk = $3.99
Carton of 1 litre milk = $1.99
Find the price per litre for a bag of milk:
[tex]\frac{3.99}{4} = \frac{x}{1}[/tex]
Cross multiply:
3.99 = 4x
Divide both sides by 4:
3.99/4 = x.
x = 0.9975 ≈ $1.00
Bag of 1 litre milk ≈ $1.00
Carton of 1 litre milk = $1.99
$1.00 < $1.99
Therefore, the bag is cheaper.
A scooter runs 40 km using 1 litre of petrol tje distance covered by it using 15/4 litres of petrol is
Answer:
150 km
Step-by-step explanation:
1 liter ............ 40 km
15/4 liter .........x km
x = 15/4×40/1 = 600/4 = 150 km
Subtracting polynomials
Answer:
The other polynomial is 11x^2 -3x
Step-by-step explanation:
12x^2 -5x - ( x^2 -2x) = other polynomial
Distribute the minus sign
12x^2 -5x - x^2 +2x
Combine terms
11x^2 -3x
The other polynomial is 11x^2 -3x
What is the domain of the relation graphed below?
Answer:
domain: (-4,4)
Step-by-step explanation:
i'm not sure if it has brackets because it doesn't have point that are on x-intervals -4 and 4
Use the formula m =
V2 - V1
X2 - X1
to calculate the slope of the
line.
The slope of the line is -1
Answer:
[tex]\displaystyle m=2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (2, 8)
Point (-6, -8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [SF]: [tex]\displaystyle m=\frac{-8-8}{-6-2}[/tex][Fraction] Subtract: [tex]\displaystyle m=\frac{-16}{-8}[/tex][Fraction] Divide: [tex]\displaystyle m=2[/tex]A 50 gram sample of a substance that's
used to treat thyroid disorders has a k
value of 0.1137.
The question is incomplete. Here is the complete question.
A 50 gram sample of a substance that's used to treat thyroid disorders has a k-value of 0.1137. Find the substance's half-life, in days. Round your answer to the nearest tenth.
Answer: [tex]t_{1/2}[/tex] = 6.1 days
Step-by-step explanation: Half-life is the amount of time necessary for a substance to reduce to half of its initial value.
To determine half-life through mass of a substance:
[tex]N = N_{0}.e^{-kt_{1/2}}[/tex]
Initially, there are 50 grams. After 1 half-life, there are 25 grams:
[tex]25 = 50.e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{25}{50} = e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{1}{2} = e^{-0.1137.t_{1/2}}[/tex]
[tex]ln (\frac{1}{2} ) = ln (e^{-0.1137.t_{1/2}})[/tex]
ln(1) - ln(2) = -0.1137.[tex]t_{1/2}[/tex]
[tex]t_{1/2} = \frac{- ln(2)}{- 0.1137}[/tex]
[tex]t_{1/2} =[/tex] 6.1
The half-life of the sample substance is 6.1 days.
The sum of two intcgers is -6. If one of them is 2, then the other is
(a) 4
(b) 4
(c) 8
(d) -8
Answer:
D) -8
Step-by-step explanation:
If you add a positive and a negative, you end up subtracting. If your sum is lower than any of the numbers you are adding together, then there is a negative. In this case, your only negative number is -8, but if there were others, you could find this equation by doing negative six minus two (because the equation was originally addition, it would still be subtraction to check your work or find the answer in this case.)
Hopefully you find this useful :)
Answer: -8
Step-by-step explanation: lets take the unknown number as x,
so we have, 2 + x= -6
by using transposition method, x= -6-2( positive becomes
negative when transpositioning)
so, x= -8
How does AC in circleE relate to DF in circleF?
Answer:
AC is four times longer than DF
Answer:
last option
Step-by-step explanation:
Let's say DF = x. DE = 2x which means DB is 4x. Since AC = DB the answer is the last option.
The total amount of deductions from an employee’s gross pay is $83.20. If the gross pay is $378.18, what percent of their gross pay is being withheld? a. 21% b. 22% c. 23% d. 24%
Answer: B. 22%
Step-by-step explanation:
Answer:
Yeah its 22%
Step-by-step explanation:
A fitness center is interested in finding a 95% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 246 members were looked at and their mean number of visits per week was 2.2 and the standard deviation was 2.6. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? distribution.
b. With 95% confidence the population mean number of visits per week is between and visits.
c. If many groups of 246 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week
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Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 156 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?
Answer:
140608 cubic in
Step-by-step explanation:
[tex]x+x+h=156[/tex]
[tex]h=156-2 x[/tex]
[tex]V=x^{2} h \quad[/tex] We eliminate one of the variables
[tex]V=x^{2}(156-2 x)[/tex]
[tex]V=156 x^{2}-2 x^{3}[/tex] Differentiating [tex]v[/tex]
[tex]V^{\prime}=312x-6 x^{2} \quad[tex] When [/tex]V=0[/tex]
[tex]312x-6 x^{2}=0[/tex]
[tex]x(312-6 x)=0 \quad=\quad\left\{\begin{array}{l}x=0 \\ x=52 \quad x=0 \text { not acceptable }\end{array}\right.[/tex]
[tex]h=156-2(52)=\Rightarrow h=52[/tex]
[tex]V=52\times52\times52= 140608 \text{ cubic in}[/tex]
A square has an area of 50 square feet what is the perimeter of the square rounded to the nearest foot
Answer:
28 feet
Step-by-step explanation:
area of a square = side times side; the sides are equal
50 = side times side or 50 = side^2
sqroot of 50 = sqroot of side^2
7 feet is about the size of the side of the square so using that information..
2 length + 2 width or 4 side
4 times 7 = 28
the perimeter is 28 feet
Select the equation that most accurately depicts the word problem. One-half of a certain number is 95. - n = 95 + n = 95 • n = 95 ÷ n = 95
Answer:
[tex] n * \frac{1}{2} = 95 [/tex]
Step-by-step explanation:
Required:
Select the equation that most accurately depicts the word problem
One-half of a certain number is 95.
Take the certain number to be n.
This statement in equation form will be:[tex] n * \frac{1}{2} = 95 [/tex]
Therefore, the equation that most accurately depicts the word problem is [tex] n * \frac{1}{2} = 95 [/tex]
Although your options are incomplete, but this answer is correct.
The * symbol can be replaced with a dot sign
Answer:
up up up up
Step-by-step explanation: