Answer with Step-by-step explanation:
We are given that
Side of cube, x=30 cm
Error in measurement of edge,[tex]\delta x=0.5[/tex] cm
(a)
Volume of cube, [tex]V=x^3[/tex]
Using differential
[tex]dV=3x^2dx[/tex]
Substitute the values
[tex]dV=3(30)^2(0.5)[/tex]
[tex]dV=1350 cm^3[/tex]
Hence, the maximum possible error in computing the volume of the cube
=[tex]1350 cm^3[/tex]
Volume of cube, [tex]V=(30)^3=27000 cm^3[/tex]
Relative error=[tex]\frac{dV}{V}=\frac{1350}{2700}[/tex]
Relative error=0.05
Percentage error=[tex]0.05\times 100=5[/tex]%
Hence, relative error in computing the volume of the cube=0.05 and
percentage error in computing the volume of the cube=5%
(b)
Surface area of cube,[tex]A=6x^2[/tex]
[tex]dA=12xdx[/tex]
[tex]dA=12(30)(0.5)[/tex]
[tex]dA=180cm^2[/tex]
The maximum possible error in computing the volume of the cube=[tex]180cm^2[/tex]
[tex]A=6(30)^2=5400cm^2[/tex]
Relative error=[tex]\frac{dA}{A}=\frac{180}{5400}[/tex]
Relative error in computing the volume of the cube=0.033
The percentage error in computing the volume of the cube=[tex]0.033\times 100=3.3[/tex]%
Roll a dice six times. Find the probability that :
a . The back of the dot appears exactly 4 times ;
Answer:
2/3???
.................
Answer:
0.804% to 3 dec places.
Step-by-step explanation:
If the first 4 throws are a dot and the next 2 are not:
Probability = (1/6)^4 * (5/6)^2
= 25/46656
There are 6C4 ways for this to happen
6C4 = (6*5*4*3)/ (4*3*2*1) = 15 ways.
So The required probability = (25*15)/46656
= 125/15552
= 0.00804
= 0.804%
Step 1: Choose the price of the house. Then calculate 20% (which will be your down payment). Write down the price and 20% of the price.
Step 2: You don't have 20% now, so you will use an annuity to save up until you have the 20%. Choose a time in the future (2 years, 3 years, 4 years, 5, 10?) that you will purchase this house. Choose an APR that the bank will give you. Calculate how much you need to deposit every month in order to have the 20% down payment down the road. Write down the numbers of years, the interest rate, the formula with all the numbers plugged in, and the monthly deposits you will need to make.
Step 3: Now you take out a mortgage on the remaining 80%. Choose an APR that the bank will charge you (to be realistic, more than the APR in step 2) and the time you will take to pay off the loan. Write down the formula with all the numbers plugged in, and write down the minimum monthly payments.
Please show me proper work and a step by step explanation on how you got your answers. Anyone who attempts to answer just to steal points will be reported. Btw this is due midnight tonight so I could really use some help with this
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Answer:
$250,000 house price. $50,000 down payment2 years, 3% from the bank, monthly: $2024.065% APR, 30 years, monthly: 1073.64Step-by-step explanation:
1. House prices vary considerably. In January, 2021, the median US house price was about $269,000, growing at the rate of about 3.2% per year. For the purpose of this problem, we have chosen a slightly lower price of ...
$250,000 . . . selected house price
20% of this price is ...
0.20 × $250,000 = $50,000 . . . amount of down payment
__
2. House prices are growing faster than the interest rate we can get at the bank, so we want to minimize the amount of time we save for a down payment. At the same time, we recognize that saving this amount quickly will put a significant strain on the budget. We choose a period of 2 years, and assume a bank rate on savings of 3%. (US rates in mid-2021 average about 0.04%.) This annuity formula gives the future value of a series of payments:
A = P((1+r/12)^(12t)-1)(12/r) . . . . monthly payment P at annual rate r for t years
Solving for P, we have ...
P = A(r/12)/((1 +r/12)^(12t) -1)
Filling in the chosen numbers, we find we need to save ...
P = $50,000(0.03/12)/(1 +0.03/12)^(12·2) -1) = $50,000(0.0025)/0.06175704
P = $2024.06
$2024.06 needs to be deposited every month for 2 years at 3%.
__
3. The mortgage will be for ...
$250,000 -50,000 = $200,000
We assume we can get an APR of 5% on a 30-year loan. (US rates in mid-2021 are around 3.2%.) The formula for the payment amount is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . principal P at rate r for t years
Filling in the chosen numbers, we find the monthly payment to be ...
A = $200,000(0.05/12)/(1 -(1 +0.05/12)^(-12·30))
= $200,000(0.0041666667)/0.77617340 = $1073.64
The monthly mortgage payment will be $1073.64.
A soft drink machine outputs a mean of 2424 ounces per cup. The machine's output is normally distributed with a standard deviation of 33 ounces. What is the probability of filling a cup between 2929 and 3030 ounces
Answer:
Step-by-step explanation:
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
If you double then triple a number, this is the same as cutting the number in half. What is the number?
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Answer:
zero
Step-by-step explanation:
3(2x) = x/2
5.5x = 0 . . . . subtract x/2
x = 0 . . . . . . . divide by 5.5
The number is zero.
plz help and explain this :)
Answer:
y=3x+6
Step-by-step explanation:
in a line graph, y=mx+c
m refers to gradient, c refers to y-intercept.
since lines are parallel, both lines have the same gradient.
the line intersects (1,9)
x=1,y=9
9=3(1)+c
c=6
so y=3x+6
Answer:
y = 3x+6
Step-by-step explanation:
Parallel lines have the same slope
y = 3x+2 is in slope intercept form (y=mx+b where m is the slope and b is the y intercept)
So the slope is 3
Y = 3x+2
Using the point given substitute into the equation and solve for b
9 = 3(1)+b
9 =3+b
9-3 =b
6=b
y = 3x+6
For the following function, solve both f'(x) = 0 and f''(x) = 0 for x.
f(x) = x(x - 3)^4
11. What is 6:12 in simplest form?
A. 2:1
B. 1:2
C. 12:6
D.2
11. What is the reciprocal of 6/5?
OA. 12/20
OB.11/5
OC.1
OD.576
Answer: The answer is D, 5/6.
Step-by-step explanation: The reciprocal of a fraction is that fraction but the numerator and denominater swapped places.
Answer:
5/6
Step-by-step explanation:
The reciprocal is where you flip the fraction
6/5 -> reciprocal -> 5/6
I'm not sure about your answer choices tho, sorry
I need help plz!!
8.57396817...•5/8 is rational or irrational?
Answer:
Irrational
Step-by-step explanation:
Any non-zero rational number multiplied by an irrational number will be irrational. We can rewrite this as (8.57... * 5) / 8, but we have no idea how to make 8.57... * 5 rational, or expressed as the quotient of two integers.
What is the vertex of the graph of this function
y= -(x+2) (x+4)
Answer:
y=-(x+2)(x+4)
y=-(x^2+4x+2x+8)
y=-(x^2+6x+8)
y=-(x^2+4x+2x+8)
Y=-x(x+4)+2(x+4)
y=-(x+2)(X+4)
So vertex is (2,4)
I need help please
Don’t skip the questions if you know the answer please I need the answers as soon as possible!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
Subtract.
7x2 - 5x+3
(2x² + 7x-4)
Answer:
7×=14
5×3=15
5+3=8
7×4=28
7-4=3
2×2=4
if add this all will get the answer as 72
if we will subtraction answer will be as -44
Step-by-step explanation:
so we will get the answer asaddition = 72
subtraction= -44
so this is the answerplease give me points
point slope of the line equation, slope=4, passing through(7,2)
Answer:
Step-by-step explanation:
Point-slope equation for line of slope m that passes through (x₀, y₀):
y-y₀ = m(x-x₀)
apply your data
y-2 = 4(x-6)
Answer:
y−2= −2(x−7)
Step-by-step explanation:
khan academy says its right
consider a study conducted to determine the average protein intake among an adult population. Suppose that a confidence level of 85% is required with an interval about 10 units wide. if a preliminary data indicates a standard deviation of 20g, what sample of adults should be selected for the study?
Answer:
made up of about 20 common amino acids. The proportion of these amino acids varies as a characteristic of a given protein, but all food proteins—with the exception of gelatin—contain some of each. Amino nitrogen accounts for approximately 16% of the weight of proteins. Amino acids are required for the synthesis of body protein and other important nitrogen-containing compounds, such as creatine, peptide hormones, and some neurotransmitters. Although allowances are expressed as protein, a the biological requirement is for amino acids.
Proteins and other nitrogenous compounds are being degraded and resynthesized continuously. Several times more protein is turned over daily within the body than is ordinarily consumed, indicating that reutilization of amino acids is a major feature of the economy of protein metabolism. This process of recapture is not completely efficient, and some amino acids are lost by oxidative catabolism. Metabolic products of amino acids (urea, creatinine, uric acid, and other nitrogenous products) are excreted in the urine; nitrogen is also lost in feces, sweat, and other body secretions and in sloughed skin, hair, and nails. A continuous supply of dietary amino acids is required to replace these losses, even after growth has ceased.
Amino acids consumed in excess of the amounts needed for the synthesis of nitrogenous tissue constituents are not stored but are degraded; the nitrogen is excreted as urea, and the keto acids left after removal of the amino groups are either utilized directly as sources of energy or are converted to carbohydrate or fat.
Fo quality control purposes, we collect a sample of 300 items and find 36 defective items in it. Construct a 90% confidence interval [a, b] for the proportion of defective items in the whole shipment.
Answer:
(0.089 ; 0.151)
Step-by-step explanation:
Given :
Sample size, n = 300
Number of defective items, x = 36
The confidence interval required here is that for a one sample proportion :
The confidence interval is defined thus :
Phat ± Zcritical * √[Phat(1 - phat) / n]
Zcritical at 90% = 1.645
Phat = x / n = 36 / 300 = 0.12
Hence,
C.I = 0.12 ± 1.645 * √[0.12(1 - 0.12) / 300]
C.I = 0.12 ± (1.645 * 0.0187616)
C.I = 0.12 ± 0.0308629
C.I = (0.089 ; 0.151)
write two properties of Zero
Answer:
the addition properties of zero and multiplication properties of zero
zero is even, not odd not neutral.
zero is neither positive or negative.
Curtis purchased a bicycle on credit. When he received his credit card statement, he noticed several charges he did not make. What should he do?
Answer: He should call the card card company and discuss the charges and make it known that he did not make those charges. He should address each charge by the amount shown. Once he has finished, the credit card company will call the company that sent in the request for payment and inform the company there are questions about the charges and request that the charges be removed.
.
Step-by-step explanation:
What is 7 1/6 - 3 4/9 =
Answer:
67/18
Step-by-step explanation:
Find common denominator:
7 9/54 - 3 24/54
Convert to improper fraction
387/54 - 186/54
201/54
67/18
Answer:
3 15/18
Step-by-step explanation:
We start by looking at the problem, and by trying to change the denominator by finding out what number than can both go into 6 and 9.
6 x 3 = 18 9 x 2 = 18
We then change the denominator to 18.
Next, we change the whole number into a fraction. If we convert 2 whole numbers into 7 1/18, we get 5 37/18. If we convert 1 into 3 4/18, we get 2 22/18.
If we then subtract the whole numbers and fractions, the answer is
3 15/18. (It can not simplify).
The expression 2(l + w) is used to calculate the perimeter of a rectangle, where l is length and w is width. If the length is Fraction 2 over 5 unit and the width is Fraction 1 over 5 unit, what is the perimeter of the rectangle in units?
Fraction 3 over 5 unit
1 unit
1Fraction 1 over 5 units
2Fraction 3 over 5 units
Answer:
Step-by-step explanation:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Answer:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Step-by-step explanation:
Solve for X
(Ignore the math I did on top)
Solve this inequality:
-12a +7<31
Answer:
a > -2
Step-by-step explanation:
-12a +7<31
Subtract 7 from each side
-12a +7-7<31-7
-12a <24
Divide by -12, remembering to flip the inequality
-12a/-12 >24/-12
a > -2
Answer:
a>-2
Step-by-step explanation:
[tex]\sf{}[/tex]
=> -12a +7 <31
=> -12a+7-7<31-7
=> -12a<24
=> a>-2
Find the equation of the tangent line at the point (0,1) of the graph of the function f(x) = x^3 - 2x + 1 ?
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Answer:
y = -2x +1
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 3x^2 -2
so the slope at x=0 is f'(0) = -2. In slope-intercept form, the equation of the tangent line is ...
y = -2x +1
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
Answer:
C. 325.
Step-by-step explanation:
The last term a5 = 85
a1 = 45
Sum of n terms = n/2 (a1 + l)
So here we have n = 5, a1 = 45 and the last term l = 85
= (5/2)(45 + 85)
= 5/2 * 130
= 325.
The required sum of the arithmetic series is 325.
Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.
The sum of the nth term of an arithmetic sequence is expressed as:
[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:
n is the number of terms
a is the first term
l is the last term
Given the following
a = 45
n = 5
an = l = 85
Substitute the given values in the formula above:
[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]
Hence the sum of the arithmetic series is 325
Learn more here: https://brainly.com/question/21473794
so sánh 198*202 và 200^2
Step-by-step explanation:
198×202=39,996
200×200=40,000
hence,
39,9996 < 40,000
hope it helps
Which proportion would you use to solve the following problem? A map has a scale of 1 cm : 5 km. Determine how far apart two cities are if they are 8 cm apart on the map. A. B. C. D.
Answer:
40 km
Step-by-step explanation:
We can use a ratio to solve
1 cm 8 cm
-------- = ----------
5 km x km
Using cross products
1 * x = 5 * 8
x = 40
40 km
[tex]\bf \large{\pink{ \implies}} \tt \: \frac{1 \: cm}{5 \: km} \: = \: \frac{8 \: cm}{x} \: \: \: \rm{\red{ (cross \: \: multiplying)}}[/tex]
[tex]\bf \large{\pink{ \implies}} \tt \:x \: = \: 40[/tex]
⇛ Distance is 40 kmIf f(x) = x2 + 9x – 14 and g(x) = x2 – x + 3, find (f – g)(x).
Answer:
10x-17
Step-by-step explanation:
f(x) = x^2 + 9x – 14
g(x) = x^2 – x + 3
(f – g)(x)=x^2 + 9x – 14 - (x^2 – x + 3)
Distribute the minus sign
(f – g)(x)=x^2 + 9x – 14 - x^2 + x - 3
Combine like terms
=10x-17
Tyler made a scale drawing of his apartment. The scale is 1 millimeter: 2 meters. The living room is 6 meters long in
real life. How long is the living room on the drawing?
(x+16)²=12 plz help me and show work
Answer:
The answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form or [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex] in decimal form.
Step-by-step explanation:
To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring [tex]x+16[/tex], which will look like [tex]x^{2} +32x+256-12=0[/tex]. Next, simplify the equation again, which will look like [tex]x^{2} +32x+244=0[/tex].
Then, use the quadratic formula to find the solutions. The quadratic formula looks like[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex].
For this problem, the quadratic variables are as follows:
[tex]a=1[/tex]
[tex]b=32[/tex]
[tex]c=244[/tex]
The next step is to substitute the values [tex]a=1[/tex], [tex]b=32[/tex], and [tex]c=244[/tex] into the quadratic formula and solve. The quadratic formula will look like [tex]\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}[/tex]. To simplify the equation, start by simplifying the numerator, which will look like [tex]x=\frac{-32(+-)4\sqrt{3} }{2*1}[/tex]. Then, multiply 2 by 1 and simplify the equation, which will look like [tex]x=-16(+-)2\sqrt{3}[/tex]. The final answer is [tex]x=-16[/tex] ±[tex]2\sqrt{3}[/tex] in exact form. In decimal form, the final answer is [tex]x=-12.535898[/tex], [tex]x=-19.464102[/tex].
The quadrilaterals JKLM and PQRS are similar. Find the length x of SP
Answer:
4.8
Step-by-step explanation:
The scale factor is (3.6)/3=1.2. Hence x/4=1.2, x=4.8
