MATHEMATICS COLLEGE

Find the surface area and volume of a rectangular solid with length 10, width 7, height 12surface area______square inches
volume_____cubic inches​

Answers

Answer 1
Answer:

Answer:

Surface area is =548

Volume = 840 in³

Step-by-step explanation:

l × w, l × w, w × h, w × h, l × h, l × h

70 + 70 + 84 + 84 + 120 + 120 = 548

l × w × h = 840

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The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?

4x<-2 como se desarrolla esta desigualdad

Answers

Answer:

x<-0.5

Step-by-step explanation:

Use the inner product〈f,g〉=∫10f(x)g(x)dxin the vector space C0[0,1] of continuous functions on the domain [0,1] to find 〈f,g〉, ∥f∥, ∥g∥, and the angle αf,g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f,g〉= ,∥f∥= ,∥g∥= ,αf,g .

Answers

Answer:

a) <f,g> = 2605/3

b) ∥f∥ = 960

c) ∥g∥ = 790

d) α = 90  

Explanation

a) We calculate  <f,g> using the definition of the inner product:

<f,g> = \int\limits^1_0 {10(-10x^(2) -6)(-9x-4)} \, dx \n        \n        =\int\limits^1_0 {900x^(3)+400x^(2) +540x+240 } \, dx\n    \n      = (225x^(4) + (400x^(3) )/(3) + 270x^(2)   +240x)\n      = (2605)/(3)

b) How

∥f∥ = <f,f> then:

∥f∥ = <f,f> = \int\limits^1_0 {10(-10x^(2) -6)(-10x^(2) -6)} \, dx \n        \n        =\int\limits^1_0 {1000x^(4)+1200x^(2) + 360} \, dx\n    \n      = (200x^(5) + 400x^(3) +  360x)\n      = 960

c)

∥g∥ = <g,g>

∥g∥ = <g,g> = \int\limits^1_0 {10(-9x-4)(-9x-4)} \, dx \n        \n        =\int\limits^1_0 {810x^(2)+720x + 160} \, dx\n    \n      = (270x^(3) + 360x^(2) +  160x)\n      = 790

d) Angle between f and g

<f,g> = ∥f∥∥g∥cosα

Thus

\alpha = cos^(-1)((2605/3)/((790)(960)) )\n\n\alpha = 90

Final answer:

The answer to this problem involves applying integrals, norms, and concepts of angles between vectors to the functions f(x) and g(x). The INNER PRODUCT is the integral of the products of the two functions, the norms are the square roots of the inner products of the functions with themselves, and the angle between the functions is calculated using the dot product and norms.

Explanation:

To find the inner product 〈f,g〉, the norms ∥f∥ and ∥g∥, and the angle αf,g between the functions f(x)=−10x2−6 and g(x)=−9x−4, we'll apply concepts from vector calculus. The inner product (also known as the dot product) is the integral from 0 to 1 of the products of the two functions. The norm of a function is the square root of the inner product of the function with itself. The angle between two vectors in a Vector Space, in this case the space of continuous functions C0[0,1], is given by cos(α) = 〈f,g〉/( ∥f∥∙ ∥g∥). Integrating and solving these equations will give us the desired values.

Learn more about Vector Calculus here:

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Need Help Fast!!!!!!!!!!!!!!!!!!

Answers

7.2, 3, 8.09, 2.22, 5.06, 2.5

In 1970, 36% of first year college students thought that being "very well off financially is very important or essential." By 2000 the percentage had increased up to 74%. These percentages are based on nationwide multistage cluster samples.a) Is the difference important? Or does teh question make sense?
b) Does it make sense to ask if the difference is statisically significante? Can you answer on the basis of the informations given?
c) Repeat b), assuming the percentages are based on independant simple random samples of 1,000 first year college students drawn each year.

Answers

Answer:

a.  The difference is important but the question does not make sense

b. Yes, it makes sense to ask if the difference is statistically significant.

c. Please check explanation

Step-by-step explanation:

From the question, we identify the following relation;

H_(o): P-P_(1) = 0

H_(A) : P-P_(1) ≠ 0

a) The difference is important as asked, but the cultural atmosphere difference of over 30 years makes the question somehow not making sense

b) Yes, it makes sense. In order to answer, it is necessary to know the sample size of the year  2000 survey.

We can answer the question on the basis of the information given.

c) We proceed here as follows;

α = 0.05 , Z_(alpha/2) = 1.96 ( This is the critical value)

Thus, z = (0.74-0.36)/√(0.36-0.64)/1000 = 25.03

We make the following conclusions; Since 25.03 > 1.96, the null hypothesisH_(o)  is rejected which means that the proportion of people who think being well officially is important has changed since 1970.

TIME REMAINING54:32
Tom would like to take out a secured loan to help pay for a vacation this summer. He has offered his car as collateral.
His car is worth $3,500. His bank can offer loans for 80% of collateral value. The vacation he has planned will cost
$4,750. Approximately how much additional collateral will Tom need to offer in order to borrow enough to go on his
vacation as planned?
$1,000.00
b. $1,362.50
c. $2,437.50
d. $2,800.00
a.
Please select the best answer from the choices provided
A
B.
ОООО
D

Answers

Tom will need to offer additional collateral of C. $2,437.50 to borrow enough for his planned vacation.

What is collateral?

Collateral refers to a valued property or financial security offered by the borrower to the lender to guarantee repayment of a loan.

Lenders sell collaterals when the borrowers fail to comply with their loan terms.

How is the additional collateral determined?

Car's value = $3,500

Collateral value in percentage = 80%

Car's collateral value = $2,800 ($3,500 x 80%)

Planned cost of vacation = $4,750

Additional cost to meet vacation cost = $1,950 ($4,750 - $2,800)

Additional collateral value to meet target = $2,437.50 ($1,950/80%)

Total collateral that Tom needs to offer = $5,937.50 ($3,500 + $2,437.50)

80% of $5,937.50 = $4,750

Another way is to work with the planned cost and the collateral percentage offered by Tom's bank:

Planned cost of vacation = $4,750

Collateral value in percentage = 80%

Total collateral to be offered by Tom = $5,937.50 ($4,750/80%)

Car's collateral value = $3,500

Additional collateral value = $2,437.50 ($5,937.50 - $3,500)

Thus, Tom needs additional collateral of C. $2,437.50.

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What is the sum of 52.38 divided by 16

Answers

52.38 divided by 16 is 3.27
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