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Which expression is equivalent to −30+(−40)+(−70) ?

Answers

Answer 1

Answer:

Answer:

−30+(−40)+(−70) = -140

Step-by-step explanation:

−30+(−40)+(−70) = -140

Answer 2

Answer:

Answer:

not what im looking for

Step-by-step explanation:

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Hope this helps, let me know if it doesn't make sense

Judith has a necklace with a mass of 65.736 grams. What is the mass of her necklace rounded to the nearest tenth?

Answers

Answer:

65.7 grams.

Step-by-step explanation:

Suppose a candy connoisseur opened a random bag of candy and found that 15 of the 62 candies were red. Using this information, determine the margin of error that would be used to construct a 95% confidence interval for the proportion of all candies that are red. Please give the answer in decimal form precise to three decimal places.

Answers

Answer: E= 0.107

Step-by-step explanation:

Formula to find the margin of error : $E=z^*\sqrt{(p(1-p))/(n)}$

, where n= sample size .

p= sample proportion

z* = critical value.

Given : Sample size : n= 62

Number of red candies out of 62 = 15

Proportion of red candies = $p=(15)/(62)\approx0.242$

We know that , the critical value for 95% confidence = z*= 1.96 [Using z-table]

Then,

$E=(1.96)\sqrt{(0.242(1-0.242))/(62)}$

$E=(1.96)\sqrt{(0.242(0.758))/(62)}$

$E=(1.96)\sqrt{(0.183436)/(62)}$

$E=(1.96)√(0.00295864516129)$

$E=(1.96)(0.0543934293945)$

$E=0.106611121613\approx0.107$

Hence, the margin of error = E= 0.107

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Answers

Answer:

Step-by-step explanation:

Tip a positive number multiplied to a negative number is negative

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

∥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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An ABC News poll asked adults whether they felt genetically modified food was safe to eat. Thirty-five percent felt it was safe, 52% felt it was not safe, and 13% had no opinion. A random sample of 120 adults was asked the same question at a local county fair. Forty people felt that genetically modified food was safe, 60 felt that it was not safe, and 20 had no opinion. At the 0.01 level of significance, is there sufficient evidence to conclude that the proportions differ from those reported in the poll

Answers

Answer:

Following is attached the detailed solution of the question.

I hope it will help you a lot!

Step-by-step explanation:

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