MATHEMATICS COLLEGE

8/4s is proportional to what value

Answers

Answer 1

Answer:

Step-by-step explanation:

$(8)/(4) = 2 \n$

Answer 2

Answer: The answer is 2.

Explanation 8 divided by 4 Is 2

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Suppose Siri (an Apple digital assistant) is known to answer general facts correctly approximately 44.52% of the time. If a consumer asked Siri 181 questions about general facts, what is the probability that less than 45.1% of them would be correct

Answers

Answer:

The probability that there will be less than 45.1% questions of general facts that Siri answers correctly is 0.5636.

Step-by-step explanation:

Let X = number of times Siri is known to answer general facts correctly.

The probability of random variable X is, P (X) = p = 0.4452.

The sample selected is of size, n = 181.

The random variable $X\sim Bin(181, 0.4452)$

As the sample size is large, i.e. n > 30 and the [probability of success is closer to 0.50, i.e.p is close to 0.50, then the binomial distribution can be approximated by the normal distribution.

Also if np ≥ 10 and n (1 - p) ≥ 10 then binomial distribution can be approximated by normal distribution.

Check the conditions as follows:

n = 181 > 30
p = 0.4452 is closer to 0.50
np = 181 × 0.4452 = 80.5812 > 10
n (1 - p) = 181 × (1 - 0.4452) = 100.4188 > 10

All the conditions are satisfied.

Then the sample proportion ( $\hat p$ ) follows a Normal distribution.

Mean = $\mu_(\hat p)=np=181*0.4452=80.5812\approx80.6$

Standard deviation = $\sigma_(\hat p)=\sqrt{(p(1-p))/(n)}=\sqrt{(0.4452*(1-0.4452))/(181)} =0.037$

Compute the probability that there will be less than 45.1% questions of general facts that Siri answers is correct as follows:

$P(\hat p<0.451)=P(\frac{\hat p-\mu_(\hat p)}{\sigma{\hat p}}<(0.451-0.4452)/(0.037))=P(Z<0.16)=0.5636$

**Use the z-table for probability.

Thus, the probability that there will be less than 45.1% questions of general facts that Siri answers correctly is 0.5636.

Sam's class voted on whether or not to do science fair projects in groups. Out of 20 votes, 14 were in favor of working in groups. What percentage of the votes were in favor of working in groups

Answers

70% were in favor so working in groups. You do 14 over 20. 14 votes divided by 20 votes is 70% of the overall votes.

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) π/2 0 3 1 + cos(x) dx, n = 4

Answers

Split up the integration interval into 4 subintervals:

$\left[0,\frac\pi8\right],\left[\frac\pi8,\frac\pi4\right],\left[\frac\pi4,\frac{3\pi}8\right],\left[\frac{3\pi}8,\frac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\frac{i-1}4\left(\frac\pi2-0\right)=\frac{(i-1)\pi}8$

$r_i=\frac i4\left(\frac\pi2-0\right)=\frac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\frac{\ell_i+r_i}2=\frac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\frac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

$p_i(x)=f(\ell_i)((x-m_i)(x-r_i))/((\ell_i-m_i)(\ell_i-r_i))+f(m)((x-\ell_i)(x-r_i))/((m_i-\ell_i)(m_i-r_i))+f(r_i)((x-\ell_i)(x-m_i))/((r_i-\ell_i)(r_i-m_i))$

so that

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

$S_i=\displaystyle\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))$

Then the integral is approximately

$\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

Final answer:

The question is asking to approximate the definite integral of 1 + cos(x) from 0 to π/2 using the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule for n=4. These are numerical methods used for approximating integrals by estimating the area under the curve as simpler shapes.

Explanation:

This question asks to use several mathematical rules, specifically the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule, to approximate the given integral with a specified value of n which is 4. The integral given is the function 1 + cos(x) dx from 0 to π/2. Each of these rules are techniques for approximating the definite integral of a function. They work by estimating the region under the graph of the function and above the x-axis as a series of simpler shapes, such as trapezoids or parabolas, and then calculating the area of these shapes. The 'dx' component represents a small change in x, the variable of integration. The cosine function in this integral is a trigonometric function that oscillates between -1 and 1, mapping the unit circle to the x-axis. The exact solution would require calculus, but these numerical methods provide a close approximation.

Learn more about Numerical Integration Rules here:

brainly.com/question/36635050

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Find the difference using fraction bars or a paper and pencil. Write your answer in simplest form. 7/8 - 3/4

Answers

Answer:

the answer would be 1/8

7/8-3/4

7/8-6/8

1/8

Write and evaluate the expression. Then, complete the statements. nine more than the product of seven and a number decreased by three The expression to model the situation is 1. 3 - 9(7n) 2. 9 + 7/n - 3 3. 9 + (7 + n) - 3 4. 9 + 7n - 3 . The value of the expression when n = 8 is 1. 6 7/8 2. 71 3. 62 4. 501