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Heather won 62 pieces of candy after bobbing apples at a Halloween party. She gave 4 pieces of candy to every student in her math class. She has six pieces of candy left. How many students are in Heather’s math class?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

62-6=56

56 divided by 4 = 14

Therefore, the answer is 14.

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According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 154 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees?
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Find four rational numbers between -3/2 and 5/3

Answers

Answer:

Four rational numbers between $-(3)/(2)$ and $(5)/(3)$ are $x_(1) = -(13)/(15)$ , $x_(2) = -(7)/(30)$ , $x_(3) = (2)/(5)$ and $x_(4) = (31)/(30)$ .

Step-by-step explanation:

First, we calculate the distance between $-(3)/(2)$ and $(5)/(3)$ :

$r = (5)/(3)-\left(-(3)/(2)\right)$

$r = (5)/(3)+(3)/(2)$

$r = (10+9)/(6)$

$r = (19)/(6)$

Then, we find four rational numbers by using the following formula:

$x = -(3)/(2)+\left((n)/(5))\cdot \left((19)/(6) \right)$

First number ( $n = 1$ )

$x_(1) = -(13)/(15)$

Second number ( $n = 2$ )

$x_(2) = -(7)/(30)$

Third number ( $n = 3$ )

$x_(3) = (2)/(5)$

Fourth number ( $n = 4$ )

$x_(4) = (31)/(30)$

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10% of the test grades. To the nearest percent, what is the dividing point between an A and a B grade? Select one:
a. 80
b. 85
c. 90
d. 95

Answers

Answer:

b. 85

Step-by-step explanation:

Average grade (μ) = 75

Standard deviation (σ) = 8

Assuming a normal distribution, the z-score corresponding to the upper 10% of the test grades is z = 1.28.

The minimum grade 'X' within the top 10% is given by:

$z=(X-\mu)/(\sigma)\n1.28=(X-75)/(8)\nX=85.24$

Rounding to the nearest percent, the dividing point between an A and a B grade is 85.

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. Click on the datafile logo to reference the data.
6 4 6 8 7 7 6 3 3 8 10 4 8
7 8 7 5 9 5 8 4 3 8 5 5 4
4 4 8 4 5 6 2 5 9 9 8 4 8
9 9 5 9 7 8 3 10 8 9 6
Develop a 95% confidence interval estimate of the population mean rating for Miami. If required, round your answers to two decimal places. Do not round intermediate calculations.

Answers

Answer:

The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:

$CI=\bar x\pm t_(\alpha/2, (n-1))\cdot\ (s)/(√(n))$

The sample selected is of size, n = 50.

The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:

$t_(\alpha/2, (n-1))=t_(0.05/2, 49)=2.000$

*Use a t-table.

Compute the sample mean and sample standard deviation as follows:

$\bar x=(1)/(n)\sum {x}=(1)/(50)* [6+4+6+...+9+6]=6.34\n\ns=\sqrt{(1)/(n-1)\sum (x-\bar x)^(2)}=\sqrt{(1)/(50-1)* 229.22}=2.163$

Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:

$CI=\bar x\pm t_(\alpha/2, (n-1))\cdot\ (s)/(√(n))$

$=6.34\pm 2.00*(2.163)/(√(50))\n\n=6.34\pm 0.612\n\n=(5.728, 6.952)\n\n\approx(5.7, 7.0)$

Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

What is (1+2+3+4+5) + (1*2*3*4*5)?

HURRY

Answers

Answer:

135

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

(1+2+3+4+5)= 15

(1*2*3*4*5)= 120

15+120=135

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Answers

Answer:

Iteration 1: $x_(2)=1.446$

Iteration 2: $x_(3)=1.337$

Step-by-step explanation:

Formula for Newton's method is,

$x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))$

Given the initial guess as $x_(1)=1.6$ , therefore value of n = 1.

Also, $f\left(x\right)=x^(9)-9$ .

Differentiating with respect to x,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)$

Applying difference rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)$

Applying power rule and constant rule of derivative,

$(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0$

$(d)/(dx)\left(f\left(x\right)\right)=9x^(8)$

Substituting the value,

$x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))$

$x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))$

Calculating the value of $f\left(1.6\right)$ and $f'\left(1.6\right)$

Calculating $f\left(1.6\right)$

$f\left(1.6\right)=\left(1.6\right)^(9)-9$

$f\left(1.6\right)=59.71947674$

Calculating $f'\left(1.6\right)$ ,

$f'\left(1.6\right)=9\left(1.6\right)^(8)$

$f'\left(1.6\right)=386.5470566$

Substituting the value,

$x_(2)=1.6-(59.71947674)/(386.5470566)$

$x_(2)=1.446$

Therefore value after second iteration is $x_(2)=1.446$

Now use $x_(2)=1.446$ as the next value to calculate second iteration. Here n = 2

Therefore,

$x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))$

$x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))$

Calculating the value of $f\left(1.446\right)$ and $f'\left(1.446\right)$

Calculating $f\left(1.446\right)$

$f\left(1.446\right)=\left(1.446\right)^(9)-9$

$f\left(1.446\right)=18.63851065$

Calculating $f'\left(1.446\right)$ ,

$f\left(1.446\right)=9\left(1.446\right)^(8)$

$f\left(1.446\right)=172.0239252$

Substituting the value,

$x_(3)=1.446-(18.63851065)/(172.0239252)$

$x_(3)=1.337$

Therefore value after second iteration is $x_(3)=1.337$

Final answer:

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.

Explanation:

To calculate two iterations of Newton's Method, we need to use the formula:

xn+1 = xn - f(xn)/f'(xn)

Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, we can proceed as follows:

Calculate f(xn) at x1: f(1.6) = (1.6)9 - 9 = 38.5432
Calculate f'(xn) at x1: f'(1.6) = 9(1.6)8 = 368.64
Calculate x2: x2 = 1.6 - f(1.6)/f'(1.6) = 1.6 - 38.5432/368.64 = 1.494
Repeat the process to find x3 using the updated x2 as the initial guess.

Learn more about Newton's Method here:

brainly.com/question/31910767

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Solve the equation
log4x=2

Answers

Change it to exponential form:

log₄(x) = 2 ⇒ 4² = x = 16

Final answer: 16

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