Jenny wrote the following expression in her notebook: 2· x + 16·y. Name all of the terms and factors in the expression. Explain the difference between a term and a factor.

Answers

Answer 1

Answer:

Answer:

In the expression 2·x + 16·y, there are two terms and three factors.

A term in an algebraic expression is a combination of variables and/or constants that are separated by addition or subtraction. In this case, the two terms are 2·x and 16·y. The term 2·x consists of the factor 2 and the variable x, while the term 16·y consists of the factor 16 and the variable y.

On the other hand, a factor is a number or variable that is multiplied by another number or variable. In this expression, the factors are 2, x, 16, and y. The factors 2 and 16 are constants, while x and y are variables.

To summarize:

Terms:

1. 2·x

2. 16·y

Factors:

1. 2

2. x

3. 16

4. y

The difference between a term and a factor lies in their roles within an expression. A term is a combination of factors that are separated by addition or subtraction, whereas a factor is an individual number or variable that is multiplied by another number or variable.

Step-by-step explanation:

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In manufacturing processes, it is of interest to know with confidence the proportion of defective parts. Suppose that we want to be reasonably certain that less than 4% of a company's widgets are defective. To test this, we obtain a random sample of 250 widgets from a large batch. Each of the 250 widgets is tested for defects, and 6 are determined to be defective, based upon the manufacturer's standards. Using α = 0.01, is this evidence that less than 4% of the company's widgets are defective? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

Answers

Answer:

Less than 4% of a company's widgets are defective.

Step-by-step explanation:

In this case we want to be reasonably certain that less than 4% of a company's widgets are defective.

The significance level of the test is, α = 0.01.

The hypothesis can be defined as follows:

H₀: At least 4% of a company's widgets are defective, i.e. p ≥ 0.04.

Hₐ: Less than 4% of a company's widgets are defective, i.e. p < 0.04.

The information provided is:

n = 250

x = 6

The sample proportion is, $\hat p=(x)/(n)=(6)/(250)=0.024$

Compute the test statistic value as follows:

$z=\frac{\hat p-p}{\sqrt{(p(1-p))/(n)}}\n\n=\frac{0.024-0.04}{\sqrt{(0.04(1-0.04))/(250)}}\n\n=-1.29$

The test statistic value is -1.29.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

$p-value=P(Z<-1.29)=0.0985$

So,

p-value = 0.0985 > α = 0.01.

The null hypothesis will not be rejected at 1% significance level.

Thus, there is not enough evidence to support the claim.

Conclusion:

Less than 4% of a company's widgets are defective.

Final answer:

This is a hypothesis testing problem where we test the claim that less than 4% of widgets are defective. We set the null and alternative hypotheses, confirm conditions for a binomial distribution, compute the test statistic, find the p-value and then make a conclusion based on the comparison of p-value with the given significance level.

Explanation:

In this scenario, we are interested in testing the hypothesis about the proportion of defective widgets. We define our null hypothesis (H0) and the alternative hypothesis (Ha) as follows:

H0: p = 0.04 (The proportion of defective widgets is 4%)

Ha: p < 0.04 (The proportion of defective widgets is less than 4%)

The conditions for a binomial distribution are met here, as each widget is either defective or not, and each widget is tested independently. Also, the quantities np and nq (where n is the sample size and q is the probability of failure) are greater than five, so we can approximate by the normal distribution.

We calculate the test statistic using the formula: z = (p' - p) / sqrt [ (p * q) / n ]

Where, p' is the sample proportion, which is 6/250, p is the hypothesized proportion which is 0.04, q is 1 - p and n is the sample size (250). This gives us a z value. Then, we find the p-value from the standard normal distribution using this z value. If p-value < α (0.01), we reject the null hypothesis. Otherwise, we do not reject it.

At the end, you will conclude. If we reject the null, we say, 'At the 1 percent significance level, there is sufficient evidence to conclude that less than 4% of the company's widgets are defective'. If we don't reject the null, 'At the 1 percent significance level, there is insufficient evidence to conclude that less than 4% of the company's widgets are defective.'

Learn more about Hypothesis testing here:

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What multiplies to 16 and adds to negative 12

Answers

factor 16 and see the - factor pairs and add them, see which add to -12
-1-16=-17 nope
-2-8=-10 nope
-4-4=-8
hmm

we will solve with math
xy=16
x+y=-12
minus x both sides
y=-12-x
sub for y in other equation
x(-12-x)=16
-12x-x^2=16
add 12x+x^2 both sides
0=x^2+12x+16
use quadratic formula
if you have
ax^2+bx+c=0
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

0=x^2+12x+16
a=1
b=12
c=16

x= $\frac{-12+/- \sqrt{12^(2)-4(1)(16) }}{2(1)}$
x= $(-12+/- √(144-64 ))/(2)$
x= $(-12+/- √(80))/(2)$
x= $(-12+/- 4√(5))/(2)$
x= $\frac{-6+/- 2√(5)$
x= $\frac{-6+ 2√(5)$ or $\frac{-6- 2√(5)$

aprox
x=-1.52786 or -10.4721

those are the numbers

the numbes are -1.52786 or -10.4721

8 times 2 8 because they are both equability right

Reduce the following fraction to lowest terms 7/14: 1/7 1/2 7/14

Answers

Answer:

1/2

Step-by-step explanation:

$(7)/(14)=(1\cdot 7)/(2\cdot 7)=(1)/(2)\cdot(7)/(7)\n\n=(1)/(2)\cdot 1=(1)/(2)$

When reducing fractions, you're trying to answer the question, "do the numerator and denominator have any common factors that can be canceled?" Knowing your multiplication tables helps answer this question.

Answer:

1/2

Step-by-step explanation:

7/14 is identical to ---------

2(7)

This can be reduced to 1/2 by cancelling out the 7s.

Wilma can mow a lawn in 40 minutes. Rocky can mow the same lawn in 120 minutes. Construct an equation that would allow you to determine how long it would take them to mow 2 lawns if they worked together. Use t to represent the number of minutes they work.

Answers

Answer:

$r_(w)*t + r_(r)*t = 2 jobs\n (1)/(40) *t + (1)/(120) *t = 2$

Step-by-step explanation:

Given are the time it takes for each worker (Wilma and Rocky) to mow one lawn.

To derive a formula to be able to find the time it takes if they work together we first need to find the rate of work of each worker

The basic formula for rate of working is as follow

$rate(r) = (Job)/(time)$

Lets calculate the rate of work for Wilma and Rocky

Wilma

$r_(w) = (1)/(40)$

Rocky

$r_(r) = (1)/(120)$

Notice the 1 at the numerator, this is because the times are given for one job.

To complete two jobs together we derive the following formula based on adding their rates together

$r_(w)*t + r_(r)*t = 2 jobs\n (1)/(40) *t + (1)/(120) *t = 2$

In which of the following stores would you pay the least amount for an item that is priced $360? Store A: Sale of 10% off and a successive discount of 10% off. Store B: Sale of 15% with no additional discount. Store C: Sale of $35 off and a successive discount of 10% off.

Answers

Given:
Price : 360

Store A: Sale of 10% off and a successive discount of 10% off.
360 * (100-10)% = 360 * 90% = 324
324 * (100-10)% = 324 * 90% = 291.60

Store B: Sale of 15% with no additional discount
360 * (100-15)% = 360 * 85% = 306

Store C: Sale of $35 off and a successive discount of 10% off
360 - 35 = 325
325 * (100-10)% = 325 * 90% = 292.50

Store A has the least amount to pay for an item at price of 291.60

Answer:

option b

Step-by-step explanation:

Sample annual salaries (in thousands of dollars) for public elementary school teachers are listed. Find the sample standard deviation. Round to two decimal places if necessary 23.9
15.3
40.2
30.3
21.0
22.8
ID: ES6L 2.4.1-9+

Answers

Answer:

The standard deviation is 9.34

Step-by-step explanation:

First we need to find mean of the sample:

$m=(23.9+15.3+40.2+30.3+12+22.8)/6=24.08$

Standard deviation will be like below:

$d=√((x-m^2)/6)=9.34$

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It a grade 9 please help me do this I don’t really understand it at all

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