Write the following fractions with a denominator 24a^3b^2 and analyze the domains.
1. 2/a^2b^2
2. 5b/8a^3

Answer:

Number of terms = 3

Degree = 6

Step-by-step explanation:

A polynomial is a mathematical expression that gives the detailed combination of variables with their coefficients, their positive exponential, and other variables using the operations of subtraction, addition, and multiplication

The number of terms in a polynomial is the number of different powers of added or subtracted in the expression

Therefore, the number of terms in the expression -3·s⁶ + 2·s⁴ + 3·s³ is 3 terms

Number of terms = 3

The degree of a polynomial is given by the highest power of the variables in the polynomial. Therefore, the degree of the given polynomial is 6

Degree = 6

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.

The sampling method described in the scenario is called systematic sampling.

Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.

However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.

To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.

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Answer:

Step-by-step explanation:

Domain: D=R-{2}

Asymptote vertical: x=2

Asymptote horizontal: y=1

Hey, I tried to graph this function, I hope you understand something here...

Answer:

x = -4

Step-by-step explanation:

A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.

To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of  the sample mean, sample standard deviation, as well as sample size.

The null hypothesis =  750 grams,

The  alternative hypothesis=  less than 750 grams.

so we need to calculate the test as:

t = (746 - 750) / (8 / √(20)) = -2.236

Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so  n-1 =19)

When you a t-distribution table, the critical t-value to be -1.734.

Therefore, know that -2.236 < (less than) -1.734,  so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.

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4. Conversion of binary to octal and hexadecimal.

1010101110₂

OCTAL: Group the binary digits into groups of three, starting from the right.

Add leadings 0's if necessary.

So, 1010101110 is 001 010 101 110.

Now, substitute each group with an octal digit.

001 010 101 110₂ = 2 5 5 6₈

HEXADECIMAL: Group the binary digits into groups of four, starting from the right.

Add leading 0's if necessary.

So, 1010101110 is 0101 0101 1100.

Now, substitute each group with a hexadecimal digit.

0101 0101 1100₂ = 5 5 C₁₆

b. 101010011100₂

OCTAL: Group the binary digits into groups of three, starting from the right.

Add leadings 0's if necessary.

So, 101010011100 is 001 010 100 111 000.

Now, substitute each group with an octal digit.

001 010 100 111 000₂ = 2 5 4 7 0₈

HEXADECIMAL: Group the binary digits into groups of four, starting from the right.

Add leadings 0's if necessary.

So, 101010011100 is 0101 0100 1110.

Now, substitute each group with a hexadecimal digit.

0101 0100 1110₂ = 5 4 E₁₆.

5. Conversion of octal to hexadecimala.

746128:

Group the octal digits into groups of three, starting from the right.

Add leadings 0's if necessary.

So, 746128 is 007 461 028.

Now, substitute each group with a hexadecimal digit.

007 461 028₈ = 0 3 1 4 0 2₁₆

b. 2746358:

Group the octal digits into groups of three, starting from the right.

Add leadings 0's if necessary.

So, 2746358 is 010 111 100 110 101 100.

Now, substitute each group with a hexadecimal digit.

010 111 100 110 101 100₈ = 2 7 C 6 5 4₁₆.

6. Conversion of hexadecimal to octal.

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To calculate the 95% confidence interval for the statistic that 80% of respondents "strongly agree" that K-12 schools should teach critical thinking, with a margin of error of 3.2%, we can use the formula for confidence intervals.

The lower limit of the confidence interval can be obtained by subtracting the margin of error from the statistic, and the upper limit is obtained by adding the margin of error. By applying these calculations, we find that the 95% confidence interval for this statistic is 78.8% to 81.2%.

The margin of error represents the range within which the true population parameter is likely to fall. To calculate the confidence interval, we subtract the margin of error from the statistic to find the lower limit and add the margin of error to find the upper limit.

For this problem, the statistic is 80% and the margin of error is 3.2%. Subtracting the margin of error from the statistic, we find the lower limit: 80% - 3.2% = 76.8%. Adding the margin of error to the statistic, we find the upper limit: 80% + 3.2% = 83.2%.

Therefore, the 95% confidence interval for the statistic that 80% of respondents "strongly agree" that K-12 schools should teach critical thinking is 78.8% to 81.2%, rounded to one decimal place.

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Answer:

6 . x = 24

Step-by-step explanation:

Answer:

z = -18

Step-by-step explanation:

I hope this helps!

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer:

Glad we helped

Step-by-step explanation:

Answer:

4*x

Step-by-step explanation:

Rachel spent 4 times more, so you multiply.

You need to multiply 4 and x.

The expression would be 4*x

Answer:

x = -7

Step-by-step explanation:

Given:

5 – x = 12

Subtract 5 from both sides

5 – x - 5 = 12 - 5

- x = 7

Note: the coefficient of -x is -1

- x = 7

Divide both sides by the coefficient of -x

- x / -1 = 7 / -1

x = -7

Check

5 – x = 12

5 - (-7) = 12

5 + 7 = 12

It is possible to subtract a number from 5 and have more than 5 as your answer when the unknown number is a negative value

Answer:

In △DBC and △BDA

proved.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

Rational

Step-by-step explanation:

As 0.70 can be represented as 70/100 or 7/10

the rental of the vacation cabin increases Piper's AGI by $2,500. She can deduct the mortgage interest and property tax as itemized deductions,

1. The rental of the vacation cabin by Piper will have an effect on her Adjusted Gross Income (AGI). The rental income of $2,500 will be included in her gross income, which will increase her AGI.

2. Piper can deduct certain expenses related to the vacation cabin, and these deductions will be classified as either "for AGI" or "from AGI."

Expenses classified as "for AGI" are deducted before calculating AGI and include:

- Mortgage interest: Piper can deduct the $10,000 in mortgage interest paid for the year as an itemized deduction on Schedule A.

- Property tax: Piper can deduct the $1,500 in property tax paid for the year as an itemized deduction on Schedule A.

Expenses classified as "from AGI" are deducted after calculating AGI and include:

- Utilities, insurance, and maintenance: The total expenses of $2,000 can be deducted from rental income, reducing the taxable rental income to $500.

- Depreciation: Piper can deduct the $3,200 in depreciation as an expense against the rental income.

the rental of the vacation cabin increases Piper's AGI by $2,500. She can deduct the mortgage interest and property tax as itemized deductions, and she can deduct the expenses of utilities, insurance, maintenance, and depreciation from the rental income to determine the taxable rental income.

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Answer:

\( \frac{20}{24} = \frac{22}{x + 22} \\ 24 \times 22 = 20x + 20 \times 22 \\ 20x = 4 \times 22 \\ x = 88 \div 20 = 4.4\)

Answer:

b. 5x + 4y = 80

Step-by-step explanation:

Let us assume the remaining balance left be Y

and, the number of songs purchased be X

Given that

Wins a gift card of $20

And, the songs purchased is 16

Now if we take the fraction

= 20 ÷ 16

= 5 ÷ 4

So if we reverse this fraction

So it could be 5x and 4y

And, the amount that would come is

= $20 × 16 ÷ 4

= 80

So, the equation is 5x + 4y = 80

Hence, the correct option is b.

Answer:

4

Step-by-step explanation:

19-3=16

16 divided by 4 is 4

The equation of the trend line is given as follows:

y = 1.33x + 20.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

Two points on the line in this problem are given as follows:

(0, 20) and (15, 40).

When x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by 15, y increases by 20, hence the slope m is given as follows:

m = 20/15

m = 1.33.

Hence the function is given as follows:

y = 1.33x + 20.

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Answer: Did you know that you should exercise regularly?

Step-by-step explanation:

Answer:

Data A - 5

Data B - 5

Data C - 5

Data D - 6

Step-by-step explanation:

Data A,

Graph for the data shows that there is a distinct value of y (output value) for every input value of x.

Therefore, Data A is a function.

Data B,

Each ordered pair shows exactly one output value for each input value.

Therefore, Data B represents a function.

Data C,

For each input value there is exactly one output value.

Therefore, Data C represents a function.

Data D,

From the given table,

For x = -1 there are two output values y = 27, 39

For x = -2 output values are y = 45, 21

Since for these input values there are two output values, Data D will not be a function.

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

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The balance of the unsubsidized loan at the time of graduation is $3,691.10.

Given:

Principal amount = $2,560

Interest rate = 6.8% = 0.068

Time period = 6 months

We can use the formula for compound interest to calculate the future value:

\(Future\; Value = P (1 + \dfrac{Interest Rate}{Number of Periods}) ^{(Periods * Time )\)

Substituting the value back into the formula as

Future Value = \($2,560 (1 + \dfrac{0.068}{12} )^{(12 * 6)\)

                      = \($2,560 (1 + 0.00566667)^{(72)\)

                      = \($2,560 (1.00566667)^{(72)\)

                      = $2,560 * 1.44044291

                       = $3,691.10

Therefore, the balance is $3,691.10.

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