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2 months ago

What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1

Mathematics

1 answer:

Inessa [12.5K]2 months ago

8 0

The outcome is "GK=37, GH=14, and JK=19".

The problem references a missing attachment file, thus please find it attached.

The provided values are:

GJ=4x+2

HK=6x-1

Given GK =37

Need to calculate:

HJ=?

From GK: GK = GJ+JK yields GJ+(HK-HJ)

= 4x+2+((6x-1)-x) yields

9x+1...(a)Substituting (a) into the equation gives: 9(4)+1 yields 37 solves to x=4... for answer (b) and (c). Substituting x=4 yields:

GH=14 and JK=19.

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After a 5% pay raise , Hermione is earning $21,000 per year. What was she earning before the pay raise?

zzz [12365]

Answer:

$\$20,000$

Explanation step-by-step:

Let

x represent Hermione's salary prior to the raise

Given:

$100\%+5\%=105\%=105/100=1.05$

Therefore, the equation that expresses this relationship is

$1.05x=21,000$

To find x, divide both sides by 1.05:

$x=21,000/1.05$

$x=\$20,000$

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3 months ago

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

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Answer:

Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.

Step-by-step explanation:

The following data set is provided: (in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ denotes data points, $\bar{x}$ represents the mean, and n indicates the number of samples.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

The sum of squares of the differences equals 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

The population mean, μ = $30,000

The sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $697.82

Initially, we formulate the null hypothesis and the alternative hypothesis.

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ A one-tailed t-test will be conducted for this analysis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

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$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

$t_{stat} < t_{critical}$

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

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2 months ago

Marc and Michelle are married and earned salaries this year of $64,000 and $12,000, respectively. In addition to their salaries,

Zina [12379]

Answer:

Total deductions available for Marc and Michelle are $24750.

Marc and Michelle's taxable income is $47750.

Further Explanation:

Income Tax refers to the additional fee imposed on an individual’s earnings that must be paid to the government. Taxable income is derived by aggregating all incomes and factoring in all claimable deductions from an individual’s income.

Here’s how to calculate the overall deductions available for Marc and Michelle:

Total Deduction Available

= The highest of Standard Deduction for MJF and Itemized Deduction + Personal and Dependency Exemptions

= Maximum of $12600 and $6000 + $12150 ($4050×3)

= $12600 + $12150

=$24750.

Consequently, Marc and Michelle's total deductions amount to $24750.

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= Marc's Salary + Michelle's Salary + Interest Yield from Corporate Bonds

= $64000 + $12000 + $500

= $76500.

Total Taxable Income of Marc and Michelle

= Gross Income – Qualified Moving Expenses – Alimony Paid – Total Deductions

= $76500 - $2500 - $1500 - $$24750

= $47750.

Thus, Marc and Michelle's entire taxable income is $47750.

Learn More:

1. Learn more about the tax on the profit from selling fixed assets

2. Learn more about personal tax

3. Learn more about the role of money

Answer details:

Grade: Senior School

Subject: Taxation

Chapter: Income Tax

Keywords: Taxable income, Marc and Michelle, Deductions, salary income, earned, corporate bond interest, interest on municipal bond, standard deductions, US tax brackets.

happy to help ya:)

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1 month ago