Find the deductions and the net pay. Social Security is 6.2 percent of the first $90,000. Medicare is 1.45 percent of all income. $90,000. For Problems 3-7, the state tax is 2 percent of gross pay and the local tax is 1.5 percent of gross pay.

The correct answer is: Both the mean and median are appropriate measures of center.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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Answer:

7.30

Step-by-step explanation:

number 13 is simple subtraction.

The four points on the graph of f(x) = √x-4  including the left most point are: (4,0), (5,1), (8,2), and (20,4).

To find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.

The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).

To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:

When x = 5: f(5) = √1 = 1, so the point is (5,1)

When x = 8: f(8) = √4 = 2, so the point is (8,2)

When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)

So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).

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Answer:

Domain: [tex]x\geq 0[/tex]

Range: [tex]y\leq 0[/tex]

Step-by-step explanation:

Recall that the domain of a function is the values that x can be, while the range of a function is the values that y can be.

Let's take a look at one part of the function: [tex]\sqrt{x}[/tex].

The square root of any positive number does exist. It may not be rational, but it exists. The square root of zero also exists -- it's zero.

However, the square root of a negative number will never exist - it's imaginary. So, x cannot be negative as long as it is under the radical.

The domain is: [tex]x\geq 0[/tex]

Now, to find the range, let's look at the coefficient: -3.

A negative number times a negative number is positive. A negative number times a positive number is negative.

However, x can never be negative, so no matter what real value you plug in for x, you will always be multiplying -3 by a positive number (or zero).

Since zero times any number is zero, and a positive number times a negative number is a negative number, y will always be either equal to zero or negative.

So, the range is: [tex]y\leq 0[/tex]

Answer:

C) 4

Step-by-step explanation:

Answer:

55°

Step-by-step explanation:

the total sum of a triangle is 180.

75+50= 125

180-125= 55

& since x is an acute angle we know x is less than 90.

The volume of the solid figure is  1795.5 metres squared. Therefore, the answer is d.

The volume of the figure is the area of the base multiplied by the height of the figure.

Therefore, let's find the volume of the figure as follows:

volume of the figure = area of the base × height of the figure

area of the base =1 / 2 (a + b)h

where

Therefore,

area of the base =1 / 2 (a + b)h

area of the base = 1 / 2 (11 + 16)9.5

area of the base = 128.25

Therefore,

volume of the figure = area × height

volume of the figure = 128.25 × 14

volume of the figure = 1795.5 metres squared

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1/2% is read as 1.2 out of one hundred

so divide 100/1.2 which the answer would be 83.33333333 or 83.3

Step-by-step explanation:

a) factorize A

A = (2x-1)²+2(3-6x)(4x-7)-4x²+1

expand the terms

(2x-1)²-52x²+108x-41

factorize

(2x-1)²-(26x-41)(2x-1)

factor out the common factor 2x-1

-(2x-1)(24x-40)

A = -8(2x-1)(3x-5)

b) show that B = (3x-11)(2x-1)

6x²-25x+11

6x²-3x-22x+11

3x(2x-1)-11(2x-1)

(2x-1)(3x-11)

c) Expand and reduce A

(2x-1)²+2(3-6x)(4x-7)-4x²+1

-48x²+108x-40

d) Calculate A for x=0 and x=-1

when x=0 -48(0)²+108(0)-40

A=0

x=-1 -48(-1)²+108(-1)-40

A=-196

e) Reduce 2A-3B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-3(6x²-25x+11)

-96x²+216x-80-18x²+75x-33

-144x²+291x-113

f) Factorize 2A-B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-(6x²-25x+11)

-96x²+216x-80-6x²+25x-11

-102x²+241x-91

x=(241 + sqrt(20953))/204

x=(241 - sqrt(20953))/204

Please Mark Me Brainliest!

Step-by-step explanation:

The range rule of thumb states that for data with a roughly bell-shaped distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Given that the standard deviation is 125.9 cm³, one standard deviation above the mean would be 1128.4 + 125.9 = 1254.3 cm³, and one standard deviation below the mean would be 1128.4 - 125.9 = 1002.5 cm³.

Thus, significantly low values would be 1002.5 cm³ or lower, and significantly high values would be 1254.3 cm³ or higher.

Since 1360.2 cm³ is higher than 1254.3 cm³, it would fall outside the range of one standard deviation above the mean and can be considered significantly high based on the range rule of thumb.

1. The solution to the system of equations is v = -3 and w = 4.

2. The solution to the system of equations is y = 6 and z = -2.

To eliminate v, we can add the two equations:

(-v + w) + (v + w) = 7 + 1

2w = 8

w = 4

Substitute w = 4 into one of the equations to solve for v:

v + 4 = 1

v = -3

To eliminate z, we can add the two equations:

(y + z) + (y - z) = 4 + 8

2y = 12

y = 6

Substitute y = 6 into one of the equations to solve for z:

6 + z = 4

z = -2.

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It only seeks a single value and does not involve collecting data to draw general conclusions.

"Which employee worked the most hours in the previous month?" is not a statistical question because it only seeks a single value and does not involve collecting data to draw general conclusions.

On the other hand, "What is the average number of hours worked by employees in the previous month?" is a statistical question because it involves collecting data on all employees and using it to draw general conclusions about the entire workforce.

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Answer:

270 counter clockwise I think I'm not sure though

When electrons are lost, a cation is formed.

When electrons are gained, an anion is formed.

An atom can lose or gain electrons to form ions. An ion is an atom or molecule that has an unequal number of protons and electrons, which gives it a net electrical charge.

When an atom loses one or more electrons, it becomes positively charged because the number of protons in the nucleus is greater than the number of electrons. This type of ion is called a cation. Cations are formed when metals lose electrons because they have relatively low electronegativity, which means they don't hold onto their valence electrons as tightly.

On the other hand, when an atom gains one or more electrons, it becomes negatively charged because the number of electrons is greater than the number of protons. This type of ion is called an anion. Anions are formed when nonmetals gain electrons because they have relatively high electronegativity, which means they attract electrons more strongly.

Therefore, When electrons are lost, a cation is formed and When electrons are gained, an anion is formed.

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Answer:

When electrons are lost, a

✔ positive

 ion is formed.

When electrons are gained, a

✔ negative

 ion is formed.

Step-by-step explanation:

Answer: He could be 47 or 46

Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.

He would be 47 years                       [tex]1945\\-\\1898\\=\\47\\[/tex]

Answer:

0.077

Step-by-step explanation:

the initial mass of the sample was 32 mg. the mass of the sample 7 weeks after the start is approximately 0.8384 mg.

What is a half-life?

the amount of time it takes for half of a radioactive substance to decay the amount of time it takes for all of a radioactive substance to decay half the time it takes for a radioactive substance to break down the reactive half of a radioactive substance

We can use the half-life formula to solve this problem. The formula is:

[tex]mass = initial mass * (1/2)^{\frac{time}{half-life} }\\[/tex]

where:

mass: the final mass of the sample

initial mass: the initial mass of the sample

time: the time that has elapsed since the start

half-life: the half-life of the substance

Let's use the formula to find the initial mass of the sample:

[tex]2 \ mg = initial mass * (1/2)^(16/4)\\\\2 = initial mass * (1/2)^4\\\\2 = initial mass * 1/16\\\\initial mass = 2 * 16 = 32 mg[/tex]

Therefore, the initial mass of the sample was 32 mg.

7 weeks × 7 days/week = 49 days

Then we can use the half-life formula again:

[tex]mass = initial mass * (1/2)^{(time/half-life)}[/tex]

[tex]mass = 32 \ mg * (1/2)^{(49/4)}[/tex]

mass = 32 mg × 0.0262

mass ≈ 0.8384 mg

Therefore, the mass of the sample 7 weeks after the start is approximately 0.8384 mg.

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x = −26

Explanation screen shot inserted below:

Answer:

[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]

The measure of angle 3 is 48°

We can see that both horizontal lines are parallel, then the measure of angle 3 and the angle below it (the 132° one) must add up to 180°.

Then we can write:

∠3 + 132° = 180°

And solve this equation for the measure of angle 3.

∠3 = 180° - 132° = 48°

That is the measure.

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Answer: C - 3a - 27

Step-by-step explanation:

We start with 2.5 + 3a - 20 - 9.5, and first solve for variables:

3a

Then we solve for constants:

2.5 - 20 - 9.5 = 2.5 - 29.5 = -27

Add the two together:

3a - 27

Answer: To calculate how many times Francisco will earn interest after keeping the money in the account for 5 years, we need to determine the number of quarters in 5 years.

Since there are 4 quarters in a year, the total number of quarters in 5 years is:

4 quarters/year x 5 years = 20 quarters

Therefore, Francisco will earn interest 20 times over the 5-year period.

To calculate the value of his account in 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time the money is invested (in years)

In this case, P = $5,000, r = 0.03, n = 4 (since the interest is compounded quarterly), and t = 5. Substituting these values into the formula, we get:

A = $5,000(1 + 0.03/4)^(4x5)

A = $5,000(1.0075)^20

A = $5,866.02

Therefore, the value of Francisco's account in 5 years, if he does not make any additional deposits or withdrawals, will be $5,866.02.

Step-by-step explanation:

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.

It consists of two steps:

Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.

Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.

Here we have

The following recursive function computes the number of comparisons used in the worst case of merge sort.

M (1) = 0

M (2k) = 2M (2k−1) + 2k for all k > 0

To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:

Base case: When k = 1,

we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.

Therefore, the base case holds.

Inductive hypothesis:

Assume that M(2k) = k × 2k holds for some positive integer k.

Inductive step:

We need to show that M(2k+1) = (k+1) × 2k+1.

Using the recursive definition of M, we have:

M(2k+1) = 2M(2k) + 2(2k+1)

= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)

= 2k(2k+2) + 2(2k+1)

= 2k(2(k+1)) + 2(2k+1)

= 2(k+1) × 2k + 2(2k+1)

= (k+1) × 2(2k+1)

Therefore, the inductive step holds.

Hence,

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

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Increased land prices and acreage on the Great Plains could be seen as negative owing to  potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.

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After solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

The boldface Z is a common mathematical symbol for the set of integers.

Numbers that are negative: -1, -2, -3, -4, -5, and so on indefinitely.

Non-negative integers include 0 and all whole numbers that are positive, such as 6, 7, 8, 9, 10, and so forth.

Positive integers include 1, 2, 3, 4, 5, and on indefinitely.

So, we have the expression:

= 2 - 0.4 ÷ 0.2

Now, evaluate using the BODMAS rule as follows:

= 2 - 0.4 ÷ 0.2

= 2 - 2

= 0

Therefore, after solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

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