An electronics store bought a flat-
screen television from its supplier
for $699 and marked up its price
by 15%. Richard makes an 8%
commission on his sales. If Richard
sells the flat-screen television at full
price, how much commission will he
earn (rounded to the nearest cent)?

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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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]

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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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

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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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

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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:

The required number of tickets sold for the semi-final matches is 12270.

                 there are 49080 tickets have been sold for the tournament. [tex]\frac{3}{5}[/tex]  of the tickets are for the qualifying matches and 15% of the tickets are for the final match.

We have to find the number of tickets that are sold for the semi-final matches.

Let s denotes the number of tickets that are sold for semi final matches.

According to the given information, we have

Number of tickets sold for the qualifying matches is

[tex]n_{q} =\frac{3}{5} *49080=29448[/tex]

and the number of tickets sold for the final match is

[tex]n_{f}=15[/tex]% * 49080=[tex]\frac{15}{100} *49080=7362[/tex]

So therefore we must have,

[tex]n_{f} +n_{q} +s[/tex]= 49080

29448+7362+s= 49080

36810 + s =49080

s = 49080-36810

s=12270

therefore the required number of tickets sold for the semifinal matches is 12270.

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Answer:

(C) 1

Step-by-step explanation:

In a function, a real zero is where the function is equal to zero, or:

[tex]f(x)=0[/tex]

which can be rewritten as:

[tex]y=0[/tex]

which is essentially the y-intercept.

Recall that the y-intercept of a graph is where the graph crosses the y-axis (the x-coordinate is equal to 0).

We can see that the graph only crosses the y-axis at one point, meaning it only has one y-intercept, meaning it has only one real zero.

Thus, the answer is (C), 1

Step-by-step explanation:

you are in college, and need help with that ?

remember,

a > b

then also

a × c > b × c

c × a > c × b

and that is what we have here

a = 20, b = 30, c = 1/2

so, 30×1/2 is larger.

because 30 > 20.

a = 2/3, b = 2, c = 15

15×2 is, of course, larger.

because 2 > 2/3.

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:

C) 4

Step-by-step explanation:

The required equation of the rational function is f(x) = -8(x-1)(x-4) (ax + 3/2)/(3(a+3/2)(x-5)(x-2))

To create a rational function with the given characteristics, we can start by setting up the general form for a rational function:

f(x) = (ax + b) / (cx + d)

To ensure that the function has vertical asymptotes at x=5 and x=2, we need the denominators of our function to be (x-5) and (x-2), respectively. So we can rewrite our function as:

f(x) = (ax + b) / ((x-5)(x-2))

To make sure that the function passes through the x-intercepts at x=1 and x=4, we need the numerator of the function to be equal to zero at those values of x. So we add two factors of (x-1) and (x-4) to the numerator:

f(x) = k(x-1)(x-4) (ax + b) / ((x-5)(x-2))

where k is a constant that we will determine shortly.

To find the value of k, we use the fact that the function has a y-intercept at (0,3). This means that when x=0, f(x) = 3. So we substitute these values into our equation and solve for k:

3 = k(0-1)(0-4) (a(0) + b) / ((0-5)(0-2))

3 = 20k b / 10

b = 3/2

Now our equation becomes:

f(x) = k(x-1)(x-4) (ax + 3/2) / ((x-5)(x-2))

To find the value of k, we can use one of the x-intercepts. Let's use x=1:

0 = k(1-1)(1-4) (a(1) + 3/2) / ((1-5)(1-2))

0 = -3k/4 (a + 3/2)

Solving for k:

k = -8/(3(a+3/2))

Now our equation becomes:

f(x) = -8(x-1)(x-4) (ax + 3/2) / (3(a+3/2)(x-5)(x-2))

Therefore, an equation for the rational function with vertical asymptotes at x=5 and x=2, x-intercepts at x=1 and x=4, and y-intercept at 3 is:

f(x) = -8(x-1)(x-4) (ax + 3/2)/(3(a+3/2)(x-5)(x-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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To complete the grouped frequency distribution for the data with a class width of 4, you can start by first obtaining the range of the data, determining the lower limit of the first class interval, and the upper limit of each class interval.

After you have determined the upper limit of each class interval, the next thing to do will be constructing a table that shows the columns for the class intervals, the frequency of each interval, and the cumulative frequency.

Count the number of data points that fall into each class interval, and record these frequencies in the frequency column of the table. Add up the frequencies to get the cumulative frequencies. Finally, use the figures obtained to determine the mean, median and mode.

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The probability that person has applied for a home mortgage this year is 0.094.

What is probability?

The likelihood of an event occurring can be calculated using probability. The only usable result is the probability that an event will occur. a scale with 0 representing impossibility and 1 representing a certain occurrence.

From the question, we get the following information:

⇒ Total Number of customers = 3000 + 24300

⇒ Total Number of customers = 27300

⇒ Persons who applied = 2430 + 150

⇒ Persons who applied = 2580

So, we get

⇒ Probability = [tex]\frac{2580}{27300}[/tex]

⇒ Probability = 0.094

Hence, the probability that person has applied for a home mortgage this year is 0.094.

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Identify which details in the figure are important. According to the graph, 40% of respondents favor flexible working hours.

Ascertain the likelihood that one person would favor flexible work hours. There is a 40% chance that one person would choose flexible hours.

Calculate the likelihood of three people using the probability of one. We must apply the binomial probability formula to find the likelihood that three people favor flexible work hours: P(X = k) is equal to (n pick k)*p*k*(1-p)(n-k) where: - P(X = k) is the likelihood that k outcomes (in this case, k individuals favoring flexible work hours) will occur. - The total number of trials (in this case, three randomly selected participants) is n. The number of successes is k. - P stands for probability of success; in this context, it refers to the likelihood that one person will favour flexible work hours. The likelihood that three randomly selected individuals will favour flexible work hours can be determined using the following formula: P(X = 3) is equal to (3 choose 3) * 0.4; 3 * (1-0.4); (3-3) = 0.064. Consequently, the likelihood that three people chosen at random would prefer flexible work hours is 0.064 or 6.4%.

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since its on a straight line we instantly know that u+100=180 since a straight line is 180 degrees. From thay we can easily find out that u=180-100=80. So u is 80 degrees. Also pls mark as brainliest answer thx.

Answer:

u=180

Step-by-step explanation:

The two angles add together to form a straight line, so they add to 180

100+u = 180

u = 180-100

u= 80

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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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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Answer:

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

So, the spread of the numbers 4, 6, 7, 9, 9 is 5.

Spread can refer to different things depending on the context. Here are a few examples:

In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).

In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.

In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).

In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.

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x = −26

Explanation screen shot inserted below:

Answer: a) Virtual School Gold Card

Step-by-step explanation: To compare the monthly interest rates of the three credit cards, we need to convert the annual and quarterly rates to monthly rates.

For Canadian Express, the monthly interest rate is 19.9% / 12 = 1.6583%.

For Virtual School Gold Card, the monthly interest rate is 1.67%.

For Bank of Brennan Super Credit Card, the monthly interest rate is (4.99% / 4) = 1.2475%.

Therefore, the Virtual School Gold Card offers the lowest monthly interest rate at 1.67%.

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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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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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.

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.