QUESTION 2 2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6 marks) Shape No. of match- sticks Rule 1 4 2 7 3 10 4 13 6 10 43 [24] 82 [6]​

Answer:

x = 27°

Step-by-step explanation:

l ║ m    Given

(x + 72) + (3x) = 180°       If parallel line then same-side angles = 180°

4x + 72° = 180°

 4x = 180° - 72°

 4x = 108°

   x = 108°/4

   x = 27°

Answer:

A

Step-by-step explanation:

when adding or subtracting (or multiplying or dividing) functions, we do this by applying the same operation to the functional expressions.

(f-g)(x) = (3x - 2) - (2x + 1) = 3x - 2 - 2x - 1 = x - 3

so, A is the correct answer.

Answer:

a) x - 3

Step-by-step explanation:

Given:

a) (f)(x) = 3x - 2

b) (g)(x) = 2x + 1

Find (f - g)(x):

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (3x - 2) - (2x + 1) [subtract]

(f - g)(x) = 3x - 2x - 2 - 1 [combine like terms]

(f - g)(x) = x - 3

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Considering the perimeter of the trapezoid, the set-builder representation of the possible values for the length of the sides labeled m is:

{m | m > 6}.

The perimeter of a polygon is calculated by the sum of the lengths of all the outer edges of the figure.

In the context of this problem, these measures of the outer edges are given as follows:

Hence the perimeter of the trapezoid is given as follows:

P = 6 + 10 + m + m = 16 + 2m.

The perimeter is greater than 28, hence the inequality is:

P > 28.

16 + 2m > 28. (replacing the equation for P into the inequality).

2m > 12

m > 12/2

m > 6.

The set-builder notation of this interval is:

{m | m > 6}.

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Answer:

22

Step-by-step explanation:

Hey There!

So if you didn't know angle H is a right angle. So we are given two angles and they want us to find the missing angle

Remember all of the angles of a triangle add up to equal 180

so we subtract the given angles from 180 to find the missing angle

180-90-68=22

so we can conclude that angle G = 22

Given:

To find:

The correct statements

Explanation:

Since the angles PCQ and SCR are vertically opposite angles.

So, we can write it as,

Therefore, the arc PQ is congruent to arc SR.

So, the first statement is correct.

Since the angles PCQ and SCR are vertically opposite angles and the angles QCR and PCS are vertically opposite angles.

So, we can write it as,

Since the central angle of a circle is 360 degrees.

Therefore,

Therefore, the measure of an arc QR is 150 degrees.

So, the second statement is correct.

Let us find the circumference of the circle.

Using the circumference formula,

Therefore, the circumference of the circle is,

So, the third statement is wrong.

Let us find the arc length of PS.

Here,

Using the formula,

Therefore, the arc length of PS is 13.1cm.

So, the fourth statement is correct.

Let us find the arc length of QS.

Here,

Using the formula,

Therefore, the arc length of QS is 15.7cm.

So, the fifth statement is correct.

Final answer: The statements 1, 2, 4, and 5 are correct.

Answer:

Out of

Step-by-step explanation:

A two-word phrase used to show division in a word problem.

Out of is a two-word phrase which is used to show division in a word problem.

Word problems in mathematics often use words such as divided by, per, average, split into, cut into, quotient of, ratio of to denote division (÷)

The graph of f(x)= 9(x-6)/x^2-7x+6 has a vertical asymptope at x= 1.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

First, we need to simplify and factorize the denominator as shown below:

f(x) = 9(x -6)/(x² -7x +6)

f(x) = 9(x -6)/(x²-6x -x +6)

f(x) = 9(x -6)/(x -6)(x -1)

f(x) = 9/(x -1)

The following points must be kept in mind:

For x=6, both the numerator and denominator are zero so we have a hole here. At x=1, only the denominator is zero, so we have a vertical asymptote here.

Thus the vertical asymptote of f(x) is at x=1

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Answer:

4(5c-2d)

Step-by-step explanation:

if you mean in factorization

Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

The probability that they were both there at exactly 6:00 PM, given that they were there at the same time at some point during the day, is 1/54 or approximately 0.0185.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Let's first consider the total time window during which Roger and Stacy could have visited the fair simultaneously.

Since Roger stayed for 2 hours and Stacy stayed for 3 hours, the maximum possible time they could have overlapped is 2 hours for Roger and 3 hours for Stacy, which gives a total of 5 hours.

We can visualize the possible overlap window as a rectangle with width 2 (for Roger) and height 3 (for Stacy), starting at some random time between 12:00 PM and 9:00 PM, and extending for 5 hours.

The probability of this happening is the ratio of the area of a 1-hour window (which is 1/9 of the total area of the time window) to the area of the overlap window (which is 2x3 = 6).

So the probability that they were both there at exactly 6:00 PM, given that they were there at the same time at some point during the day, is:

= (1/9) / 6

= 1/54

Therefore, The probability that they were both there at exactly 6.00 pm: 1/54

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The complete question:

Roger and Stacy each go to the county fair on the same day. They each separately show up at a random time between 12:00 PM and 9:00 PM. Roger stays for 2 hours and Stacy stays for 3 hours.

Given that, at some time, Roger and Stacy were at the fair simultaneously, what is the probability that they were both there at exactly 6:00 PM?

There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.

In this question, we have been given a customer ordered 15 pieces of gourmet chocolate. the order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate.

Any box that is used must be full.

We need to find the number of different combinations of boxes can be used for the customer's 15 chocolate pieces.

In 15 pieces, there would be maximum 3(4-piece boxes), maximum 7(2-piece boxes) and maximum 15(1-piece boxes).

For small boxes that contain 1 piece of chocolate:

∑(i = 0 to 15) x^(i)

For small boxes that contain 2 pieces of chocolate:

∑(i = 0 to 7) x^(2i)

For small boxes that contain 4 pieces of chocolate:

∑(i = 0 to 3) x^(4i)

Consider an expression,

∑(i = 0 to 15) x^(i) * ∑(i = 0 to 7) x^(2i) * ∑(i = 0 to 3) x^(4i)

If we solve above expression, the coefficient of x¹⁵ is 20

Hence, there are 20 possibilities.

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Total arrangement = Case 1 + Case 2 – Case 3

Total arrangement = 15 + 15 - 81 = -51

What is Sitting Arrangement ?

In mathematics, seating arrangement refers to the various ways in which individuals can be seated in a certain arrangement or order. This term is often encountered in combinatorics, which is a branch of mathematics that deals with counting arranging objects.

To find the number of seats satisfying a given condition, we can approach the problem using the inclusion-exclusion principle.

Let's look at these two cases: no girls are sitting together and no boys are sitting together.

Case 1: No girls are sitting together

In this case, we have to divide the five girls into three rows so that no two girls sit in any row. We can use a technique called stars and bars. Think of the girls as stars and the spaces between them and the ends as rods. We need to divide the five girls between the three rows, so we have four spaces between the stars and two ends, giving us (4 + 2)C2 = 15 ways to divide the girls.

Case 2: No boys sit together

Similarly, we have to divide the five boys among three rows so that no two boys sit in any row. Using the same stars and bars technique, we have (4 + 2)C2 = 15 ways to divide the boys.

However, we must exclude cases where boys and girls sit together. To find this, we need to find the number of arrangements where both conditions are violated.

Case 3: Boys and girls are sitting together

In this case, we can consider the pair of boy and girl sitting together as one entity. So we have four pairs (BB, GG, GB, BG) to split between the three rows, giving us 3^4 = 81 ways to split these pairs.

Now we can use the inclusion-exclusion principle to find the number of arrangements that satisfy at least one of the conditions. The total number of arrangements is the sum of arrangements without girls together, arrangements without boys, minus arrangements where both boys and girls sit together:

Total arrangement = Case 1 + Case 2 – Case 3

Total arrangement = 15 + 15 - 81 = -51

However, a negative value has no meaning in this context. It means that there are no valid seating arrangements that meet the given conditions. It may not be possible to seat students in such a way as to prevent two girls or two boys from sitting together in any row of five seats. The teacher may need to explore alternative seating arrangements or adjust conditions to find a suitable solution.

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Answer:

  116 °F

Step-by-step explanation:

We presume the temperature of interest is ...

  (100 °F)×(1 +16%) = 116 °F

The highest recorded temperature in Indiana was 116 °F.

_____

Comment on the question

Temperature in degrees Fahrenheit is reported using an interval scale, not a ratio scale. The notion of a percentage change in temperature measured by such a scale makes no mathematical sense.

Yes, you can perform percentage-like operations on the numbers (which is what we did here), but the idea that 116 °F is a 16% higher temperature than 100 °F is complete nonsense. For such ratios to be meaningful, an absolute temperature scale is needed, such as the Kelvin or Rankine scales.

Answer:

1/5, 30%, 0.8, 4/3

Answer:

The break-even point is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business.

Step-by-step explanation:

Answer:

Its Pretty Simple

Step-by-step explanation:

What Is a Break-Even Price?

A break-even price is the amount of money, or change in value, for which an asset must be sold to cover the costs of acquiring and owning it. It can also refer to the amount of money for which a product or service must be sold to cover the costs of manufacturing or providing it.

In options trading, the break-even price is the price in the underlying asset at which investors can choose to exercise or dispose of the contract without incurring a loss.

KEY TAKEAWAYS

A break-even price describes a change of value that corresponds to just covering one's initial investment or cost.

For an options contract, the break-even price is that level in an underlying security when it covers an option's premium.

In manufacturing, the break-even price is the price at which the cost to manufacture a product is equal to its sale price.

Break-even pricing is often used as a competitive strategy to gain market share, but a break-even price strategy can lead to the perception that a product is of low quality.

Break-Even Price Formula

The break-even price is mathematically the amount of monetary receipts that equal the amount of monetary contributions. With sales matching costs, the related transaction is said to be break-even, sustaining no losses and earning no profits in the process. To formulate the break-even price, a person simply uses the amount of the total cost of a business or financial activity as the target price to sell a product, service, or asset, or trade a financial instrument with the goal to break even.

For example, the break-even price for selling a product would be the sum of the unit's fixed cost and variable cost incurred to make the product. Thus if it costs $20 total to produce a good, if it sells for $20 exactly, it is the break-even price. Another way to compute the total breakeven for a firm is to take the gross profit margin divided by total fixed costs:

Business break-even = gross profit margin / fixed costs

​​For an options contract, such as a call or a put, the break-even price is that level in the underlying security that fully covers the option's premium (or cost). Also known as the break-even point (BEP), it can be represented by the following formulas for a call or put, respectively:

BEP call = strike price + premium paid

BEPpu = strike price - premium paid

Break-Even Price Strategy

Break-even price as a business strategy is most common in new commercial ventures, especially if a product or service is not highly differentiated from those of competitors. By offering a relatively low break-even price without any margin markup, a business may have a better chance to gather more market share, even though this is achieved at the expense of making no profits at the time.

Being a cost leader and selling at the break-even price requires a business to have the financial resources to sustain periods of zero earnings. However, after establishing market dominance, a business may begin to raise prices when weak competitors can no longer undermine its higher-pricing efforts.

The following formula can be used to estimate a firm's break-even point:

Fixed costs / (price - variable costs) = break-even point in units

The break-even point is equal to the total fixed costs divided by the difference between the unit price and variable costs.

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The matrix can be organized using a spreadsheet, with each row representing a month and columns for each expense category, due dates, and amounts. This will allow Tina to easily track her budget and ensure all expenses are paid on time.

In order to effectively track Tina's expenses and their due dates, it's important to consider the following elements: income, fixed expenses, variable expenses, and savings goals.

First, let's start by listing all sources of income and their frequency, e.g. monthly salary or weekly allowances. Next, identify Tina's fixed expenses, which are regular and predictable payments such as rent or mortgage, utilities, insurance, and loan repayments. These expenses can be added to the matrix with their respective due dates.

Variable expenses are those that may change each month, such as groceries, entertainment, and transportation costs. To keep track of these, you can allocate a monthly budget and update the matrix as expenses occur. Also, make a note of any annual or semi-annual payments, like property taxes or subscriptions, and include them in the appropriate months.

Finally, establish Tina's savings goals and decide on a monthly contribution. Include this as a fixed expense to ensure regular savings progress. The matrix can be organized using a spreadsheet, with each row representing a month and columns for each expense category, due dates, and amounts. This will allow Tina to easily track her budget and ensure all expenses are paid on time.

Remember to review and update the budget check-off matrix periodically to make adjustments as necessary and maintain accurate financial planning.

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The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of the line as -

y = 14x - 4

The given equation of line is -

y = 14x - 4

Slope of the line perpendicular to the given line is -

m{p} = -1/14

The equation of this line will be -

y = -(1/14)x + c

For the point (28, 16), we can write -

16 = -(1/14) x 28 + c

c = 16 + 2

c = 18

So, the equation will be -

y = - (1/14)x + 18

Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

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Answer:

8p - 9

Step-by-step explanation:

→ Expand brackets

6p - 15 + 2p + 6

→ Collect like terms

8p - 9

The answer would be f(-7) = 224.

To solved you simply plug the -7 in for x. So, it would be f(-7) = 4(-7)^2 - 4(-7).

The first thing you would do is square the 4(-7)^2, to get 4(49) - 4(-7).

Then, multiply these out to the numbers outside the parentheses, to get f(-7) = 196 - (-28).

Remember, negatives cancel out negatives and turn positive, so the equation would actually be f(-7) = 196 + 28.

Simplify this, and you get f(-7) = 224.

The number of bacteria after 5 hours with initial numbers 3500 increased double in each hour is equal to 112,000.

Initially number of bacteria in a culture =  3500

Total hours the number of bacteria double = Each hour

Then the growth rate is equal to  2

As the number of bacteria after each hour is twice the previous numbers.

Formula used for the number of bacteria after t hours ,

N = N₀ x 2^t

where N₀ is the initial number of bacteria.

Time in hours = t hours

And N is the number of bacteria after t hours.

After 5 hours, the number of bacteria present is equal to,

⇒N = 3500 x 2^5

⇒N = 3500 x 32

⇒N = 112,000

Therefore, number of bacteria present after 5 hours is equal to 112,000.

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Answer:

a , b

Step-by-step explanation:

ans this are the variables

Answer: Binomial

Monomial= 1 term

Binomial= 2 terms

Trinomial=3 terms

Polynomial= 4 terms or more

Answer:

the answer should be 5

Step-by-step explanation:

Remove parentheses.

3(3x-8)-5(3x-8)=4x-16-6(x-2)3(3x−8)−5(3x−8)=4x−16−6(x−2)

2 Simplify  3(3x-8)-5(3x-8)3(3x−8)−5(3x−8)  to  -2(3x-8)−2(3x−8).

-2(3x-8)=4x-16-6(x-2)−2(3x−8)=4x−16−6(x−2)

3 Expand.

-6x+16=4x-16-6x+12−6x+16=4x−16−6x+12

4 Simplify  4x-16-6x+124x−16−6x+12  to  -2x-4−2x−4.

-6x+16=-2x-4−6x+16=−2x−4

5 Add 6x6x to both sides.

16=-2x-4+6x16=−2x−4+6x

6 Simplify  -2x-4+6x−2x−4+6x  to  4x-44x−4.

16=4x-416=4x−4

7 Add 44 to both sides.

16+4=4x16+4=4x

8 Simplify  16+416+4  to  2020.

20=4x20=4x

9 Divide both sides by 44.

\frac{20}{4}=x

​4

​

​20

​​ =x

10 Simplify  \frac{20}{4}

​4

​

​20

​​   to  55.

5=x5=x

11 Switch sides.

x=5x=5

The standard deviation of a probability distribution must be a non-negative value. It represents the measure of the dispersion or spread of the data in the distribution. The standard deviation quantifies how much the values in the distribution deviate from the mean.

Mathematically, the standard deviation (σ) is calculated as the square root of the variance (σ^2) of the probability distribution. The variance is obtained by calculating the average of the squared differences between each data point and the mean, weighted by their respective probabilities.

The standard deviation provides important information about the shape and characteristics of the distribution. A smaller standard deviation indicates that the data points are closer to the mean, resulting in a more concentrated or less dispersed distribution. Conversely, a larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider or more dispersed distribution.

The standard deviation of a probability distribution must be a non-negative value and is a measure of the dispersion or spread of the data in the distribution.

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The probability that more than the expected number of Sikh youths wear a turban in a random sample of five is 0.3671 (rounded to 4 decimal places).

a. Using the binomial distribution formula, we can determine the likelihood that two out of a random sample of five Sikh teenagers are turban-wearing:

\(P(X = 2) = (5 pick 2) (5 choose 2) * (0.75)^3 * (0.25)^2\)

"X" indicates the proportion of Sikh adolescents who wear turbans, "5 choose 2" indicates the number of possible methods to select 2 Sikhs from a group of 5, and "0.75" and "0.25" indicate the likelihoods that a Sikh youngster will not be wearing a turban and will be wearing one, respectively.

This expression can be made simpler by using a calculator to become:

P(X = 2) = 10 * 0.421875 * 0.0625 = 0.2659

Hence, 0.2659 percent chance exists that two out of every five Sikh youngsters in a random sample will be turban-wearing (rounded to 4 decimal places).

Using the complement rule, we can determine the likelihood that two or more of a random sample of five Sikh teenagers are wearing turbans:

P(X >= 2) = 1 - P(X 2)

where X is the proportion of young Sikhs who are turban-wearing.

P(X 2) is the likelihood that fewer than 2 of five Sikh teenagers chosen at random will be turban-wearing.

This can be calculated as:

P(X 2) equals P(X = 0) plus P(X = 1).

P(X = 0) = (5 select 0) * (0.75) * (5 select 0) * (0.25) * 0 = 0.2373

P(X = 1) = (5 select 1) * (0.75) * (4 select 1) * (0.25) * 1 = 0.3956

P(X 2) = 0.2373 + 0.3956 = 0.6329 as a result.

We can then compute P(X >= 2) = 1 - 0.6329 = 0.3671 using the complement rule.

Consequently, there is a 0.3671 percent chance that two or more of five Sikh teenagers chosen at random will be turban-wearing (rounded to 4 decimal places).

c. The following formula can be used to determine how many Sikh teenagers in a random sample of five are likely to wear a turban:

E(X) = n * p = 5 * 0.25 = 1.25

Using the cumulative binomial distribution function, we can determine the likelihood that more Sikh teenagers than predicted in a random sample of five wear turbans:

P(X > 1) = 1 - P(X <= 1)

P(X = 1) equals P(X = 0) plus P(X = 1).

P(X = 0) = (5 select 0) * (0.75) * (5 select 0) * (0.25) * 0 = 0.2373

P(X = 1) = (5 select 1) * (0.75) * (4 select 1) * (0.25) * 1 = 0.3956

Therefore,

P(X <= 1) = 0.2373 + 0.3956 = 0.6329

The complement rule can then be used to determine:

P(X > 1)

P(X > 1) = 1 - 0.6329 = 0.3671

Hence, in a random sample of five Sikh adolescents, the likelihood that there are more turban-wearing Sikh youths than expected is 0.3671. (rounded to 4 decimal places).

d. To determine the likelihood that more than predicted will occur.

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Answer:

D

Step-by-step explanation:

The submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures. Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented.

Given that, the sonar system detects an icicle 4000 measures ahead, with an angle of depression of 34 ∘ to the bottom of the icicle.

What are trigonometric angles?

Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

a) We know that, tan θ = ( vertical/ Base)

Let the number of measures must the submarine lower to pass under the icicle bex.

tan θ = x/ 4000

⇒ tan 34 ° = x/ 4000

⇒0.6745 = x/ 4000

⇒ x = 0.6745 × 4000

⇒ x = 2698 measures

b) Let the number of measures must the submarine rise to pass over the sunken boat bey.

tan θ = y/ 1500

⇒ tan 19 ° = y/ 1500

⇒0.3443 = y/ 1500

⇒ y = 0.3443 × 1500

⇒ y = 516.45 measures

thus, the submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures.

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The weight of the motor is both 475.6 pounds and can be expressed as an improper fraction, 475.6/1.

To find the weight of the motor, we need to determine one-fifth of the weight of Mr. Smith's bass boat, which is 2378 pounds.

Step 1: Calculate one-fifth of the weight:
To find one-fifth of a number, we divide it by 5.
2378 pounds ÷ 5 = 475.6 pounds

Step 2: Express the weight of the motor as an improper fraction:
The weight of the motor can be expressed as 475.6/1, since the whole weight is in the numerator and the unit "pounds" is in the denominator.

Step 3: Express the weight of the motor as a decimal number:
The weight of the motor can be written as 475.6 pounds.

So, the weight of the motor is both 475.6 pounds and can be expressed as an improper fraction, 475.6/1.

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