X
0 1 2 3 4
frequency 4 6 18 7 1
Based on the table, what is P (2 > 1)?
Leave your answer in decimal form to three places.

Answer:

4(x + 3) + 2x and 6(x + 2) are equivalent

Step-by-step explanation:

The best prove why two expressions must be equivalent is,

1. Simplify each expression to its simplest form

2. Show that the simplest form of them are equal

Let us do that with the given expressions

∵ The 1st expression is 4(x + 3) + 2x

→ At first, multiply the bracket (x + 3) by 4

∵ 4(x + 3) = 4(x) + 4(3) = 4x + 12

∴ The 1st expression = 4x + 12 + 2x

→ Add the like terms

∴ 4x + 12 + 2x = (4x + 2x) + 12 = 6x + 12

∴ The 1st expression = 6x + 12

∴ The simplest form of the 1st expression is 6x + 12

∵ The 2nd expression is 6(x + 2)

→ Multiply the bracket (x + 2) by 6

∵ 6(x + 2) = 6(x) + 6(2) = 6x + 12

∴ The 2nd expression = 6x + 12

∴ The simplest form of the 2nd expression is 6x + 12

∵ 6x + 12 = 6x + 12

∴ The simplest form of the two expressions are equal

∴ The expressions are equivalent

∴ 4(x + 3) + 2x and 6(x + 2) are equivalent

Answer:

8 and 5

Step-by-step explanation:

I was messing around with the numbers in my head

Answer:

\(2x-y=-3\)

Step-by-step explanation:

\(\mathrm{The\: standard\: form\: of\: a \:linear \:equation \:is}:\mathrm{A}x+\mathrm{B}y=\mathrm{C.}\)

\(\underline{\sf{Solve\:for\:}y}:\)

\(y+7=2(x+5)\)

\(=y+7=2x+2\cdot5\)

\(= y+7=2x+10\)

\(=(y+7)+(-7)=(2x+10)+(-7)\)

\(=y+7-7=2x+10-7\)

\(\underline{y=2x+3}\)

Let's consider first what equation we must use:

 ⇒ use Combination Formula ⇒ \(._{n} C_{r}=\frac{n!}{r!(n-r)!}\)

      ⇒ where 'n'  is the total number of items and 'r'

      is the number of items to choose

Let's look at the problem:

Let's plug it in:

 \(\frac{18!}{4!*(18-4)!} =\frac{18!}{4!*14!} =\frac{18*17*16*15}{4*3*2*1} =18*17*2*5=3060\)

Thus there are 3060 ways

Answer: 3060 ways

Hope that helps!

The initial amount and rate of change given a table for a linear function are $65 and $86, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 476) and (10, 736)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (736 - 476)/(10 - 6)

Evaluate

Rate = 65

This means that the rate of change is $65

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 65

So, we have

y = 65(x - x1) + y1

Using one of the points, we have

y = 65(x - 6) + 476

Set x = 0

So, we have

y = 65(0 - 6) + 476

Evaluate

y = 86

Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively

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If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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The probability that both cards drawn are face cards, without replacement, is 12/221.

To find the probability, we need to determine the number of favorable outcomes (drawing two face cards) and the total number of possible outcomes.

First, let's calculate the number of face cards in a standard deck of 52 cards. There are 12 face cards in total (4 kings, 4 queens, and 4 jacks).

Now, for the first draw, any of the 52 cards can be chosen. However, since the first card is not replaced before the second draw, there are only 51 cards left in the deck for the second draw.

If the first card drawn is a face card, there are 12 face cards remaining in the deck. So, the probability of drawing a face card on the first draw is 12/52.

For the second draw, if the first card was not a face card, there are still 12 face cards remaining in the deck. However, the total number of cards remaining is reduced to 51.

Therefore, the probability of drawing a face card on the second draw, given that the first card was not a face card, is 12/51.

To find the probability that both cards drawn are face cards, we multiply the probabilities of the individual events:

P(both face cards) = P(first face card) * P(second face card | first card not a face card)

                = (12/52) * (12/51)

                = 12/221

The probability of drawing two face cards, without replacement, is 12/221.

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Answer:

It takes 70 minutes for 9 team members (painting 60 sq ft per minute) to paint a 4200 sq ft wall.

Step-by-step explanation:

According to the situation the calculation is shown below:-

= \(\frac{4800}{20}\)

= 240 sq ft each member of the team in 36 minutes

= \(\frac{240}{36}\)

= 6.67 sq ft each member of the team within 1 minute

\(= 6.67\times 9\)

= 60 sq ft for every 9 team members in one minute

= \(\frac{4200}{60}\)

= 70 minutes (or 1 hour and 10 minutes)

Hence, the 70 minutes is taken for 9 team members

Answer:

a) (f + g)(x) = 8x + 2

b) (f - g)(x) = 4x - 6

Step-by-step explanation:

Given:

a) Find (f + g)(x):

a. (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (6x - 2) + (2x + 4)

⇒ (f + g)(x) = 6x + 2x - 2 + 4

⇒ (f + g)(x) = 8x + 2

b) Find (f - g)(x):

b. (f - g)(x) = f(x) - g(x)

⇒ (f - g)(x) = (6x - 2) - (2x + 4)

⇒ (f - g)(x) = 6x - 2x - 2 - 4

⇒ (f - g)(x) = 4x - 6

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The object whose distance is three times its displacement is object Z.  

The distance is defined as a scalar quantity representing the total distance traveled.

Displacement is a vector representing the distance between the end and start points.

Distance, Displacement, Ratio To calculate r = 3

Object    Motion                                    Distance     Displacement  ratio

 X          3 units left, 3 units right        3 + 3 = 6       3 - 3 = 0            ∞

 Y          6 units right, 18 units right    6 + 18 = 24    6 + 18 = 24       1

 W         8 units left, 24 units right      8 + 24 = 32   -8 + 24 = 16     2

 Z          16 units right, 8 units left       16 + 8 = 24    16 - 8 = 8         3

Ratio is calculated by dividing the distance by the displacement.

distance/displacement.

For object Z it is 24/8 = 3. So the object whose distance is three times its displacement is object Z.  

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Answer:

A. $ (5 + 2x), B. = $ 305

Step-by-step explanation:

x miles

A. cost for x miles = 5 + 2x ($)

B. cost for 150 miles = 5 + 2*150 =305 ($)

Answer:

A. let the mile driven = x

5 + 2x

B. × = 150 mile

taxi service = $5 + $2(150)

= $305

*in an equation u dont have to write the symbol . for example, $, ml, km, etc.

The firm's cash coverage ratio can be calculated using the formula:

Cash Coverage Ratio = (Operating Income + Depreciation) / Interest Expense.  Therefore, the firm's cash coverage ratio is approximately 6.93.

The cash coverage ratio is a financial metric used to assess a company's ability to cover its interest expenses with its operating income. It provides insight into the company's ability to generate enough cash flow to meet its interest obligations.

In this case, we first calculated the operating income by subtracting the cost of goods sold (COGS) and selling, general, and administrative expenses (SG&A) from the sales revenue. The resulting operating income was $143,106.

Since the question didn't provide information about the depreciation expenses, we assumed it to be zero. If depreciation expenses were given, we would have added them to the operating income.

The interest expense was given as $20,650, which we used to calculate the cash coverage ratio.

By dividing the operating income by the interest expense, we found the cash coverage ratio to be approximately 6.93. This means that the company's operating income is about 6.93 times higher than its interest expenses, indicating a favorable position in terms of covering its interest obligations.

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Answer:

\(f(-7) = 20\)

Step-by-step explanation:

Given:

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

Solving for \(f(-7)\):

\(f(-7) = 2(3 -(-7)) \\ f(-7) = 2(3 +7) \\ f(-7) = 2(10) \\ f(-7) = 20\)

From the hypothesis test, it is found that that the p value is of  0.6683

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

H₀ : µ > 10.2

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

H₁: µ > 10.2

10 students were surveyed, so there are 9 df (degree of freedom).

The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value

Thus, p test:

X = 10.2 hours

n = 10

test statistics = 0.45

Thus, using a t-distribution calculator, the p-value of the test is of 0.6683

Pvalue = 0.6683

p value is greater is than 0.10 which indicates that the amount of time is not greater than 10.2 hours for this year.

Hence we get the value of p as 0.6683.

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To determine what the net income would have been if the allowance method had been used and the company estimated that 1% of sales would be uncollectible, you would need the following information:

Sales Revenue: The total amount of sales made during the specified period.

Estimated Uncollectible Percentage: The estimated percentage of sales that the company expects to be uncollectible.

Once you have these two pieces of information, you can calculate the estimated uncollectible amount and subtract it from the net income. Here's the calculation:

Calculate the Estimated Uncollectible Amount:

Estimated Uncollectible Amount = Sales Revenue * Estimated Uncollectible Percentage

Calculate the Net Income:

Net Income = Sales Revenue - Estimated Uncollectible Amount

Let's say the company's sales revenue for the period is $1,000,000 and they estimate that 1% of sales will be uncollectible. We can plug these values into the formulas above:

Estimated Uncollectible Amount = $1,000,000 * 0.01 = $10,000

Net Income = $1,000,000 - $10,000 = $990,000

Therefore, if the allowance method had been used and the company estimated that 1% of sales would be uncollectible, the net income would have been $990,000.

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We can use trigonometric ratio to find the value of x

From the question,

θ=22 opposite = x hypotenuse = 15

substitute the values into the formula and evaluate

cross-multiply

Therefore, the closest value is 5.6

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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Answer:

27\(x^{14}\)\(y^{13}\)

Step-by-step explanation:

When a power is raised to a power, you multiply the exponents. If you do not see an exponent, it is understood that the exponent is one.

\((xy^{5})^{2}\)\((3x^{4}y)^{3}\)

\(x^{2}\)\(y^{10}\)\(3^{3}\)\(x^{12}\)\(y^{3}\)  Now we multiple 3(3)(3) to get 27 and we add the exponents for the variables that are the same.

27\(x^{14}\)\(y^{13}\)

Answer:

the number of players being seniors is 24

Step-by-step explanation:

For every 7 players at least 2 were seniors so you can make it into a ratio 2:7. When you divide 84 by 7 you get 12 then multiply 12 with 2 and you get 24.

have good day ( ^﹏^)

All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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Answer:

i think its b

Step-by-step explanation:

Answer:

Susan is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.

23

20

Equation:

j(x) = -3x² - 5

Which part of the equation tell us that the graph opens downward?

Here see that the leading coefficient of x² which is (-3) is less than 0, meaning negative. a < 0 Hence, the graph will open from downwards.

Answer:

The coefficient of x²

Step-by-step explanation:

The part of the function j(x) which shows the graph opens downward is the coefficient of x². Depending on whether the value is positive or negative, we will understand if it opens upward or downward.

The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

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Answer:

1)Area; A = ¼πr²

Perimeter; P = πr/2 + 2r

2)A = 19.63 cm²

P = 17.85 cm

3) r = 8.885 cm

4) r = 14 cm

Step-by-step explanation:

This is a quadrant of a circle. Thus;

Area of a circle is πr². A quadrant is a quarter of a circle. Thus;

Formula for Quadrant Area is; A = ¼πr²

A) Perimeter of a circle is 2πr. Thus, perimeter of a quadrant is a quarter of the full circle perimeter.

Formula for the quadrant perimeter in the image given is;

P = 2πr/4 + 2r

P = πr/2 + 2r

B) When r is 5 cm;

A = ¼π(5)²

A = 19.63 cm²

P = π(5)/2 + 2(5)

P = 17.85 cm

C) when A is 100cm²:

¼πr² = 100

r² = 100 × 4/π

r² = 78.9358

r = √78.9358

r = 8.885 cm

D) when P = 50 cm.

50 = πr/2 + 2r

50 = (½π + 2)r

r = 50/(½π + 2)

r = 14 cm

The value of c: -0.0018.

We first find the derivative of f(x) using the product and chain rule:

f(x) = cx ln(cos(x))

f'(x) = c ln(cos(x)) + cx * (-sin(x)/cos(x))

f'(x) = c ln(cos(x)) - cx tan(x)

Then we can find the fourth derivative:

\(f''''(x) = c * (- 2sec^4(x) - 16sin^2(x)sec^2(x) + 12sin^4(x)sec^2(x)) - cx * (24sin^3(x)/cos^3(x) + 12sin(x)/cos(x))\)

Now we evaluate the fourth derivative at x = 4:

\(f''''(4) = c * (- 2sec^4(4) - 16sin^2(4)sec^2(4) + 12sin^4(4)sec^2(4)) - c*4 * (24sin^3(4)/cos^3(4) + 12sin(4)/cos(4))\)

We set this equal to 7 and solve for c:

\(7 = c * (- 2sec^4(4) - 16sin^2(4)sec^2(4) + 12sin^4(4)sec^2(4)) - c*4 * (24sin^3(4)/cos^3(4) + 12sin(4)/cos(4))\)

Using a calculator, we find that the value of c that satisfies this equation is approximately -0.0018.

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Answer:

49π cm^2

Step-by-step explanation:

\(A = \pi r^2\)

For this equation, we need the radius but we have the diameter so we divide the diameter by 2.

14 ÷ 2 = 7

Then we substitute that into the equation.

\(A = \pi (7)^2\)

\(A = \pi(49)\)

So the area of the circle in terms of pi is \(49\pi cm^{2}\)

The number 7 emerged in human history through cultural and mathematical developments.

The significance of the number 7 can be observed in various aspects of human history. One of the earliest instances is found in ancient Mesopotamia, where the Sumerians developed a base-60 numeral system called sexagesimal.

This system contributed to the use of 60 as a highly divisible number and influenced the concept of dividing the day into 24 hours, each consisting of 60 minutes.

In ancient Egypt, the division of the week into seven days was based on the observation of celestial bodies.

The Egyptians associated each day with a different planet or celestial object, namely Sunday (Sun), Monday (Moon), Tuesday (Mars), Wednesday (Mercury), Thursday (Jupiter), Friday (Venus), and Saturday (Saturn). These planetary associations were later adopted by the Romans, and their names in English still reflect these origins.

The number 7 also holds religious and symbolic significance. In Judaism, the seventh day of the week, Saturday, is considered a day of rest, known as the Sabbath.

This tradition is rooted in the biblical story of creation, where God rested on the seventh day. In Christianity, the Book of Genesis describes the world being created in six days, with the seventh day being designated as holy.

Furthermore, the number 7 appears in mathematics and geometry. The seven colors of the rainbow, the seven musical notes, and the seven wonders of the ancient world are all examples of the cultural significance attributed to this number.

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The correct answer include the following: A) The given value is a parameter for the week because the data collected represent a population.

In Statistics and Mathematics, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.

In this context, we can reasonably infer and logically deduce that the amount of voltage that was supplied to this homeowner's home represent a parameter for the week since the data collected represents a population.

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Complete Question:

A homeowner measured the voltage supplied to his home on all 7 days of a given week​, and the average​ (mean) value is 120.6 volts.

Choose the correct answer below.

A) The given value is a parameter for the week because the data collected represent a population.

B) The given value is a statistic for the week because the data collected represent a sample

C) The given value is a statistic for the week because the data collected represent a population.

D)The given value is a parameter for the week because the data collected represent a sample.