A party will have pentagonal tables placed together. The number of people, P, who can sit at the tables is a function of the number of tables, n.

A. Explain why the equation
P=3n+2 defines this function.

B. How many tables are needed if 47 people come to the party?

C. How many tables are needed if 99 people come to the party?

D. Write the inverse of this function and explain what the inverse function tells us?

The length of TS  in ΔTRS using Similarity of triange is 12 cm .

If two items have the same shape or have the same shape as their mirror images, they are said to be Similar. One can be produced from the other more accurately by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.

If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varying individual side lengths, but they must have equal angles and the same scale factor or matching ratio of the side lengths. If two triangles resemble one another, then

In ΔTPQ and ΔTPS

∠T is common in both triangle

PQ ║ RS

∴∠TPQ = ∠TRS (Corresponding Angles)

similarly ,

∠TQP = ∠TSR

∴ Δ TPQ ~ ΔTRS

So,

PQ/ RS = TQ/ TS

⇒ 2/ 6 = 4 / TS

⇒TS = (4*6)/2  = 12

The length of TS  in ΔTRS using Similarity of triange is 12 cm .

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The series ∑(n=1 to ∞) 8/n! converges. The limit of the absolute value of the ratio of consecutive terms, lim(n→∞) |a(n+1)/a(n)|, is 0, indicating convergence.

To determine the convergence or divergence of the series ∑(n=1 to ∞) 8/n!, we can use the Ratio Test. The Ratio Test states that if the limit of the absolute value of the ratio of consecutive terms, lim(n→∞) |a(n+1)/a(n)|, is less than 1, the series converges. If the limit is greater than 1 or if the limit is equal to 1 but inconclusive, further analysis is needed.

In this case, let's compute the ratio of consecutive terms:

|a(n+1)/a(n)| = |8/(n+1)!| * |n! / 8|

= 8 / (n+1)

Taking the limit as n approaches infinity:

lim(n→∞) |a(n+1)/a(n)| = lim(n→∞) 8 / (n+1) = 0

Since the limit is 0, which is less than 1, the Ratio Test tells us that the series converges.

Therefore, the series ∑(n=1 to ∞) 8/n! converges.

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Answer:

Amelia is 5 years old

Let x be Amelia and y by Etta.

[] Amelia is 3 years younger than Etta.

x = y - 3

[] The product of their ages is 40.

x * y = 40

We can use a system of equations to solve

[] The system

a = e - 3

a * e = 40

[] Graphing

-> See attached

[] The answer is 5

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

The margin of error for this poll is approximately 0.01 or 1%.

The margin of error is determined by the formula:

\($$ME = z*\frac{\sigma}{\sqrt{n}}$$\)

Where sigma is the standard deviation, z is the z-score for the confidence level, and n is the sample size.

In this case, we have a sample of 1103 adults and we want 95% confidence in our estimate of the percentage of American adults who do not use e-mail.

This means that the z-score will be 1.96 (for a two-tailed test). The standard deviation is unknown, so we use the sample proportion as an estimate for the population proportion.

The sample proportion is p = 0.38.

The formula for the standard deviation of a sample proportion is:

\($$\sigma = \sqrt{\frac{p(1-p)}{n}}$$\)

Plugging in the values:

\($$\sigma = \sqrt{\frac{0.38(1-0.38)}{1103}}$$\)

\($$\sigma \approx 0.0198$$\)

Now we can find the margin of error:

\($$ME = 1.96*\frac{0.0198}{\sqrt{1103}}$$\)

\($$ME \approx 0.01$$\)

Therefore, the margin of error for this poll is approximately 0.01 or 1%.

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Given z²+1/z² =14

using above equation,

z²+1/z² = 14

add 2 on both side,

z² + 1/z² + 2 = 14 + 2

the LHS is whole square of z + 1/z

so we can write it

(z + 1/z)² = 16z + 1/z = 4

Now we know,

(a + b)³ = a³ + b³ + 3ab(a+b)

here, a = z and b = 1/z,

substituting a and b in equation we will get,

(z + 1/z)³ = z³ + 1/z³ + 3z/z( z+ 1/z)

4³ = z³ + 1/z³ + 3×4

z³+ 1/z³ = 64-12

z³ + 1/z³ = 52

Answer:

52.

Step-by-step explanation:

Using the identity a^3 + b^3 = (a + b)(a^2 - ab + b^3):

z^3 + 1/z^3 = (z + 1/z)(z^2 - z *1/z + 1/z^2)

= (z + 1/z) (z^2 - 1 + 1/z^2)

= (z + 1/z) (14 - 1 )

= 13(z + 1/z).

Now using the identity a^2 + b^2 = (a + b)^2 - 2ab:

z^2 + 1/z^2 = ( z + 1/z)^2 - 2(z * 1/z)  = 14 So:

( z + 1/z)^2 - 2 = 14

( z + 1/z)^2 = 16

Taking z + 1/z = 4 we therefore have:

z^3 + 1/z^3 =  13 * 4 = 52.

Answer:

I see a fish writing on paper

Answer: A girl/boy writing

Step-by-step explanation:

Answer:

8 1/3

Step-by-step explanation:

We want to find a number, x, that when divided by 10/3 equals 2.5.  We can write that as:

  x/(10/3) = 2.5

x = (2.5)*(10/3)    [MULTIPLY BOTH SIDES BY (10/3)

x = 25/3

x = 8 1/3             [

Answer:

its all about reletives so if u take the number then multiply by five u get 56.3

Step-by-step explanation:

u know

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Step-by-step explanation:

"Domain' is the x values a graph can have

  this one appears to have an asymptope at x = minus 2 ...it approaches but never reaches minus2  

    and then goes on up to + inf

 ( - 2, +inf)

Answer:

c = 10

Step-by-step explanation:

The pythagoras theorem :

a² + b² = c²

a = 6 and b = 8

6² + 8² = c²

36+64 = c²

100 = c²

c = √100

c= 10

Hope this helped and brainliest please

Answer:

Answer: 31

Step-by-step explanation:

\({ \rm{45 - ( {}^{ + } 14)}} \\ \\ = { \rm{45 - 14}} \\ \\ = { \rm{31}}\)

Answer:

31

Step-by-step explanation:

(45)-(+14)

This is asking us to take 45 [(45)] and subtract 14 [-(+14)]

That is 45 - 14 = 31

The expression "-(+14)" is a deliberate attempt to confuse.  It says "subtract a positive 14."  There was no need to add the "+" sign in the parentheses, since a positive value is always assumed.  But it was added here to promote heartburn and the sale of TUMS.  When I see something like "-(+10000)," I immediately change it to "-10000" and move on, adding one demerit to the author of the problem.

Answer:

She spent two times as long on the phone then she did cleaning the kitchen.

Step-by-step explanation:

1/4 times 2 is 1/2.

Answer:

In total she spent 45 minutes on the phone and in the kitchen cleaning

Step-by-step explanation:

1/4 of an hour is 15 minutes and 1/2 of an hour is 30 min. You add them together to get 45 minutes and that how much time she has spent in total on the phone and in the kitchen.

Decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

The expression SS stands for "sum of squares", which is a statistical concept used in analysis of variance (ANOVA) to quantify the variation in a dataset. The components of this expression, a, b, c, and d, represent different sources of variation in the dataset, and their meanings are as follows:

a. (df)(s^2): This component represents the sum of squares due to the effect of the independent variable, also known as the factor or treatment. It is calculated by multiplying the degrees of freedom (df), which is the number of levels of the factor minus one, by the variance of the data within each level (s^2). This component quantifies the amount of variation in the dependent variable that can be explained by the independent variable.

b. (df)(s): This component represents the sum of squares due to the interaction between the independent variable and other factors, also known as the interaction effect. It is calculated by multiplying the degrees of freedom (df) by the standard deviation (s) of the data. This component quantifies the amount of variation in the dependent variable that is due to the joint effect of the independent variable and other factors.

c. (n)(s^2): This component represents the sum of squares due to the variation within groups, also known as the error or residual sum of squares. It is calculated by multiplying the sample size (n) by the variance of the data within each group (s^2). This component quantifies the amount of variation in the dependent variable that is not explained by the independent variable or other factors.

d. (n)(s): This component represents the sum of squares due to the variation between the sample mean and the overall mean, also known as the total sum of squares. It is calculated by multiplying the sample size (n) by the standard deviation (s) of the data. This component quantifies the total amount of variation in the dependent variable.

In summary, the expression SS = a. (df)(s^2) + b. (df)(s) + c. (n)(s^2) + d. (n)(s) represents the decomposition of the total sum of squares into its components due to the independent variable, interaction effect, error, and total variation. This decomposition is used to perform ANOVA and test the significance of the independent variable and its interaction effect on the dependent variable.

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Answer:

60%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

9/15=0.6 which is 60%

\( \cos(x) = \frac{b}{h} \\ \cos(x) = \frac{4 .9}{6.8} \\ \cos(x) = 0.720 \\ x = \cos^{ - 1} (0.720) \\ x = 44 \degree\)

Answer:

x ≈ 44°

Step-by-step explanation:

        We will use a trigonometry function to solve for x. We can see that we have values for the adjacent side and hypotenuse. This means we will be using cosine. Cosine is \(\frac{adjacent }{hypotenuse}\)

cos(x) =  \(\frac{adjacent }{hypotenuse}\)        [Given]

cos(x) =  \(\frac{4.9}{6.8}\)                   [Plug-in the values we have]

x ≈ 43.8969                 [Find the inverse cosine function of both sides]

x ≈ 44°                          [Rounding to nearest degree]

Therefore, the equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2) is y = -x + 2.

To find an equation of the tangent line to the curve xe^y + ye^x = 2 at the point (0, 2), we need to use the concept of differentiation.

First, we differentiate both sides of the equation with respect to x using the product rule and the chain rule:

(d/dx)[xe^y] + (d/dx)[ye^x] = (d/dx)[2]

e^y + xe^y(dy/dx) + e^x(dy/dx) + ye^x = 0

Simplifying this expression and evaluating it at the point (0, 2), where x = 0 and y = 1, we get:

e^1 + 0 + e^0(dy/dx) + 2e^0 = 0

dy/dx = -1

Therefore, the slope of the tangent line at the point (0, 2) is -1.

Next, we can use the point-slope form of a line to find the equation of the tangent line. We know the slope is -1 and the point (0, 2) lies on the line, so we can write:

y - 2 = -1(x - 0)

Simplifying this expression, we get:

y = -x + 2

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Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

What do you mean by rates?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

1. Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

2. From 1988 to 1989 the cost of a ticket decreased. Also from 1991 to 1992 the cost decreased a little. The graph slants a little downward.\

3. From 1990 to 1994 the cost stayed pretty much the same. Those years on the graph look almost level... not sloping upward or downward.

4.  1980-1988 price increased from about $2.75 to about $4.25 $1.50 over 8 years = $0.19 per year 1989-1993 price increased from about $4.00 to about $4.20 = $0.20 over 4 years = $0.05 per year 1994-2011 price increased from about $4.20 to about $8.00 $3.80 over 7 years = $0.54 per year

5. Maybe 2012 will be $8.20, 2013 will be $8.30, 2014 will be $8.50, 2015 will be $8.60 ish
Maybe I should make the price go up about $0.17 cents per year ... on average.

6.  1979 maybe $2.52
     1978 maybe $2.36
     1977 maybe $2.19
     1976 maybe $2.02
      975 maybe $1.85
I figured that the price was going down, on average, at about $0.17 per year.

7. one possibility might be y=$5.30/31 x + $2.70 or y = 0.17x+2.7.

8.Using the equation that we fit to this data y = 0.17x + 2.7 we get 0.17(40) + 2.7= $9.50 for the year 2020 and for the year 2030 we get 0.17(50)+2.7 $11.20

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Answer:

Step-by-step explanation:

its b like this the aetter  number g

The probability that the committee will consist of two teachers and two students is 28/65.

To determine the probability that the committee will consist of two teachers and two students, we need to first find the total number of ways to select four people from the group of 15:

Total number of ways = C(15,4) = 15! / (4!11!) = 1365

Next, we need to find the number of ways to select two teachers and two students:

Number of ways = C(7,2) * C(8,2) = (7! / (2!5!)) * (8! / (2!6!)) = 21 * 28 = 588

Finally, we can find the probability by dividing the number of ways to select two teachers and two students by the total number of ways:

Probability = 588/1365 = 28/65

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The break-even quantity is 3 units. The profit for producing 470 units is $5624. 13 units must be produced for a profit of $120.here both cost and revenue are in dollars.

(a) To find the break-even quantity, we set the cost function C(x) equal to the revenue function R(x) and solve for x:

\(11x + 36 = 23x\)

\(36 = 12x\)

\(x = 3\)

Therefore, the break-even quantity is 3 units.

(b) The profit for producing 470 units can be calculated by subtracting the cost from the revenue:

\(Profit = Revenue - Cost\)

\(Profit = R(470) - C(470)\)

\(Profit = 23(470) - (11(470) + 36)\)

\(Profit = 10810 - 5186\)

\(Profit = $5624\)

The profit for producing 470 units is $5624.

(c) To find the number of units that must be produced for a profit of $120, we set the profit equation equal to $120 and solve for x:

\(Profit = Revenue - Cost\)

\($120 = R(x) - C(x)\)

\($120 = 23x - (11x + 36)\)

\($120 = 12x - 36\)

\(12x = 156\)

\(x = 13\)

Therefore, 13 units must be produced for a profit of $120.

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Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.

The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.

cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53

So, the cosine of ∠U is 28/53, written as a proper fraction.

Now let's convert cosine of ∠U is 28/53 in improper fraction:

The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.

gcd(28, 53) = 1, so the fraction cannot be further simplified.

Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.

Now let's convert cosine of ∠U is 28/53 in whole number:

The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.

28 ÷ 53 = 0.526087

So, the cosine of ∠U expressed as a whole number is approximately 0.52609

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_____ The given question is not correct, so correct Question is:

Find the cosine of ∠U in Triangle UTV with side:

UV=28

VT=45

TU=53

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.

In case the 95 % confidence interval would be given by

\($0.582 \leq \mu_1-\mu_2 \leq 3.178$\)

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".

The margin of error exists the range of values below and above the sample statistic in a confidence interval.

Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".

\($\bar{X}_1=5.84$\) represent the sample mean 1

\($\bar{X}_2=3.96$\) represent the sample mean 2

n 1 = 25 represent the sample 1 size

n 2 = 25 represent the sample 2 size

\($s_1=2.211334$\) sample standard deviation for sample 1

\($s_2=2.35372$\) sample standard deviation for sample 2

\($\mu_1-\mu_2$\) parameter of interest.

The confidence interval for the difference of means exists given by the following formula:

\($\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$\)

The point of estimate for \($\mu_1-\mu_2$\) exists just given by:

\($\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$\)

In order to estimate the critical value \($t_{\alpha / 2}$\) we require to estimate first the degrees of freedom, given by:

\($d f=n_1+n_2-1=25+25-2=48$$\)

Since the Confidence is 0.95 or 95 %, the value of \($\alpha=0.05$\)and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that \($t_{\alpha / 2}=2.01$\)

In order to replace into formula (1), we get

\($1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$\)

\($1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$\)

In case the 95 % confidence interval would be given by

\($0.582 \leq \mu_1-\mu_2 \leq 3.178$\)

Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.

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Answer:

x= 1.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

5(x−2 2/5) = −5.2

1. We need to use distibutaive property

5×x and 5×-2.4

5x - 12 = -5.2

2. We need to get x alone.

5x - 12 = -5.2

    -12      -12

5x = 6.8

3. We need to divide

5x = 6.8

/5     /5

x = 1. 36

check:

5(1.36−2 2/5)=−5.2

6.8 - 12 = 5.2

An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.

Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.

The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.

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a) The probability that the murder was committed with a knife: 0.55

b) The probability that the cook did it, given that the murder was committed with a knife: 0.275

To determine the probability that the murder was committed with a knife, we first need to find the total number of weapons.

The butler has four poison tipped pens, two crowbars and four knives and the cook has three rolling pins and seven knives.

So, the total knives: 4 + 7 = 11

crowbars: 2

poison tipped pens: 4

and rolling pins: 3

So, the total number of weapons: 11 + 2 + 4+ 3 = 20

The probability that the murder was committed with a knife:

p = 11/20

p = 0.55

Now we need to find the probability that the cook did it, given that the murder was committed with a knife.

P = 0.55 × 0.5

P = 0.275

The required probability is 0.275

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The graph along the coordinate plane is attached below

To find the graph of the points along the coordinate plane, we simply need to use a graphing calculator to plot the points M - N, N - P, P - Q, Q - R and R - M.

These individual points in this coordinates cannot form a quadrilateral on the plane.

The total perimeter or distance of the plane cannot be calculated by simply adding up all the points along the line.

However, these lines seem not to intersect at any point as they travel across the plane in different directions.

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