A log is 16 m long, correct to the nearest metre. It has to be cut into fence posts which must be 70 cm long, correct to the nearest 10
What is the largest number of fence posts that can possibly be cut from the log?

Answers

Answer 1

The largest number of fence post that can possibly be cut from the log is 23.8( nearest tenth)

What is word problem?

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

For us to know the number of fence post that can be obtained from the log, we need to convert the length of the log into cm

Therefore;

1m = 100cm

16m = 16× 100 = 1600 cm

Therefore the maximum number of fence post that can be obtained is

1600/70 = 160/7

= 23.8 ( nearest tenth)

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Related Questions

a rectangle is drawn so the width is 4 inches longer than the height. if the rectangle's diagonal measurement is 56 inches, find the height. give your answer rounded to 1 decimal place

Answers

We have the height of the rectangle equal to h = 37.5 inches.

A rectangle is actually about a right triangle. We can use the Pythagorean theorem to generate an expression to find the height of the rectangle.

We know that:

[tex]c^2=a^2+b^2[/tex] so replacing it with the width and length of the rectangle, we get :

[tex]c^2=h^2+w^2[/tex]

We were not given values for the width and length, just their relationship to each other, and we can use that to find an equation in the variable h:

So, [tex]c^2=h^2+w^2[/tex]

[tex](56)^2=h^2+(h+4)^2[/tex]

[tex]3136=h^2+h^2+8h+16[/tex]

[tex]0=2h^2+8h+16-3136[/tex]

[tex]0=2h^2+8h-3,120[/tex]

Since we cannot factor this, we can use the quadratic formula to solve for the height h, where, a = 2 , b = 8, c = -3,120

h = (-b ±[tex]\sqrt{b^2-4ac}[/tex]) /2a

Now, Plug all the values:

h = (-8 ± [tex]\sqrt{8^2-4(2)(-3120)})/4[/tex])

h = -8 ± [tex]\sqrt{64+24,960}/4[/tex]

h =( -8 ± [tex]\sqrt{25,024})/4[/tex]

h = (-8 ± 158.180)/4

There are two possible solutions, so we have:

[tex]h_1=\frac{-8+158.180}{4}[/tex]                      [tex]h_2=\frac{-8-158.180}{4}[/tex]

[tex]h_1 = 37.545[/tex]                           [tex]h_2=-41.545[/tex]  

[tex]h_1[/tex] ≈ 37.5 in.                          [tex]h_2[/tex] ≈ -41.5 in.

We cannot use [tex]h_2[/tex] because a negative height is absurd and undefined. Thus, we have the height of the rectangle equal to h = 37.5 inches.

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Which is smallest?
0.2, 0.019, 0.12, 0.02

Answers

From the given decimals which are 0.2, 0.019, 0.12, 0.02, the smallest number is 0.019.

To compare the given decimals, we need to look at the digits to the right of the decimal point. Starting from the left, the first decimal is 0.2, which has one decimal place. The second decimal is 0.019, which has three decimal places. The third decimal is 0.12, which has two decimal places. Finally, the fourth decimal is 0.02, which has two decimal places.

To compare them, we can line them up vertically by decimal place and see which one has the smallest value in the first decimal place. In this case, the smallest value in the first decimal place is 0.019. Therefore, 0.019 is the smallest decimal among the given options.

In summary, the decimals listed from smallest to largest are: 0.019, 0.02, 0.12, 0.2.

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The line L is normal to the curve defined by 2xy2 -3y = 18 at the point (3,2). The slope of line L is:

(A) 21/8 (B) 32/3 (C) - 10/21 (D) 8/21 (E) - 8/21

Answers

Slope of the normal L is 21/8.

Hence the correct option is (A).

Slope of normal to a function f(x) = y is given by = -dx/dy

Given the equation of the curve is,

2xy² - 3y = 18

Differentiating the function with respect to 'x' we get,

2x*2y*dy/dx + 2y²*1 - 3 dy/dx = 0

4xy*dy/dx + 2y² - 3dy/dx = 0

(3 - 4xy)dy/dx = 2y²

dy/dx = 2y²/(3 - 4xy)

-dx/dy = (4xy - 3)/2y²

Slope of the normal L at the point (3, 2) = (4*3*2 - 3)/(2*2²) = (24 - 3)/8 = 21/8

Hence the correct option is (A).

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Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%

Answers

The amount in the savings account after each number of years are as follows

2 years = $3413.6

5 years = $3434

8 years = $3454.4

How to calculate the simple interest and future value?

In Mathematics, simple interest can be calculated by using this formula:

S.I = PRT or S.I = A - P

Where:

S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.

By substituting the given parameters into the simple interest formula, we have;

SI = 3400 × 0.2/100 × 2

SI = $13.6

A = SI + P = 13.6 + 3400 = $3413.6

After 5 years, we have:

SI = 3400 × 0.2/100 × 5

SI = $34

A = SI + P = 34 + 3400 = $3434

After 8 years, we have:

SI = 3400 × 0.2/100 × 8

SI = $54.4

A = SI + P = 54.4 + 3400 = $3454.4

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Complete Question:

Charlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.

2 years $

5 years $

8 years $

According to a research​ survey, 34​%
of adults are pessimistic about the future of marriage and family. That is based on a random sample of about 1900 people from a much larger body of adults. Is it reasonable for research team to use a Normal model for sampling distribution of sample​ proportion?Why or why​ not?

Choose the correct answer below.

A.Yes. The data are from a random​ sample, meeting the Randomization Condition. The data have at least 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.

B.No. The data are not from a random​ sample, failing the Randomization Condition. The data have at least 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.

C.Yes. The data are from a random​ sample, meeting the Randomization Condition. The data have less than 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.

D.No. The data are from a random​ sample, meeting the Randomization Condition. The data have less than 10 successes and 10​ failures, failing the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.

Answers

Yes.

The data are from a random sample, meeting the Randomization Condition.

The data have at least 10 successes and 10 failures, meeting the Success/Failure Condition.

The population is much larger than the sample, meeting the 10% Condition. A

It is reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion.

A Normal model for the sampling distribution of a sample proportion, three conditions must be met:

The Randomization Condition, the Success/Failure Condition, and the 10% Condition.

The Randomization Condition is met as the sample is selected randomly from a much larger population of adults.

The Success/Failure Condition is also met because the sample size is large enough (n = 1900) for us to expect at least 10 successes (those who are pessimistic about the future of marriage and family) and 10 failures (those who are optimistic about the future of marriage and family).

The sample proportion of pessimistic adults is 34%, which corresponds to 646 successes in the sample.

The 10% Condition is also met as the sample size (n = 1900) is less than 10% of the total population of adults.

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the table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars. speeding ticket no speeding ticket total red car 141 194 335 not red car 200 89 289 total 341 283 624 find the probability that a randomly chosen person: a) has a red car. b) has a speeding ticket. c) has a speeding ticket given they have a red car. d) has a red car given they have a speeding ticket. e) has a red car and got a speeding ticket. f) has a red car or got a speeding ticket. write your answers in decimal form, rounded to the nearest thousandth.

Answers

Therefore, the required probabilities are:

a) P(red car) = 0.537

b) P(speeding ticket) = 0.546

c) P(speeding ticket | red car) = 0.421

d) P(red car | speeding ticket) = 0.413

e) P(red car and speeding ticket) = 0.226

f) P(red car or speeding ticket) = 0.857

a) The probability that a randomly chosen person has a red car is the number of people with red cars divided by the total number of people, which is:

P(red car) = 335/624

= 0.537 (rounded to the nearest thousandth).

b) The probability that a randomly chosen person has a speeding ticket is the number of people with speeding tickets divided by the total number of people, which is:

P(speeding ticket) = 341/624

= 0.546 (rounded to the nearest thousandth).

c) The probability that a randomly chosen person has a speeding ticket given they have a red car is the number of people with red cars and speeding tickets divided by the number of people with red cars, which is:

P(speeding ticket | red car) = 141/335

= 0.421 (rounded to the nearest thousandth).

d) The probability that a randomly chosen person has a red car given they have a speeding ticket is the number of people with red cars and speeding tickets divided by the number of people with speeding tickets, which is:

P(red car | speeding ticket) = 141/341

= 0.413 (rounded to the nearest thousandth).

e) The probability that a randomly chosen person has a red car and got a speeding ticket is the number of people with red cars and speeding tickets divided by the total number of people, which is:

P(red car and speeding ticket) = 141/624

= 0.226 (rounded to the nearest thousandth).

f) The probability that a randomly chosen person has a red car or got a speeding ticket is the sum of the probabilities of having a red car and having a speeding ticket minus the probability of having both, which is:

P(red car or speeding ticket) = P(red car) + P(speeding ticket) - P(red car and speeding ticket)

= 0.537 + 0.546 - 0.226

= 0.857 (rounded to the nearest thousandth).

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Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
A. x + x + 6 – 7 + x
B. 2x + 2 + x
C. 3 – x + 2x – 4 + 2x
D. x – 1
E. x + 1

(The answer is A and C)

Answers

The expressions are equivalent to the given expression are x + x + 6 – 7 + x and 3 – x + 2x – 4 + 2x. Therefore, the options A and C are correct answer.

The given expression is 6+(-x)+2x+(-7)+2x.

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Here, group the like terms, we get

(-x+2x+2x)+(6-7)

= 3x-1

Therefore, the options A and C are correct answer.

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Answer:

yo

Step-by-step explanation:

the answers are A and C

x + x + 6 – 7 + x and  3 – x + 2x – 4 + 2x

Edge 2023

Please answer!!! Simplify [tex]\frac{\sqrt 7 + \sqrt 3}{2\sqrt 3 - \sqrt 7}[/tex]

Answers

The simplified rational expression for this problem is given as follows:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

How to simplify the rational expression?

The rational expression in the context of this problem is defined as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}}[/tex]

The first step in simplifying the expression is removing the root from the denominator, multiplying numerator and denominator by the conjugate, as follows:

[tex]\frac{\sqrt{7} + \sqrt{3}}{2\sqrt{3} - \sqrt{7}} \times \frac{2\sqrt{3} + \sqrt{7}}{2\sqrt{3} + \sqrt{7}}[/tex]

Applying the subtraction of perfect squares, the denominator is given as follows:

2² x 3 - 7 = 12.

The numerator is:

[tex](\sqrt{7} + \sqrt{3})(2\sqrt{3} + \sqrt{7}) = 2\sqrt{21} + 7 + 6 + \sqrt{21} = 3\sqrt{21} + 13[/tex]

Thus the simplified expression is:

[tex]\frac{3\sqrt{21} + 13}{12}[/tex]

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in a survey, 75% of household reported to have some kind of board games. out of 10 households, what is the probability that less than 3 households have board games?

Answers

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

To find the probability that less than 3 households have board games, we can use the binomial probability formula. The terms involved in this problem are:

1. n: number of trials (households)
2. k: number of successful outcomes (households with board games)
3. p: probability of success (having board games)
4. q: probability of failure (not having board games)

Given that 75% of households have board games, p = 0.75, and q = 1 - p = 0.25. In this case, n = 10 households. We need to find the probability of k = 0, 1, or 2 households having board games.

The binomial probability formula is:
P(X = k) = C(n, k) * p^k * q^(n-k)

Step 1: Calculate the probability for k = 0, 1, and 2 separately:
P(X = 0) = C(10, 0) * 0.75^0 * 0.25^10
P(X = 1) = C(10, 1) * 0.75^1 * 0.25^9
P(X = 2) = C(10, 2) * 0.75^2 * 0.25^8

Step 2: Add the probabilities for k = 0, 1, and 2 to get the total probability:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

After performing the calculations, you'll find that the probability of less than 3 households having board games out of 10 households is approximately 0.0038 or 0.38%.

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What is the median of this data set?
Rainfall (in inches)

Answers

Answer:

2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5

The median is 3.

Subtract 1/2h-1 from 3/4h +4

Answers

To subtract 1/2h-1 from 3/4h+4, we can distribute the negative sign to the expression 1/2h-1 and then combine like terms. This gives:

(3/4h + 4) - (1/2h - 1)

= 3/4h + 4 - 1/2h + 1 (distributing the negative sign)

= (3/4h - 1/2h) + (4 + 1) (combining like terms)

= 1/4h + 5

Therefore, the result of subtracting 1/2h-1 from 3/4h+4 is 1/4h+5.

The article referenced in this lesson also stated that the pig landed on its right side lesson also stated that the pig landed on its right side 4,172 times out of 11,954 tosses. You will construct a 90% confidence interval for the population proportion of tosses of a plg die in which the pig lands on A Are the criteria for approximate normality met? es of a pig die in which the pig lands on its right side. B Find the sample proportion and the critical value: 0571 and Z= C Find the estimated standard error, SA, and compute the margin of error, m. 0349U-2349) = 0,004 11,954 m=2 si: 2x 0,004 -0.008 D Find the 90% confidence interval. Provide an interpretation of the confidence interval in context of this problem. E Would you support the claim that 33% of all tosses have the pig landing on its right side? Explain your reasoning. F What is the best way to decrease the margin of error and create a more precise estimate for the population proportion? Why would you want a smaller margin of error? G If you were to compute the 99% confidence interval, would it be wider or narrower than the 90% confidence interval? Explain briefly.

Answers

To determine if the criteria for approximate normality is met, we need to check if both the sample size and sample proportion are large enough. The sample size is n = 11,954 which is greater than 10.

Additionally, the sample proportion of landing on its right side is p = 0.571 which is also greater than 10. Therefore, the criteria for approximate normality is met.


A 99% confidence interval would be wider than the 90% confidence interval. This is because a higher confidence level requires a larger range to ensure the true population proportion is captured within the interval with a higher degree of certainty.

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) two adults are selected at random. find the probability that at least one of the two smokes.round your answer to 4 decimal places.leave your answer in decimal form.

Answers

The probability that at least one of the two adults smokes is approximately 0.4375, or 0.438 rounded to 4 decimal places.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that at least one of the two adults smokes, we can calculate the probability that neither of them smokes and then subtract that from 1.

Let's assume that the probability that an adult smokes is p. Then, the probability that an adult does not smoke is (1-p). Since the two adults are selected randomly, the probability that both of them do not smoke is (1-p)*(1-p), or (1-p)².

Therefore, the probability that at least one of the two adults smokes is:

1 - (1-p)²

Simplifying this expression, we get:

1 - (1 - 2p + p²)

= 2p - p²

We don't know the value of p, but we can assume a reasonable value based on smoking rates in the population. Let's say that p is 0.25, or 25%.

Substituting this value into the equation, we get:

2(0.25) - (0.25)²

= 0.5 - 0.0625

= 0.4375

Therefore, the probability that at least one of the two adults smokes is approximately 0.4375, or 0.438 rounded to 4 decimal places.

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26
In the xy-plane, a parabola has vertex (9,-14) and
intersects the x-axis at two points. If the equation of
the parabola is written in the form y = ax²+bx+c₁
where a, b, and c are constants, which of the
following could be the value of a +b+c?
A) -23
B) -19
C) -14
D) -12

Answers

The possible values of the sum of a, b and c is (c) - 14

Calculating the possible values of the sum of a, b and c

From the question, we have the following parameters that can be used in our computation:

Vertex = (9, -14)

It intersects the x-axis at two points.

So, we have (x₁, 0) and (x₂, 0)

The equation of a parabola in vertex form is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

So, we have

y = a(x - 9)² - 14

Expanding the equation, we have

y = a(x² - 18x + 81) - 14

Open the brackets

This gives

y = ax² - 18ax + 81a - 14

Set a = 0

So, we have

y = (0)x² - 18(0)x + 81(0) - 14

Evaluate

y = 0x² - 0x - 14

This means that

a = 0

b = 0

c = -14

Add the constants a, b and c

So, we have

Sum of constant = 0 + 0 - 14

Evaluate the sum

Sum of constant = - 14

Hence, the possible value of a + b + c is -14

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can density curves occur in other shapes?

Answers

Density curves can occur in a variety of shapes, depending on the distribution of the underlying data.

The normal distribution is the most commonly encountered density curve, other shapes are also possible, including skewed, bimodal, uniform, and multimodal distributions.

A skewed density curve can be either positively skewed, where the tail is longer on the right-hand side, or negatively skewed, where the tail is longer on the left-hand side.

A density curve for income data might be positively skewed, since there are more people with lower incomes than with higher incomes, and the higher incomes have a longer tail to the right.

Another type of density curve is the bimodal distribution, which has two peaks or modes.

This can occur when there are two distinct groups or populations within the data, such as in the case of height data for men and women.

Density curves can also take on other shapes, such as a uniform distribution where all values are equally likely, or a multimodal distribution where there are more than two modes.

Density curves can occur in a variety of shapes depending on the underlying distribution of the data.

The normal distribution is the most commonly encountered density curve, other shapes are also possible, including skewed, bimodal, uniform, and multimodal distributions.

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Write an expression that can be a rule for the number sequence below.

5, 9, 13, 17, 21, …Write an expression that can be a rule for the number sequence below.

5, 9, 13, 17, 21, …

5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4

5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4

Answers

The arithmetic sequence is given by the expression A = 5 + 4n

Given data ,

Let the number sequence be represented as A

Now , the value of A is

A = 5 + 9 + 13 + 17 + 21 ...

On simplifying , we get

The first term of the series is a₁ = 5

Let the second term be a₂ = 9

So , the common difference d = a₂ - a₁

d = 9 - 5 = 4

And , let the number of terms be n

So , the expression is

A = 5 + 4n

when n = 4

A = 5 + 4 ( 4 ) = 25

Hence , the arithmetic sequence is A = 5 + 4n

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PLS HELP
(Will give the brainliest)

Answers

Answer:

5

Step-by-step explanation:

Given a=12 and c=13,

b = 5

∠α = 67.38° = 67°22'48" = 1.17601 rad

∠β = 22.62° = 22°37'12" = 0.39479 rad

h = 4.61538

area = 30

perimeter = 30

inradius = 2

circumradius = 6.5

Julie was assigned to take her statistics class with Professor Fisher, whose final scores follow a normal distribution with mean 75
and a standard deviation of 6
. Her score on the final was 84
.
What is Julie's z-score?

Answers

Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To calculate Julie's z-score, we need to use the formula:

z = (x - μ) / σ

where:

x is Julie's score on the final (84)

μ is the mean score of the class (75)

σ is the standard deviation of the class (6)

Plugging in the values, we get:

z = (84 - 75) / 6

z = 1.5

Therefore, Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln 3x, y = 2, y = 3, x= 0; about the y-axis
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9x^6, y = 9x, x greaterthanorequalto 0; about the x-axis

Answers

The volume of solid generated by rotating the region bounded by curves y = ln( 3x), y = 2, y = 3, x= 0; about the y-axis is equals to the [tex] \frac{π}{18}({e^6}- e^4)[/tex]. The volume of solid generated by rotating the region bounded by curves = 9x⁶, y = 9x, x ≥0; about x-axis is equals to the [tex]\frac{81π}{13} \\ [/tex].

We have a solid obtained by rotating the region bounded by the curves with equations, y = ln 3x, y = 2, y = 3, x= 0; about the specified line, y-axis. We have to determine the volume, V of that solid. First, see the above diagram where red line, green line, blue line and purple lines represent y = ln 3x, y = 3, y = 2, x= 0 respectively. The volume of shaded region will be determine. Using formula, [tex]V = \int_{y = 2}^{y = 3} πx² dy \\ [/tex]

Now, y = ln( 3x)

taking exponential both sides,

[tex]e^ y = 3x [/tex]

[tex]x = \frac{ e^y}{3}[/tex]

so, [tex]V = \int_{y = 2}^{y = 3} π ( \frac{e^y}{3})² dy \\ [/tex]

[tex]= \int_{y = 2}^{y = 3} π ( \frac{e^{2y}}{9})dy \\ [/tex]

[tex]=[π(\frac{e^{2y}}{9 \times 2})]_{2}^{3} [/tex]

[tex]= π ( \frac{e^6}{18} -\frac{ e^4}{18})[/tex]

[tex]= \frac{π}{18}({e^6}- e^4)[/tex]

Hence, required value is [tex]= \frac{π}{18}({e^6}- e^4)[/tex].

Solid obtained by rotating the region bounded by the curves with equations, y = 9x⁶, y = 9x, x ≥0; about the specified line, x-axis. We have to determine the volume, V of that solid. First we determine the intersection points of y = 9x² and y = 9x

=> 9x = 9x²

=> x = 1

Using the formula, [tex]V = \int_{x= 0}^{x = 1} πy² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} π(9x⁶)² dx \\ [/tex]

[tex] = \int_{x= 0}^{x = 1} 81πx¹² dx \\ [/tex]

[tex] = 81π [ \frac{x¹³}{13}]_{x= 0}^{x = 1} \\ [/tex]

[tex] = 81π [ \frac{1¹³}{13} - 0] \\ [/tex]

[tex] = \frac{81π}{13} \\ [/tex]. Hence, required value is [tex]\frac{81π}{13} \\ [/tex].

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determine if the function is an exponential function

f (x) = x^3

Answers

Answer:

Yes, the function is exponential.

Step-by-step explanation:

The "^" represents an exponet. If you want to know, the exponent is 3.

A fair coin is tossed 10 times. If is the number of times that heads is tossed, what is P(3<≤6)?

Answers

The probability of P(3 < X ≤ 6) is approximately 0.6575.

What is probability?

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To find P(3 < X ≤ 6), where X represents the number of times heads is tossed when a fair coin is tossed 10 times, we need to calculate the probability of obtaining more than 3 but less than or equal to 6 heads.

Since the coin is fair, the probability of getting heads on any single toss is 0.5, and the probability of getting tails is also 0.5.

We can use the binomial probability formula to calculate the probability for a specific number of heads in a given number of coin tosses:

P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^{(n-k)[/tex],

where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.

In this case, n = 10 (10 coin tosses), p = 0.5 (probability of heads), and we want to calculate the probability for 4, 5, and 6 heads.

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6)

Using the binomial probability formula, we can calculate these probabilities:

P(X = 4) = (10 choose 4) * [tex](0.5^4) * (0.5^6)[/tex] = 210 * 0.0625 * 0.015625 = 0.2063

P(X = 5) = (10 choose 5) * [tex](0.5^5) * (0.5^5)[/tex] = 252 * 0.03125 * 0.03125 = 0.2461

P(X = 6) = (10 choose 6) * [tex](0.5^6) * (0.5^4)[/tex] = 210 * 0.015625 * 0.0625 = 0.2051

Finally, we can calculate the desired probability:

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2063 + 0.2461 + 0.2051 = 0.6575

Therefore, P(3 < X ≤ 6) is approximately 0.6575.

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the probability of winning a certain lotter is 1/51,949. for people who play 560 times, find the standard deviation for the random variable x, the number of wins

Answers

The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery [tex]= 1/51,949[/tex]

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is [tex]p = 1/51,949[/tex]. The probability of not winning in one play is [tex]q = 1 - p[/tex]

[tex]q = (51,949 - 1) / 51,949[/tex]

[tex]q = 51,948 / 51,949.[/tex]

What X should actually be is:

[tex]E(X) = np[/tex]

[tex]E(X) = 560 * (1/51,949)[/tex]

[tex]E(X) = 0.010793[/tex]

The variance of X is:

[tex]Var(X) = npq[/tex]

[tex]Var(X) = 560 * (1/51,949) * (51,948/51,949)[/tex]

[tex]Var(X) = 0.010699[/tex]

The value of X's standard deviation is

[tex]SD(X) = \sqrt{Var(X)}[/tex]

[tex]SD(X) = \sqrt{0.010699}[/tex]

[tex]SD(X) = 0.10341[/tex](approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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What is the simplified form of the following expression? Assume x > 0.

3

2x

4/6x

O2x

√24x3

2x

24x3

16x4

O√12x²

Answers

The simplified form of expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex] is  [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex]

The correct answer is an option (B)

Consider an expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex]

Multiply the fraction by an expression to form a perfect square in the denominator.

[tex]\sqrt[4]{\frac{3}{2x} }[/tex]

[tex]=\sqrt[4]{\frac{3\times 2^3\times x^3}{2x\times 2^3\times x^3} }[/tex]

We know that the cube of 2 is 8. So, substitute 2³ = 8

[tex]=\sqrt[4]{\frac{3\times 8\times x^3}{2x\times 8\times x^3} }[/tex]

Now, we multiply the monomials.

[tex]=\sqrt[4]{\frac{24\times x^3}{16\times x^4} }[/tex]

We know that the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex]

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{16\times x^4} }[/tex]

We know that 2⁴ = 16

[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4\times x^4} }\\\\=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4}\times \sqrt[4]{x^4} }[/tex]        ............(using the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex])

[tex]=\frac{\sqrt[4]{24\times x^3}}{2x }[/tex]           .......(Simplify the radical expressions)

Here, [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex] is the simplified form of expression.

Therefore, the correct answer is an option (B)

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Find the complete question below.

one day, a downtown hotel in san jose had to walk a guest to another hotel. the room rate for another hotel in downtown was $150. it cost $15 for the guest to take an uber to another hotel. the overbooked hotel also gave the guest a gift card of $25. how much is the cost of walking this guest? group of answer choices $150 $180 $190 $160

Answers

The cost of walking this guest is $190.

The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.

The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.

In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.

Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.

Therefore, the total cost incurred by the hotel for walking the guest is:

$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190

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The distinction between real variables and nominal variables is known as.

Answers

The distinction between real variables and nominal variables is based on the type of measurement used to represent the variable.

A variable is a characteristic that can take different values or levels. Real variables are measured on a numerical scale and can take any value within a certain range.

On the other hand, nominal variables are categorical variables that represent non-numerical attributes. They are used to classify data into different groups or categories based on their characteristics. Examples of nominal variables include gender, race, nationality, and occupation. These variables cannot be measured using a numerical scale, but they can be represented using labels or codes.

The distinction between real variables and nominal variables is important because they require different methods of analysis. Real variables can be analyzed using statistical methods such as mean, standard deviation, and correlation, while nominal variables require different methods such as frequency tables and chi-square tests.

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Please help me on this.

Answers

Answer:

B No solution

Step-by-step explanation:

What is the surface area of the triangular prism.

Answers

Answer:480cm^3

Step-by-step explanation:

The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?

Answers

The polynomial is P(x)= 2/5x(x-4)²(x+4)

What in mathematics is a polynomial?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. x²- 4x + 7 is an illustration of a polynomial with a single indeterminate x.

If the polynomial has a root of multiplicity 2 at  x=4, the (x−4)² is a factor.

Multiplicity 1 at x=0, then x is a factor.

Multiplicity 1 at x= -4 then (x+4) is a factor.

So P(x) = Ax(x-4)²(x+4)

As it passes through (5,18) so

18 = A.5.(5-4)² . (5+4)

So, A = 18/5 .(1/9)

= 2/5

Therefore, The polynomial is P(x)= 2/5x(x-4)²(x+4)

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Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?

33%
0%
100%
66%

Answers

In a case whereby there is a spinner with three equal sections colored red, white, and blue the  P(yellow) is 33%

What is probability?

Probability can be described as trhe act of showing how likely something is to happen it should be noted that this usually comes into play when we were not sure about the outcome of an event,  and the analysis of events governed by probability can be regarded as statistics.

P(yellow) =  1/3

= 0.33

0.33 * 100

= 33 percent

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a coach is hosting a cookout for their kick ball team. the coach wants to have two hot dogs for each guest, and 8 extra hot dogs in case some teammates bring friends. the coach writes an equation to determine how many hot dogs are needed for the cookout. which variable is independent?

Answers

The independent variable in this scenario is the number of guests that will be attending the cookout. The number of hot dogs needed is dependent on the number of guests, as the coach plans to provide two hot dogs for each guest and an additional 8 hot dogs for potential extra guests.


. In this situation, the coach needs to determine the number of hot dogs required for the cookout based on the number of guests. Let's represent the number of guests as "g" (independent variable) and the total number of hot dogs needed as "h" (dependent variable).

The coach wants 2 hot dogs for each guest and 8 extra hot dogs. So, the equation would be:

h = 2g + 8

In this equation, the independent variable is "g" (number of guests) because the total number of hot dogs needed (dependent variable "h") depends on how many guests are attending the cookout.

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