Least common denominator of 9/8 and 7/12

The t-percentile defines the boundaries of the confidence interval and is equal to the critical value of t with a positive or negative sign, depending on whether the confidence interval is one-sided or two-sided.

A t-distribution table determines the t-percentile required to construct two-sided confidence intervals. The first step in determining the t-percentile is to know the degrees of freedom and confidence level. The next step is to find the critical value of t from a t-distribution table. The t-distribution table lists values for the probability density function, cumulative distribution function, and percentile points of the t-distribution.

The table is arranged in rows and columns, with the rows corresponding to the degrees of freedom and the columns corresponding to the significance level. The critical value of t is the value that separates the central area of the t-distribution from the tails of the distribution. It is used to define the boundaries of the confidence interval. The t-value is the same as the critical value of t, but it has a positive or negative sign depending on whether the confidence interval is one-sided or two-sided. The t-percentile that is required to construct two-sided confidence intervals is given by the following steps:

Step 1: To determine the t-percentile, the degrees of freedom and confidence level are needed.

Step 2: Find the critical value of t from a t-distribution table.

(a) 95% confidence level, 15 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 15, a 95% confidence level, the value of t is found to be 2.1318. Therefore, to construct the confidence interval, the t-value is ± 2.1318.

(b) 95% confidence level, 24 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 24, a 95% confidence level, the value of t is 2.064. Therefore, to construct the confidence interval, the t-value is ± 2.064.

(c) 99% confidence level, 13 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 13, a 99% confidence level, the value of t is 3.012. Therefore, to construct the confidence interval, the t-value is ± 3.012.

(d) 99.9% confidence level, 15 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 15, a 99.9% confidence level, the value of t is found to be 3.579. Therefore, to construct the confidence interval, the t-value is ± 3.579.

The t-percentile can be found using a t-distribution table, which lists the critical value of t for different degrees of freedom and significance levels. The t-percentile defines the boundaries of the confidence interval and is equal to the critical value of t with a positive or negative sign, depending on whether the confidence interval is one-sided or two-sided.

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Answer:

Yes, that is enough statistical evidence to suggest to conclude that residents of Legacy Ranch use less water on average

Step-by-step explanation:

The data given by the American Water Works Association are;

The per capita water use in a single-family home, μ = 76 gallons per day

The number of responders in the sample, n = 27

The sample mean water used by the sample, \(\overline x\) = 71 gallons

The standard deviation, s = 9.5 gallons per day

The level of significance, α = 0.01

The test statistics is given as follows;

The null hypothesis, H₀; μ ≥ 76 gallons

The alternative hypothesis, Hₐ; μ < 76 gallons

\(t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}\)

Therefore, we have;

\(t=\dfrac{71-76 }{\dfrac{9.5}{\sqrt{27}}} \approx -2.734817\)

At n - 1 = 27 - 1 = 26 degrees of freedom, the critical-t = 2.5

From the test statistic, of t ≈ -2.734817, the p-value < 0.01, and from a graphing calculator, the p-value is given as Prob = 0.005544418

Therefore, given that the p-value is less the significant level, and less than 0.01, is therefore statistically significant, and therefore, there is sufficient statistical evidence against the null hypothesis, therefore we reject the null hypothesis, and there is enough statistical evidence to suggest to conclude that residents of Legacy Ranch use less water on average.

This is the answer through graphs.

a) Median will be an appropriate measure for the distribution. b) Mean will be an approprate measure for the distribution.

Here we already have the data available to us. From the data, we can clearly see that

Mode < Mean < Median

Hence this is a negatively skewed distribution.

Therefore the appropriate measure of central tendency for this distribution will be the median. The median will tell us the point at which the frequency is divided by 50%.

Hence we can say that the median will a more appropriate measure.

Now if the data has another aspect of sex included, then the frequency column would be divided into separate columns with each gender identity taking up its own column.

Since now this will become multivariate data, the best measure of central tendency will be Mean.

The difference in the measure of central tendency will depend upon how skewed the data for every sex will be. For example, if in a country, men preferred to be educated over women, then the mean for men will be a lot higher than that of women. On the other hand, the EDUC for women will be a lot lower.

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Answer:

30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,8,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100

Step-by-step explanation:

100!

1. To estimate the probability of catching a bass in a lake using a special type of bait, the forest ranger could employ the following process:  Random Sampling, Bait Experiment, Data Collection,  Probability Calculation.

2. a.  the probability of selecting 'S' at random is P(S) = 2/12 = 1/6.

b. The probability of selecting a vowel at random is P(vowel) = 4/12 = 1/3.

1. To estimate the probability of catching a bass in a lake using a special type of bait, the forest ranger could employ the following process:

a. Random Sampling: The ranger could randomly select a sample of fishermen or anglers who frequently fish in the lake. This would ensure a representative sample of individuals who are likely to have experience with different fishing techniques and bait preferences.

b. Bait Experiment: The ranger could provide each participant in the sample with the special bait and observe the outcomes of their fishing attempts. It would be important to control for other variables such as fishing location, time of day, and weather conditions to isolate the impact of the bait.

c. Data Collection: The ranger would record the number of successful bass catches and the total number of fishing attempts for each participant. This data would be used to calculate the observed probability of catching a bass with the special bait.

d. Probability Calculation: The ranger could calculate the proportion of successful bass catches out of the total fishing attempts for the sample. This proportion would serve as an estimate of the probability of catching a bass in the lake using the special bait.

2. a. P(S): The letter 'S' appears twice in the word "RECKLESSNESS." The probability of selecting 'S' at random is determined by the ratio of the number of occurrences of 'S' to the total number of letters in the word. Since there are two 'S's in the word and a total of 12 letters, the probability of selecting 'S' at random is P(S) = 2/12 = 1/6.

b. P(vowel): To determine the probability of selecting a vowel at random from the word "RECKLESSNESS," we need to identify the vowels in the word. The vowels in the word are E, E, E, and the letter O. Therefore, there are four vowels out of a total of 12 letters. The probability of selecting a vowel at random is P(vowel) = 4/12 = 1/3.

In both cases, the probabilities are calculated by dividing the number of favorable outcomes (occurrences of 'S' or vowels) by the total number of possible outcomes (total letters in the word).

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The objective of a hypothesis test is to "Reject the null hypothesis when it is false and not reject the null hypothesis when it is true."

In hypothesis testing, we start with a null hypothesis (H0) that represents a statement of no effect or no difference.

The alternative hypothesis (Ha) represents the opposite, suggesting there is an effect or difference.

The objective is to gather evidence from the data to make a decision about the null hypothesis.

If the evidence strongly suggests that the null hypothesis is false (i.e., there is evidence of an effect or difference), we reject the null hypothesis.

On the other hand, if the evidence does not provide sufficient support to reject the null hypothesis, we fail to reject the null hypothesis.

The objective is not to reject the null hypothesis when it is true, as that would be a Type I error (false positive).

It is also not to decrease the probability of committing a Type I error and increase the probability of committing a Type II error.

The aim is to make an informed decision based on the evidence and the pre-specified significance level, which leads to either rejecting or failing to reject the null hypothesis based on the observed data.

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In(x) - In(x - 4) = 0

From the step-by-step explanation, the equation has zero solution.

The z-scores for the different values of random variable x;

(a) Z = 2.25

(b) Z = 1.50

(c) Z = -1.75

(d) Z = 3.25

(e) Z = -2.25

(f) Z = 3.50

We are given different values of x which is a random variable along with the values of the mean and the standard deviation. We have to calculate the z-score for the given values of x. We will use the following formula to calculate the z-score.

z = (x - μ)/σ

In all the parts we have;

μ = 23

σ = 4

(a)x = 32

z = (x - μ)/σ

z = (32 - 23)/4

z = 9/4 = 2.25

(b) x = 29

z = (x - μ)/σ

z = (29 - 23)/4

z = 6/4 = 1.50

(c) x = 16

z = (x - μ)/σ

z = (16 - 23)/4

z = 7/4 = -1.75

(d) x = 36

z = (x - μ)/σ

z = (36 - 23)/4

z = 13/4 = 3.25

(e)  x = 14

z = (x - μ)/σ

z = (14 - 23)/4

z = -9/4 = -2.25

(f)  x = 37

z = (x - μ)/σ

z = (37 - 23)/4

z = 14/4 = 3.50

Therefore, the z-scores will be;

(a) Z = 2.25

(b) Z = 1.50

(c) Z = -1.75

(d) Z = 3.25

(e) Z = -2.25

(f) Z = 3.50

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The complete question is "Suppose the random variable x is best described by a normal distribution with μ=23 and σ=4. Find the z-score that corresponds to each of the following x-values.

(a) x=32

z=

(b) x=29

z=

(c) x=16

z=

(d) x=36

z=

(e) x=14

z=

(f) x=37

z=                    "

When ax = b has infinitely many solutions, it means that there is no single value of x that will make the equation true.

This is because the equation is true for any value of x, so it is impossible for ax = b (new right-hand side) to have only one solution. It is also possible for ax = b to have no solution, which would occur if the right-hand side of the equation is not equal to any value of the left-hand side.

For example, if ax = 5 and b = 6, then there is no value of x that will make the equation true. Therefore, when ax = b has infinitely many solutions, it means that there is no single value of x that will make the equation true.

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Answer:

40

Step-by-step explanation:

you first said 10 times the difference of 8-4 which 8-4=4×10=40

Hey there!

Guide:

Sum means add/addition

Difference means subtract/subtraction

Product means multiply/multiplication

Quotient means divide/division

ANSWERING the QUESTION

10 * 8 - 4

= 80 - 4

= 76

Therefore, your answer is: 76

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

To find the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7, let's analyze the given information.

The sum of the second term (s2), fifth term (s5), and seventh term (s7) themselves form an arithmetic sequence.

Let's denote the second term as a + 2d, the fifth term as a + 5d, and the seventh term as a + 7d, where 'a' is the first term and 'd' is the common difference.

Using the arithmetic sequence formula for the sum of terms, we have:

s2 = (2/2) * (2a + (2-1)d) = 2a + d

s5 = (5/2) * (2a + (5-1)d) = 5a + 6d

s7 = (7/2) * (2a + (7-1)d) = 7a + 12d

Since the sums s2, s5, and s7 themselves form an arithmetic sequence, we can express their differences:

s5 - s2 = (5a + 6d) - (2a + d) = 3a + 5d

s7 - s5 = (7a + 12d) - (5a + 6d) = 2a + 6d

Now, equating the differences, we have:

3a + 5d = 2a + 6d

Simplifying the equation, we find:

a = d

Therefore, the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7 is 'd'.

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Answer:

±1/4, ±5/4 (If you could mark as brainliest that would be great!)

Step-by-step explanation:

The possible rational roots of H(x) can be found using the Rational Root Theorem, which states that any rational root of a polynomial must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is 5 and the leading coefficient is 4, so the possible rational roots are:

±1/4, ±5/4

These are the factors of 5 divided by the factors of 4. However, it's important to note that not all of these possible roots will necessarily be actual roots of the polynomial.

We can find the customer who can get popcorn and drink for free by using the concept of Least common Multiple.

The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.

The popcorn is given free to every 20th customer.

The drink is given free to every 30th customer.

The multiples of 20 are 20,40,60,80,100,120.....

The multiples of 30 are 30,60,90,120,150......

The number 60 appears as multiple of 20 as well as 30.

So, this implies every 60th customer will receive a free drink and popcorn.

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Using the slope concept, supposing the horizontal distance is of 1500 feet, the angle of depression will be of 37º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we suppose an horizontal distance of 1500 feet, with a vertical distance of 2000 feet, hence:

\(\tan{\alpha} = \frac{1500}{2000}\)

\(\alpha = \tan^{-1}{\left(\frac{1500}{2000}\right)}\)

\(\alpha = 37^\circ\)

The angle of depression will be of 37º.

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The value of x = 16, y = 172 and z = 2.

x - 4z = 12x - y - 6z = 42x + 3y - 2z = 8

let x - 4z = 8 be equation (1), 12x - y - 6z = 8 be equation (2) and 42x + 3y - 2z = 8 be equation (3)

x - 4z = 8

x = 8 + 4z

12x - y - 6z = 8

12(8 + 4z) -y - 6z =8

96 + 48z - y - 6z = 8

42z - y = -88

y = 42z + 88

42x + 3y - 2z = 8

42(8+4z) + 3(42z + 88) - 2z = 8

336 + 168z + 126z + 264 - 2z = 8

168z + 126z + 2z = 336+264 - 8

296z= 592

z = 2

substituting the value of z

x = 8 + 4z

= 8 + 4(2)

8+8 = 16

y = 42z + 88

42(2) + 88

84 + 88= 172

The value of x = 16, y = 172 and z = 2.

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Answer:

2.3333333333333333333333333333333 sec

The remaining root of f(x) will be 3 - \(\sqrt{11}\)

To answer this question we have to find the conjugate of 3+\(\sqrt{11}\),

For example, the conjugate of p+q will be p-q or vice versa.

Let us consider x= 2+\(\sqrt{11}\)

To simplify the equation let us subtract 3 on both sides of the equation

x - 3 = 3+\(\sqrt{11}\) - 3

x - 3 = \(\sqrt{11}\)

Square both,

\((x - 3)^{2}\) = 11

\((x - 3)^{2}\) - 11 =0

Now we will use the principle of Square difference to factorize both sides-

\((d^{2} - e^{2}) = (d - e)(d + e)\)

(x - 3) - 11 × (x - 3) + 11 = 0

on solving the equation we get,

(x - 3) - 1 = 0  let us consider this first equation

or (x - 3) + 11 = 0 let us consider this second equation

Add \(\sqrt{11}\) on both sides of the first equation,

\(x - 3 = \sqrt{11}\)

Subtract \(\sqrt{11}\) on both sides of the second equation,

\(x - 3 = -\sqrt{11}\)

Now by adding 3 on both sides of the first and second equation,

\(x = 3 + \sqrt{11}\) or \(x = 3 - \sqrt{11}\)

Therefore, the remaining root of f(x) will be = \(3 - \sqrt{11}\)

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Complete Question - If a polynomial function f(x), with rational coefficients, has roots 0, 4, and 3 + \(\sqrt{11}\), what must also be a root of f(x)?.

Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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Answer:

|-3.9-(-15.1)|=11.2

Step-by-step explanation:

the last one is the answer

Lets check one by one

#1

Wrong

#2

Wrong

#3

Still wrong

#4

Distance must be positive so it's correct

The zeros of the function f(x) are x = 0, x = 2/5, x = i, and x = -i.

A unique kind οf relation called a function is οne in which each input has precisely οne οutput. Inοther words, the function produces exactlyοne value for each input value. The graphic above shows a relation rather than a function becauseοne is mapped to two different values. The relation above would turn into a function, though, ifοne were instead mapped to a single value. Additionally,οutput values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its οperations andοutputs the y-values. The function within can be any function.

To find the zeros οf the function f(x) = x(5x-2)(x² +1), we need to find the valuesοf x that make f(x) equal to zero.

We can do this by setting each factor equal to zero and solving for x:

x = 0 or 5x-2 = 0 or x² +1 = 0

Solving for x in the second equation, we get:

5x - 2 = 0

5x = 2

x = 2/5

Solving for x in the third equation, we get:

x² + 1 = 0

x² = -1

x = ±√(-1)

x = ±i

So the zeros of the function f(x) are x = 0, x = 2/5, x = i, and x = -i.

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Answer:

7/40

17/1000

9/3125

3/200

Step-by-step explanation:

Brainliest pls tried hard

The total pieces at the fruit stand is 60.

Let the number of apples, bananas and oranges sold be 3x, 2x and 1x. We have actual number of bananas. So equating them to find the value of x.

2x = 20

x = 20/2

Performing division

x = 10

So, number of apples = 3x

Number of apples = 3×10

Number of apples = 30

Similarly, number of oranges = 10

Total number of fruits = sum of the number of apples, bananas and oranges

Total number of fruits = 30 + 20 + 10

Total number of fruits = 60

Thus, there are 60 fruits to sell.

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Answer:

The answer is 20

Step-by-step explanation:

6/8 = 15/y

(6) × y = (8) × (15)

6y = 120

6y/6 = 120/6

y = 20

Thus, The value of y is 20

Answer:

\( \sf \: y = 20\)

Step-by-step explanation:

Given equation,

\( \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} \)

Now the value of y will be,

\( \sf \rightarrow \: \frac{6}{8} = \frac{15}{y} \)

\( \sf \rightarrow \: 6y = 15 \times 8\)

\( \sf \rightarrow \: 6y = 120\)

\( \sf \rightarrow \: y = \frac{120}{6} \)

\( \sf \rightarrow \boxed{ \sf y = 20}\)

Hence, the value of y is 20.

6 kilogram of fertilizer were used by a gardener over the course of 8 weeks. They use 0.75 kilogram per week.

Given that,

6 kilogram of fertilizer were used by a gardener over the course of 8 weeks.

We have to find how much did they use each week.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

In the apparent reasons, you would need to place four donuts in each group in order to divide 12 donuts into three similar groups. Thus, 12 divided by 3 will result in the number 4.

Divide the weight by time

That is

6kg/8week

3kg/4week

0.75 kilogram per week

Therefore, they use 0.75 kilogram per week.

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Answer:

2.05m

Step-by-step explanation:

Answer:

the answer is O 2 in.

Step-by-step explanation: