convert 0.25 to a fraction in its simplest form​

(a) The probability that a person drinks between 10 and 15 gallons of milk a year is 0.558

(b) The maximum gallons of milk a person can consume and still be in the bottom 10% of all milk drinkers is 8.3 gallons

(c) The probability that a person consumes less than 11 gallons is 0.12

(a) To find the probability that a person drinks between 10 and 15 gallons of milk a year, we need to calculate the area under the normal curve between the values of 10 and 15.

This probability turns out to be approximately 0.558.

(b) Using the standard normal distribution table, we can find the z-score that corresponds to the 10th percentile, which is approximately -1.28.

Substituting these values, we get x = 14 - 1.28 × 3.71, which is approximately 8.3 gallons.

(c) To find the probability that a person consumes less than 11 gallons of milk per year, we can use the normal cumulative distribution function with a mean of 14 and a standard deviation of 3.71. This probability turns out to be approximately 0.12.

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The net would be 51 feet long to stretch from one side of the court to the other.

Scale drawings are drawings that shows a diagram with another proportional dimensions

The scale ratio of the diagram is given as:

Scale = 1 inch = 12 feet

The length of the net is given as:

Length = 4.25 inches

So, the actual length of the net is:

\(Length=4.25*12\)

Evaluate the product

\(Length=51\)

Hence, the net would be 51 feet long, if stretched across the court

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x is shifted 5 units right

y is shifted one units up

The graph is attached

Answer:

g(x) is a translation of f(x) by 5 units right and 1 unit up.

Step-by-step explanation:

Translations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

Parent function:  

f(x) = x²

Translated 5 units right:

f(x - 5) = (x - 5)²

Then translated 1 unit up:  

f(x - 5) + 1 = (x - 5)² + 1

Therefore, g(x) is a translation of f(x) by 5 units right and 1 unit up.

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Answer:12

Step-by-step explanation:

Answer:

$5.67

Step-by-step explanation:

All you have to do is 17 divided by 3 to figure out how much it costs for one hour, that equals 5.666, but you have to round it to the nearest cent, which equals 5.67. ;)

The probability of drawing 2 successive red pens is \(\frac{1}{66}\)

Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.

Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.

Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of drawing a red pen on the first draw is 2/12 = 1/6. After the first red pen is drawn, there is 1 red pen left in the bag, so the probability of drawing another red pen is 1/11.

Therefore, the probability of drawing 2 successive red pens is 1/6 * 1/11 = 1/66.

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\(\huge\sf{Answer :- }\)

Exterior angle of the polygon = ( 360/ n )°

where,

➙ ( 360/ 20 )°

➥ 18°

Answer:

answer of this qn will 360÷20= 18degree

We need to find out the common multiples in the given number of years. So, 48 years will pass before the bird and the expedition have just arrived to the mountain at the same time.

It is given to us that -

Every 24 years, a bird flies to a mountain to sharpen its beak

Every 9 years, a bird watching expedition journeys to the mountain

If the bird and the expedition have just arrived to the mountain at the same time, we have to find out the number of years that will pass before this happens again.

From the given information, it is known to us that -

Bird watching expedition journeys occur every 9 years

and, bird flies to a mountain every 24 years

So, the number of years for both the events to happen again can be determined by finding the first multiple of 24 which is also a multiple of 9.

Now, 24 * 2 = 48. But 48 is not a multiple of 9.

Again, 24 * 3 = 72 which is also a multiple of 9.

Thus, we can conclude that in 72 years both the events of bird watching expedition journeys and bird flying to a mountain will occur again.

So, the number of years that will pass before these two events happen again is equal to 72 - 24 = 48 years.

Therefore, 48 years will pass before the bird and the expedition have just arrived to the mountain at the same time. We find out this by finding the common multiples in the given number of years.

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The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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Answer: \(y=\dfrac12 x\) .

Step-by-step explanation:

We know that \(a f (x)\)  compresses f(x) vertically such that

If we vertically compress the linear parent function, F(x) = x, by multiplying by \(\dfrac12\).

Then, the equation of the new function is \(y=\dfrac12 F(x)=\dfrac12 x\) .

i.e. \(y=\dfrac12 x\) .

Answer: Your answer would be 12 pencils and 9 pens

Step-by-step explanation:

have a nice day

The number of pencils that Anna sold, given the cost of each pen and pencil was 12 pencils.

P = number of pencils Anna sold,

N = number of pens Anna sold.

From the problem, we know that:

P + N = 21 (the total number of items sold is 21)

$1P + $2N = $30 (the total money made from selling the items is $30)

So therefore:

P = 21 - N

By substitution:

$1*(21 - N) + $2*N = $30

21 - N + 2N = 30

21 + N = 30

N = 30 - 21

N = 9

So, Anna sold 9 pens. Substituting N back into the first equation to find P:

P = 21 - N

P = 21 - 9

P = 12 pencils

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The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

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Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

Answer: 1. 12x+13

2. 13y−12

3. x=2

Step-by-step explanation:

The prediction thay the shopper can make about buying mystery bags in the future is A.There will be 4 more spy novels in 8 bags than in 6 bags.

Since the shopper bought 3 mystery bags and found that 6 books were spy novels, it means that there are 6/3 = 2 spy novels in each bag.

There, the prediction thay the shopper can make about buying mystery bags in the future is that there will be 4 more spy novels in 8 bags than in 6 bags.

This is because there's an extra 2 bags which will be equal to 4 spy novels

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The given statement "The fallacy of equivocation occurs whenever a word has one meaning in one premise and the same meaning in another premise or the conclusion." is false because it will lead to invalid conclusion.

The fallacy of equivocation occurs when a word or phrase is used in multiple senses within an argument, leading to a misunderstanding or invalid conclusion. This can happen when a word or phrase is used ambiguously, with different meanings in different contexts or definitions.

Equivocation can occur not only between different premises, but also within a single premise or conclusion. To avoid equivocation, it is important to clarify the intended meaning of terms and to ensure that they are used consistently throughout the argument.

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Answer:

2 \(\frac{67}{100}\)

Step-by-step explanation

The decimal 2.67 is:

2 ones and 67 hundredths.

Because of the hundredths, we know that the 67 will be 67/100. 2 is just 2. We cannot simplify this further. The answer is 2 67/100.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=19\\ V=4100 \end{cases}\implies 4100=\pi r^2(19)\implies \cfrac{4100}{19\pi }=r^2 \\\\\\ \sqrt{\cfrac{4100}{19\pi }}=r\implies 8.29\approx r\)

Using expression (L/3) / (36t) = L / (108t),  the fraction of the total singing time that all three are singing at the same time is L / (108t).

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. Expressions can be composed of one or more terms, which are separated by addition or subtraction symbols.

For example, the expression 2x + 3y - 5 represents a value that depends on the values of the variables x and y. The term 2x represents a quantity that is twice the value of x, the term 3y represents a quantity that is three times the value of y, and the term -5 represents a constant value of negative five.

Now,

Let's call the length of the song "L" and the time it takes to sing one line "t". Then, we know that:

Rachel starts singing at t = 0, and she sings for a total of 4L.

Jenny starts singing at t = t, and she sings for a total of 4L.

Angela starts singing at t = 2t, and she sings for a total of 4L.

Since each line of the song is the same length, we can divide the total singing time for each person into three equal parts, one for each line. So, each person sings for a total of 12t.

Now, let's think about when all three people are singing at the same time. This happens during the second line of the first repetition of the song. Rachel is singing the first line, Jenny is singing the second line, and Angela is starting to sing the third line. The total length of time that all three people are singing together is just the length of one line, which is L/3.

Since each person sings for a total of 12t, the total singing time for all three people is 36t. Therefore, the fraction of the total singing time that all three are singing at the same time is:

(L/3) / (36t) = L / (108t)

So, the fraction of the total singing time that all three are singing at the same time is L / (108t).

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a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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Answer:

Step-by-step explanation:

lim cot(x) as x ---> 0 from below x = -∝

lim cos (x) as x ---> 0 from above = ∝

The equation of the vectors are

35. y = (-1/2)x + 2

36. y = (1/2)x + 5/2

37. y = 2x + 3

38. y = (2/3)x - 52/3

Exercise 35:

P(2, 1)

v = i + 2j

To find the equation of the line passing through P and perpendicular to v, we need to determine the slope of the line. The slope of a line perpendicular to a vector is the negative reciprocal of the slope of the vector.

The vector v = i + 2j has a slope of 2/1 = 2. The negative reciprocal of 2 is -1/2. Therefore, the slope of the line perpendicular to v is -1/2.

Using the point-slope form of a line, we can write the equation of the line passing through P as follows:

y - y₁ = m(x - x₁)

Substituting the values of P(2, 1) and the slope (-1/2), we get:

y - 1 = (-1/2)(x - 2)

Simplifying the equation, we have:

y - 1 = (-1/2)x + 1

y = (-1/2)x + 2

Exercise 36:

P(-1, 2)

v = -2i - j

The slope of the vector v = -2/1 = -2. The negative reciprocal of -2 is 1/2.

Using the point-slope form, we can write the equation of the line passing through P(-1, 2) as:

y - 2 = (1/2)(x + 1)

Simplifying the equation, we have:

y - 2 = (1/2)x + 1/2

y = (1/2)x + 5/2

Exercise 37:

P(-2, -7)

v = -2i + j

The slope of the vector v = 1/(-2) = -1/2. The negative reciprocal of -1/2 is 2.

Using the point-slope form, the equation of the line passing through P(-2, -7) is:

y - (-7) = 2(x - (-2))

Simplifying the equation, we have:

y + 7 = 2(x + 2)

y = 2x + 3

Exercise 38:

P(11, 10)

v = 2i - 3j

The slope of the vector v = -3/2. The negative reciprocal of -3/2 is 2/3.

Using the point-slope form, the equation of the line passing through P(11, 10) is:

y - 10 = (2/3)(x - 11)

Simplifying the equation, we have:

y - 10 = (2/3)x - 22/3

y = (2/3)x - 52/3

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Complete Question:

In Exercises 35–38, find an equation for the line through P perpendicular to v. Then sketch the line. Include v in your sketch as a vector starting at the origin.

35. P(2, 1), v = i + 2j

36. P(-1, 2), v =-2i - j

37. P(-2, -7), v =-2i + j

38. P(11, 10), v = 2i - 3j.

Answer:

y=1/3x+6

Step-by-step explanation:

Answer:

y=1/3x+6

Step-by-step explanation:

Answer:

the answer is 71

Step-by-step explanation:

423/6

42÷6=7

42-42=0

6÷3=×

30÷6=5

70.5--> 71

Answer:

364

Step-by-step explanation:

If the number of research papers in Dr. Carey's area of expertise is increasing by 3% every year and 34,176 research papers were published this year, then approximately 35,168 research papers will be published two years from now.

To calculate the number of research papers that will be published two years from now, we need to apply the 3% annual increase for two consecutive years to the initial count of 34,176 papers.

First, we calculate the increase for the first year:

Increase = 34,176 * 3% = 34,176 * 0.03 = 1,025.28 (approximately)

Next, we add this increase to the initial count to get the count after one year:

Count after one year = 34,176 + 1,025.28 = 35,201.28 (approximately)

Now, we calculate the increase for the second year based on the count after one year:

Increase = 35,201.28 * 3% = 35,201.28 * 0.03 = 1,056.04 (approximately)

Finally, we add this increase to the count after one year to get the count after two years:

Count after two years = 35,201.28 + 1,056.04 = 36,257.32 (approximately)

Therefore, approximately 36,257 research papers will be published two years from now.

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Answer:

x = 2

Step-by-step explanation:

-4x + 136 + 52 = 180             {supplementary  angles}

        -4x + 188 = 180

Subtract 188 from both sides

                -4x = 180 - 188

                -4x = -8

Divide both sides by (-4)

          x = -8/-4

x = 2

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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a) It is unlikely that either of these measurements could have been made with either of the calipers. b) Volume is 57.457 \(cm^3\) c) Density is 0.731 g/\(cm^3\) d) The percent error is 2.24%.

a. Calipers typically have a measuring range and precision that may not be suitable for measuring such small variations in dimensions. The given uncertainties for each dimension (0.1 cm, 0.05 cm, and 0.01 cm) are relatively small, which suggests that more precise measuring instruments would be required to obtain such precise measurements.

b. To calculate the volume of the block, we multiply the dimensions together:

Volume = Length * Width * Height

Volume = (3.8 cm) * (2.15 cm) * (7.31 cm)

Volume ≈ 57.457 \(cm^3\)

c. To calculate the density of the block, we divide the mass by the volume:

Density = Mass / Volume

Density = (42.0 g) / (57.457 \(cm^3\))

Density ≈ 0.731 g/\(cm^3\)

d. To calculate the percent error, we compare the calculated density to the accepted density and express the difference as a percentage:

Percent Error = |(Calculated Density - Accepted Density) / Accepted Density| * 100

Percent Error = |(0.731 g/\(cm^3\) - 0.715 g/\(cm^3\)) / 0.715 g/\(cm^3\)| * 100

Percent Error ≈ 2.24%

Therefore, the percent error is approximately 2.24% if the block is made of spruce wood with an accepted density of 0.715 g/\(cm^3\).

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