What is 14 2/7 as a fraction?

Answer:

4.5

Step-by-step explanation:

You calculate it. look 1 yard is 36 inches. so 1/8 of a yard is 36 divided by 8. 4.5!

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]f(x)= 2x^2 + 12x +16 \qquad \begin{cases} x_1=-3\\ x_2=-2 \end{cases}\implies \cfrac{f(-2)-f(-3)}{-2 -( -3)} \\\\\\ \cfrac{[2(-2)^2 + 12(-2) + 16]~~ - ~~[2(-3)^2 + 12(-3) + 16]}{-2+3} \\\\\\ \cfrac{[8-24+16]~~ - ~~[18-36+16]}{1}\implies 0-(-2)\implies \text{\LARGE 2}[/tex]

To multiply the division expression 3/4 ÷ 1/3 is 9/4. Division expressions are mathematical expressions using division

  3/4 : 1/3

= 3/4 · 3/1

= 3·3/4.1

= 9/4

Hence this proved.

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The two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking are; (0, 320) and (4, 0)

From the table in the attached file, we see that;

Justine started when Michael was 320 yards from the top.

This coordinate is expressed as (0,320)

where;

0 represents the time Justine started

320 represents the number of yards left.

Now, it is clear that every minute, Justine covers 80 yards.

Thus;

After 1 minute, Justine will have:

(320 - 80) yards left

After 2 minutes, Justine will have:

(320 - 80 - 80) yards left

After 3 minutes, Justine will have:

(320 - 80 - 80 - 80) yards left

After n minutes, Justine will have;

(320 - 80n) yards left

Thus, the possible coordinates are:

(0, 320), (1, 240), (2, 160), (3, 80), (4, 0)

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Answer:

Question 1: Calculate the coordinates of 2 points. You know that the value of the Y coordinate in a point is 4 times the value of the x in the same point. Once you figure out the points, put them on the graph and draw a straight line through them with a ruler.

Question 2: What number do you multiply 5 by to get 12? You multiply that same number by the 375 to get the value in the corresponding row. That's called proportion.

Question 3: You can find the proportion between the two values (distance and energy). Its how many times bigger (or smaller) the values are in relation to each other. You can use this proportion for the scale of the graph so that the location of points are easier understood in relation to each other and discernable all by your eye.

The average cost function is C(x) = 5000x + 20,000/x, where x is the number of machines used in the production. The critical value is C(x) = 20,000 and it happens when x = 2.

If we have a function f(x), the critical point happens when its first derivative is equal to zero.

             f '(x) = 0

In the given problem, the function is:

C(x) = 5000x + 20,000/x

Take the derivative:

C '(x) = 5000 - 20,000/x² = 0

5000 x² = 20,000

x² = 4

x = ±2

Since x is within the interval: 0<x<∞, the solution is x = 2

Substitute x = 2 into the function:

C(2) = 5000 (2) + 20000/2

C(2) = 10000 + 10000 = 20,000

Hence, the critical value is C(x) = 20,000 and it happens when x = 2.

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Answer:

Step-by-step explanation:300 mStep-by-step explanation:20 meters per minute. 15 minutes it dives. 20x15 is 300

Yes, g(x) is a 3 unit translation down after a reflection of f(x) over the x-axis.

The set of ordered pairs with the f(x) = y is the graph of a function f in mathematics. These pairs, which are Cartesian coordinates of points in two-dimensional space and thus constitute a subset of this plane in the typical case where x and f(x) are real numbers, are examples of real numbers.

Pie charts, line graphs, bar graphs and histograms, and Cartesian graphs are likely the four most popular types. They are typically utilized for, and are most effective for, very different purposes. You'd employ: Bar graphs are used to display numbers that are unrelated to one another.

Use line/area charts if your data is continuous, or bar charts or histograms if your data is nominal. Use a scatter plot, bubble chart, or line chart to illustrate how the values in your dataset relate to one another.

y = −f(x) Reflects it about x-axis

y = f(x) + C   C < 0 moves it down

The complete question is:

Consider the function f(x) = x3 + 0.5x – 1. Marjan needs to graph f(x) and g(x) = –f(x) – 3. His graphs are shown below. Which statement describes whether Marjan’s graphs are correct? No, the reflection should be over the x-axis, not the y-axis. No, the reflection should be over the y-axis, not the x-axis. Yes, g(x) is a reflection of f(x) over the y-axis followed by a translation of 3 units down. Yes, g(x) is a reflection of f(x) over the x-axis followed by a translation of 3 units down.

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The linear function is f(x) and the exponential function is g(x).

The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.

In this case, the function for g(x) is 2^x.

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The classification model is used to define the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Percentage:

In math,  number or ratio that can be expressed as a fraction of 100 refers the percentage.

Given,

Here we have a dollar general sends out a $5 off coupon to its email subscribers.

And we need to find the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Then the model used to define the this type of situation is refers as the classification model, because in this model, we have classify the given group of people based on the constraint.

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Answer:

d = 9.43398113206

Step-by-step explanation:

d=√((x2 – x1)² + (y2 – y1)²)

d = √((-4-1)² + (5+3)²)

d = √((-5)² + (8)²)

d = √(25 + 64)

d = √89

d = 9.43398113206

The standard median value of the data set is -0.25.

The standard value of any data is the converted value of the variable, such that the mean of the data set is 0 and the standard deviation is 1.

To convert any data set to its standard form we use the equation

(X - μ)/σ

where,

μ = mean

σ = standard deviation

here,

μ = 6

σ = √64 = 8

Now median is that value which gives the midpoint of the frequencies.

Hence the standard median should be the standard value of the median obtained from the data set which is 4

Hence standard median

= (4 - 6)/8

= -2/8

= -0.25

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Answer:

C,D

Step-by-step explanation:

C and D  are multiplying 250 by  a number greater than one so the result will be greater than 250

 The first two are multiplying 250 by a frction less than one....the result will be less than 250

Answer:

x = - 4

Step-by-step explanation:

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 4, 2 ) with x- coordinate - 4 , then

x = - 4 ← equation of line

The decimal number 24.7 represents the average mileage of the vehicle.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

A famous magazine tests vehicles and trucks for mileage out and about and around the city. the magazine reports that half of the vehicles tried had mileages beneath 24.7 mpg out and about, and the other half of the vehicles tried had mileages above 24.7 mpg.

The decimal number 24.7 means the vehicle can cover 24.7 miles with each gallon of gas.

The decimal number 24.7 represents the average mileage of the vehicle.

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Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer:

(3/4)a + 1/3

Step-by-step explanation:

3/4a + 2/3 - 1/2a - 1/3 + 1/2a

(3/4)a + (2/3) - (1/2)a - (1/3) + (1/2)a   [added () to clarify.  Is "3/4a" (3/4)a or 3/(4a)?

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

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

(3/4)a  - (1/2)a + (1/2)a - (1/3)  + (2/3)  [Rearrange:  like terms together]

a[(3/4)  - (1/2) + (1/2)] - (1/3)  + (2/3)    [bring out the "a"]

a[(3/4)] + (1/3)                                         [simplify]

(3/4)a + 1/3

An approximate 95% confidence interval for the difference in the mean tooth damage is  (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

For sweetened samples

The value of n = 10

The mean of the samples = 6.14

The standard deviation of the sample = 5.0

For unsweetened samples

The value of n = 15

The mean of  the sample = 5.20

The standard deviation of the sample = 15.0

We have to assume that necessary conditions for inference are met

The confidence interval = 95%

The equation will be

(6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

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Following the Sampling Theorem of statistics, the answer is True.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

Each member of the group or community has an equal chance of being chosen when using probability sampling. According to probability-based statistical theory, this indicates that the sample is more likely to match the larger population, allowing for the drawing of more precise conclusions about the latter.

Yes, the quota sampling process occurs when the available or accessible people or material are selected. Due to large population size, Sampling process is preferred.

Since, Statistics convey characteristics of data to us. So yes, The sample is weighted so that predetermined characteristics are represented.

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The probability that the entire batch will be accepted.

What is Acceptance Sampling?

Acceptance sampling is a statistical measure used in quality control. It allows a company to determine the quality of a batch of products by selecting a specified number for testing.

abc Electronics Company manufactured 1200 write-rewrite cds, and 150 are defective. Since 150 are defective, the number of write-rewrite cds that would be accepted is (1200 - 150 = 1050).

Since the items at selected without replacement, the number of write-rewrite cds will continue to decrease anytime a write-rewrite cds is taken out. For example if they are 1050 accepted write-rewrite cds if one is taken out they would then be 1049 accepted write-rewrite cds, and if another one is taken out they would be 1049 accepted write-rewrite cds and so on.

If 3 of these cds are randomly selected for testing without replacement,

The probability that the entire batch will be accepted

= (1050/1200) × (1049/1200) × (1048/1200) × (1047/1200)

= 0.8750 × 0.8742 × 0.8733 × 0.8725

=0.5828

The probability that the entire batch will be accepted is 0.5828 .

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As the tree grows 1& 3/4 feet per year, it will take 9 years to reach a height of 37 feet.

Division is a basic procedure in which an integer is divided. It's best to imagine of it as a number of things being distributed among a particular number of persons, such as in the previous example. In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 implies dividing 15 into three equal groups of five. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number, which divides the number (dividend) into equal parts.

Here,

37 - 21 and 1/4 = 36 and 4/4 - 21 and 1/4 = 15 and 3/4 = 63/4

63/4 divided by 1 and 3/4 = 63/4  divided by 7/4 = 63/4 * 4/7 = 9 years

It will take 9 years to reach at the height of 37 feet as the tree grow 1& 3/4 feet per year.

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Complete question:

A tree grow 1& 3/4 feet per year. How long will it take the tree to grow from a height of 21 & 1/4 feet to a height of 37 feet?

The equation x² + y² = 49 can be written in standard form as (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.

The equation for a circle is (x-h)² + (y-k)² = r², where (h, k) represents the center of the circle and r represents the radius.

In order to find the center (h, k) and radius (r) of the circle, we need to rearrange the equation to put it in the standard form. To do this, we subtract 49 from each side of the equation, which will give us x² + y² - 49 = 0. Then, we can factor the equation to get (x² + y²) - 7(7) = 0. This can be further simplified to (x + 7)(x - 7) + (y + 7)(y - 7) = 0.

Since there are no solutions for (x + 7) or (x - 7) when set equal to 0, we can conclude that the equation for the circle is (x-0)² + (y-0)² = 49, which is the equation for a circle with a center at (0, 0) and a radius of 7.

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The graph of the function square root of the square root of x + 2 in the given domain is given by the image shown at the end of the answer.

The function for this problem is defined as follows:

f(x) = √√x+2

The double square root means that in reality, we have the fourth root of the function, hence the function is then defined as follows:

f(x) = fourth root(x + 2).

The fourth root function is defined for values of x for which the inner term is zero and greater, hence:

x + 2 >= 0

x >= -2.

Then the graph is made over a domain that goes until x = 7, and is given by the image presented at the end of the answer.

(the domain is chosen because it is the domain given by the problem).

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Answer: 8

Step-by-step explanation:

=(1) ^3×(2) ^3

=1×1×1×2×2×2

=1×8

=8

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The percentage of total hours was spent skiing is 10%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, total number of hours =5+20+10+5+10 =50

Number of spent on skiing is 5

Now, percentage is 5/50 ×100

=10%

Therefore, percentage of hours spent on skiing is 10%

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"Your question is incomplete, probably the complete question/missing part is:"

What percentage of total hours were spent skiing?

Soccer 5

Jogging 20

walking 10

skiing 5

football 10

The probability that the battery lasts between 12,000 and 14,000 miles is approximately 0.084.

The number of miles that a car can run before its battery wears out follows an exponential distribution with an average value of 11,000 miles. The probability that the battery lasts between 12,000 and 14,000 miles can be calculated as follows:

P(12,000 < x < 14,000) = P(x < 14,000) - P(x < 12,000)

To calculate the probabilities on the right-hand side of the equation, we can use the formula for the cumulative distribution function (CDF) of an exponential distribution:

F(x) = 1 - e^(-x/λ)

where λ is the mean value of the distribution. In this case, λ = 11,000 miles.

Plugging in the values and solving, we get:

P(12,000 < x < 14,000) = F(14,000) - F(12,000)

= (1 - e^(-14,000/11,000)) - (1 - e^(-12,000/11,000))

= e^(-12,000/11,000) - e^(-14,000/11,000)

≈ 0.242 - 0.158

≈ 0.084

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By simplifying the above equation i.e 27^(3/4) we get, 9 x (3)^(1/4).

Simplification is the process of substituting a mathematical expression with a simpler (typically shorter) counterpart. A fraction is simplified to an irreducible fraction. In computer algebra, expressions are simplified.

In order to simplify the given equation we need to factorize the bases. You can see that in the following steps :

(a^b)^c=a^(bc)

a^(b+c)=a^b x a^c

By using this above equation, we can factorize the bases.

So, factorization would be equal to :

27 ^(3/4) = ((3^3) )^ (3/4)

       = 3^(9/4)

      = 3^ (2+1/4)

       = 3^2 x 3^(1/4)

      = 9 x 3^(1/4)

That’s how we simplified the given equation.

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The value of x is 23.22°. By using the Cosine rule

The Cosine Rule of trigonometry states that the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle included between them. The Law of cosines and Cosine Formula are other names for the cosine rule.

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given,

a = 26

b = 50

c = 29

Substituting the value to the equation:

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C

cos C = [tex]\frac{2335}{2660}[/tex]

C = 23.22°

The value of x is 23.22°

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Answer: 23.2 rounded to nearest tenth

Step-by-step explanation: