For revision purpose
In 350 words or less, answer the following: ..
Mathematics is described as a Science and not an Art. Do you
agree? Justify your answer.
Describe two different examples of Mathemat

The Answer is A. 6.67 in

Step-by-step explanation:

Given : The aspect ratio of a rectangular shape is its length divided by its width (L/W).

Let's Make  'L'  to be the length of the rectangular shaped chalkboard.

If  the aspect ratio of a chalkboard is 4:3 and the width is 5 in then we have To Multiply 5 on each side , we get the length of the chalkboard = 6.67 in.

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Bacon Hair

The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Population: The containers of blueberries that are being sent to Stop and Shop.

Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.

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Answer:

10a + 7b + 4

Step-by-step explanation:

3a + 7b + 4 +7a

3a + 7a = 10a

10a + 7b + 4

Answer:

x=334

Step-by-step explanation:

log(3x-2)=3

log(3x-2)=3

3x-2=10^3

3x-2=1000

3x=1000+2

3x=1002

x=1002/3

x=334

Answer:

-3/4

Step-by-step explanation:

rise/run

^^^you go up 3 and move left 4

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

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Answer:

equilateral and acute

Step-by-step explanation:

Answer:

4'5

Step-by-step explanation:

The expression √75x³y in radical form is 5x√(3xy).

The given expression is √75x³y

Square root of seventy five times of x cube times of y

We have to write in radical form

We can simplify √75x³y as follows:

√75x³y

= √(25×3×x²×x×y)

= 5x√(3xy)

Therefore, the expression √75x³y in radical form is 5x√(3xy).

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The equation of the line passing through the point (2,6)  and perpendicular to the given line is y = 6.

Given data;

The line is horizontal, and the slope of the line is infinity.

The slope of the line perpendicular will be expressed as \(\frac{-1}{∞}\) = 0

To get the equation of the line and passes through the point (2,6),

A line's equation in point-slope form is written as;

\(m = \frac{y-yo}{x-xo}\)

As m is the slope of the line then,

The required equation will be:

y - 6 = 0*(x-2)

y - 6 = 0

y = 6

Hence, the equation of the line that is perpendicular to the given line and passes through the point (2,6) is y = 6.

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the 90% confidence interval for the population mean is approximately (111.95, 133.05).

To construct confidence intervals for the population mean, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)

a) 95% Confidence Interval:

For a 95% confidence level, the critical value can be found using the t-distribution with (n-1) degrees of freedom, where n is the sample size. Since the sample size is 18, the degrees of freedom is 18 - 1 = 17.

Using a t-table or calculator, the critical value for a 95% confidence level and 17 degrees of freedom is approximately 2.110.

The standard error can be calculated using the formula:

Standard Error = Sample Standard Deviation / √(Sample Size)

In this case, the sample mean is 122.5, and the sample standard deviation is 33.20.

Standard Error = 33.20 / √18 ≈ 7.81

Now we can construct the 95% confidence interval:

95% Confidence Interval = 122.5 ± (2.110 * 7.81)

Lower Bound = 122.5 - (2.110 * 7.81)

Upper Bound = 122.5 + (2.110 * 7.81)

Lower Bound ≈ 105.63

Upper Bound ≈ 139.37

Therefore, the 95% confidence interval for the population mean is approximately (105.63, 139.37).

b) 90% Confidence Interval:

For a 90% confidence level, the critical value can be found using the t-distribution with (n-1) degrees of freedom. Again, with a sample size of 18, the degrees of freedom is 17.

Using a t-table or calculator, the critical value for a 90% confidence level and 17 degrees of freedom is approximately 1.740.

Now we can construct the 90% confidence interval:

90% Confidence Interval = 122.5 ± (1.740 * 7.81)

Lower Bound = 122.5 - (1.740 * 7.81)

Upper Bound = 122.5 + (1.740 * 7.81)

Lower Bound ≈ 111.95

Upper Bound ≈ 133.05

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The proportion of people who spend at least 5.25 hours per day on their computers is approximately 6.68%.

The question is asking for the proportion of people who spend at least 5.25 hours per day on their computers, given that the average time spent is 4 hours per day with a standard deviation of 0.75 hour.

We can use the normal distribution to find the proportion of people who spend at least 5.25 hours per day on their computers. First, we need to calculate the z-score for this value using the formula:

z = (x - μ) / σ

Where x is the value we are interested in (5.25 hours), μ is the mean (4 hours), and σ is the standard deviation (0.75 hour).

z = (5.25 - 4) / 0.75
z = 1.5

Next, we can use a standard normal distribution table or calculator to find the proportion of values that are greater than or equal to 1.5. This represents the proportion of people who spend at least 5.25 hours per day on their computers.

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Given:

A figure of a right angle triangle.

To find:

The value of x.

Solution:

First, label the vertices figure as shown below.

In triangle ABC and DBA,

\(\angle BAC\cong \angle BDA\)         (Right triangles)

\(\angle ABC\cong \angle DBA\)         (Common angle)

\(\triangle ABC\sim \triangle DBA\)         (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional.

\(\dfrac{BC}{BA}=\dfrac{AB}{DB}\)

Substituting the given values from the below figure, we get

\(\dfrac{x}{8\sqrt{3}}=\dfrac{8\sqrt{3}}{12}\)

\(x=\dfrac{8\sqrt{3}}{12}\times 8\sqrt{3}\)

\(x=\dfrac{192}{12}\)

\(x=16\)

Therefore, the value of x is 16 and correct option is B.

Answer:

42

Step-by-step explanation:

6+12+8+16=42 ft

The area of this irregular figure is 42 sq.ft

I hope I helped you :)

Answer:

12000 In 12 days

Step-by-step explanation:

12÷4=3

4000×3=12000

Answer:

4.00

Step-by-step explanation:

Given

x:   2  ,      5   ,     8     , 12

y: 8.50, 15.25, 22.00. 31.00

Required

Determine the y intercept

First, we calculate the slope:

\(m = \frac{y_2- y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (2,8,50)\)

\((x_2,y_2) = (12,31.00)\)

\(m = \frac{31.00 - 8.50}{12 - 2}\)

\(m = \frac{22.5}{10}\)

\(m = 2.25\)

Next, we calculate the equation:

\(y - y_1 = m(x - x_1)\)

Where:

\((x_1,y_1) = (2,8,50)\)      

\(m = 2.25\)

The equation becomes:

\(y - 8.50 = 2.25(x - 2)\)

\(y - 8.50 = 2.25x -4.5\)

Make y the subject

\(y = 2.25x -4.5+8.50\)

\(y = 2.25x +4\)

Take \(x =0\); to get the y intercept

\(y = 2.25*0 +4\)

\(y = 4\)

Hence, the y intercept is 4.00

Answer:

The answer is B

Step-by-step explanation:

Answer:

The retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38

Step-by-step explanation:

The given information are;

The number of bags of synthetic hair bundles the owner buys = 700

The number of bags of natural hair bundles the owner buys = 400

The number of synthetic hair bundles the Forestville location receives = 300

The number of natural hair bundles the Forestville location receives = 250

The total retail value of the hair bundles the Forestville location receives = $23,600

The number of synthetic hair bundles the Largo location receives = 400

The number of natural hair bundles the Forestville location receives = 150

The total retail value of the hair bundles the Largo location receives = $24,500

Let the price of a bag of synthetic hair bundle = x

Let the price of a bag of natural hair bundle = y

∴ 300·x + 250·y = $23,600...(1)

400·x + 150·y = $24,500...(2)

Making y the subject of the formula in both equations gives;

For equation (1)

y = 23,600/250 - 300/250·x = 94.4 - 1.2·x

y = 94.4 - 1.2·x

For equation (2)

400·x + 150·y = 24,500

y = 24,500/150 - 400/150·x = 490/3 - 8/3·x

y = 490/3 - 8/3·x

Finding the common solution gives;

490/3 - 8/3·x = 94.4 - 1.2·x

490/3 - 94.4 = 8/3·x  - 1.2·x

1034/15 = 22/15·x

x = 1034/15/(22/15) = 47

x = 47

∴ The price of a bag of synthetic hair bundle = x = $47

The price of a bag of synthetic hair bundle = $47

y = 490/3 - 8/3·x = 490/3 - 8/3 × 47 = 38

y = 38

The price of a bag of natural hair bundle = y = $38

The price of a bag of natural hair bundle = $38.

Therefore, the retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38.

Answer:its 5

Step-by-step explanation: cuz

y/x is equivalent to a constant and is equal to [m].

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                                {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)      {Two point - slope form}

x/a + y/b = 1                                        {intercept form}

x cos(β) + y sin(β) = L                          {Normal form}

We have a relationship that is proportional when the ratio of [y] over [x].

The equation of a straight line -

y = mx + c

can be used to represent proportional relationship when [c] = 0. Now -]

y = mx

m = y/x

Now, y/x is equivalent to a constant and is equal to [m].

Therefore, y/x is equivalent to a constant and is equal to [m].

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Answer:

Php 210

Step-by-step explanation:

Basic pizza = Php 150

each additional slice of meat topping = Php 5

y = 150 + 5x

Where,

y = Total cost of pizza

x = number of additional meat topping

How much will the pizza cost if it has a dozen slices of meat

toppings?

A dozen slices of meat

toppings = 12 slices of meat

toppings

y = 150 + 5x

= 150 + 5(12)

= 150 + 60

= 210

y = Php 210

Using a linear function, it is found that the pizza will cost Php 210.

A linear equation has the following format:

\(y = mx + b\)

In which:

In this problem:

Then:

\(y = 5x + 150\)

The cost if it has a dozen slices of meat  toppings is y when x = 12, thus:

\(y = 5(12) + 150 = 210\)

The pizza will cost Php 210.

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Answer:64 ounce bottle of orange juice has a greater percent of water Step-by-step explanation:Case ...

Step-by-step explanation: An 80 ounce bottle of apple juice contains 32 ounces of water a 64 ounce bottle of orange juice has 48 ounces of water which juice has a greater ...

The probability that a child is not allergic to nuts is 0.986, or 98.6%.

The probability that a child is not allergic to nuts can be calculated by subtracting the probability of being allergic to nuts from 1.

Given the probabilities of a child being allergic to nuts, dairy, and gluten, we are interested in finding the probability that a child is not allergic to nuts.

The probability of being allergic to nuts is given as 0.014.

To find the probability that a child is not allergic to nuts, we subtract this value from 1.

P(Not allergic to nuts) = 1 - P(Allergic to nuts) = 1 - 0.014 = 0.986

Therefore, the probability that a child is not allergic to nuts is 0.986, or 98.6%.

This calculation is based on the assumption that being allergic to nuts and being allergic to other foods are independent events.

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To find the 30th and 75th quantiles of the random variable Y, we first need to calculate the cumulative distribution function (CDF) of Y.

CDF of Y:
F(y) = ∫ f(y) dy from 0 to y (since f(y) = 0 for y < 0)
= ∫ e^(-y) dy from 0 to y
= -e^(-y) + 1

Now, to find the 30th quantile, we need to find the value y_30 such that F(y_30) = 0.3.
0.3 = -e^(-y_30) + 1
e^(-y_30) = 0.7
y_30 = -ln(0.7) ≈ 0.357

Similarly, to find the 75th quantile, we need to find the value y_75 such that F(y_75) = 0.75.
0.75 = -e^(-y_75) + 1
e^(-y_75) = 0.25
y_75 = -ln(0.25) ≈ 1.386

Therefore, the 30th quantile of Y is approximately 0.357, and the 75th quantile of Y is approximately 1.386.
Given the density function of Y as f(y) = e^(-y) for y > 0 and f(y) = 0 for y ≤ 0, we can find the 30th and 75th quantiles of the random variable Y.

First, let's find the cumulative distribution function (CDF) F(y) by integrating the density function f(y):

F(y) = ∫f(y)dy = ∫e^(-y)dy = -e^(-y) + C

Since F(0) = 0, C = 1. So, F(y) = 1 - e^(-y) for y > 0.

Now, we can find the quantiles by solving F(y) = p, where p is the probability:

1. For the 30th quantile (p = 0.3):

0.3 = 1 - e^(-y)
e^(-y) = 0.7
-y = ln(0.7)
y = -ln(0.7)

2. For the 75th quantile (p = 0.75):

0.75 = 1 - e^(-y)
e^(-y) = 0.25
-y = ln(0.25)
y = -ln(0.25)

So, the 30th quantile of the random variable Y is -ln(0.7), and the 75th quantile is -ln(0.25).

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To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer: the slope of AC is 4

the slope of EG is 2

the polygons are not dilations of eachother because the corresponding sides are not parallel

Answer:

D, D, C

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

A=l*w

32*2=64

A=s*s

s=√A

√64

=8

The length in centimeters of the side of the square is 8 cm.

The area of a rectangle and a square are -

A{R} = Length x Breadth

A{S} = Side x Side

Given is that a square and a rectangle have the same area. The length of the rectangle is 32 cm and the width of the rectangle is 2 cm.

It is given that -

A{R} = A{S}

Length x Breadth = Side x Side

32 x 2 = (Side)²

(Side)² = 64

Side = 8

Therefore, the length in centimeters of the side of the square is 8 cm.

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