How many square feet of outdoor carpet will we need for this hole?

The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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When a number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

The sample space describing all possible outcomes is {1, 2, 3, 4, 5, 6}

Then outcomes for the event of rolling an even number. {2, 4, 6}

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to foretell the likelihood of many events.

In probability, sample space refers to the list of all potential outcomes of an experiment. Regardless of the number of ways an event could occur, each potential result is represented by a single point in the sample space.

The sample space is the numbers from 1 to 6 while event of rolling an even number is 3/6 = 1/2

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The function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given is a function under some transformations, 3 h(x) + 4 ;

If we consider h(x) as a parent function, then the result after the transformation is 3h(x)+4,

We see that, it is being multiplied by 3, we know that if a function is being multiplied by a number greater than 1 in transformation then it is dilated by a scale factor of the number, hence, the function is being dilated by a scale factor of 3.

Also, we see, here is an addition of 4, we know that, when function is added by a certain number then in the transformed function the function is shifted vertically and addition mean it shifted vertically upwards, sine, 4 is added to the function it means, the function is shifted 4 unit vertically upwards.

Hence, the function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

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Answer:

top right graph

Step-by-step explanation:

5y=-10x+20

y=-2x+4

Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

Given :

=> B = 8

=> S = 40

Tangent :

=> Angle ∠A = 40/9

For tangent ∠B:

=> Angle ∠B = 41/9

Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

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Answer:

D. 2r2 + 23r > 645

Step-by-step explanation:

The equation "2r^2 + 23r > 645" represents the situation because it states that the number of spaces in the parking lot, represented by the left-hand side of the equation (2r^2 + 23r), is greater than the maximum number of spaces that the parking lot can hold (645). This is consistent with the information given in the problem, which states that the parking lot has been expanded and can now hold more spaces.

The other equations given (A, B, C) do not accurately represent the situation because they do not take into account the expansion of the parking lot and the addition of new rows and spaces.

The measure of ∠EFJ is 60°. Option B is the correct option.

What is a linear pair?

When two lines cross at one point, a linear pair of angles are created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

∠EFG is a linear pair of angle.

This means ∠E F G = 180°

Given that ∠J F K = 90° and ∠E F J = 2∠K F G.

∠E F G is the sum of angles ∠E F J, ∠J F K  and ∠K F G

∠E F G = ∠E F J + ∠J F K + ∠K F G

Now putting the value of ∠E F G, ∠J F K

180° = ∠E F J +  90° + ∠K F G

Again putting ∠K F G = 1/2∠E F J:

180° = ∠E F J +  90° + 1/2∠E F J

180° -  90° = 3/2 ∠E F J

90° = 3/2 ∠E F J

∠E F J = 90° ×(2/3)

∠E F J = 60°.

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The number of square inches of fabric that Alicia would need to create the logo is equal to 141.135 square inches.

Based on the information provided, we can logically deduce that a mathematical expression that represents the number of square inches of fabric that Alicia would need to create the logo is given by:

s . s + 0.5s . s

where:

s represents the length of the side of the square in inches.

By simplifying the mathematical expression, we have the following:

Number of square inches of fabric = s² + 0.5s²

Substituting the given parameters into the mathematical expression, we have the following;

Number of square inches of fabric = 9.7² + 0.5(9.7)²

Number of square inches of fabric = 94.09 + 0.5(94.09)

Number of square inches of fabric = 94.09 + 47.045

Number of square inches of fabric = 141.135 square inches.

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Complete Question:

Alicia, a graphic designer, is designing a new logo for a company. The logo will contain a square and a triangle. The triangle’s base and height will be the same length as the side of the square. Alicia wants to use fabric to create the shapes to use during her presentation to the company. The expression s · s + 0.5s · s represents the number of square inches of fabric she will need to create the logo, where s is the length of the side of the square in inches.

If a side of the square is 9.7 inches long, how many square inches of fabric will Alicia need?

let's firstly convert the mixed fractions to improper fractions and then sum them up.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2\frac{2}{5}} \implies \cfrac{2\cdot 5+2}{5} \implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{equal sides}}{x+x}~~ + ~~\stackrel{\textit{third side}}{\left( x+\cfrac{4}{3} \right)} ~~ = ~~\stackrel{perimeter}{\cfrac{12}{5}}\implies 3x+\cfrac{4}{3}=\cfrac{12}{5}[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( 3x+\cfrac{4}{3} \right)=15\left( \cfrac{12}{5} \right)}\implies 45x+20=36\implies 45x=16 \\\\\\ \stackrel{\textit{equal sides}}{\boxed{x=\cfrac{16}{45}}}\hspace{10em}x+\cfrac{4}{3}\implies \cfrac{16}{45}+\cfrac{4}{3}\implies \stackrel{\textit{third side}}{\boxed{\cfrac{76}{45}}}[/tex]

The graph that shows that y is less than or equal to 3x - 4 is plotted and attached

The graph is plotted by forming a table of value, then tracing eaching point in the table and marking the points of intersection of the x and y

The points intersections later joined with a line

The table of value is formed for x = -2, 0, and2

y ≤ 3x - 4

for x = -2, y ≤ 3 * -2 - 4 = -10

for x = 0, y ≤ 3 * 0 - 4 = -4

for x = 2, y ≤ 3 * 2 - 4 = 2

table of value

x      y

-2    -10

0     -4

2      2

The graph is attached, the line is a solid line since the inequality is less than or "equal to". The shading is below because it is less than

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The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of  

The formula for the area of a rectangle is the product of length and wide. This is written mathematically as

= length * wideness

In the problem the rectangular array made by Casey has a the following dimensions

length = 1167 units

wide = 7 units

Area of rectangle = length * wideness

substituting the values

Area of rectangle = 1167 * 7

Area of rectangle = 8169 square units

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Answer:

(9b-4c)(9b+4c)

Step-by-step explanation:

81b^2-16c^2

Using the the difference of square formula: a^2-b^2=(a-b)(a+b)

(9b-4c)(9b+4c)

Answer:

Yes.

(2, 23) is a solution for the equation y = 9x + 5

Step-by-step explanation:

(2, 23) means that for an x value of 2, the y value should be 23

The equation is y = 9x + 5

Substitute x = 2 on the right side

y = 9(2) + 5 = 18 + 5 = 23

Since this matches the given value of y =23, we can conclude that

(2, 23) is a solution for y = 9x + 5

Answer:

The annual percentage yield (APY) is the effective annual rate of return on an investment, taking into account the effects of compounding. To calculate the APY, we can use the formula:

APY = (1 + (APR / n))^n - 1

Where APR is the annual percentage rate (the stated interest rate), and n is the number of times the interest is compounded per year.

In this case, the APR is 4.86% and the interest is compounded daily, so n = 365 (the number of days in a year).

APY = (1 + (0.0486 / 365))^365 - 1

Plugging in the numbers, we get:

APY = (1 + 0.000132876712328767123)^365 - 1

APY ≈ 4.87%

So, the annual percentage yield is 4.87%

There are 45 pounds are needed for 6045 square​ feet.

What is pounds?

The United Kingdom and nine of its associated territories use the sterling as their currency. The pound is the primary unit of sterling, and the term "pound" is also frequently used to refer to the British pound or the pound sterling in international contexts.

Given:

3 pounds of grass seed cover 403 square​ feet.

We have to find the how many pounds are needed for 6045 square​ feet.

As 3 pounds of grass seed cover 403 square​ feet.

⇒ 403/3 = 134.33

⇒  1 pound of grass seed cover 134.33 square feet.

Let x pounds needed for 6045 square feet.

⇒ x = 6045 / 134.33 = 45

Hence, there are 45 pounds are needed for 6045 square​ feet.

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The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as 4y+16x=28 or y+4x=7

putting (1,3) in the equation we get 3+4×1=7

Similarly we can find the ordered pair as (2, -1) , (3,-5) , (4,-9)

Hence, The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)

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Answer:

1, 2, 7, 14

Step-by-step explanation:

its all of those

The probability that the two bills together will be worth at least 30 dollars is, 4/7

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

Marya has 3 bills worth 10 dollars each

4 bills worth 20 dollars each

she chooses two of these bills at random

the probability that the two bills together worth at least 30 dollars =?

So,  total possible combinations  (10, 10, 10, 20, 20, 20, 20) = ⁷C₂ = 21

favorable combinations = ³C₁ × ⁴C₁ = 12

Probability = 12/21

Probability = 4/7

Hence, the probability is 4/7

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Answer:

[tex]\frac{10}{7}x^4[/tex]

Step-by-step explanation:

There is an exponent rule which essentially states: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

All this is doing is essentially cancelling out the terms, since you can think of it as: [tex]\frac{x^a}{x^b}\implies \frac{x*x*x...\text{ "a" amount of times}}{x*x*x...\text{"b" amount of times}}[/tex], and if you recall, multiplication and division cancel. So we cancel out "b" amount of x's, leaving us with "a - b" amount of x's. Which can also be expressed as: [tex]x^{a-b}[/tex]

We can use this logic to solve our problem: [tex]\frac{20x^6}{14x^2}[/tex], here we can separate this into two different fractions: [tex]\frac{20}{14}*\frac{x^6}{x^2}[/tex] and we can use basic division on the left side and our exponent rule on the right side. This gives us the following:  [tex]\frac{10}{7}x^{6-2}\implies \frac{10}{7}x^4[/tex] which is our solution!

Answer: The summer monsoon rains are a crucial source of rainfall for India, bringing in 80% of the country's annual rainfall. These rains are essential for the country's agriculture as they provide the necessary water for crops to grow and thrive. The monsoon season typically runs from June to September, and the amount of rainfall received during this time period can greatly impact the success of the agricultural season. With the majority of the rainfall coming during this season, farmers and agricultural experts closely monitor the monsoon forecast to ensure that enough rainfall is received to support the crops. Without the summer monsoon rains, the agricultural production of the country would be greatly impacted and the livelihoods of many farmers would be at risk.

Step-by-step explanation:

On solving the provided question we can say that 1,000,000 nanometers =  1 millimeter; 1e-6 millimeter = nanometers

A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.

1,000,000 nanometers =  1 millimeter

1e-6 millimeter = nanometers

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Answer:

$101.75

Step-by-step explanation:

You work 4 hours in the morning from 8-12 and 5 hours and 15 minutes in the afternoon from 12:45 to 5:30 (a.k.a. 17:30)

15 minutes is a quarter of an hour.  1/4 = 0.25

4 + 5.25 = 9.25

You worked for 9.25 hours

Multiply that by $11 per hour.

9.25 · 11 = 101.75

You make $101.75 on Monday.

The coordinates of the square are 2.8

A square is a polygon whose all sides are equal.  the if the sides are equal, the coordinates of the vertices are also equal to each other.

The length of the diagonal of the square is gotten by the use of the formula for distance between two points

d = √(y₂-y₁)²+(x₂-x₁)²

distance = √(6-2)²+(-2-2)²

distance = √4²+-4²

Distance = √16+16

distance = √32 = 5.7 units

This implies that the sides of the square = 5.7/2 = 2.8

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Answer:

Step-by-step explanation:

y2-y2/x2-x1

Answer:

1267 people

Step-by-step explanation:

The area of the 10 feet by 10 feet square is 100 square feet. If 20 people fit comfortably in this area, we can use this information to estimate the number of people in a larger area.

Since we know that 20 people fit in 100 square feet, we can calculate how many people would fit in a larger area by multiplying the number of square feet by 20.

A 1 mile section of a parade route is approximately 5280 feet long and 12 feet deep (on one side of the street). Therefore, the area that the crowd is occupying is approximately 5280*12 = 63,360 square feet.

So, the number of people that would fit in this area would be approximately:

63,360 square feet * 20 people/100 square feet = 1267.2 people.

So we can estimate that 1267 people will comfortably fit in a 1 mile section of a parade route that is 12 feet deep on one side of the street.

Answer:

389 people

Step-by-step explanation:

Step 1 we convert 1500 inches to feet

Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

Answer:

14 inches is to 56 miles

Step-by-step explanation:

First, let's convert the question into an "equation"

1in : 4mi as xin:56mi

Since we need to multiply 4mi by 14 to 56mi, we will multiply 1in by 14 to find the value of x. 1 * 14 = 14. So, x must be equal to 14 and 1 inch is to 4 miles as 14 inches is to 56 miles.

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It is given to us in the question that we have a proportion of 1 inch is to 4 miles.

The proportion we need to solve is, 1 : 4 :: x : 56  as given in the question.

To solve this,

If 1 inch is equal to 4 miles, that means 4 miles is equal to 1/4 inch.

i.e. 1x = 4y; where x is inches and y is miles

1y = 1x/4....................(i)

Similarly, from the above-given proportion, we see that

x = 56y;

Taking the value of y from (i),

x = 56 * (1/4)

= 14

So the proportion becomes,

1 inch : 4 miles :: 14 inch : 56 miles

Hence, it can be determined that 1 inch is to 4 miles as 14 inches is to 56 miles.

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Answer:

2670 feet

Step-by-step explanation:

x = [tex]\frac{19341}{tan14}[/tex]

I preserve shape but not size.

My image and pre-image will be similar.

I am created by using a scale factor that is less than one.

I am Dilation (decrease).

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The points given are -

1. I preserve shape but not size.

2. My image and pre-image will be similar.

3. I am created by using a scale factor that is less than one.

During dilation if the scale factor is between 0 and 1, then the image shrinks.

The new image will be same but smaller in size than the original image.

The size of the image decreases from its original size but the shape remains the same.

Therefore, this is known as dilation (decrease).

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