Patricia is checking the distance between two towns on a map. The map uses a scale in which 3 inches equals 200 feet. If the actual distance between the towns is 8250 feet, how far is it between the towns on the map, in inches? Your answer can be exact or rounded to two decimal places. ​

If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:

Total number of hours of work / Number of hours of work done by 4 men in a day

= 224 / (4 x 8)

= 7

So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.

II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:

Total number of men x Total number of days x Number of hours worked by each man per day

= 4 x 7 x 8

= 224 hours

Therefore, the total cost of employing all 4 men is:

Total number of hours x Rate per hour

= 224 x $57.50

= $12,880

III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:

Total number of hours of work / Total number of days to complete the project

= 224 / 4

= 56 hours

Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:

Number of hours of work per day - Number of hours worked by each man per day

= 56 - 8

= 48 hours

Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.

IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:

l x $57.50

= $57.50l

Let the overtime rate of payment be $r per hour. Then:

r = $57.50l

The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:

Number of regular hours x Regular hourly rate

= 4 x 8 x 7 x $57.50

= $16,240

The cost of overtime hours is:

Number of overtime hours x Overtime hourly rate

= 4 x 6 x 7 x $57.50l

= $12,180l

So, the total cost of the project is:

Total cost = Cost of regular hours + Cost of overtime hours

= $16,240 + $12,180l

Answer:

Step-by-step explanation:

(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:

Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days

So it will take 4 men, each working 8 hours per day, 7 days to complete the project.

(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:

Total cost = 4 men x $57.50/hour x 56 hours = $12,320

(iii) If the project is to be completed in 4 days, each man will need to work for a total of:

224 total hours / (4 men x 4 days) = 14 hours per day

Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.

(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:

Overtime rate = $57.50 x 1.5 = $86.25/hour

To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:

Regular hours cost = 224 regular hours x $57.50/hour = $12,880

The cost of the overtime hours is:

Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour

= 96 x $86.25

Therefore, the total cost of the project is:

Total cost = Regular hours cost + Overtime cost

= $12,880 + $8,280

= $21,160

where the overtime rate is 1.5 times the regular hourly rate.

The formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

The geometric sequence equations has the general form an=a1rⁿ⁻¹, where r denotes the common ratio, a1 denotes the first term, and n denotes the term's position in the sequence.

sequence: 2, 4, 8, 16, 32, …

a1 = 2

r = 4/2 = 2

So,

an = 2(2)ⁿ⁻¹

Thus, the formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

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The two fractions' sum is therefore (a + b) / (a² × b²).

A sum, usually referred to as a summation, is the product of combining two or more quantities or numbers. A summation always has an even term count. It could be two terms simply, or it might total 100,000 or a million. Many terms can be included in some summations.

We require a common denominator in order to add these two fractions.

The first fraction's denominator is a² × b, and the second fraction's denominator is a × b².

Get the supreme strength of each component that exists in either denominator, then utilize the result of these factors to determine the least frequent multi of these two denominators:

LCM (a² × b, a × b²) = a² × b²

The two fractions can now be rewritten using the following common denominator:

1/(a² × b) + 1/(a × b²) = (1 × b + 1 × a) / (a² × b²)

If we condense this phrase, we get:

1/(a² × b) + 1/(a × b²) = (a + b) / (a² × b²)

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Answer:

Where's the question...

Answer:

7m + 20 ≥ 150

Closest option is 7m + 20 > 150 which is the second choice

Step-by-step explanation:

The words "at least" indicate a ≥ inequality.

There is a fixed earning of $20 for entering the race. So this amount will be earned on regardless of how much Carol runs

For each mile she runs she earns $7. For running m miles, she earns 7m dollars

Total amount earned for running m miles = 7m + 20
This must be at least $150
So the correct inequality is
7m + 20 ≥ 150

I don't see this exact inequality in any of the answer choices but that is the correct answer.

π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.

The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.

Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.

π - This is an irrational number.

22/7 - The number is rational but not an integer.

3.3 - The number is an integer but not a whole number.

The number is a whole number but not a natural number.

9 -This number can be written as a natural number.

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Based on the 2009 season, the Texas Rangers have a winning percentage of .533. The probability that the Rangers win 4 of their next 5 games is 18.8%.

We can use the binomial distribution formula to find the probability that the Texas Rangers win exactly 4 of their next 5 games:

P(4 wins) = (5 choose 4) * (.533)^4 * (1-.533)^1

= (5! / (4! * 1!)) * (.533)^4 * (.467)^1

= 5 * 0.533^4 * 0.467^1

= 18.8%

where "choose" is the binomial coefficient, which represents the number of ways to choose a subset of size k from a set of size n, and is given by:

(n choose k) = n! / (k! * (n-k)!)

So the probability that the Rangers win 4 of their next 5 games is 18.8%,.

Therefore, the answer is B.

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Answer:

19,306 = 10 + 90 + 30 + 60

Step-by-step explanation:

The scale factor for the given transformation is -

{k} = 2/3.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given is a figure {Q} that is a transformation of figure {P}.

The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -

{K} = 10/15

{K} = 2/3

Therefore, the scale factor for the given transformation is -

{k} = 2/3.

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The sections of each course it should offer are 3 finite maths, 2 applied calculus and 2 computer methods

Let's use the following variables to represent the unknowns:

From the problem, we can write the following system of equations:

x + y + z = 7 (total number of sections)

40x + 40y + 10z = 220 (total number of students)

40000x + 60000y + 29000z = 298000 (total revenue)

Simplify

x + y + z = 7

4x + 4y + z = 220

40x + 60y + 29z = 298

We can solve this system of equations using substitution

So, we have

x = 7 - y - z

By substitution, we have

4(7 - y - z) + 4y + z = 22

This gives

28 - 4y - 4z + 4y + z = 22

So, we have

28 - 3z = 22

This gives

3z = 6

Divide

z = 2

Recall that

40x + 60y + 29z = 298

So, we have

40x + 60y + 29*2 = 298

40x + 60y + 58 = 298

This gives

40x + 60y = 240

Divide by 20

2x + 3y = 12

Also, recall that x = 7 - y - z

So, we have

2(7 - y - z) + 3y = 12

This gives

2(7 - y - 2) + 3y = 12

2(5 - y) + 3y = 12

Open brackets

10 - 2y + 3y = 12

Evaluating the like terms, we have

y = 2

Lastly. we have

x = 7 - y - z

x = 7 - 2 - 2

x = 3

Hence, the number of sections of Finite Math is 3

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The surface area of the shape is 110 square units.

The area of a two-dimensional figure is the area enclosed by its perimeter. The area of a closed figure is the number of unit squares that cover its surface. Area is measured in square units such as cm2 and m2. The area of a shape is measured in two dimensions.

The rectangle's surface area is:

Area = 10 × 9 = 90 unit square

The area of the triangle is:

Area = 0.5 × 10 × 4 = 20 unit square

The figure's area is as follows:

Total = 90 + 20

Total = 110 unit square

Hence, the shape's area is 110 unit square.

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The expression for the quadratic function can be written as:

g(x + a) - g(x) = 4ax + 2a² - 4a

Here we want to find the expression:

g(x + a) - g(x)

For the quadratic function:

g(x) = 2x² - 4x

So just let's evaluate the function in these values, we will get:

g(x + a) =2*(x + a)² - 4*(x + a)

Expanding that we will get:

            = 2(x² + 2ax + a²) - 4x - 4a

            = 2x² + 4ax + 2a² - 4x - 4a

Subtracting the original equation we will get:

g(x + a) - g(x) = 2x² + 4ax + 2a² - 4x - 4a - 2x² - 4x

                     = 4ax + 2a² - 4a

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The solution to the inequalities, y < 6 and y > x + 3 is the common intersecting region.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, y < 6.

Now, To determine wether it inclues the origin or not we'll set, y = 0.

So, 0 < 6 is true so y < 6 includes the origin.

Now, y > x + 3.

0 > 0 + 4 is not true therefore, y > x + 3 doest not inclue the origin.

The solution to these now can be determine by the common intersecting region.

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Answer:

The polynomials are:

-7x²+ 5/3x

6x² + 5x

-x^2+5x

The expression x^2+ 5x1/5 is not a polynomial because it contains a fraction with x in the denominator.

Step-by-step explanation:

V = P(1 - r)^t

where V is the value of the car after t years, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the number of years.

Plugging in the values given in the problem, we get:

V = 42000(1 - 0.15)^7

V = 42000(0.85)^7

V = 42000(0.327)

V = $13734.00

Therefore, the car will be worth $13,734.00 after 7 years. Rounded to the nearest dollar, the value is $13,734.

Answer:

A) $12,800.00. B) $13,629.44. The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years? C) ...

Therefore , the solution of the given problem of function comes out to be  height is 64 feet .

What is meant by the word function?

The study of mathematics includes histology, architecture, and both actual and fictitious geographic locations, as well as arithmetic, numerals, and their divisions. A function explains the relationships between different components, each of which has a corresponding result. A function is made up of a variety of components that, when put together, produce specific outputs for each input.

Here,

The highest spot on the ball's trajectory, which is at the vertex of the parabolic path, must be identified in order to calculate the maximum height the ball has ever attained.

The following equation describes the height of the projectile as a function of time:

s = -16t² + 64t

We can apply the following method to determine the parabola's vertex:

t = -b/2a

where b = 64 and a = -16.

By replacing these numbers, we obtain:

t = -64/(2*(-16)) = 2

Thus, after two seconds, the utmost height is reached.

We can enter t = 2 into the calculation to get the height at this point:

s = -16(2)² + 64(2) = 64 feet

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Answer: PP(Percentage) + PP or PP(1.%)

Step-by-step explanation:

We can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

The identity matrix is the only idempotent matrix with non-zero determinant.

Given is the matrix relation as -

(I + 2A)

We can write the addition of matrix as -

(I + 2A) →

[1  0]

[0  1]  

+

2[-1  2]

2[4  5]

(I + 2A) →

[1  0]

[0  1]  

+

[-2  4]

[8  10]

(I + 2A) →

[- 1  4]

[8  11]  

Therefore, we can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

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Answer:

Your blank answer is 4.68

Step-by-step explanation:

Well lets make the missing blank into a variable.

12 - x = 7.32

This way we can solve for x. Simplify.

Add x to both side.

12 = 7.32 + x

Subtract 7.32 to both side leaving you x.

12 - 7.32 = x

x = 4.68

Answer:

12 - 4.68 = 7.32

Step-by-step explanation:

Now we have to,

→ Find the missing number in the equation.

Let us assume that,

→ Missing number = m

Forming the equation,

→ 12 - m = 7.32

Then the value of m will be,

→ 12 - m = 7.32

→ -m = 7.32 - 12

→ -m = -4.68

→ [ m = 4.68 ]

Hence, the answer is 4.68.

Answer: C

Step-by-step explanation:

Answer:

11%

Step-by-step explanation:

110 divided by 10 is 11% or 11 times 10 is 110

Answer:

10% of 110 is 11

Step-by-step explanation:

Finding the fraction of a number is the same as multiplying a fraction with the number

10/100 of 110 = 10/100 x 110

so the answer is 11

Answer:

Malleability and ductility refer to a material's ability to be shaped, bent, or stretched without breaking. Malleability is a measure of how easily a material can be hammered, pressed, or rolled into different shapes, while ductility is a measure of how much a material can be stretched before it breaks. Metals and alloys are generally highly malleable and ductile, while concrete and glass are less so

Step-by-step explanation:

The type of triangle AABC is an equilateral triangle, as it is formed by the midsegments of the equilateral triangle ADEF.

Since the midsegments of a triangle are parallel to its opposite sides and half the length of the opposite sides, the midsegments of an equilateral triangle are congruent to each other, and their length is half the length of the sides of the equilateral triangle.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2} and y = \dfrac{q+n}{2}[/tex]

We are given that;

An equilateral triangle DEF

AAB is formed by the midsegments of triangle ADEF, which means that AAB is also an equilateral triangle. To see why this is true, we can use the following argument:

The midsegment of DE is parallel to AB and has half the length of AB.

The midsegment of EF is parallel to AA' and has half the length of AA'.

The midsegment of FD is parallel to BB' and has half the length of BB'.

Therefore, AB = AA' = BB', and the angles at A and B are both 60 degrees (since DEF is equilateral).

Thus, AAB is an equilateral triangle, because all its sides are equal in length and all its angles are equal to 60 degrees.

Therefore, by midpoint the answer will be equilateral triangle.

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In response to the supplied query, we may state that there is a proportionality  statistically significant difference between the two population proportions because the interval comprises 0.

Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an orchard and the number of apples in a harvest of apples depend on the average number of apples produced by each tree. A linear relationship between two numbers or variables is referred to as being proportional in mathematics.

The following is the point estimate for the variance between the two sample proportions:

ME is equal to z/2 * [p1(1 - p1) / n1 + p2(1 - p2) / n2]

where:

The z-score that corresponds to the required degree of confidence, in this case 90%, is z/2, or 1.645.

The proportions of the sample are p1 and p2.

These are the sample sizes, n1 and n2.

When we enter the values, we obtain:

ME = 1.645 * √[(0.9512)(1 - 0.9512) / 820 + (0.9891)(1 - 0.9891) / 804]

ME = 0.0528

-0.0379 ± 0.0528

or

-0.0907 to 0.0149

As a result, we have 90% confidence that the actual change in population proportions is between -0.0907 and 0.0149. We cannot infer that there is a statistically significant difference between the two population proportions because the interval comprises 0.

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Answer:

Step-by-step explanation how do I use this appp :

The remaining feet long is A. 3 7/12 feet long

How to determine this

Kelsey has a board of 6 1/3 feet long

When he uses 2.75 feet

To calculate the remaining feet

= 6 1/3 - 2.75 feet long

By converting 2.75 to fraction

2.75 = 2 3/4

= 11/4

6 1/3 = 19/3

So, 19/3 - 11/4

= 43/12

= 3 7/12

Therefore, the remaining piece is 3 7/12 feet long

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Answer:

33.02 centimeters of cloth

Step-by-step explanation:

Since 1 inch is equal to 2.54 cemtimeters then all you need to do is multiply 13x2.54 and you have your answer of 33.02

The number of apples after the increase will be 18.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %.  In order to change a number to a percentage, multiply by 100.

After the apples are increased, the new number of apples would be half more than the initial number of apples.

The formula that can be used to determine the new number of apples is: New number of apples = original number of apples x (1 + increase/100)

= 12 x (1 + 50/100)

= 12 x (1 + 0.5)

= 12 x 1.5 = 18

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In response to the aforementioned query, we may say that Point M's slope coordinates are therefore (39/25, 69/25).

A line's slope determines how steep it is. The gradient is mathematically expressed as gradient overflow. By dividing the vertical change (run) between two spots by the height change (rise) between the same two locations, the slope is determined. The equation for a straight line, y = mx + b, is written as a curve form of an expression. When the slope is m, b is b, and the line's y-intercept is located (0, b). For instance, the y-intercept and slope of the equation y = 3x - 7 (0, 7). The location of the y-intercept is where the slope of the path is m, b is b, and (0, b).

A and B's respective y-coordinates are at the midpoint of the triangle AB.

[tex]((x A + x B)/2, (y A + y B)/2)[/tex]is the midpoint.

[tex]((-4 + 2)/2, (2 + 10)/2)[/tex] is the midpoint.

Midway = [tex]( -1, 6 )\\[/tex]

Slope of AB: The slope of AB is equal to the product of the y-value and the x-value, or:

slope is equal to [tex](y B-y A) / (x B-x A).\\[/tex]

slope = [tex](10 - 2) / (2 - (-4))\\[/tex]

slope = 8/6 = 4/3

[tex]y - y 1 = m * (x - x 1)\\y - 6 = (-3/4) * (x + 1)\\y - 6 = (-3/4)\\x - (3/4)\sy = (-3/4)x + (21/4)[/tex]

Point M's coordinates are:

[tex]y = (-3/4)x + (21/4)\\4x/3 + 2 = (-3/4)x + (21/4)\\16x + 24 = -9x + 63\s25x = 39\ = 39/25\\y = (-3/4)(39/25) + (21/4) = 69/25\\[/tex]

Point M's coordinates are therefore (39/25, 69/25).

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all of them are equivalent