A construction company can remove 1/2 metric tons of dirt from a construction site in
1/4 hours.
What is the unit rate in metric tons per hour?

Write your answer in simplest form.

The function g(x, y) is defined as 15x^2 + 2y^2. To compute g(3,3), g(0,-2), and g(a,b), we substitute the given values into the function.

To find g(3,3), we substitute x = 3 and y = 3 into the function g(x, y) = 15x^2 + 2y^2:

g(3,3) = 15(3)^2 + 2(3)^2

g(3,3) = 135 + 18

g(3,3) = 153

To find g(0,-2), we substitute x = 0 and y = -2 into the function g(x, y) = 15x^2 + 2y^2:

g(0,-2) = 15(0)^2 + 2(-2)^2

g(0,-2) = 0 + 8

g(0,-2) = 8

To find g(a,b), we substitute x = a and y = b into the function g(x, y) = 15x^2 + 2y^2:

g(a,b) = 15a^2 + 2b^2

Note: The function g(a,b) cannot be simplified further without knowing the values of a and b.

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To the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.

A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always adds up to 180 degrees. There are many different types of triangles, including equilateral triangles (where all three sides are equal in length and all three angles are 60 degrees), isosceles triangles (where two sides are equal in length and two angles are equal in measure), and scalene triangles (where no sides are equal in length and no angles are equal in measure).

Let x be the length of the shorter leg of each right triangle. Then, the longer leg will be twice as long, so its length will be 2x. Using the Pythagorean theorem, we can write:

x² + (2x)² = 6²

Simplifying and solving for x, we get:

x² + 4x² = 36

5x² = 36

x² = 7.2

x ≈ 2.7

Therefore, to the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.

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The equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.

To find the equation of a line that goes through the point (-2, -5) and is parallel to y = x + 2, we will follow these steps:

1. Identify the slope of the given line.
2. Use the slope and the given point to find the equation of the new line.

Step 1: Identify the slope of the given line.
The equation of the given line is y = x + 2. This is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 1, as it is the coefficient of x.

Step 2: Use the slope and the given point to find the equation of the new line.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 1.

Now, we will use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.

Plugging in the values, we have:
y - (-5) = 1(x - (-2))
y + 5 = 1(x + 2)

Now, let's rewrite the equation in slope-intercept form:
y + 5 = x + 2
y = x + 2 - 5
y = x - 3

So, the equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.

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If Juan does not read any books before day 4 and he starts reading at the same rate as Patti for the rest of the month, he would have read 6 books by day 12. The correct option is A.

If Juan does not read any books before day 4, it means he has missed out on the opportunity to read for the first three days. Assuming Patti and Juan have been reading at the same rate since day 4, we can calculate the total number of books they would have read by day 12.

Patti reads one book per day, so by day 12, she would have read a total of 9 books (from day 4 to day 12). If Juan starts reading at the same rate as Patti from day 4, he would also have read 9 books by day 12.

However, we have to account for the fact that Juan did not read any books before day 4. This means that he missed out on the opportunity to read 3 books (one book per day for the first three days). Therefore, by day 12, Juan would have read a total of 6 books (3 books missed + 3 books read from day 4 to day 12).

Therefore, the answer is A. Juan would have read 5 books less than Patti by day 12, since Patti would have read a total of 9 books and Juan would have only read 6.

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a4 = 2

It is given that,

[tex]a_{1} = 5[/tex], and

[tex]a_{n} = (a_{n-1}) - 1[/tex]

Therefore, it can be said,

[tex]a_{2} = a_{1} - 1\\a_{3} = a_{2} - 1\\a_{4} = a_{3} - 1\\[/tex]

That is,

[tex]a_{2} = 5-1=4\\a_{3} = 4-1=3\\a_{4} = 3-1=2[/tex]

So, a4 = 2

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For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.

To find the number of grams of peanuts for every 1 gram of raisins, you need to set up a ratio and solve for the missing value.

1. Set up the ratio: grams of peanuts / grams of raisins.
2. You are given three sets of values: (14, 4), (21, 6), and (35, 10).

For the first set (14, 4):
3. Calculate the ratio: 14 grams of peanuts / 4 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

For the second set (21, 6):
4. Calculate the ratio: 21 grams of peanuts / 6 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

For the third set (35, 10):
5. Calculate the ratio: 35 grams of peanuts / 10 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.

Your answer: For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.

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The predicted exam grade for 1 hour of studying is 66. Therefore the residual for 1 hours of studying can be calculated as Residual = Actual Exam Grade - 66.

To find the residual for 1 hour of studying, we first need to determine the predicted exam grade and compare it to the actual exam grade for that specific data point.

Using the line of best fit equation y = 6x + 60, we can find the predicted exam grade for 1 hour of studying:

y = 6(1) + 60
y = 6 + 60
y = 66

So, the predicted exam grade for 1 hour of studying is 66. To calculate the residual, you need the actual exam grade for 1 hour of studying. If that information is not provided, the residual cannot be calculated. If the actual grade is provided, subtract the predicted grade from the actual grade to find the residual:

Residual = Actual Exam Grade - Predicted Exam Grade

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There is no one definitive list of steps to solving a word problem, as different types of problems may require different approaches.

However, a general set of steps that can be useful in solving many word problems is:

1. Read the problem carefully to understand what it is asking.

2. Identify the relevant information and the unknown quantity you need to find.

3. Translate the problem into an equation or set of equations that relate the given information to the unknown quantity.

4. Solve the equation(s) to find the value of the unknown quantity.

5. Check your answer to make sure it makes sense in the context of the problem.

Additional steps or variations on these steps may be necessary depending on the specific problem, but this general framework can be a useful starting point.

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The percentage of $7,200 that was donated to charity would be = 2%

To calculate the percentage of the total sales that was donated, the following should be carried out.

The total sales at the shoe store = $7,200

The amount of money that was donated = $144

Therefore to calculate the percentage the following is done ;

= 144/7200 × 100/1

= 14400/7200

= 2%

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To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.

∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.

To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.

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The height of the CN tower which is 320m away from the Mr.Thayer is 555.85 meters.

Please look at the attached diagram for a clear explanation,

From the diagram point A represents, the Mr.Thayer's eyes, point B represents Mr.Thayer's foot, point C represents the base of the CN tower along with point E represents the top of the tower.

From the following diagram lets find out the height of the tower,

In right-angled triangle ADE, Tan theta = opposite/adjacent

So, Tan (60°) = DE/AD

√3 = DE/320m

DE = 320m x √3

DE= 554.25m

DE represents the height of the CN tower from the eyes of Mr.Thayer.

To find out the total height of the CN tower, the height of Mr.Thayer + the height of the CN tower from Mr. Thayer's eyes = 554.25m + 1.6m = 555.85m.

From the above explanation, we can conclude that the height of the CN tower from the base = 555.85m.

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After 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

a) To write an exponential function that models the mass of Francium remaining after t minutes, we can use the formula:

N = N0 * [tex](1/2)^{(t / t1/2)}[/tex]

where N is the amount remaining after time t, N0 is the initial amount, t1/2 is the half-life, and (t/t1/2) means raised to the power of t/t1/2.

In this case, the initial amount is 480 grams, the half-life is 22 minutes, and we want to find the amount remaining after t minutes. Therefore, the exponential function that models the mass of Francium remaining after t minutes is:

N = 480 * [tex](1/2)^{t/22}[/tex]

b) 2 hours is equal to 120 minutes. To find how many grams of Francium remain after 2 hours, we can substitute t = 120 into the exponential function we found in part a):

N = 480 *[tex](1/2)^{ (120 / 22) }[/tex] ≈ 4.38 grams

Therefore, after 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.

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The equivalent expression is $\boxed{4^{15} \cdot 5^{10}}$.

We can simplify the expression inside the parentheses first, using the rule that says when you raise a power to another power, you multiply the exponents:

$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$

Now, we can use the rule that says when you raise a product to a power, you raise each factor to the power:

$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$

Simplifying further:

$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$

we can substitute this expression back into the original expression:

$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$

To simplify this expression further, we can use the rule that says when you raise a product to a power, you raise each factor to the power:

$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$

Simplifying the exponents, we get:

$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$

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lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers. We can verify lcmm,n∙gcdm,n=mn for each pair of numbers as follows:

For 60 and 90:

lcm(60,90) = 180

gcd(60,90) = 30

180 * 30 = 5400

60 * 90 = 5400

Since both sides of the equation are equal to 5400, the equation is verified.

For 220 and 1400:

lcm(220,1400) = 3080

gcd(220,1400) = 20

3080 * 20 = 61600

220 * 1400 = 61600

Since both sides of the equation are equal to 61600, the equation is verified.

For 3273∙11 and 23∙5∙7:

lcm(3273∙11, 23∙5∙7) = 15015

gcd(3273∙11, 23∙5∙7) = 161

15015 * 161 = 2418315

3273∙11 * 23∙5∙7 = 2418315

Since both sides of the equation are equal to 2418315, the equation is verified.

Therefore, lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers.

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The equation of the line in point-slope form is y - 2 = -3(x + 9), and in slope-intercept form is y = -3x - 25.

To find the equation of the line passing through(- 9,2) and parallel to the line y =  – 3x 3, we need to use the fact that  resemblant lines have the same  pitch.  

The  pitch of the given line y =  – 3x 3 is-3,

so the  pitch of the  resemblant line we want to find is also-3.   Point-  pitch form  Using the point-  pitch form, the equation of the line is given by

 y- y1 =  m( x- x1),

where( x1, y1) is the given point and

m is the  pitch.  

Substituting the given values,

we get   y- 2 = -3( x-(- 9))  

y- 2 = -3( x 9)  

y- 2 = -3 x- 27  

y = -3 x- 25

Hence in slope-intercept form is y = -3x - 25.

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a) The characteristic equation is r^2 + 11r + 28 = 0.

b) The associated homogeneous equation are y1(x) = c1e^(-4x) and y2(x) = c2e^(-7x).

c) The form of the particular solution is y_p(x) = Ae^(5x) + Bx + C.

d) By solving the system of equations, it gives A = 1/28, B = 1/28, and C = -211/196.

e) The general solution is y(x) = c1e^(-4x) + c2e^(-7x) + (1/28)e^(5x) + (1/28)x - 211/196.

a) The characteristic equation of the associated homogeneous equation is r^2 + 11r + 28 = 0.

b) Factoring the characteristic equation gives (r + 4)(r + 7) = 0, so the solutions to the associated homogeneous equation are y1(x) = c1e^(-4x) and y2(x) = c2e^(-7x).

c) The form of the particular solution is y_p(x) = Ae^(5x) + Bx + C. Taking the first and second derivatives of y_p(x) gives y_p'(x) = 5A + B and y_p''(x) = 0.

d) Substituting y_p(x), y_p'(x), and y_p''(x) into the original nonhomogeneous equation gives:

0 + 11(5A + B) + 28(Ae^(5x) + Bx + C) = e^(5x) + x + 4

Simplifying this equation gives:

(28A)e^(5x) + (28B)x + 11(5A) + 11B + 28C = e^(5x) + x + 4

Comparing coefficients gives the system of equations:

28A = 1

28B = 1

11(5A) + 11B + 28C = 4

Solving this system of equations gives A = 1/28, B = 1/28, and C = -211/196.

e) The general solution to the nonhomogeneous equation is y(x) = y_h(x) + y_p(x), where y_h(x) = c1e^(-4x) + c2e^(-7x) and y_p(x) = (1/28)e^(5x) + (1/28)x - 211/196. Therefore, the general solution is:

y(x) = c1e^(-4x) + c2e^(-7x) + (1/28)e^(5x) + (1/28)x - 211/196.

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Using various laws of integers we can say that if a is a positive integer and b is a negative integer, statement A is False, B is True, C s True and D is false.

Here we are given that a is a positive integer while b is a negative integer.

A. The statement says that the difference (a - b) could be negative.

According to the subtraction law of integers, when a negative number is subtracted from a positive number, that is we have

2 - (-3)

Here the 2 minus signs will make a positive to give

2 + 3 = 5

Hence (a - b) will be a positive number since b is negative.

B.

The difference (b - a) cannot be positive.

Since a is positive and b is negative, according to the above example we will get

-3 - 2 = -5

Hence it is true that the difference (b - a) can't be positive.

C.

The sum (a + b) could be positive.

Here, we can see that a is a positive number while b is a negative number. In the light of above example, we will get

2 - 3 = -1

Here the sum is nagative as 3 > 2, but if we had

3 + (-2), then the answer would have been 1. Hence (a + b) can be positive. Hence the statement is true.

D.

The sum (b + a) must be negative.

Integers have commutative properties. Hence a + b = b + a

Hence if a + b can be positive, then b + a can also be positive.

Hence the statement is False.

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Spencer will be on the phone for 56 minutes in total if he routes 28 calls.

Using unit rates, we can calculate how long Spencer will spend on the phone when routing 28 calls if he spent 10 minutes on the phone while routing 5 calls.

The amount of time spent on each phone call is the unit rate. In this instance, the unit fee is 10 minutes / 5 phone calls = 2 minutes each call.

In order to determine how much time Spencer will spend on the phone when routing 28 calls, we can use this unit rate as follows:

Therefore, Spencer will be on the phone for 56 minutes in total if he routes 28 calls.

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The volume of the prism in 120 cubic centimeter.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is a scalar quantity that characterizes the "size" or "capacity" of an object in three dimensions.

A prism is a three-dimensional geometric shape that has two parallel and congruent bases connected by lateral faces that are typically rectangular or parallelogram-shaped. Prisms are classified based on the shape of their base, such as rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on. The lateral faces of a prism are perpendicular to the bases, and the bases are usually parallel to each other.

According to the given information:

Given the measures of prism is length = 8cm, breadth = 6 cm, height = 5 cm

The formula for volume of prism = 1/2 l*b*h

                                                      = 1/2 8*6*5

                                                      = 120 cubic centimeter

Hence the volume of prism is 120 cubic centimeter.

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The evaluated missing length in right triangle by using the Pythagorean theorem is  9 yards under the condition given the triangle is a right triangle.

The Pythagoras theorem projects that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides,
It is given to us that in a right triangle,
Hypotenuse = 15 yd
Perpendicular = 12 yd

Therefore, applying Pythagoras theorem;
Base² = 15² - 12²

Base² = 225 - 144

Base² = 81

Base = √81

Base = 9 yards

Hence, The missing length present in the right triangle by applying the Pythagorean theorem is,
9 yards

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The complete question is

Determine the missing length in each right triangle using the Pythagorean theorem. Round the answer to the nearest tenth, if necessary

_______________________________

_______________________________

Based on the equation, when Lisa sells 24 copies of Math is Fun, her total pay will be $3140.

The equation relating P to N is:

P = 1700 + 60N

This is because her base salary is $1700, and she earns an additional $60 for each copy of Math is Fun she sells.

In order to find her total pay if she sells 24 copies of Math is Fun, we simply need to substitute N = 24 into the equation:

P = 1700 + 60(24)

P = 1700 + 1440

P = 3140

Therefore, if Lisa sells 24 copies of Math is Fun, her total pay will be $3140.

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So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.

To find the value of xa where the function is discontinuous, we need to look for any points where the function is undefined or where the left and right limits of the function are not equal.
(a) From the given information, we know that the function is undefined at xa = 16. So, this is the point of discontinuity.
(b) To find the left and right limits at xa = 16, we need to approach the point from both sides of the function. So,
lim f(x) as x approaches 16 from the left (denoted as lim-) = Im = 0
lim f(x) as x approaches 16 from the right (denoted as lim+) = Im = 16
Since the left and right limits are not equal, the limit as x approaches 16 does not exist. So,
lim f(x) as x approaches 16 (denoted as lim) does not exist.
(c) To determine which conditions for continuity are not met, we need to check if the function satisfies the three conditions for continuity at xa = 16.
i) The function must be defined at xa = 16. Since the function is undefined at xa = 16, this condition is not met.
ii) The left and right limits of the function must exist and be equal at xa = 16. Since the left and right limits are not equal, this condition is not met.
iii) The value of the function at xa = 16 must be equal to the limit of the function at xa = 16. Since the limit does not exist, this condition is also not met.
Therefore, none of the conditions for continuity are met at xa = 16.
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
Note: The terms "discontinuous" and "continuity" are used throughout the explanation to describe the concept and the point of interest. The term "function" refers to the given function that we are analyzing.

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C. All rectangles have four sides. All squares are rectangles. Therefore, all squares have four sides.

This is an example of deductive reasoning because it starts with a general statement (all rectangles have four sides) and then applies a specific example (squares are rectangles) to come to a logical conclusion (all squares have four sides).

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Answer:

rita and john are susseful the job

js school

The price of a new ticket after reducing the ticket price by 25% is $6. Maddy will need to sell 400 more tickets this year to raise the same amount of money as last year.

Number of tickets sold = 1200

Cost of each ticket = $8

Part A:

If Maddy lowers ticket costs by 25%, The price of a new ticket will be:

Ticket price = $8 - (25% of $8)

Ticket price = $6

The New ticket price will be calculated by multiplying 0.75 for reducing the 25% tickets

New ticket price = $8 x 0.75 = $6

Part B:

To find how many tickets Maddy requires to sell to equal the same amount of money collected in the previous year:

Total revenue = total number of tickets x Ticket price

1200 tickets x $8 per ticket = $9,600

= $9,600 / $6

= 1,600

Total tickets need to sell = 1600-1200 = 400

Therefore we can conclude that Maddy will need to sell 400 more tickets this year.

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Answer:

D. 53

Step-by-step explanation:

To calculate total length, just add all those lengths:

5.5 + 6 + (6.5 x 3) + (7 x 2) + 8

5.5 + 6 + 19.5 + 14 + 8

11.5 + 19.5 + 14 + 8

31 + 14 + 8

45 + 8

53

The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.

Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,

0.89x = 68

Solving for x,

x = 68 / 0.89

x ≈ 76.4

Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).

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