Let's denote crew A's work per week as A and crew B's work per week as B.
We are given that A = 58 ft per week and B = 59 ft per week.
We have to calculate how many weeks it will take both crews to complete the tunnel.
585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.
Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.
Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)
= (7020 ft) / (58 ft/week + 59 ft/week)
= 120.20 weeks
Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.
in long division what is the working and answer for 348 divided by 4?
4 will divide the 348 is 8 and 2 left, so you will write the two and move the 8 down, which is now 28, then divide the 28 by 4. It will be 7.
find the quotient : 6x/(3x+15) divided by (x^2+2x)/ (x^2+7x+10)
The quotient of[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.
To simplify the expression[tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10)),[/tex] we can use the rule for dividing fractions, which states that dividing by a fraction is the same as multiplying by its reciprocal.
Let's simplify the expression :
Simplify the numerator and denominator of the first fraction.
The numerator is 6x, and the denominator is (3x+15).
We can factor out a common factor of 3 from the denominator, which gives us 3(x+5).
So the first fraction simplifies to 6x / 3(x+5).
Simplify the numerator and denominator of the second fraction.
The numerator is (x^2+2x), and the denominator is [tex](x^2+7x+10).[/tex]
We can factor both the numerator and denominator:
Numerator: x(x+2)
Denominator: (x+5)(x+2)
Canceling out the common factor of (x+2), we are left with x / (x+5).
Multiply the two simplified fractions.
Multiplying the fractions, we get:
[tex](6x / 3(x+5)) \times (x / (x+5))[/tex]
Simplify the resulting expression.
Canceling out the common factor of (x+5) in the numerator and denominator, we are left with:
2x / 1
So the quotient simplifies to 2x.
Therefore, the quotient of [tex](6x/(3x+15)) / ((x^2+2x)/ (x^2+7x+10))[/tex] is 2x.
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How many of which types of roots does f(x) = 7x5 - 3x³ + 5x + 2 have?
Answer:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x = 5/7,−3,3
Step-by-step explanation:
These shapes are similar.
Find X.
5
X
5
30
24
30
The value of x is 4.
To determine the value of x, we can use the concept of similarity between shapes.
Similar shapes have corresponding sides that are proportional to each other.
Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:
5/x = 30/24
To solve for x, we can cross-multiply:
30 · x = 5 · 24
30x = 120
Dividing both sides of the equation by 30:
x = 120 / 30
x = 4
Therefore, the value of x is 4.
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Determine the first five terms of the following generalized Fibonacci sequence. Please enter the five terms in the boxes provided in sequential order. Please simplify your solution.
The first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4
Finding the first five terms of the following generalized Fibonacci sequenceFrom the question, we have the following parameters that can be used in our computation:
The generalized Fibonacci sequence
In the sequence, we can see that the last two terms are added to get the new term
Also, we have
a(1) = -19
a(2) = 14
Using the above as a guide, we have the following:
a(3) = -19 + 14 = -5
a(4) = -5 + 14 = 9
a(5) = 9 - 5 = 4
Hence, the first five terms of the following generalized Fibonacci sequence are -19, 14, -5, 9, 4
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what is equivalent to 3³
Answer:
Step-by-step explanation:
3x3x3= 27
A merchant has 1500 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Answer:
900 kg
Step-by-step explanation:
Let's assume the cost price (C.P.) of sugar is Rs. x per kg.
The total quantity of sugar is 1500 kg.
Let the quantity of sugar sold at 8% profit be represented by y kg.
The quantity of sugar sold at 18% profit would then be (1500 - y) kg.
Using the rule of alligation, we can set up the following proportion:
(8% profit) y kg
-------------- = ------
(18% profit) (1500 - y) kg
Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).
The ratio of these differences is 2:3.
This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.
Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:
(2 kg) * (3/2) = 3 kg
Therefore, the quantity sold at 18% profit is 900 kg.
If 9x - 3y = -10 and 3x - 4y = 1 are true equations, what would be the value
of 12x-7y?
Answer:
Step-by-step explanation:
9x-3y=-10 ...............(1)
3x-4y=1...............(2)
multiplying equation (2) by 3
9x-12y=3...................(3)
Using elimination method, then
9x-3y=-10 ...............(1)
9x-12y=3...................(3
9y= -13
y= -13/9
substituting y= -13/9 in equation (1) then
9x-3(-13/9)= -10
9x+13/3= -10
multiplying throughout by 3
27x+13= -30
27x= -30-13
27x= -43
x= -43/27
since x and y values are known, then
12x-7y = 12(-43/27) - 7(-13/9)
12x-7y = -516/27 + 91/9
12x-7y = -9
Please and this question ASAP. Multiply 31.5 percent times 600
Answer:
189
Step-by-step explanation:
To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.
31.5 percent = 31.5/100 = 0.315
Multiplying 0.315 by 600 gives us:
0.315 * 600 = 189
Therefore, 31.5 percent of 600 is equal to 189.
find the length represented by x for each pair of similar triangles 12in x 20in 15in 40in 25in
The length x in the similar triangles is given as follows:
x = 15 cm.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The proportional relationship for the side lengths in this triangle is given as follows:
x/25 = 9/15 = 18/30
Hence the value of x is obtained as follows:
x/25 = 9/15
15x = 25 x 9
x = 25 x 9/15
x = 15 cm.
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7. How a change in fixed costs affects the profit-maximizing quantity
Manuel owns and operates a hot dog stand in downtown New York City. In order to operate his hot dog stand, regardless of the number of hot dogs sold, Manuel must purchase a permit from the local government in New York City. Manuel's initial profit hill is plotted in green (triangle symbols) on the following graph.
Suppose the price Manuel must pay for a permit decreases by $10 per day.
On the following graph, use the purple diamond symbols to plot Manuel's new profit hill, for 0, 10, 20, 30, 40, 50, 60, and 70 hot dogs, after the decrease in the price of a permit (with all other factors remaining constant).
you can tell that Manuel initially faces a fixed cost of $ per day.
Initially, Manuel's profit-maximizing level of output is hot dogs per day. After the price of a permit falls, Manuel's profit-maximizing level of output is hot dogs per day.
Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.
In order to answer your question accurately, I would need the specific values for Manuel's profit and cost functions. The information you provided is incomplete, as you mentioned Manuel's initial profit hill is plotted in green on a graph, but the graph itself is not available for reference.
To determine how a change in fixed costs affects the profit-maximizing quantity, we typically analyze the cost and revenue functions. Without these functions or the corresponding data, it is not possible to provide an exact numerical answer.
However, I can explain the general concept. Fixed costs are expenses that do not change with the level of output or production. Examples of fixed costs in Manuel's case might include the permit cost, rent for the hot dog stand, or insurance premiums.
When fixed costs decrease, it reduces the overall cost of production for each level of output. This means that Manuel can achieve higher profits or reduce losses for any given level of sales. Consequently, the profit-maximizing quantity may change as a result.
If we assume that the decrease in the price of the permit is the only change in fixed costs and all other factors remain constant, the new profit hill can be expected to shift upward. This is because the reduction in fixed costs increases the potential for higher profits at each level of output.
Without more specific information about Manuel's profit and cost functions, it is not possible to determine the exact profit-maximizing levels before and after the decrease in the price of the permit.
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Which expression represents the total surface area of the prism shown?
The expression represents the total surface area of the prism is
2 (5 * 7) + 2 (4 * 7) + 2 (4 * 5)
How to solve for the TSA of the prismThe term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the sum of the areas of all the faces (including the bases) of the prism.
for the rectangular prism, the Total Surface Area can be calculated using the formula:
TSA = 2lw + 2lh + 2wh
where
l = 5
w = 4
h = 7
plugging in the values gives
TSA = 2 (5 * 7) + 2 (4 * 7) + 2 (4 * 5)
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Solve for a. Round your answer to the nearest tenth if necessary. 10.7 N X P 22.2 R 17.8
Answer:
Step-by-step explanation:
the answer is 69 the if we round of
The express that is equivalent is?
Step-by-step explanation:
Multiply the L side of the equation by d/d ( this is just multiplying by 'one' )
2/d * d/d = 2d / d^2
Here is a rectangle:
2
3
2 cm
Find the area of the rectangle.
cm²
The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².
To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.
Area of the rectangle = Length * Width
Plugging in the given values:
Area = 3 cm * 2 cm
Multiplying 3 cm by 2 cm gives us:
Area = 6 cm²
Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².
The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).
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if f(x)=x+2/x^2-9 and g(x)=11/x^2+3x
A. find f(x)+g(x)
B. list all of the excluded values
C. classify each type of discontinuty
To receive credit, this must be done by Algebraic methods, not graphing
The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
A. To find f(x) + g(x), we add the two functions together:
f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)
To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:
f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]
Simplifying the numerator:
f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]
Combining like terms:
f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]
B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:
(x^2 - 9) = 0 --> x = -3, 3
(x^2 + 3x) = 0 --> x = 0, -3
So, the excluded values are x = -3, 0, and 3.
C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.
At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.
At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.
Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.
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6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable
The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.
What is the solutuon to the given equation?Given the equation in the question:
6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31
To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.
Apply distributive property:
6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31
18x + 24 + 4x + 4 + 2 = 22x + 31
Collect and combine like terms on both sides:
22x + 30 = 22x + 31
Next, we want to isolate the variable x on one side.
22x - 22x + 30 = 22x - 22x + 31
30 = 31
However, we notice that the x terms cancel out when subtracted:
30 ≠ 31
This means that there is no solution.
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The graph shows a function of the form () = ab
.
Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function.
Answer:
When [tex]x=0[/tex], the value of f(x) is 1.
Each time x increases by 1, f(x) is multiplied by 4.
Equation of function: [tex]f(x)=1\cdot 4^x[/tex]
Step-by-step explanation:
The detailed explanation is attached below.
6 in.
3.2 in.
2 in.
3.2 in.
1 in.
square inches
1 in.
The container will be made from cardboard. How many
square inches of cardboard are needed to make one
container? Assume there are no overlapping areas.
The square inches of cardboard paper used is 56.8 square inches
Calculating the square inches of cardboard paperFrom the question, we have the following parameters that can be used in our computation:
The prism
The square inches of cardboard paper is the surface area of the pyramid
And this is calculated as
Area = bh + L(Sum of side lengths)
Using the above as a guide, we have the following:
Area = 2 * 3.2 + 6 * (2 + 3.2 + 3.2)
Evaluate
Area = 56.8
Hence, the square inches of construction paper used to make the container is 56.8 square inches
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The class had 7 tests, on which he scored 85, 93, 78, 90, 88, 97, and 88.
What is the mean?
A class contains 5 girls and 7 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.
Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.
Determine the total number of students in the class. That is 5 + 7 = 12.
Determine the number of ways to select two students from the class.
Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.
In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).
C(12, 2) = 12! / (2!(12-2)!) = 66.
Determine the number of favorable outcomes.
In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.
To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):
Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.
So, the probability of selecting a girl and a boy for the class committee is 5/6.
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-) Aspirin has a half-life of 6 hours in the blood stream. If a person takes 625mg, how long will it take for there to be 150mg left in the bloodstream?
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
We have,
To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.
The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.
Let's calculate the number of half-lives required to reach 150mg:
Initial amount of aspirin = 625mg
Final amount of aspirin = 150mg
625mg / 150mg = 4.17
This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.
Since each half-life is 6 hours, we can calculate the total time it will take:
Total time = Number of half-lives * Half-life duration
Total time = 4.17 x 6 hours
Total time ≈ 25 hours and 1 minute
Therefore,
It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.
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answer right all 3 and all the points go to you
The length of the arc can be obtained as follow:
Radius (r) = 7 ftAngle (θ) = 210 °Length of arc =?Length of arc = 2πr × (θ / 360)
Length of arc = (2 × π × 7) × (210 / 360)
Length of arc = 49π / 6 ft (option D)
How do i determine the area of the sector?
i. The area of the sector can be obtained as shown below:
Radius (r) = 19 inAngle (θ) = 135 °Area of sector =?Area of sector = πr² × (θ / 360)
Area of sector = (π × 19²) × (135 / 360)
Area of sector = 1083π / 8 in² (option D)
ii. The area of the sector can be obtained as shown below:
Radius (r) = 10 mAngle (θ) = 165 °Area of sector =?Area of sector = πr² × (θ / 360)
Area of sector = (π × 10²) × (165 / 360)
Area of sector = 275π / 6 m² (option B)
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what is an example of "The restriction of a function f"?
The restriction of a function f is when the domain of f is limited to a subset of its original domain.
What is an example of "The restriction of a function f"?The restriction of a function f can be demonstrated by considering a function f: R -> R, where R represents the set of real numbers.
Let u say f(x) = x^2. Now, if we restrict the domain of f to the interval [0, 5], the new function becomes f restricted: [0, 5] -> R and its expression would be f restricted(x) = x^2 for x in the interval [0, 5].
This means that the function f restricted only takes inputs from the interval [0, 5] and behaves the same way as the original function within that interval.
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enter the number that belongs in the green box 4 29 10
Answer:
Set your calculator to degree mode.
x^2 = 4^2 + 10^2 - 2(4)(10)(cos 29°)
x^2 = 46.0304
x = 6.78
The number that belongs in the green box is 6.78.
dos aviones de parte de una ciudad a las 8 AM el primer avión quiso regresar a la ciudad 5 horas y el segundo avión regresa casa 3 horas en cuanto tiempo volverán a dentrar a la ciudad
Both planes will reach the city at the same time again at 11 PM.
How to deal with periodic events?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for this problem are given as follows:
5 hours.3 hours.As 5 and 3 are prime numbers, the least common factor is given as follows:
5 x 3 = 15.
15 hours after 8 AM is of 11 PM.
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the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
Find the equation of a parabola with focus (3, 4) and directrix y = 1.
The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]
To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:
[tex]4p(y - k) = (x - h)^2[/tex]
where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.
In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).
The directrix is given as y = 1.
First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.
Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.
Now that we have the value of p, we can substitute it into the equation:
[tex]4p(y - k) = (x - h)^2[/tex]
Plugging in the values (h, k) = (3, 4) and p = 3, we get:
[tex]4(3)(y - 4) = (x - 3)^2[/tex]
Simplifying further:
[tex]12(y - 4) = (x - 3)^2[/tex]
Expanding the equation:
[tex]12y - 48 = x^2 - 6x + 9[/tex]
Bringing all terms to one side:
[tex]x^2 - 6x - 12y + 57 = 0[/tex]
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From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
,
,
The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3
How to determine the x-coordinates where the graphs of the equations intersect?From the question, we have the following parameters that can be used in our computation:
y = 2x
y = x² - 3
The x-coordinates where the graphs of the equations intersect is when both equations are equal
So, we have
x² - 3 = 2x
Rewrite the equation as
x² - 2x - 3 = 0
When the equation is factored, we have
(x + 1)(x - 3) = 0
So, we have
x = -1 and x = 3
Hence, the x-coordinates are x = -1 and x = 3
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Question
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
y = 2x
y = x² - 3
factor completely using distributive law -14-(-8)
Answer: To factor the expression -14 - (-8) completely using the distributive law, we need to simplify it first.
Remember that when we subtract a negative number, it is equivalent to adding the positive number. Therefore, -(-8) is the same as +8.
So the expression becomes:
-14 + 8
To factor it further using the distributive law, we can rewrite the addition as multiplication by distributing the -14 to both terms:
(-14) + (8) = -14 * 1 + (-14) * 8
This can be simplified as:
-14 + 8 = -14 * 1 + (-14) * 8 = -14 + (-112)
Finally, we can add the two negative numbers to get the result:
-14 + (-112) = -126
Therefore, the expression -14 - (-8) factors completely as -126.
