Road surfacing gangs are made up of a fixed number of workers and machines.Three gangs have surfaced 20 km of road in 10 days.How many additional gangs should be brought in if all the work is to be finished in another 15 days and there is still 50 km of road to be surfaced?(You should assume that their work does not interfere with each other.)Please use algebra if possible and state any formulas used.

Answer:

Step-by-step explanation:

The difference:

If Tito took a loan of $10000 from a bank to be repaid within 4 years, at 12% Simple interest per annum, then, he will have to pay overall $4800 as interest to the bank over 4 years and a total payment of $14800 at the end of the 4th year to repay and close off the loan.

As per the question statement, a bank charges 12% Simple interest per annum on cash loans to its clients and Tito took a loan of $10000 from the same bank to be repaid within 4 years.

We are required to calculate the overall interest Tito has to pay to bank if he repays and closes the loan at the end of 4th year, and also to calculate the total payment required to repay and close off the loan at the end of the 4th year.

To solve this question, we need to know the formula to calculate the interest amount in case of simple interest which goes as

Interest (I) \(=(\frac{P*R*T}{100} )\)

where, "P" = Principle amount of Loan,

"R" = Rate of simple interest charged on the principle per annum, and

"T" = Time period within which, the loan is to be repaid.

Here, (P = 10000), (R = 12%) and (T = 4). Then, the overall interest Tito will have to pay at the end of 4th year  = \((\frac{10000*12*4}{100}) = (100*12*4)=(48*100)=4800\)

And total amount to be paid to repay and close of the loan at the end of 4th year will be = $[4800 + 10000] = $14800.

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Answer: 135 x 5 = 655 it took 655 miles park city to Rainey

Answer:

$520.437

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

a)

The value of k is 0.61.

b)

The population in 2010 is 739013.

The population in 2015 is 15604434.

c)

In 5.2 years, the population will reach 2.5 million.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

P = 1657.5 \(e^{kt}\)

P is the population in t years.

Now,

In 2000, t = 0,

a)

In 2005, t = 5 and P = 1940,000

So,

P = 1657.5 \(e^{kt}\)

1,940,000 = 1657.5 \(e^{5k}\)

1940000/1657.5 = \(e^{5k}\)

1170.44 = \(e^{5k}\)

Taking logs on both sides.

log 1170.44 = 5k

3.07 = 5k

k = 0.61

b)

In 2010, t = 10

So,

kt = 0.61 x 10 = 6.1

P = 1657.5 \(e^{6.1}\)

P = 1657.5 x 445.86

P = 739012.95

P = 739013

In 2015, t = 15

So,

P = 1657.5 \(e^{9.15}\)

P = 1657.5 x 9414.44

P = 15604434

c)

P = 2.5 million = 2,500,000

Now,

P = 1657.5 \(e^{6.1}\)

Solve for t.

2,500,000 = 1657.5 \(e^{0.61t}\)

2500000/1657.5 = \(e^{0.61t}\)

1508 = \(e^{0.61t}\)

Taking logs on both sides.

log 1508 = 0.61t

3.18 = 0.61t

t = 3.18/0.61

t = 5.21

t = 5.2

Thus,

a)

k = 0.61

b)

P = 739013 in 2010

P = 15604434 in 2015

c)

In 5.2 years, the population will reach 2.5 million.

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The measure of the arc AT in this problem is given as follows:

mAT = 159º.

The measure of arc AT is obtained applying the two secant theorem, which states the angle measure of intersection of the two secant segments is half the difference of the measure of the far arc by the measure of the near arc.

The parameters for this problem are given as follows:

Hence the measure of the arc AT in this problem is given as follows:

(mAT - 59)/2 = 50

mAT - 59 = 100

mAT = 159º.

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Answer: angle 1 = 51, angle 2 = 18, angle 3 = 123, angle 4 = 39

Step-by-step explanation:

72+57=129 180-129= 51 degrees for 1

90-72= 18 degrees for 2

180-57= 123 degrees for 3

123+18=141 180-141= 39 degrees for angle 4

The number of men which it will take which will be needed for the same job to be completed in 2 days is; Choice A; 9 men.

It follows from the task content that 6 men did the work in 3 days and hence, to determine the number of men capable of completing the work 2 days, we must evaluate as follows;

Total work = 6men × 3 days = 18 men days.

Hence, for 2 days; = 18/2 = 9 men.

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Answer:

78

Step-by-step explanation:

you have to multipy 13 and 12 then divide it by 2.(13*12=156/2=78)

Answer: 5x 5y

Step-by-step explanation: because of the length

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

B. g(x)=(2x)^2

Step-by-step explanation:

this is right

Answer:

t = 2 and t = 3.

Step-by-step explanation:

To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:

2^t = 4Taking the logarithm base 2 of both sides:

t = log2(4)

t = 2For u = 8:

2^t = 8Taking the logarithm base 2 of both sides:

t = log2(8)

t = 3

Answer:

9 students chose duck

Step-by-step explanation:

The question says "6 more students chose duck than chose penguin"

This means that you would add 6 to the number that chose penguin, which is 3.

6 + 3 = 9

Answer:

9

Step-by-step explanation:

6+3=9

and this is very is easy

The measure of the angle of the trapezoid is:

∠W = 110°

∠X =  110°

∠Y = 70°

∠Z = 70°

For an isosceles trapezoid, the base angles are equal. That is:

∠Z = ∠Y

∠W = ∠X

Since ∠X = (13x -7)° and ∠Y = (8x -2)°. Thus:

∠Z = (8x -2)°

∠W = (13x -7)°

Also, the sum of opposite angles an isosceles trapezoid is 180°. That is:

∠W + ∠Y = 180° and ∠Z + ∠X = 180°

Thus, we can say:

(13x -7)° + (8x -2)° =  180°

21x - 9 = 180

21x = 180 + 9

21x = 189

x = 189/21

x = 9

Substitute x = 9:

∠W = (13x -7)°

∠W = 13(9) - 7

∠W = 110°

∠X =  110° (∠X = ∠W)

∠Y = (8x -2)°

∠Y = 8(9) -2

∠Y = 70°

∠Z = 70°  (∠Z = ∠Y)

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The required conjecture is framed. And the coordinates are plotted.

The loci of point 5 units from the origin is a circle of radius 5 centred on the origin (red)

The loci of points 3 units from the x-axis is two parallel lines y=±2(blue)

Visually we can see there are 4 such points of intersection.

The loci of the circle is:

x²+y² = 25

The loci of the two lines are:

y = ±2

At a point of intersection we have both equation satisfied simultaneously; thus:

x² + (±2)² = 25

x² + 4 = 25

x² = 21

x = ±√21

Thus we have the four coordinates (all possible permutations) of:

coordinates (±√21 , ±2)

(-√21,2) , (-√21,-2) , (√21,2) and (√21,-2)

Hence we get the required conjecture.

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Your question is incomplete. Please find the missing content below.

Make a Conjecture Find as many points as you can that are 5 units from

the origin and 2 units from the x axis. Make a conjecture about the shape formed if all the points

5 units from the origin were connected.

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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Answer:

Option C.

Step-by-step explanation:

If we have two functions:

f(x) and g(x)

the product is given by:

(f*g)(x) = f(x)*g(x)

So, if here we have

f(x) = √(3*x)

g(x) = √(48*x)

And remembering that the square root is distributive, so:

√a*√b = √(a*b)

We can write:

(f*g)(x) = f(x)*g(x) = √(3*x)*√(48*x) = √(3*x*48*x)

          = √(3*48*x*x) = √(144*x^2) = √(144)*√(x^2)

And here we can use that:

12*12 = 144, then √144 = 12

and

x*x = x^2, then √x^2 = x

So:

√(144)*√(x^2) = 12*x

Then the correct option is C.

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

(a) for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.

(b) f(x, y) = |x| - |y| is not onto.

(a) To show that the function f(x, y) = 2x - 4y is onto, we need to show that for every integer z, there exists integers x and y such that f(x, y) = z.

Let z be an arbitrary integer. Then we need to find integers x and y such that 2x - 4y = z. We can rewrite this equation as x = (z + 4y)/2.

Now, if z is even, then we can choose any even number for y and solve for x using the above equation. Conversely, if z is odd, we can choose any odd number for y and solve for x.

Therefore, for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.

(b) To show that the function f(x, y) = |x| - |y| is not onto, we need to find an integer z such that there does not exist integers x and y such that f(x, y) = z.

Let z = -1. Then we need to find integers x and y such that |x| - |y| = -1. However, the absolute value of any integer is non-negative, so |x| and |y| are both non-negative.

Therefore, |x| - |y| is non-negative, and it is impossible for f(x, y) to equal -1.

Hence, there does not exist integers x and y such that f(x, y) = -1, and thus f(x, y) is not onto.

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Both representations are equivalent and describe the same function.the function rule for this table is:   f(x) = -1/2 x 2

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.

To write a function rule for a given array, we need to determine how the values ​​in the output column (y) relate to the values ​​in the input column (x).

Looking at the given data, we notice that the output values ​​decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .

The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values ​​decrease by 1 every time the input values ​​increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.

Therefore, the function rule for this table is:

f(x) = -1/2 x 2

where x is the input value and f(x) is the output value.

Alternatively, we can also represent the function in table entries, for example:

f(0) = 2

f(2) = 1

f(4) = 0

f(6) = -1

Both representations are equivalent and describe the same function.

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Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

20=5(4)

Step-by-step explanation:

make it a linear function make the x-axis adults and the y-axis students and for every 1 adullt go up by 5 student

Answer:

C)  y = -3x + 5

Step-by-step explanation:

(0,5) represents the point where the line intersects the y-axis; we can eliminate answers A and D as they don't indicate that

to find the slope we can use these two points:

(-1,8)(0,5)

slope = (8-5)/(-1-0) = -3

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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Answer:

180

Step-by-step explanation:

IF  you

Answer:

38.465

i used 3.14 for pi

Step-by-step explanation:

The restriction of a function f is when the domain of f is limited to a subset of its original domain.

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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The graph of the function g(x) = x + 3 is a straight line that passes through the point (0, 3) on the y-axis and has a slope of 1.

To understand how to plot the graph, let's consider a few points on the line.

We can choose any values for x and calculate the corresponding values for g(x).

Let's start with x = 0.

Substituting this value into the function, we get g(0) = 0 + 3 = 3.

So, the point (0, 3) is on the graph.

Next, let's choose x = 1.

Substituting this value into the function, we get g(1) = 1 + 3 = 4.

This gives us another point on the line, (1, 4).

Similarly, we can choose more values for x and calculate the corresponding values for g(x).

For example, if we let x = -1, we get g(-1) = -1 + 3 = 2, giving us the point (-1, 2).

By connecting these points and extending the line in both directions, we obtain a straight line that represents the graph of g(x) = x + 3.

The line has a positive slope of 1, which means it rises by 1 unit vertically for every 1 unit it moves horizontally.

Overall, the graph of g(x) = x + 3 is a straight line that passes through the point (0, 3) and has a slope of 1.

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Answer:

Donde esta el foto

Step-by-step explanation:

translation: how do we answer the mf question without context

Answer:

45% value looked it up

Step-by-step explanation:

byéeeee