(06.04 HC)

Two friends wash cars to make extra money. The profit P(x) of one friend after x days can be represented by the function P(x) = −x2 + 5x + 12. The second friend's profit can be determined by the function Q(x) = 6x. Solve the system of equations. What solution is a viable answer to the question, "After how many days will the two students earn the same profit?" and which solution is a nonviable answer? Show your work and justify your answer.

The given function is f(x) = 5x³ - 40x² + 20x + 240, and we are given that f(4) = 0. We need to find the other two solutions to this function and determine the positive and negative solutions.

To find the other two solutions, we can use the fact that f(4) = 0. This means that when x = 4, the function evaluates to zero. By substituting x = 4 into the function, we get:

f(4) = 5(4)³ - 40(4)² + 20(4) + 240 = 0

Simplifying this equation, we have:

320 - 640 + 80 + 240 = 0

-320 + 320 = 0

Therefore, we see that the equation holds true, and x = 4 is one solution to the function.

To find the other two solutions, we can factor the given function or use numerical methods such as the Newton-Raphson method. Factoring the function is not possible in this case, so we will use numerical methods.

Using numerical methods, we find that the other two solutions to the function are approximately x ≈ -3.081 and x ≈ 2.581.

The positive solution is x ≈ 2.581, and the negative solution is x ≈ -3.081.

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The two triangles are said to be congruent by the SSS rule if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

Segments, or "triangles," are three-sided plane enclosed figures that can be classified according to their sides and angles. The typical variations include isosceles, equilateral, scalene, etc. So what exactly are congruent triangles? Triangles are said to be in congruence when all corresponding sides and interior angles are congruent (of the same length).

The triangles will be the same size and shape, but they will appear to be mirror images of one another. Simply put, objects that appear to be identical when placed over their opposites or that are Xerox copies of one another are said to be congruent.

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We would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g by using properties of the normal distribution.

To find the range in which you would expect to find the middle 68% of amounts of nicotine in these cigarettes, we can use the properties of the normal distribution.

Given:
Mean (μ) = 0.946 g
Standard deviation (σ) = 0.289 g

For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can expect the middle 68% of amounts of nicotine to fall within the range:

μ ± σ

Substituting the given values:

0.946 ± 0.289

To calculate the range, we have:

Lower bound = 0.946 - 0.289 ≈ 0.657 g
Upper bound = 0.946 + 0.289 ≈ 1.235 g

Therefore, we can expect to find the middle 68% of amounts of nicotine in these cigarettes to be between approximately 0.657 g and 1.235 g.

Now, if we were to draw samples of size 41 from this population, the standard deviation of the sample mean (also known as the standard error) can be calculated as:

Standard error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size.

Substituting the given values:

SE = 0.289 / √41 ≈ 0.045 g

To find the range in which we would expect to find the middle 68% of the sample means, we multiply the standard error by 1 to capture approximately 68% of the data, giving us:

Lower bound = μ - SE ≈ 0.946 - 0.045 ≈ 0.901 g
Upper bound = μ + SE ≈ 0.946 + 0.045 ≈ 0.991 g

Therefore, we would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g.

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Answer:

Nick get = $10

Pam get = $28.25

Step-by-step explanation:

Given:

Total amount paid = $38.25

Nick work = 1 hour 5 minutes = 1.0833 hr

Pam work = 3 hour

Find:

Amount they get

Computation:

Assume each get x in 1 hour

So,

3x + 1.0833x = 38.25

4.0833x = 38.25

x = 9.3674

Nick get = 1.0833(9.3674) = 10.14 = $10

Pam get = $38.25 - $10 = $28.25

The largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) is 15

Divisor of a Number :  

A Divisor is any number that divides a given number completely or with a reminder. Where a factor, is a divisor that divides the number entirely and leaves no remainder.

Here we have,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9)  

And n is a positive even integer  

For n = 2 ⇒  (2 + 1)(2 + 3)(2 + 5)(2 + 7)(2 + 9) = (3× 5 × 7 × 9 × 11 )    

For n = 4 ⇒   (4 + 1)(4 + 3)(4 + 5)(4 + 7)(4 + 9) = (5× 7 × 9 × 11 × 13 )

and so on.

From the above calculations,

we can say that (n + 1); (n + 3); (n + 5); (n + 7); (n + 9) are 5 consecutive odd numbers  

In every 5 consecutive odd positive integers,

One of them is always divisible by 3

And one of them is always divisible by 5.

Therefore,

(n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5

As we know product of 3 and 5 = 15

then (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15

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The complete question is

What is the largest integer that is a divisor of (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n?  

(A) 3         (B)  5        (C)  11          (D) 15             (E)  165    

The value of the given logarithm function is found to be  log3 a3log3 3 = 3.

The logarithm of a number in a given base is the power to which the base must be raised to obtain that number. The logarithm of x is written as logb(x) (read "log base b of x") and is defined as the power to which the base, b, must be raised to give the value x.  

Mathematically, it can be written as:logb(x) = y if by = x where b is the base of the logarithm, x is the number whose logarithm is to be found, and y is the logarithm of x in base b.

We are given log3a = −0.631 and we are to find the value of the expression log3 a3log3 3.

Step 1: Let's recall some properties of logarithm:

logb(b) = 1

logb(1) = 0

logb(xy) = logb(x) + logb(y)

logb(x/y) = logb(x) - logb(y)

We can simplify the given expression using these properties of logarithm:

log3 a3

log3 3= log3 (a3) + log3 3

Now we can simplify a³. We have a = 3log3a, therefore

a³ = (3log3a)³ = 33

log3a = 27log33

= 27

Therefore, a³ = 2

7Now, we can replace a³ with 27 in the expression log3 a³, and we have:

log3 27 = log3 (3³) = 3(log3 3)

We can substitute log3 3 with its value 1 and we have:

3(log3 3) = 3(1) = 3

Therefore, log3 a3log3 3 = 3.

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Answer:

1.631 on edge 2023 :}

Step-by-step explanation:

Answer:

2x+3r+16

Step-by-step explanation:

If you mean by simplify, here's the solution

2(x+6)+3r+4

2x+12+3r+4

2x+3r+16

Answer:

Other whole numbers that can be raised to a power to get 4,096 are  4, 8, 16 and 64

Step-by-step explanation:

Given;

2¹² = 4096

Other whole numbers that can be raised to a power to get 4,096 are obtained as follows;

\(if \ (a^x)^y = a^{xy}\\\\ (2^2)^6 = 4,096\\\\(4)^6 = 4,096\\\\Thus, \ the \ first \ whole \ number \ is \ 4\\\\(2^3)^4 = 4,096\\\\(8)^4 = 4,096\\\\Thus, \ the \ second \ whole \ number \ is \ 8\\\\(2^4)^3 = 4,096\\\\(16)^3 = 4,096\\\\Thus, \ the \ third \ whole \ number \ is \ 16\\\\(2^6)^2 = 4,096\\\\(64)^2 = 4,096\\\\Thus, \ the \ fourth \ whole \ number \ is \ 64\)

Therefore, Other whole numbers that can be raised to a power to get 4,096 are  4, 8, 16 and 64

The next term of the geometric sequence is 32

From the question, we have the following parameters that can be used in our computation:

2, -4, 8, -16, ___

The above definitions imply that we multiply -2 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

Next term = -2 * -16

Evaluate

Next term = 32

Hence, the next term is 32

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Since 1/4 is greater than 1/6 we can infer that Tiffany painted more of the room's wall.

Since most walls are square or rectangular, their surface area may be calculated by multiplying the width and height values, then taking out any spaces for doors or windows. However, unusual architecture and design might lead to the combination of the rectangle with triangular, round, or trapezoidal shapes. Using the fundamental formulas for estimating the area of two-dimensional forms is the key to accurately determining the surface area of a wall.

We must determine the precise dimensions of the parts Tiffany and Roberto painted in order to compare the quantity of each.

Assume for the moment that the wall is one unit in size. Tiffany then painted 1/4.

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Step-by-step explanation:

525 - 75 = 450

18 for ever one

equals to 450

18x = 450

450÷18 = x

450 ÷ 18 is

comment and i will check

please put brainest

Answer: 7e-5 millimeters, and the nanometer scale is more appropriate

Step-by-step explanation: PLEASE MARK ME BRAINLIEST!!!!!!

-divide the length value by 1e+6

-The millimeter scale and the centimeter scale are two huge, while the nanometer scale is too small. The nanometer scale is often used to measure atoms and viruses.

Answer:

a) The length of the virus in millimetres is 0.000 07 mm.

b) Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

Step-by-step explanation:

SI is the abbreviation for The International System of Units.

The SI base unit for length is metres (m).

Milli and nano are SI prefixes used to form decimal multiples or submultiples of SI units.

Therefore, to convert nanometres to millimetres, multiply the nanometres by 10⁻⁶:

So 70 nanometres is:

Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

Answer:

its 11.

hope it helps!!

Answer:

1stone is 8

2nd one is 15

3rd one is 6  

4th one is 48.5

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

\(x^2-8x=48\)

To solve for x, turn one side of the equation into 0 and solve. Therefore:

\(x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12\)

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

\(x+10\\(-4)+10\\=6\)

Beth drinks 7.2 ounces of orange juice, she will consume approximately 408 milligrams of potassium.

To find out how many milligrams of potassium Beth will consume when she drinks 7.2 ounces of orange juice, we can set up a proportion using the given information.

Let's set up the proportion:

12 ounces of orange juice contains 680 milligrams of potassium.

7.2 ounces of orange juice will contain x milligrams of potassium (unknown).

Using the proportion:

12 ounces / 680 milligrams = 7.2 ounces / x milligrams

Cross-multiplying, we get:

12 × x = 7.2 × 680

Simplifying:

12x = 4896

Dividing both sides by 12:

x = 4896 / 12

x ≈ 408

We may build up a percentage using the above data to determine how many milligrammes of potassium Beth will ingest when she drinks 7.2 ounces of orange juice.

Let's establish the ratio:

680 milligrammes of potassium are present in 12 ounces of orange juice.

The amount of potassium in 7.2 ounces of orange juice is x milligrammes (unknown).

Making use of the proportion

7.2 ounces / x milligrammes is equal to 12 ounces / 680 milligrammes.

The result of cross-multiplying is: 12 x = 7.2 680

To put it simply: 12x = 4896

x = 4896 / 12 x equals 408 when both sides are divided by 12.

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1. x-3y -3=0, 3x-9y-2=0 has no solution

2. 2x+y=5,3x+2y=8 has a unique solution

3. 3x-5y=20,6x-10y=40 has infinitely many solution

4.  x-3y-7 =0,3x-3y-15=0 has No solution

5. 8x+5y=9,3x+2y=4 has a unique solution

(i) To solve using substitution method, we can rearrange the first equation to x=3y+3 and substitute it into the second equation:

3(3y+3) - 9y - 2 = 0

9y + 9 - 9y - 2 = 0

7 = 0

This is a contradiction, so the pair of equations has no solution.

(ii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

3x + 2y = 8

(4x + 2y = 10)

-x = -2

So, x = 2. Substituting this value into the first equation, we get:

2x + y = 5

2(2) + y = 5

y = 1

Therefore, the unique solution is (x,y) = (2,1).

(iii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

6x - 10y = 40

(6x - 10y = 40)

0 = 0

This equation is true for any value of x and y, so the pair of equations has infinitely many solutions.

(iv) To solve using elimination method, we can subtract the first equation from the second equation:

3x - 3y - 15 - (x - 3y - 7) = 0

2x - 22 = 0

x = 11

Substituting this value into the first equation, we get:

11 - 3y - 7 = 0

-3y = -4

y = 4/3

Therefore, the unique solution is (x,y) = (11,4/3).

(v) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:

3x + 2y = 4

(16x + 10y = 18)

-29x - 18y = -14

Solving for y, we get:

y = (29/18)x + (7/9)

Substituting this expression for y into the first equation, we get:

8x + 5((29/18)x + (7/9)) = 9

(143/18)x = 2/9

x = 2/13

Substituting this value into the expression for y, we get:

y = (29/18)(2/13) + (7/9) = 41/117

Therefore, the unique solution is (x,y) = (2/13,41/117).

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Answer:

B

Step-by-step explanation:

60+40+x=180(angles in a triangle)

x= 180-100

x=80°

80+z=180(angles on a str line)

z= 100°

100+15+y=180(angles in a triangle)

y=180-115

y=65°

Answer:

c: x = 80, y = 65, z = 100

Step-by-step explanation:

The sum of all angles in a triangle is 180

so 40 + 60 + x = 180 and 15 + y + z = 180

40 + 60 + x = 180

100 + x = 80

x = 80

supplementary angles are equal to 180

x and z are supplementary

80 + z = 180

z = 100

15 + 100 + y = 180

115 + y = 180

y = 65

Answer:it's c

Step-by-step explanation:

It's - -1/4

Answer:

-1/4

Step-by-step explanation:

just did it

it A

Step-by-step explanation:

Answer:

The answer is H. I think :)

Input, output, domain, range, and inequality are all important concepts in mathematics.

The input is the value that is put into a function or equation to produce an output. It is typically denoted by the variable x. The output is the value that results from a function or equation when a given input is used.

The domain of a function is the set of all possible input values that can be used with the function. The range of a function is the set of all possible output values that can be produced by the function. An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as <, >, ≤, or ≥.

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Answer:

0

Step-by-step explanation:

The size of angle DAB in the quadrilateral is 49°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

∠A + ∠B + ∠C + ∠D = 360°

∠A + 34° + ∠C + 228° = 360°

∠A  + ∠C + 262° = 360°

∠A  + ∠C = 360 - 262

∠A  + ∠C = 98

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

∠A  + ∠A = 98

2∠A  = 98

∠A = 98/2

∠A  = 49°

Therefore, the size of angle DAB is 49°.

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Complete Question

Check the attached image

If person A and person B have equal positive amounts of goods X and Y and person A values good X more than good Y and person B values good Y more than good X, there are mutually beneficial trades available.

Mutually beneficial trades are the kind of trades that benefit both parties in a trade agreement. A mutually beneficial trade occurs when two countries or individuals trade and both benefit from the transaction. In the case where person A and person B have equal positive amounts of goods X and Y and person A values good X more than good Y and person B values good Y more than good X, there are mutually beneficial trades available. This is because person A would be more willing to trade his good Y for Person B’s good X since person A values good X more than good Y and person B would be more willing to trade his good X for person A’s good Y since person B values good Y more than good X. In this way, both parties would benefit from the transaction because they would be trading the goods they value less for the ones they value more.

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Answer:

4/3

Step-by-step explanation:

gradient=

\( \frac{change \: in \: y}{change \: in \: x?} \)

7--5=12

16-7=9

12÷9=4/3

the gradient is the same as slope

thus the answer is 4/3

Answer:

Yes

Step-by-step explanation:

they are both equal to 3:4

21:28 can be reduced by 7

21/7=3

28/7=4

and 6:8 can be reduced by 2

6/2=3

8/2=4

Answer:

We know that 6² = 36 , which is very close to 37 . Thus square root of 37 will be very close to 6