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In linear equation, 57 cents per cubic foot  should clint charge for a cubic foot .

What are a definition and an example of a linear equation?

cubic meter =  [3.28 ft ]^3  ≈ 35.29 cubic feet

So,

 price [ in cents] / 35.29  cubic feet  = 2000 / 35.29  ≈  57 cents per cubic foot

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The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

Answer

4: 22 degrees

3: (9,2)

Step-by-step explanation:

The charge on the capacitor for t > 0 is q(t) = (7/2)e^(-t/4)cos((3/4)t) + (35/6)e^(-t/4)sin((3/4)t) - (40/13)sin(2t) + (40/39)cos(2t).

The charge on the capacitor for t > 0 in an RLC series circuit with a voltage source E(t), a resistor of R ohms, an inductor of L henrys, and a capacitor of C farads, with initial current i(0) and initial charge q(0), is given by the solution to the differential equation q''(t) + (R/L)q'(t) + (1/LC)q(t) = E(t)/L with initial conditions q(0) = q(0) and q'(0) = i(0)/C.

In this case, we have E(t) = 40cos(2t), R = 2 ohms, L = 1/4 henrys, and C = 1/13 farads. We also have initial current i(0) = 0 and initial charge q(0) = 7/2 coulombs.

Using the characteristic equation of the differential equation, we find that the roots are complex conjugates with a real part of -R/2L = -1/4 and an imaginary part of sqrt((1/LC)-(R/2L)^2) = 3/4. Thus, the general solution is of the form q(t) = Ae^(-t/4)cos((3/4)t) + Be^(-t/4)sin((3/4)t).

Using the initial conditions, we can solve for A and B to get q(t) = (7/2)e^(-t/4)cos((3/4)t) + (35/6)e^(-t/4)sin((3/4)t) - (40/13)sin(2t) + (40/39)cos(2t).

Therefore, the charge on the capacitor for t > 0 is q(t) = (7/2)e^(-t/4)cos((3/4)t) + (35/6)e^(-t/4)sin((3/4)t) - (40/13)sin(2t) + (40/39)cos(2t).

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The linear equation that gives the rule for this table is y = -5x + 15

The table of values is given as:

x y

1 10

2 5

3 0

4 –5

On the above table, we can see that:

As x increases by 1, the value of y decreases by 5

This means that the slope is

Slope = -5

Also, the above table can be modified as follows (using the slope of -5)

x y

0 15

1 10

2 5

3 0

4 –5

This means that the y-intercept is

y-intercept = 15

A linear equation is represented as

y = slope * x + y-intercept

So, we have

y = -5x + 15

So, the equarion is y = -5x + 15

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Answer:

\(a + b = 5 \\ a \: = 5 - b \\ a - b = 4 \\ 5 - b - b = 4 \\ 5 - 2b = 4 \\ 5 - 4 = 2b \\ 1 = 2b \\ \frac{1}{2} = \frac{2b}{2} \\0.5 = b \\ b = 0.5 \\ a = 5 - b \\ = 5 - 0.5 \\ = 4.5 \\ {a \: }^{2} - {b}^{2} = ( {4.5}^{2}) - ( {0.5}^{2} ) \\ = 20.25 - 0.25 \\ = 20 \\ {a}^{2} - {b}^{2} = 20\)

Step-by-step explanation:

HOPE THAT THIS IS HELPFUL.

HAVE A GREAT DAY.

Answer:

2+2 = 4

Step-by-step explanation:

1+1= the answer

Multiplication: 4 significant figures

Division: 4 significant figures

Addition: 4 significant figures

To determine the number of significant figures, we need to count the non-zero digits in each number and any zeros between them.

For the number 6.429×10³, there are four significant figures: 6, 4, 2, and 9.

For the number 3.18785×10², there are six significant figures: 3, 1, 8, 7, 8, and 5.

When multiplying two numbers, the result should have the same number of significant figures as the least precise number in the calculation. In this case, the least precise number is 6.429×10³ with four significant figures. Therefore, the product will also have four significant figures.

When dividing two numbers, the result should have the same number of significant figures as the dividend (the number being divided). In this case, the dividend is 6.429×10³ with four significant figures. Therefore, the quotient will also have four significant figures.

When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places. However, since we are adding whole numbers here, the decimal places are not relevant. We only need to consider the significant figures. In this case, both numbers have four significant figures, so the sum will also have four significant figures.

In summary:

Multiplication: 4 significant figures

Division: 4 significant figures

Addition: 4 significant figures

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The equation given results in a cylinder with radius 3 as shown in the attached sketch.

An equation involving three variables can be represented as a three-dimensional domain. For those involving only two variables, we can use our knowledge of the plane equations to get an idea of ​​what the surface will look like.

Represented by the equation x² + z² = 9

We observe  that there is no y term, and as such y can be any value.

x² + z² = 9 is a circle in the xz plane with a radius of 3

We are then "pushing this along the y-axis, resulting in a cylinder with radius 3.

The sketch of the surface is as shown in the attached file.

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Answer:

3 + y = 18

y = 18 - 3

y = 15

Step-by-step explanation:

brainliest plz

15 is the answer.

3+15=18

A 90° rotation around the origin characterised the transition.

A logical principle that specifies the circumstances in which one assertion can be legitimately inferred from one or more other statements, particularly in codified languages.

(x, y)(x, y) is the formula for a reflection over the x-axis.

Triangle ABC was changed utilizing the (x, y) rule (–y, x). The triangles' vertices are displayed. A (–1, 1) B (1, 1) C (1, 4) (1, 4) A' (–1, –1) (–1, –1) B' (–1, 1) C' (–4, 1) (–4, 1) Which phrase best sums up the change? A 90° rotation around the origin characterised the transition. A 180° rotation of the origin occurred during the transformation.  The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

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Answer: A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'.

Step-by-step explanation: Took the test, no thanks neeeded :)

Total distance represented by the simplified expression for which the car was tested equals option c. x² + 2x - 4 .

Total distance drive on flat road = x miles

Total distance drive on downhill =  (x²+ 3) miles

Total distance drive on uphill =  ( x - 7 ) miles

Simplified expression which is equivalent to total distance drive by a car

= Distance drive on ( flat road + downhill + uphill )

= ( x +  x²+ 3 + x - 7 ) miles

= ( x² + 2x - 4 ) miles

Therefore, the simplified expression equivalent to the total distance drive by a tested car is equal to option c.  ( x² + 2x - 4 ) miles.

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The above question is incomplete , the complete question is:

A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road,    (x²+ 3) miles downhill, and (x - 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?

a.3x² _ 4

b. 3x² + 10

c. x² + 2x - 4

d. x² + 2x + 10

Answer:

\(2 log(x )- (3 log(y) + log(z) ) \\ \equiv log( {x}^{2} ) - log( {y}^{3} ) - log(z) \\ \equiv log( \frac{x {}^{2} }{ {y}^{3} + z} ) \)

The number of Grade 6 students were asked in total is 100 students.

Let the number of students who choose Natural History be x.

Since the number of students who chose the Museum of Math was 50 more than the number of students who chose the Museum of Natural History. This will be x + 50

The ratio of students who chose the Museum of Math to students who chose the Museum of Natural History was 3 to 1. The expression will be illustrated thus:

1/3 = x/x+50

Cross multiply

3x = x + 50

Collect like terms

3x - x = 50.

2x = 50

Divide

x = 50/2

x = 25

Also, x + 50 = 25 + 50 = 75

The number of Grade 6 students that were asked will be:

= 25 + 75

= 100

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Answer:

Step-by-step explanation:

                                                           4x + 1

The quotient   (f/g)(x) is    (f/g)(x) = ---------------

                                                          x^2 - 5

Note that x^2 means "square of x," whereas "x2" is ambiguous.

Answer:

30%

Step-by-step explanation:

1L = 1000ml

--------------------

100%-> 1000

1%-> 10

300 ÷ 10 = 30%

The limit of the given expression as x approaches 1 is 0.

To evaluate the limit of the given expression as x approaches 1, we can use L'Hopital's rule, which states that if the limit of a quotient of functions is of the form 0/0 or ±∞/±∞, then the limit can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the same point.

Using L'Hopital's rule on the given expression, we get:

lim x→1 [5x/(x-1) - 5/x] = lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)]

Plugging in x = 1 directly to this expression, we get:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = (5 - 10 + 5)/(1 - 1) = 0/0

Since the limit is still in an indeterminate form, we can apply L'Hopital's rule once again:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = lim x→1 [(10x - 10)/(2x - 1)] = 0

Therefore, the limit of the given expression as x approaches 1 is 0.

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Answer:

it's "urgent" not "ergent"

Step-by-step explanation:

hope this helps you learn how to spell! :)

The job will take 6 days if 5 workers are assigned to it.

we can use the concept of "worker-days." If it takes 2 workers 15 days to finish the landscaping job, we can calculate the total worker-days required to complete the job. Since 2 workers worked for 15 days, the total worker-days is 2 workers × 15 days = 30 worker-days.

If we increase the number of workers to 5, we can find the number of days required to complete the job by dividing the total worker-days by the number of workers. So, the job will take 30 worker-days ÷ 5 workers = 6 days.

Therefore, the landscaping job will take 6 days if 5 workers are assigned to it.

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Step-by-step explanation:

the distance between 2 points is the Hypotenuse of a right-angled triangle with the legs being the x coordinate difference and the y coordinate difference.

so, Pythagoras applies.

c² = a² + b²

distance² = (2 - -7)² + (11 - 9)² = 9² + 2² = 81 + 4 = 85

distance = sqrt(85) = 9.219544457... ≈ 9.2

The distance between the points A(2,11) and B(−7,9) is d = √85.

There are two points (a, b) and (c, d) then the distance between two points is

d= √(c -a)² + (d-b)²

We have the points A(2, 11) and B(-7, 9).

Using the Distance Formula

d = √(-7-2)² + (9-11)²

d= √(-9)² + (-2)²

d= √81 + 4

d = √85

Thus, the distance between points is √85 unit.

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Answer: Y= -9 + 3x/2

Step-by-step explanation: Down below Have a brilliant day-Lily ^_^

Answer:

The diameter of the floor is 6 yards

Step-by-step explanation:

Here, we are to calculate the diameter of a circular floor that has a circumference of 18.84 yards

Mathematically,

C = π * D

where C is the circumference

Plugging the values of the circumference , we have ;

18.84 = 22/7 * D

7 * 18.84 = 22D

D = (7* 18.84)/22 = 5.99 which is approximately 6 yards

Answer:

Answer choices A and D. E would also be correct but it's a perfect correlation and the question said "strong but not perfect"

Step-by-step explanation:

(c) To find the unique Bayesian Nash Equilibrium (BNE), we need to consider player 1's beliefs about nature's move and player 2's strategies.

In this game, player 1 observes nature's move, so player 1's information set is {A, B}. Player 1's strategy is to choose either L or R given their beliefs about nature's move. Let's denote player 1's strategy as s1(L) and s1(R). Player 2's strategies are U and D. Let's denote player 2's strategy as s2(U) and s2(D).

To find the BNE, we need to find the combination of strategies that maximize the expected payoffs for both players. In this case, the BNE can be determined as follows: If nature chooses A, player 1 should choose s1(L) to maximize their payoff (0). If nature chooses B, player 1 should choose s1(R) to maximize their payoff (-3). For player 2, they should choose s2(U) to maximize their payoff (-20) regardless of nature's move. Therefore, the unique BNE is (s1(L), s2(U)). The expected equilibrium payoffs for both players are:  Player 1: E1 = 0.5(0) + 0.5(-3) = -1.5. Player 2: E2 = 0.5(-20) + 0.5(-20) = -20

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The mean of the given data is approximately 39.7.

The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.

In the given data set, the mean can be calculated as the sum of all the values divided by the number of entity in the data.

mean = {33.2+38.6+41.9+44.0+42.9+36.2+41.7+39.8+43.5+30.5+39.2} / 12

mean = 119 / 3

mean = 39.7

The mean of the data set is calculated as 39.66666 which is approximately 39.7.

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Answer:

868.5

Step-by-step explanation:

18 times 40 = 720

720 + 5 times 27 =135

135 + 27 divided by 5 = 13.5

720+135+13.5= 868.5

The P-value for this test is the probability of observing a z-score as extreme or more extreme than 22.75, assuming the null hypothesis is true.

To conduct this hypothesis test, we can use the normal distribution as an approximation to the binomial distribution. Since the sample size is large (963 babies), we can assume that the sampling distribution of the sample proportion of girls is approximately normal. The sample proportion of girls is 873/963=0.906, which is the point estimate of the population proportion of girls born to parents using the new method.

To calculate the test statistic, we need to determine the standard error of the sample proportion.

Where p is the hypothesized population proportion (0.5 for boys and 0.5 for girls), and n is the sample size (963).

Using this formula, we get SEp=√[(0. 5x (1-0.5))/963]=0.016.

The z-score can be calculated as:

z=(p-p)/SEp

where p is the sample proportion and p is the hypothesized population proportion (0.5).

Using the values from the sample, we get z=(0.906-0.5)/0.016=22.75.

This can be calculated using a standard normal distribution table or a statistical software such as Statcrunch. The P-value turns out to be very small, much less than the chosen significance level of 0.01.

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