The values in the table represent a function.

A 2-column table with 5 rows. The first column is labeled x with entries negative 2, 1, 4, negative 3, 0. The second column is labeled f of x with entries 1, 3, negative 2, 0, 4.

Use the drop-down menus to complete the statements.



The ordered pair given in the first row in the table can be written using function notation as
.

f(x) = –2 when x is

Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

The equation of the line shown in the graph, from (–2,2) to (–3,–1) is y = -5/4x – 7/4.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

To solve for the equation of the line, we can use the point-slope formula, y – y1 = m(x – x1), where m is the slope of the line and (x1, y1) is a point on the line. In this case, the point (x1, y1) is (–2,2) and the slope of the line is m = (–1 – 2)/(–3 – (–2)) = –3/–1 = 3. Therefore, the equation of the line is y – 2 = 3(x – (–2)).

Simplifying, we get y = 3x + 2. To put the equation in the slope-intercept form, y = mx + b, we can rewrite the equation as y = 3x + 2 = 3x + 2 – 2 = 3x – 2 + 2 = 3x – 2, which is the equation of the line, y = –5/4x – 7/4.

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The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3.

Equation is a mathematical statement that states the equality of two expressions. It contains an equal sign (=) and expresses the relationship between two values, expressions or functions. Equations are used to solve for unknown values, to describe relationships between variables, and to model and solve real-world problems.

The equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This line is a horizontal line, which means that all points on the line have the same y-coordinate.

To verify this equation, we can use the two points given on the graph: (-2,-3) and (3,-3). Using the slope-intercept form of a line, we can plug in the points to determine the equation of the line.

The slope-intercept form is y = mx + b, where m is the slope, x is the x-coordinate, and b is the y-intercept. The slope is calculated by finding the change in y over the change in x. In this case, both points have the same y-coordinate, so the slope is 0. Therefore, the equation of the line is y = 0x + b.

Plugging in the coordinates of one of the points, (-2,-3), we get -3 = 0x + b. By solving for b, we get b = -3. Substituting b into the equation, we get y = 0x - 3. This is the equation of the line shown in the graph.

In conclusion, the equation of the line shown in the graph is y = -3. This equation states that for every y-coordinate on the graph, the corresponding x-coordinate is -3. This equation was verified by using the slope-intercept form of a line and plugging in the two points given on the graph.

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Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then then corresponding sides are in proportion , that is

\(\frac{NP}{ST}\) = \(\frac{NM}{SR}\) , substitute values

\(\frac{x}{25}\) = \(\frac{18}{30}\) ( cross- multiply )

30x = 450 ( divide both sides by 30 )

x = 15

Similarly

\(\frac{UT}{QP}\) = \(\frac{NM}{SR}\) , that is

\(\frac{y}{15}\) = \(\frac{18}{30}\) ( cross- multiply )

30y = 270 ( divide both sides by 30 )

y = 9

The similarity ratio is the ratio of corresponding sides , that is

\(\frac{NM}{SR}\) = \(\frac{18}{30}\) = \(\frac{3}{5}\)

SRUT is \(\frac{3}{5}\) of NMQP

The probability that the average grade in a statistics course is more than 74, given a sample of 52, is approximately 0.1446 or 14.46%.

To calculate the probability that the average grade is more than 74, we need to standardize the distribution using the z-score and then find the corresponding probability using the standard normal distribution table (Appendix B.1).

First, we calculate the z-score using the formula:

z = (x - μ) / (σ / √n)

Where:

x = desired average grade (74)

μ = population mean (71)

σ = population standard deviation (8.5)

n = sample size (52)

Plugging in the values, we get:

z = (74 - 71) / (8.5 / √52)

Now, let's calculate the z-score:

z = 1.0607

Next, we find the probability corresponding to this z-score using the standard normal distribution table or a calculator. The probability of obtaining a z-score of 1.0607 or more can be determined as:

P(z > 1.0607)

Looking up the z-value in the standard normal distribution table, we find that the probability is approximately 0.1446.

Therefore, the probability that the average grade is more than 74 is approximately 0.1446 or 14.46%.

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Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

Step-by-step explanation:

please mark me as brainlest

The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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( − 5 ) ( + 5 ) ( 2 + 2 5 )

The given expression represents a collection of equations and properties related to Legendre polynomials. These equations involve various properties and relations that characterize the behavior and properties of Legendre polynomials. Each equation represents a specific property or relation, such as evaluation at specific points, recurrence relations, or differential equations. It is important to study and understand these properties to work with Legendre polynomials effectively.

The equations mentioned in the given expression involve properties such as the evaluation of Legendre polynomials at specific points, the recurrence relation between consecutive polynomials, and the differential equation they satisfy. These properties are essential in understanding the behavior and properties of Legendre polynomials.

Each equation represents a specific property or relation associated with Legendre polynomials. For example, equation (67) shows the evaluation of Pn(x) at x = -1, equation (72) represents the recurrence relation between consecutive polynomials, and equation (76) shows the relation between Pn(x) and Pn-1(x).

To fully understand and work with Legendre polynomials, it is important to study their properties and equations systematically. The given expressions provide a glimpse into some of these properties and relationships.

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Tuppy should report a 95% confidence interval for the mean parameter as (3.4547, 8.213) based on Bertie's simulated values with a sample average of 5.88 and a sample standard deviation of 1.96.

To calculate the 95% confidence interval for the mean parameter, Tuppy can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value * (Sample Standard Deviation / √n)),

where:

Sample Mean is the average of the simulated values (5.88 in this case).

Critical Value is the value corresponding to the desired confidence level (95% in this case).

Sample Standard Deviation is the standard deviation of the simulated values (1.96 in this case).

n is the number of draws (5 in this case).

To find the critical value for a 95% confidence level, we need to look up the value associated with the Student's t-distribution with (n - 1) degrees of freedom. Since we have 5 draws, the degrees of freedom is 5 - 1 = 4. Looking up the value in a t-distribution table or using a statistical calculator, the critical value for a 95% confidence level with 4 degrees of freedom is approximately 2.776.

Now, we can substitute the values into the formula:

Confidence Interval = 5.88 ± (2.776 * (1.96 / √5)).

Calculating the expression inside the parentheses:

2.776 * (1.96 / √5) ≈ 2.4333

Therefore, the confidence interval for the mean parameter that Tuppy should get is:

Confidence Interval = 5.88 ± 2.4333

This means Tuppy should report a 95% confidence interval for the mean parameter as (3.4547, 8.213).

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Answer:

if it's area the area would be the length of the diameter of the semi circle which is the height of the triangle multiplied by the base of the triangle to find the area of the triangle then to find the area of the circle would be pie multiplied by the diameter divided by two squared

\(\pi \ \times 7 {}^{2} \)

then the total area would be the area of the triangle plus the area of the half circle

The least-square equation for the given (x,y) data pairs is: y = 0.9048x + 0.6190

To find the least-square equation for the given (x,y) data pairs, we can use the method of linear regression. The equation of a line is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept. The values of m and b can be calculated using the following formulas:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

b = (Σy - mΣx) / n

where n is the number of data points.

Using the given data, we can calculate the values of Σx, Σy, Σxy, and Σ(x^2) as follows:

Σx = 2 + 1 + 5 = 8

Σy = 4 + 3 + 8 = 15

Σxy = (24) + (13) + (5*8) = 42

Σ(x^2) = (2^2) + (1^2) + (5^2) = 30

Substituting these values into the formulas for m and b, we get:

m = ((342) - (815)) / ((330) - (8^2)) ≈ 0.9048

b = (15 - (0.90488)) / 3 ≈ 0.6190

Therefore, the least-square equation for the given data is:

y = 0.9048x + 0.6190

Rounded to four digits after the decimal, the equation becomes:

y = 0.9048x + 0.6190

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Answer: x <- -8

x is less than negative eight.

Step-by-step explanation:

First, subtract 11 from both sides. Then divide both sides by 11. The arrow should be open and pointing to the left.

Answer:

x <- -8

Step-by-step explanation:

A stream of hot water at 80°C flowing at a rate of 50 1/min is to be produced by mixing water at 15°C and steam at 10 bars and 350 °C in a suitable mixer. The required flow rates of steam and cold water are 0.024 kg/s and 0.8093 kg/s, respectively.

The required flow rates of steam and cold water are to be determined.

Given, Q = 0 (i.e. no heat loss or gain).Water has a specific heat of 4.187 kJ/kg-K. The enthalpy of water at 80°C is (h1) 335.23 kJ/kg.

The enthalpy of water at 15°C is (h2) 62.33 kJ/kg.

Superheated steam at 350°C and 10 bar has an enthalpy of 3344.28 kJ/kg (h3).

The enthalpy of saturated steam at 10 bar is 2773.9 kJ/kg (h4).

The enthalpy of saturated water at 10 bar is 191.81 kJ/kg (h5).Let m1, m2, and m3 be the mass flow rates of steam, cold water, and hot water respectively.

The heat balance equation for the mixer is given by,m1h3 + m2h5 + m3h1 = m1h4 + m2h2 + m3h1We know that Q = 0.

Therefore,m1h3 + m2h5 = m1h4 + m2h2

Rearranging,m1 = (m2/h3) (h2 - h5) / (h4 - h3)

Substituting the values,m1 = (m2/3344.28) (62.33 - 191.81) / (2773.9 - 3344.28)m1 = -0.024 m2

The negative sign indicates that the mass flow rate of steam is opposite in direction to that of water.

Therefore, the flow rate of steam required to produce the given flow rate of water is 0.024 kg/s.

The total mass flow rate is given as,m3 = m1 + m2 = (0.024 - 1) m2m2 = (50 / 60) kg/s = 0.8333 kg/s

Therefore, m3 = -0.8093 kg/s

The mass flow rate of cold water is 0.8093 kg/s.

The required flow rates of steam and cold water are 0.024 kg/s and 0.8093 kg/s, respectively.

Note: The negative sign for the mass flow rate of water implies that the direction of flow is opposite to that of the steam flow.

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To find the required flow rates of steam and cold water, we need to equate the energy entering the mixer from the steam to the energy entering from the cold water and solve for the mass flow rates.

To determine the required flow rates of steam and cold water, we need to use the principle of energy conservation. The total energy entering the mixer must equal the total energy leaving the mixer.

First, let's calculate the energy entering the mixer from the steam. We can use the formula Q = m × h, where Q is the heat energy, m is the mass flow rate, and h is the specific enthalpy. The specific enthalpy of steam at 10 bars and 350°C can be found using steam tables.

Next, we need to calculate the energy entering the mixer from the cold water. Using the same formula, Q = m × h, we can find the energy using the specific enthalpy of water at 15°C.

Since we assume Q=0, the energy entering the mixer from the steam and cold water must be equal. Equating the two energy expressions, we can solve for the mass flow rate of the steam and cold water.

Let's assume the mass flow rate of the steam is m₁ and the mass flow rate of the cold water is m₂. We can write:

m₁ × h₁ = m₂ × h₂

where h₁ and h₂ are the specific enthalpies of the steam and cold water, respectively.

By substituting the given values and solving the equation, we can find the required flow rates of steam and cold water.

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Answer:

  6

Step-by-step explanation:

If x represents the last number, to get zero you must subtract 6 from it:

  x - 6 = 0

  x = 6 . . . . . . add 6 (undo the subtraction)

The last number before zero is 6.

The total amount that Asher needs to save to buy a new playstation is 208.53.

The keyword "total" is crucial in this problem because we are trying to find the total amount of money that Asher needs to save to buy a new playstation. It's essential to understand that 78.20 is only a fraction of the total amount, and we need to determine what that fraction is.

To start, we can set up a proportion that represents the relationship between the fraction of the total amount saved (3/8) and the actual amount saved (78.20). We can use x to represent the total amount Asher needs to save:

3/8 = 78.20/x

To solve for x, we can cross-multiply the equation:

3x = 8 * 78.20

3x = 625.6

x = 625.6/3

x = 208.53

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Answer:

8

Step-by-step explanation:

Answer:

8mph

Step-by-step explanation:

Because it took Ruthene 1/4 of an hour or 15 minutes to run two miles, if she were to run for an entire hour she would go 4 times as far, or 8 miles. This means that Ruthene had an average speed of 8mph.

Let 'x' gallons of first brand and 'y' gallons of second brand antifreeze is used.

Given that the first brand is 70% pure antifreeze. It means that each gallon of this brand contains 0.70 gallons of the solute. So the amount of solute in x gallons will be,

Also, it is given that the second brand is 95% pure antifreeze. So the amount of solute in 'y' gallons will be,

The total mixture is 110 gallons, so we can write,

Also the mixture is 75% antifreeze. It means that each gallon of this mixture will contain 0.75 gallon solute. So the amount of solute in 110 gallons will be,

The total quantity of solute in this mixture should be equal to the sum of quantity of solutes in first and second brand,

Substitute the value of 'y' from equation (1) in equation (2),

Substitute this value in equation (1) to obtain 'y' as,

The values of 'x' and 'y' are 22 and 88 respectively.

So, the 22 gallons of first brand and 88 gallons of second brand must be used to obtain the required mixture.

Answer:

x=7

Step-by-step explanation:

HI + IJ = HJ

3x-5 + x-1 = 7x-27

Combine like terms

4x-6 = 7x-27

Subtract 4x from each side

4x-6 -4x= 7x-27-4x

-6 = 3x-27

Add 27 to each side

-6+27 = 3x-27+27

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

Answer:

x=7

Step-by-step explanation:

Answer:

d-b                d=b
___   =  
c-a                 c-a

Step-by-step explanation:

that is the formual to slove it
y2 - y1
__________
x2 - x1

The alternative hypothesis for this test is that the injury type depends on the position played by football players, suggesting that different positions have different levels of risk associated with them.

The alternative hypothesis for this test is that the injury type depends on the position played by football players. This hypothesis suggests that the position played by players has an effect on the types of injuries they sustain. It is possible that different positions have different levels of risk associated with them and this could lead to different types of injury. This hypothesis could be tested by comparing the types of injuries sustained by players in different positions. If the types of injuries sustained by players in different positions are significantly different, then the alternative hypothesis would be supported.

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No, a pair of angles cannot be both supplementary and congruent.

Supplementary angles are two angles whose measures add up to 180 degrees. If two angles are supplementary, their sum is 180 degrees.

Congruent angles, on the other hand, have the same measure. If two angles are congruent, their measures are equal.

If a pair of angles were both supplementary and congruent, it would mean that their measures are equal and their sum is 180 degrees. However, this is not possible because if two angles have the same measure, their sum cannot be 180 degrees unless both angles are right angles (90 degrees).

In summary, a pair of angles cannot be both supplementary and congruent, as the conditions of being supplementary and congruent are contradictory.

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Answer:

no

Step-by-step explanation:

Answer:

No, a parallelogram means that the opposite sides don't meet (are parallel), so a triangle isn't. A triangle has only three sides, and they all meet up.

Step-by-step explanation:

Answer:

1440000

Step-by-step explanation:

Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.

The interval of convergence is (-111/16, -15/16), and the radius of convergence is R = 15/16.

To find the interval of convergence and radius of convergence of the power series ∑n=1[infinity](−4)nn‾√(x 7)n, we can use the ratio test:

|(-4)nn‾√(x 7)n+1 / (-4)nn‾√(x 7)n| = 4√(x 7) → as n → infinity

The ratio test tells us that the series converges if 4√(x 7) < 1, and diverges if 4√(x 7) > 1. Solving for x, we get:

4√(x 7) < 1
√(x 7) < 1/4
x 7 < 1/16
x < -111/16

and

4√(x 7) > 1
√(x 7) > 1/4
x 7 > 1/16
x > -15/16

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Answer:

C

Step-by-step explanation:

1 1/4 = 1.25

1 4/5 = 1.8

1.8+1.25=3.05=3 1/20

Answer:

C. 3 1/20

Step-by-step explanation:

Answer:

24 is the answer

Step-by-step explanation:

2a + 5 = 53

     -5      -5

      0      48

2a/2= a

48/2= 24

THEREFORE a=24

Hey there! I'm happy to help!

How many times does 30 minutes go into 60 minutes?

60/30=2

This means we are traveling 32 miles two times!

32(2)=64

Therefore, Kathryn and her mom drive 64 miles in an hour.

Have a wonderful day! :D

Answer:

This is a sequence, so we have to move forward step by step

Step-by-step explanation:

4,3,9/4,27/16

Because this sequence has no exponential arithmetic or geometry, we perform the sequence with the help of a matrix

\(y = y\)

\(x = x\)

\(x = 4.4.4.4.4\)

\(x = 4\)

Matrix determinants allowed us to achieve both geometric and arithmetic progression by sequence guidance

The answer is

\(x \times y = 144 = 614.88\)

When everyone is sitting down, the number of free seats is 26, using arithmetic addition and subtraction.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are arithmetic addition and subtraction. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

The initial number of passengers on board=29

After 4 people get off at the first stop,

Using arithmetic addition and subtraction, we get,

Number of passengers left=29-4=25

After 11 people get on,

Number of passengers=25+11=36

At the second stop, when 7 people get off,

Number of passengers=36-7=29

When 23 people get on,

Number of passengers=29+23=52

Total number of passenger seats in the bus=78

Number of free seats, when everyone is sitting=78-52

                                                                              =26

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