Find the domain for the rational function f of x equals quantity x plus 4 over quantity 3 times x minus 5. negative infinity to negative five thirds and negative five thirds to infinity negative infinity to five thirds and five thirds to infinity (−∞, −4)( −4, ∞) (−∞, 4)(4, ∞)

Step-by-step explanation:

4 + x = -9

x = -9 +4

x = - 5

-x = -5

x = 5

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

Step-by-step explanation:

Mark has left with 44 inches. The correct option is C.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences.

To solve this problem, we need to first convert the measurements to a common unit. Let's convert everything to inches:

To find out how much rope Mark had left after cutting off 4 feet 6 inches, we need to subtract 54 inches from 98 inches:

98 inches - 54 inches = 44 inches

Therefore, the answer is C. 44 inches.

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

Acute angle

Step-by-step explanation:

45°= Acute Angle

‘Cause It's less than 90°

Answer:

Step-by-step explanation:

It's an acute angle. Acute, in this case, means anything between 0 and 90 written 0<x<90. Notice that you are using < and not ≤. The endpoints are not included. They have their own names. 90 is a right angle. 0 is called a zero degree angle.

Answer:

261.1

Step-by-step explanation:

Wizardry

Step-by-step explanation:

Patel could use the Quadratic Formula to solve it    

   or

    he could 'complete the square' to solve it after dividing thru by 8                          or he could solve it graphically  

{   or he could use factoring to solve it   (difficult)  }

Identities are given as cos(a + B) = cosa cosß-sina sinß, cos²p+ sin²p=1,(a) cos(a+B) =cosa cosß + sina sinß (b)  (27 - (a− p)) = cos((2-a) + B)=cos(2-a + B) (c) sin(7/12)cos(7/12)= (√6+√2)/4

Part (a)To prove the identity for cos(a-B) = cosa cosß+ sina sinß, we start from the identity

cos(a+B) = cosa cosß-sina sinß, and replace ß with -ß,

thus we getcos(a-B) = cosa cos(-ß)-sina sin(-ß) = cosa cosß + sina sinß

To prove the identity for sin(a-B)=sina-cosß-cosa sinß, we first replace ß with -ß in the identity sin(a+B) = sina cosß+cosa sinß,

thus we get sin(a-B) = sin(a+(-B))=sin a cos(-ß) + cos a sin(-ß)=-sin a cosß+cos a sinß=sina-cosß-cosa sinß

Part (b)To prove that as (27 - (a− p)) = cos((2-a) + B),

we use the identity cos²p+sin²p=1cos(27-(a-p)) = cos a sin p + sin a cos p= cos a cos 2-a + sin a sin 2-a = cos(2-a + B)

Part (c)Given cos²a= 1+cos2a 2 , sin² a= 1-cos2a 2We are required to calculate cos(7/12) and sin(7/12)cos(7/12) = cos(π/2 - π/12)=sin (π/12) = √[(1-cos(π/6))/2]

= √[(1-√3/2)/2]

= (2-√3)/2sin (7/12)

=sin(π/4 + π/6)

=sin(π/4)cos(π/6) + cos(π/4) sin(π/6)

= √2/2*√3/2 + √2/2*√1/2

= (√6+√2)/4

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Answer:

Answer:

Tens

PART B: 18

PART C: 24

Step-by-step explanation:

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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The distributions that a person  would be more likely to find the mean and median the same is  (E) A, B, and C.

The term  frequency distribution is known to be commonly used in statistics.

It is seen as a graph or data set that is put together to depict the frequency of  the occurrence of all the possible outcome of any kind of repeatable event that is seen to be observed a lot of times.

Note that from the image attached, you can see that the points ranges from 20 -30 and the heights of measurement is similar across all of them.

Therefore, The distributions that a person  would be more likely to find the mean and median the same is  (E) A, B, and C because the same value is used.

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The statement "2.2% of all people in the nation always eat out" is a descriptive statement.

A descriptive statement provides information or describes a specific characteristic or attribute of a population or sample without making any inferences or generalizations beyond the data itself. In this case, the statement simply presents a specific percentage (2.2%) indicating the proportion of people in the nation who always eat out.

It is important to note that descriptive statements are based on observed data or facts and do not involve any statistical analysis or generalizations beyond the given information. The statement does not make any claims about the entire population or draw conclusions about other groups or individuals who are not specifically mentioned.

In contrast, an inferential statement would involve making inferences, generalizations, or conclusions about a population based on sample data and statistical analysis. It would involve drawing broader conclusions beyond the observed data. However, the statement provided does not involve any inferences or generalizations, making it descriptive in nature.

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Answer:

(2x+ 3) ( x-4)

2x (x-4) + 3(x-4)

2x^2 -8x + 3x -12

2x^2 - 5x - 12

hope it helps

Answer:

the product is: 2 x ^2 − 5 x − 12

Step-by-step explanation:

Expand the polynomial using the FOIL method.

The expected value of the sample mean of the values obtained in these 300 tosses is 3.5

Given :

A fair six sided die is tossed 300 times

We have to find the expected value of the sample mean of the values obtained in these 300 tosses.

A dice have six sides:

In a fair dice every side has equal chance of occurrence,

Now the probability of presence of each side = 1/6

Now the expected value of the sample mean of the values obtained in these 300 tosses is given by:

E(x) = Σx P(x =x)

= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6

= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6

= 1/6 (1+2+3+4+5+6)

= 1/6 (21)

= 21/6

E(x) = 3.5

Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5

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Answer:

75 miles squared

Step-by-step explanation:

First we have to convert 1 inch = 5 miles to square miles as that is what we are trying to get

So, 1 inch squared = 25 miles squared

To get 75 miles squared, we multiply both sides by 3.

So 3 * 1 inch squared = 3 * 25 miles squared

Gets us 3 inch squared = 75 miles squared

Answer:

Hope this helps :D

The answer is 27(If i`m not mistaken)

Answer:

Step-by-step explanation:

There are options:

Number of  possible combinations:

Answer:

20

I hope this helps!

Answer:

20

Step-by-step explanation:

hope this helps I know I'm too late.

a. The complete table for the ordered pairs that are solutions to y = x³ - 4 is

x             y

-1            -5

0            -4

1             -3

2            4

b. The graph of the equation is shown below

From the question, we are to complete the given table of ordered pairs that are solutions to the given equation.

The given equation is

y = x³ - 4

Now, we will determine the values of y for the given values of x

When x = -1

y = x³ - 4

y = (-1)³ - 4

y = -1 - 4

y = -5

(-1, -5)

When x = 0

y = x³ - 4

y = (0)³ - 4

y = 0 - 4

y = -4

(0, -4)

When x = 1

y = x³ - 4

y = (1)³ - 4

y = 1 - 4

y = -3

(1, -3)

When x = 2

y = x³ - 4

y = (2)³ - 4

y = 8 - 4

y = 4

(2, 4)

Thus,

The table is

x             y

-1            -5

0            -4

1             -3

2            4

The graph is shown below

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The given field is F = − yi + xj. We are required to find the circulation and the flux of this field around and across the following curves.

A) \(The circle r(t) = (cost) i + (sint) j, 0 ≤ t ≤ 2πCirculation: For a vector field F = P i + Q j, the circulation of F around a simple closed curve C oriented counterclockwise is given by: circulation = ∮cF(r) · drHere, P = 0 and Q = x.∴ F(r) = P i + Q j = xj\)

\(The parameterization of the given curve is r(t) = (cost) i + (sint) j.\)

\(The differential element of the curve is given by:dr = dx i + dy j= -sin(t) i + cos(t) j\)

\(The circulation is given by:circulation = ∮cF(r) · dr= ∫₀²π F(r(t)) · dr/dt dt= ∫₀²π(xj)·(-sin(t)i+cos(t)j)·(-sin(t)i+cos(t)j)dt= ∫₀²πxdt= ∫₀²πcostdt= 0Flux:The flux of F across C is given by:flux = ∮cF(r) · n dsHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The outward unit normal vector to the given curve is given by:n = sin(t) i − cos(t) j\)

\(The parameterization of the given curve is r(t) = (cost) i + (sint) j.\)

\(The differential element of the curve is given by:ds = |dr|=√((dx)²+(dy)²)=√(sin²t+cos²t)dt= dtThe flux is given by: flux = ∮cF(r) · n ds= ∫₀²π F(r(t)) · n(t) ds/dt dt= ∫₀²π(xj)·(sin(t)i-cos(t)j)·(1)dt= ∫₀²πxsin(t)dt= 0B)\)

\(The ellipse r(t) = (cost) i + (7sint) j, 0 ≤ t ≤ 2πCirculation: For a vector field F = P i + Q j, the circulation of F around a simple closed curve C oriented counterclockwise is given by: circulation = ∮cF(r) · drHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The parameterization of the given curve is r(t) = (cost) i + (7sint) j.\)

\(The differential element of the curve is given by:dr = dx i + dy j= -7sin(t) i + 7cos(t) j\)

\(The circulation is given by:circulation = ∮cF(r) · dr= ∫₀²π F(r(t)) · dr/dt dt= ∫₀²π(xj)·(-7sin(t)i+7cos(t)j)·(-7cos(t)i-7sin(t)j)dt= ∫₀²π49xdt= 0Flux:The flux of F across C is given by:flux = ∮cF(r) · n dsHere, P = 0 and Q = x.∴ F(r) = xj\)

\(The outward unit normal vector to the given curve is given by:n = 7sin(t) i − cos(t) j\)

\(The parameterization of the given curve is r(t) = (cost) i + (7sint) j.\)

\(The differential element of the curve is given by:ds = |dr|=√((dx)²+(dy)²)=√(49sin²t+cos²t)dt=√(50cos²t-48)dt\)

\(The flux is given by: flux = ∮cF(r) · n ds= ∫₀²π F(r(t)) · n(t) ds/dt dt= ∫₀²π(xj)·(7sin(t)i-cos(t)j)·(7sin(t))√(50cos²t-48)dt= ∫₀²π7xsin(t)√(50cos²t-48)dt= 0\)

Hence, the circulation is zero and the flux is zero for both the given curves.

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Answer:

mean: 2.6, mode: 1, median: 1

Step-by-step explanation:

The mean is essentially the average of the data set which can be defined as: \(\frac{\text{sum of data set}}{\text{amount of data in data set}}\). So adding all the values together you get: \(26\). and counting all the numbers in the data set you find the data set has 10 numbers. This gives you the equation: \(\frac{26}{10} = 2.6\) which is the mean

To find the mode, you find which number occurs most frequently, this is of course 1, which can really be determined by just looking at the data set for a second. all the other numbers only occur once, while 1 is in the data set 5 times. So 5 is the mode

To find the median you sort the data, from min to max, and then find the middle number. Sorting the data set gives you. -2, 1, 1, 1, 1, 1, 4, 5, 6, 8. Since this data set has an even amount of numbers, there is not going to be an exact middle. If you go the "middle" which is the 5th and 6th number, you add these two numbers and divide the sum by 2. This gives you: (1+1)/2 = 1 So the median is 1

Answer:

15

Step-by-step explanation:

y= 15 because 5 x 15 is 75 and 51+54+75= 180

Answer:

y=15

Step-by-step explanation:

51+54=105

180-105=75

75÷5=15

y=15

OR

5y+51+54=180⁰

5y+51=126

5y=75

y=75÷5

y=15

Answer:

B

Step-by-step explanation:

Circumference=(pi)d

3*3.14=9.42