Determine when the following expression is undefined: 17+12r / 3r2-15r-120

Answer:

It is A and D

The city streets are overcrowded with cars

There is a lot of noise pollution

Step-by-step explanation:

The correct answers are the city streets are overcrowded with cars and there is a lot of noise pollution.

A government is the system or group of people governing an organized community, generally a state

The following statements represent possible problems:

The city streets are overcrowded with cars.

The noise level is raising.

And the following statements are possible solutions:

More money from the city government should go to public transportation.

A subway system should be built.

People should be encouraged to carpool to work and school.

Therefore, the correct answers are the city streets are overcrowded with cars and there is a lot of noise pollution.

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SOLUTION:

Step 1:

In this question, we are given the following:

Solve the following equations.

Express your answer as an ordered pair in the format (a,b) with no spaces between the numbers and symbols:

Step 2:

We multiply equation 1 by 2, so we have that:

Then, we evaluate equation 3 minus equation 4, we have that:

Next, we put the value of y = 1 in equation 1, we have that:

CONCLUSION:

In ordered pair, the value of:

Answer:

The order is

Sherry >> Rachel>>Bobby

Step-by-step explanation:

Step one:

We want to find the smallest unit rate

given data

1. Bobby fills his bucket at a rate of 3/4 gallon in 2 minutes.

unit rate

=3/4/2

=3/4*1/2

=3/8

=0.375 gallons per minute

2. Rachel can fill her bucket at 1/5 gallon in 1/2 minute.

unit rate

=1/5/1/2

=1/5*2/1

=2/5

=0.4 gallons per minute

3.  Sherry can fill 3/8 gallon in 3/4 minute.

unit rate

=3/8/3/4

=3/8*4/3

=12/24

=0.5 gallons per minute

Answer:

Step-by-step explanation:

Your first equation is y=10x+20

Your slope is 10 and your y-intercept is 20 in this first equation

Your second equation after it has changed, your new equation is y=30x+45

Your slope is 30 and your y-intercept is 45 in this second equation

I hope this helps!

The equation of line is y = 30x + 45 , where x is the number of hours

The slope of the line = 30

The y intercept of the line = 45

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the initial amount of charge for the stable be = $ 45

Let the amount per hour for the stable be = $ 30

Let the total number of hours be = x

Now , the total amount for the stable in x hours = initial amount of charge for the stable + ( total number of hours x amount per hour for the stable )

Substituting the values in the equation , we get

y = 30x + 45

The equation is of the form y = mx + b , where m is the slope and b is the y intercept

Therefore, the value of A is y = 30x + 45

Hence , the equation of line is y = 30x + 45

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a)  As long as the slope of the objective function stays between -8/7 and -1/2 the current optimal solution point will remain optimal.                                                                                                                                                                                                                        

b) The objective functions that lead to the same optimal solution are Z = 2X + Y and Z = 25X + 35Y.

a. The binding constraints for the given linear programming problem are 5X + 3Y ≤ 30 and 2X + 5Y ≤ 20. We need to find the range of slope of the objective function for which the current optimal solution point will remain optimal.

First, we graph the two binding constraints on the X-Y plane and find their intersection point as (X, Y) = (3, 3). This is the current optimal solution point.

Next, we need to check the slope of the objective function at this point. Let the objective function be Z = aX + bY. At the optimal solution point, the slope of the objective function is given by -b/a.

For the current optimal solution point (3, 3), we can compute the slope of the objective function for different values of a and b as follows:

When a = 2 and b = 1, the slope of the objective function is -1/2.

When a = 7 and b = 8, the slope of the objective function is -8/7.

When a = 80 and b = 60, the slope of the objective function is -3/4.

When a = 25 and b = 35, the slope of the objective function is -7/5.

Since the binding constraints have negative slopes, we know that the objective function must have a negative slope for an optimal solution to exist. Therefore, the range of slope of the objective function for which the current optimal solution point will remain optimal is between -8/7 and -1/2.

b. To find the objective functions that lead to the same optimal solution, we need to find the objective functions that have the same slope at the current optimal solution point (3, 3). We can compute the slope of each objective function as follows:

For Z = 2X + Y, the slope at (3, 3) is -1/2.

For Z = 7X + 8Y, the slope at (3, 3) is -8/7.

For Z = 80X + 60Y, the slope at (3, 3) is -3/4.

For Z = 25X + 35Y, the slope at (3, 3) is -7/5.

Therefore, the objective functions that lead to the same optimal solution are Z = 2X + Y and Z = 25X + 35Y

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Answer:

5.2seconds

Step-by-step explanation:

Fredrick threw a ball from the top of a building. The height of the ball, in feet, after it is thrown is modeled by the function

The modeled function is given as

h(t) = –16t^2 +64t + 100,

We can see this is a quadratic equation, we can solve using quadratic formula, Below

= -b±(√b^2 -4ac)/2a

Where

a=-16, b=64, c=100

FROM THE ATTACHMENT

We have too answers t= -1.20s and t=5.20s

Therefore,it take 5.20s for the ball to reach the ground (h=0). Because "t" cannot be negative here

CHECK THE ATTACHMENT FOR THE QUADRATIC SOLUTION

Answer:

Is there multiple choice or just calculations?

Step-by-step explanation:

Step-by-step explanation:

1) 6*26 = 156

2) 156 + 9 = 165

Answer:

option C is correct

x^4 - x^2 - 2.5

If we add any constant c in the function then it gets shifted upward by the c unit. Then the function g(x) is above the function f(x) by 2.5 units.

The function is an expression, rule, or law that defines the relationship between one variable to another variable.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The functions are g(x) and f(x) are given below.

f(x) = x⁴-x²

g(x) = x⁴-x²+2.5

We know that if we add any constant c in the function then it gets shifted upward by the c unit.

The graph is shown.

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Answer:

A.  Correct

B.  Correct

C.  Not correct

D.  Correct

E.  Not correct

Step-by-step explanation:

We are told that Michael's race numbers are:

5.25 miles

45.75 minutes

Divide the miles by the minutes to get mIchael's running rate:

0.114754098 mi/min

This result matches option B. " Michael's average pace was about 0.11 miles per minute."

======

Check all the answer options:

A. Michael's unit rate of minutes per mile was about 8.7.  

  Take 0.11475409 mi/min and invert it to find min/mile:

      1/(0.11475409 mi/min) = 8.71 min/mile

This is a correct statement.

B. Michael's average pace was about 0.11 miles per minute.

From above:  This is a correct statement.

C. Michael's unit rate of minutes per mile was about 6.9.

Take the given numbers:   (45.75 minutes)/(5.25 miles) = 8.71 min/mile

This is not a correct statement.

D. Michael's average speed during the race was about 6.9 miles per hour.  

Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:

  Use the conversion factor (60 min/1 hr)

   (0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr

This is a correct statement.

E.  Michael ran about 8.7 miles in 1 minute.

We know from above that he runs at 6.89 miles per hour.  Running 8.7 miles in 1 minute  would mean he is running at (8.7)*(60) = 413 miles/hour.    

Perhaps he had some good energy bars, but the data do not support this conclusion.

This is not a correct statement.

Answer:

x = 23 degrees

Step-by-step explanation:

Angle on a straight line = 180 degrees

therefore 180 - 75 = 105 degrees

105 + 52 = 157 degrees

Angle in a triangle is 180 degrees

therefore 180 - 157 = 23 degrees

The probability  that the average scholarshi[s in the samle greater than 20,000 is (69.729, 74.271).

Let X: Marks of students and be the population average marks.

X ~ N(72, 16)

The formula for the CI for is,

CI = mean + tₐ/₂ , ₙ₋₁ s/n

= 72 ± 2.539 × 4/20

= 72 ± (2.539 × 0.8944)

= 72 ± 2.27

= 72 - 2.27 , 72 + 2.27

= (69.729, 74.241)

Therefore, the required 98% CI for the average marks of the students is (69.729, 74.271).

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Answer:

Step-by-step explanation:

it woulkd be 200 gallons

We prove that ABCD is isosceles trapezoid because diagonals AC and BD are equal and unparallel side AB and DC also equal.

A two-dimensional geometrical shape having four straight sides including one pair of parallel sides is termed as trapezoid.

There are different types of trapezoids. If a trapezoid is such that two diagonals is equal in length, then it has equal sizes of unparallel side length. This trapezoid is termed as isosceles trapezoid due to its two equal sides and two parallel sides with different length.

given, ABCD is a trapezoid with equal diagonal AC and BC. Two sides AD and BC are parallel but different side length. As diagonals are same so side AB and side DC are also equal in length.

hence, ABCD is an isosceles trapezoid.

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The value of the of your quarters incense is a function of and the number of quarters, then the output when input is 10 is 250.

Quarters:

In mathematical terms, quartering is the division of a whole into 4 equal parts, where 1 is the part referred to and 4 is the number of parts the whole is divided into.

Let the quarter be 25 cents then value(v) of quarter (cents) is functions of n then equation,

         v = 25n

Putting input (n =10)

   V =  25× 10

      = 250

The independent value is: n

The dependent value is : v

The equation is: v = 25n

And, the output when input is 10 is 250.

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Answer:

Here,

x+(-5) = 4

x = 4+5

x = 9

Therefore, 9+(-5) = 4

Answer:

66.03 so 70

Step-by-step explanation:

since hypotunees has no value it cancels.

aso it leaves with an adjacent and oppisite

using trig function you will get

tan(x)=(9/4)

inverse tan to get x on its own

(x)=tan^-1(9/4)

put that on the calculater and you will get the angle

therefore

(x)=66.04 round it the nearest ten which is

70

Answer:

Interest= $516.93

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $1,200

Number of periods (n)= 12*3= 36 months

Interest rate (i)= 0.12/12 = 0.01 monthly

First, we need to calculate the future value of the investment using the following formula:

FV= PV*(1 + i)^n

FV= 1,200*(1.01^36)

FV= $1,716.93

Now, the interest earned:

Interest= 1,716.93 - 1,200

Interest= $516.93

We must invest  396.90, at an interest rate of 8.

Hobby is the fee you pay to borrow cash or the cost you price to lend money. interest is most customarily contemplated as an annual percent of the amount of a mortgage. This percent is called the interest price on the loan. for example, a bank will pay you interest when you deposit your money in a savings account.

The forms of interest consist of simple hobby, accumulated hobby, and compounding hobby. while money is borrowed, generally via the way of a loan, the borrower is required to pay the interest agreed upon by the two events.

There has been a energetic hobby inside the elections inside the final  weeks. She'd appreciated him in the beginning, but soon lost interest. Synonyms: significance, issue, importance, moment extra Synonyms of interest. countable noun.

value = Amount*(1+i)n

                     = 500*(1+.08)3

                         = 500*0.7938

                  Present value = 396.90

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Answer:

Since Manish hit the target 25 - 5 = 20 times, he earned 15 * 20 = ₹ 300. Since he missed 5 times, he lost 5 * 5 = ₹ 25, therefore, he only earned 300 - 25 = ₹ 275.

Answer:

Manish hit the target=25-5=20times

He he earned=15×20=₹300

Since he missed 5 times he lost 5×5=₹25

Therefore,he only earned 300-25=₹275

I HOPE YOU LIKE IT. THIS IS THE CORRECT ANSWER

Answer:

\(\textsf{B)} \quad \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5cm} \underline{Binomial Theorem}\\\\$\displaystyle (a+b)^n=\sum^{n}_{k=0}\binom{n}{k} a^{n-k}b^{k}$\\\\\\where \displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}\\\end{minipage}}\)

Given expression:

\((2x^2y^3+y)^7\)

Therefore:

Therefore:

\(\displaystyle (2x^2y^3+y)^7=\sum^{7}_{k=0}\binom{7}{k} (2x^2y^3)^{7-k}(y)^{k}\)

To find the 4th term in the binomial expansion, substitute k = 4 into the equation:

\(\implies \displaystyle \sum^{7}_{k=0}\binom{7}{4} \left(2x^2y^3\right)^{7-4}\left(y\right)^{4}\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{(7-4)!4!} \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(35 \cdot 8x^6y^9y^4\right)\)

\(\implies \displaystyle \sum^{7}_{k=0} \left(280x^6y^{13}\right)\right)\)

Therefore, the expression that correctly shows how to use the binomial theorem to determine the 4th term in the expansion is:

\(\displaystyle \sum^{7}_{k=0} \left(\frac{7!}{3!\:4!} \cdot \left(2x^2y^3\right)^{3}\left(y\right)^{4}\right)=280x^6y^{13}\)

Given :

Diameter of pizza , \(D=10\dfrac{1}{3}=\dfrac{31}{3}\) .

To Find :

Is square box of size equal to diameter big enough to fit pizza inside it .

Solution :

Area of pizza :

\(A_p=\pi(\dfrac{D}{2})^2\\\\A_p=\pi\times (\dfrac{31}{3\times 2})^2\\\\A_p=83.86\ inch^2\)

Area of square with side equal to diameter :

\(A_s=D^2\\\\A_s=(\dfrac{31}{3})^2\\\\A_s=106.78\ inch^2\)

Since , the area of square is more than area of pizza .

Therefore , pizza can easily be fitted .

Hence , this is the required solution .

The arc length of the curve x = 9 cos(3t), y = 9 sin(3t) with 0 ≤ t ≤ 7 is 5103 units.

To find the arc length of the curve described by the parametric equations x = 9 cos(3t) and y = 9 sin(3t) with 0 ≤ t ≤ 7, we can use the arc length formula for parametric curves:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 dt

In this case, a = 0 and b = 7, so we need to calculate the derivative of x with respect to t (dx/dt) and the derivative of y with respect to t (dy/dt):

dx/dt = -27 sin(3t)

dy/dt = 27 cos(3t)

Now, substitute these derivatives into the arc length formula:

L = ∫[0,7] √[(-27 sin(3t))^2 + (27 cos(3t))^2] dt

Simplifying the expression inside the square root:

L = ∫[0,7] √[(-27)^2 sin^2(3t) + (27)^2 cos^2(3t)] dt

L = ∫[0,7] √[729 sin^2(3t) + 729 cos^2(3t)] dt

L = ∫[0,7] √[729 (sin^2(3t) + cos^2(3t))] dt

Since sin^2(3t) + cos^2(3t) = 1, the expression simplifies to:

L = ∫[0,7] 729 dt

L = 729t | [0,7]

Finally, evaluate the integral at the upper and lower limits:

L = 729(7) - 729(0)

L = 5103 - 0

L = 5103

Therefore, the arc length of the curve x = 9 cos(3t), y = 9 sin(3t) with 0 ≤ t ≤ 7 is 5103 units.

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Answer:

So the formula of area of the circle A=πr2. The answer is 153.86.

Step-by-step explanation:

You first divide 14/2=7 then do 7^2 which equals 49 lastly multiplying 3.14 X 49. So how is the radius 7 because half of a diameter is a radius.Therfore the answer is 153.86.

The ratio of the rotational partition functions of these molecules, at temperatures above 100 K assuming H₂ and HD having equal bond lengths is 1/2.

Rotational partition functions refer to the number of ways that a molecule can be oriented in space without considering its electronic state. When the bond length between the two atoms in H2 and HD is considered, the partition function changes, which is taken into account in the formula:

QR = \((8\pi^2I/ kT)^{1/2}\) where QR refers to the rotational partition function, k refers to the Boltzmann constant, T refers to the temperature, and I refers to the moment of inertia.

In the present problem, H₂ and HD have equal bond lengths, and thus the value of the moment of inertia is the same for both. Therefore, the ratio of the rotational partition functions of these molecules, at temperatures above 100 K is proportional to the square root of their reduced masses. Since the reduced mass of HD is 2/3 that of H₂, the ratio of the rotational partition functions is given by:

QR(HD) / QR(H₂) =\((μ(H₂) / μ(HD))^(1/2)\)

= \((3/2)^(1/2)\)

= 1.225

So, the answer is not given in the options. However, we can approximate it as the value lies between 1 and 1.5. The closest answer to the approximation is 1/2. Hence, option (c) is the closest to the approximation.

Therefore, the ratio of the rotational partition functions of these molecules, at temperatures above 100 K assuming H₂ and HD having equal bond lengths is 1/2.

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Answer:

Sides: a = 9.165   b = 4   c = 10

Step-by-step explanation:

Is that check mark supposed to be square root?

Answer:

\((4^{2} +(\sqrt{84} ^{2} )\\=100\)

Step-by-step explanation:

Answer: 171.19

V=lwh

w=3.65

l=14

h=7-3.65

=3.35

V=171.185 ≈171.19

Step-by-step explanation:

Se calcula que la aceleración es - 8,35 m/s.

Ahora sabemos lo siguiente de la pregunta;

Velocidad inicial (u) = 60 km/h o 16,7 m/s

Tiempo empleado (t) = 2 s

Dado que;

v = tu + en

v = 0 m/s porque el carro se detenía

tu = -en

a = -(u/t)

 a= -1(6,7 m/s/2 s)

a =- 8,35 m/s

La aceleración es negativa porque la velocidad disminuye con el tiempo.

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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