Simplify rational expression
16 – 4y?
3y2 – 12y + 12
8 + 4y
3y – 6
Which values of y make the expression undefined?

The possible number of nickels that Alison would have had is given as  [14, 15, 16, 17]

We would first have to define the variables x and y. We have x as the number of pennies that she has while y is the number of nickels that she has.

We would have the inequality equation as

x + y ≤ 23

Let us define an equation

0.01x + 0.05y ≥ 0.75   ------ 1

Given that she is said to have 6 pennies then x would be = 6

6 + y ≤ 23

we would have to solve the equation above

y ≤ 23 - 6

y ≤ 17

put the value of 6 as x in the equation 1 above

0.01(6) + 0.05y ≥ 0.75

simplify the equation

0.05y ≥ 0.69

divide through by 0.05

y ≥ 13.8

y ~ 14

Hence we would have the range of values to be between  14 ≤ y ≤ 17.

This would be listed as y = [14, 15, 16, 17]

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Answer:

k=30

Step-by-step explanation:

The formula for calculating the mean from a frequency table is:

\( \displaystyle \overline{x} = \frac{ \sum \: fx}{ \sum f} \)

we have

So our equation is

\( \displaystyle 7= \frac{ 120 + 3k}{30} \\ \implies \dfrac{120 + 3k}{30} = 7\)

Solving the equation yields:

\(\implies 120 + 3k = 210 \\ \implies 3k = 90 \\ \implies \boxed{k = 30}\)

Answer:

k = 30

Step-by-step explanation:

The formula for the mean is:

\(\boxed{\displaystyle \text{Mean}=\overline{x}=\dfrac{\sum fx}{\sum f}}\)

where:

Given:

  \(\displaystyle \sum f=30\)

  \(\displaystyle \sum fx=120+3k\)

  \(\overline{x}=7\)

Substitute the given values into the formula and solve for k:

\(\implies 7=\dfrac{120+3k}{30}\)

Multiply both sides by 30 to eliminate the denominator on the right side:

\(\implies 210=120+3k\)

Subtract 120 from both sides:

\(\implies 90=3k\)

Divide both sides by 3:

\(\implies k=30\)

Therefore, k = 30.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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The latitude and longitude coordinates on our globe are essential for locating a specific location on earth. They are measured in degrees, with the equator serving as the reference point for latitude and the Prime Meridian serving as the reference point for longitude.

Latitude specifies a location's north-south position relative to the equator, while longitude specifies a location's east-west position relative to the Prime Meridian. Latitude is expressed in degrees north or south of the equator, while longitude is expressed in degrees east or west of the Prime Meridian. As we compare our conclusion with latitude and longitude on our globe, we found that both are equally important.

Longitude and latitude help to pinpoint any location on the globe with extreme accuracy, which is why they are so important. These coordinates are used in GPS devices, mapping software, and more.In conclusion, we can say that the importance of latitude and longitude cannot be overstated. They are critical components of modern navigation and have transformed how we travel and interact with the world around us.

Latitude and longitude are essential for determining the precise location of a particular place on earth. Latitude is the imaginary line that runs east to west around the earth's circumference, which is perpendicular to the earth's axis. Longitude is the imaginary line that runs north to south around the earth's circumference, which is parallel to the earth's axis. Latitude and longitude are represented in degrees, and they are used to determine the exact location of a particular place on earth.In comparison to our conclusion, we find that both latitude and longitude are essential for locating a particular place on earth.

They help in determining the precise location of a place on earth. They are essential components of modern navigation and have revolutionized how we travel and interact with the world around us.

We can say that latitude and longitude are critical components of modern navigation. They help in pinpointing the exact location of a place on earth. They are represented in degrees, and they are used to determine the precise location of a particular place on earth. Thus, they have revolutionized the way we travel and interact with the world around us. We must know the importance of latitude and longitude in our daily life, as it helps us in determining the location of a particular place.Coordinates of a particular location that you know or would like to know:The coordinates of the place I would like to know is the Niagara Falls. The coordinates of Niagara Falls are 43.0828° N, 79.0742° W.

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Answer:  1144

Step-by-step explanation:

Given: Machine A makes 7 parts every 10 minutes.

i.e. it makes \(\dfrac{7}{10}\) parts in 1 minute.

Machine B makes 16 parts every 15 minutes.

i.e. it makes \(\dfrac{16}{15}\) parts in 1 minute.

On Monday,

machine A makes parts for 12 hours(720 minutes).    [1 hour = 60  minutes, 12 hours = 12 x 6 = 720 minutes]

i.e. Total parts made = \(\dfrac{7}{10}\times720\)

i.e. Total parts made = 504

machine B makes parts for 10 hours(=60x 10=600 minutes)

i.e. Total parts made = \(\dfrac{16}{15}\times600\)

i.e. Total parts made = 640

Total parts made by both machines = 504+640 =1144

Hence, the total number of parts made by the two machines on Monday=1144.

The value of x as an int variable is 0

An int(integer) variable is a variable containing only whole numbers.

Given the expression;

x = - 3 + 4 % 6/ 5

Let's make into proper fraction, we have

x = - 3 + {}4/ 100 × 6/ 5

Multiply through

x = -3 + 6/ 5/ 4/ 100

x = -3 + {6/ 5 ÷ 0. 4}

x = -3 + {3}

expand the bracket

x = -3 + 3

Add like terms

x = 0

Thus, the value of x as an int variable is 0

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Complete question;

Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;

Answer:

x = 15

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{MP}{XZ}\) = \(\frac{NP}{YZ}\) ( substitute values )

\(\frac{x+5}{30}\) = \(\frac{4x-10}{75}\) ( cross- multiply )

30(4x - 10) = 75(x + 5) ← distribute parenthesis on both sides

120x - 300 = 75x + 375 ( subtract 75x from both sides )

45x - 300 = 375 ( add 300 to both sides )

45x = 675 ( divide both sides by 45 )

x = 15

Answer:

1/10

Step-by-step explanation:

first you find the common denominator.

multiply 1/2 by 5 and 2/5 by 2

now you have 5/10-4/10

now its easy and the answer is 1/10

Step-by-step explanation:

answer is 5/10-4/10= 1/10 sorry if im wrong

Answer:5.67* 10^7

Step-by-step explanation:

A) we would send Order A to Factory 3.

B) we would send both Order B and Order C to Factory 3.

B 7,000 Factory 3

C 30,000 Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

To make decisions about which factory to send the orders to on Monday and Tuesday, we need to compare the costs per unit for each factory and consider the total number of units to be produced. Let's go through each day's scenario and make the production decisions.

a) Monday: Order A for 15,000 units

To decide which factory to send the order to, we compare the costs per unit for each factory. We select the factory with the lowest cost per unit to minimize the average cost per unit for the company.

Let's assume the costs per unit for each factory are as follows:

Factory 1: $10 per unit

Factory 2: $12 per unit

Factory 3: $9 per unit

To calculate the total cost for each factory, we multiply the cost per unit by the number of units:

Factory 1: $10 * 15,000 = $150,000

Factory 2: $12 * 15,000 = $180,000

Factory 3: $9 * 15,000 = $135,000

Based on the calculations, Factory 3 has the lowest total cost for producing 15,000 units, with a total cost of $135,000. Therefore, we would send Order A to Factory 3.

b) Tuesday: Order B for 7,000 units and Order C for 30,000 units

We have two options: sending each order to a separate factory or sending both orders to the same factory. We need to compare the average cost per unit for each option and select the one that results in the lowest average cost per unit.

Let's assume the costs per unit for each factory remain the same as in the previous example. We will calculate the average cost per unit for each option:

Option 1: Sending orders to separate factories

For Order B (7,000 units):

Average cost per unit = ($10 * 7,000) / 7,000 = $10

For Order C (30,000 units):

Average cost per unit = ($9 * 30,000) / 30,000 = $9

Total number of units produced for the company today = 7,000 + 30,000 = 37,000

Average cost per unit for all production today = ($10 * 7,000 + $9 * 30,000) / 37,000 = $9.43 (rounded to two decimal places)

Option 2: Sending both orders to the same factory (Factory 3)

For Orders B and C (37,000 units):

Average cost per unit = ($9 * 37,000) / 37,000 = $9

Comparing the two options, we see that both options have the same average cost per unit of $9. However, sending both orders to Factory 3 simplifies the production process by consolidating the orders in one factory. Therefore, we would send both Order B and Order C to Factory 3.

Production Report for Tuesday:

Order # of Units Factory

B   7,000      Factory 3

C  30,000    Factory 3

Total number of units produced for the company today: 37,000

Average cost per unit for all production today: $9.00

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The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

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Answer: A ratio is one thing or value compared with or related to another thing or value; it is just a statement or an expression, and can only perhaps be simplified or reduced. On the other hand, a proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved.

Step-by-step explanation: looked it upp

Answer: 4 :1 , 2

(The explanation is in the .pdf)

The position of the mean and standard deviation are shown in the diagram below:

The mean is value at the center of the distribution

The standard deviation is the difference between the mean and the first value to the right

Comparing the given graph to the diagram above, we can conclude that:

Answer:

Answer:

25.981 seconds

Step-by-step explanation:

because X represents the magnitutde of falling height substitute 1200 into the original equation and you will find the above answer

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

To divide polynomials by a polynomial, we use the long division method.

When there is no common factor in both the numerator and the denominator, we can use the long division.

It may be used to find reminders and quotients while dividing.

Here we have

Divide 3x² + 6 by 3x – 3    

On dividing 3x² + 6 by 3x – 3 in long division method

we get the remainder as 9 and the quotient as (x - 1)

For more understanding understand the long division in the given picture.

Therefore,    

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

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Answer:

(a) Three numbers that could be Jenny's favorite number are;

2, 8, and 18

(b) Yes

Step-by-step explanation:

(a) Let Jenny's favorite integer be X, we have;

√X × √2 = Y where Y is an integer

Therefore, the square root of Jenny's favorite number has a factor of √2 which gives the possible options as

2 with √2 being the square root

8 with √8 = 2·√2

18 with √18 being 3·√2

(b) By dividing each of the square root of the possible Jenny's favorite number, we have;

i) For the integer 2 we have;

√2/√2 = 1 which is an integer

ii) For the integer 8 we have;

√8/√2 = 2·√2/√2 = 2 which is an integer

ii) For the integer 18 we have;

√18/√2 = 3·√2/√2 = 3 which is an integer

Answer:

180,000

Step-by-step explanation:

7*10^5 is 700,000. 5.2*10^5 is 520,000

700,000-520,000 is 180,000

The readability of a double-pan torsion balance is typically very small, usually in the range of a few milligrams (mg). This is because the double-pan torsion balance is a highly sensitive instrument used to measure very small masses.

The readability of a double-pan torsion balance is determined by the sensitivity of the torsion spring which is used to measure the mass on the scale pans. The higher the sensitivity of the torsion spring, the higher the readability of the double-pan torsion balance. The readability of a double-pan torsion balance is typically in the range of 0.1 to 0.5 mg.

This allows the balance to measure very small increments with a high degree of accuracy and precision. The readability of a double-pan torsion balance is critical for accurate measurements of very small masses, such as in the pharmaceutical, chemical and food industries.

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Answer:

put the equations in tiger math

Step-by-step explanation:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

|

|

|

|

| x

|

|

|

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

|

|

|

|

|

|

|

|

|

B

|

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|

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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The angle which the velocity of electron make with the magnetic field is :  Smaller value = 88.3°, Larger value = 91.7°.

The angle that the velocity of the electron makes with the magnetic field is given by:

θ = arctan(F/mv²B)

where F is the magnetic force on the electron,

m is the mass of the electron,

v is the velocity of the electron, and

B is the magnetic field.

Substituting the given values, we have:

θ = arctan((1.40 × 10⁻¹⁶ N)/(9.11 × 10⁻³¹ kg × (4.10 × 10³ m/s)² × 1.28 T))≈ arctan(2.35 × 10⁷)

The angle θ lies between 0° and 90° because the tangent function is positive in the first quadrant.

Using a calculator, we find that:θ ≈ 88.3°

Therefore, the smaller value is 88.3° and the larger value is 180° - 88.3° = 91.7°.

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Answer:

1/10

Step-by-step explanation:

not sure

The dimensions required to minimize the cost of fencing is 180ft and 360 ft.

According to question

The cost of fence on opposite side of river is $40.

The cost of fence on other sides of river is $10.

Total yield = 64800 sq. feet

Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.

Area of fence = xy = 64800 sq feet

⇒ \(y = \frac{64800}{x}\)

Let C be the cost of making fence.

For cost to be minimum, dC/dx should be equal to zero.

C = 40x + 10y * 2

⇒ C = \(40x + 10(\frac{64800}{x})*2\)

⇒ \(\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0\)

⇒ \(40x^{2} = 20 * 64800\)

⇒ \(x^{2} = 32400\)

⇒ \(x = 180\)

⇒ \(y = \frac{64800}{180} = 360\)

So, the dimensions needed will be 180 ft and 360 ft.

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compute the dot product ∇f • dr = (∂f/∂x)(dx/dt) + (∂f/∂y)(dy/dt), and integrate it with respect to t over the interval [0, 1] to obtain the line integral.

To find the value of Cnablaf�dr, we need to use the formula: Cnablaf�dr = f(b) - f(a), where a and b are the endpoints of the given curve. In this case, a = (1,1) and b = (5,3) as per the given parametric equations.
To find the value of f at each point, we can refer to the given table of values and interpolate between the points if needed.
So,
f(a) = f(1,1) = 6
f(b) = f(5,3) = 10
Therefore,
Cnablaf�dr = f(b) - f(a) = 10 - 6 = 4
Given the table of values for function f and parametric equations x = t^2 + 1 and y = t^3 + t, we want to find the line integral ∫C∇f • dr from t = 0 to t = 1. First, compute the derivatives dx/dt = 2t and dy/dt = 3t^2 + 1. Next, find the gradient ∇f, which is (∂f/∂x, ∂f/∂y). Using the table, we can estimate these partial derivatives at the points along C. Finally, compute the dot product ∇f • dr = (∂f/∂x)(dx/dt) + (∂f/∂y)(dy/dt), and integrate it with respect to t over the interval [0, 1] to obtain the line integral.

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Answer:

y = 1

Step-by-step explanation:

When x= -4, the value for y is 1.

hope this helps! <3

Yes, these values indicate a difference in popularity. Using a 0.01 significance level, the p-value for this test is 0.0018, which is less than the significance level.

This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.

1. The candidate has a population of voters that he wishes to test to see if there is a difference in his popularity between men and women.

2. He conducts a survey of 250 men and 250 women, 44% of the men favoring his candidacy and 52% of the women favoring his candidacy.

3. To determine if there is a significant difference between the two samples, we first calculate the difference in proportions between the two groups:

52% - 44% = 8%.

4. We then use a 0.01 significance level to conduct a two-tailed z-test for proportions to determine if there is a statistically significant difference between the two groups.

5. The p-value for this test is 0.0018, which is less than the significance level of 0.01.

6. This means that there is statistical evidence to support the claim that there is a difference in the candidate's popularity between men and women.

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