2. Which of the following best represents the
range of the function?
a. All real numbers.
b. y ≤ 3
c. y = 3
d. x ≤ 3

The decimal equivalent of the binary string 01001010001101 using the 14-bit simple model with an exponent bias of 15 is 51/32

What is a binary string?

A binary string is a finite sequence of characters or digits that consists of only two possible symbols, typically represented as "0" and "1". These symbols correspond to the binary numeral system, where each digit represents a power of two. Binary strings are commonly used in computer science and digital communication systems to represent and manipulate binary data.

To convert the binary string 01001010001101 to its decimal equivalent using the 14-bit simple model with an exponent bias of 15, we can follow these steps:

Identify the sign bit: The leftmost bit (bit 0) represents the sign of the number. In this case, the sign bit is 0, indicating a positive number.

Determine the exponent: The next 5 bits (bits 1-5) represent the exponent. Convert these bits to decimal and subtract the bias to obtain the actual exponent value. In this case, the exponent bits are 10010. Converting 10010 to decimal gives us 18. Subtracting the bias of 15, the actual exponent is \(18 - 15 = 3.\)

Calculate the significand: The remaining 8 bits (bits 6-13) represent the significand or mantissa. To obtain the significant value, we convert these bits to decimal and divide by 2^8 (since there are 8 bits). In this case, the significant bits are 00110011. Converting 00110011 to decimal gives us 51. Dividing 51 by \(2^8,\)we get \(51/256.\)

Determine the decimal value: To calculate the decimal equivalent, we multiply the significand value by 2 raised to the power of the exponent. In this case, the decimal value is\((51/256) * 2^3 = 51/32.\)

Therefore, the decimal equivalent of the binary string 01001010001101 using the 14-bit simple model with an exponent bias of 15 is \(51/32.\)

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Answer:

4 different rays that can be formed from 3 collinear points.

Step-by-step explanation:

A ray is a part of a line that starts at a single point (called the endpoint) and extends infinitely in one direction.

A ray is named using its endpoint first, and then any other point on the ray, with an arrow on top, pointing in the direction of the ray. For example, the ray starting at point A and extending in the direction of point B is denoted as \(\overrightarrow{AB}\).

Collinear points are points that lie on the same straight line. Three or more points are said to be collinear if there exists a single straight line that passes through all of them.

Let the three collinear points be A, B and C (see attachment).

Each point can be the endpoint of a ray.

As point A if the left-most point, we can form one ray with point A as the endpoint. As this ray extends in the direction of points B and C, we can use either point B or point C as the directional point when naming the ray:

\(\overrightarrow{AB}\;\;\left(\text{or}\;\;\overrightarrow{AC}\right)\)

As point C if the right-most point, we can form one ray with point C as the endpoint. As this ray extends in the direction of points A and B, we can use either point A or point B as the directional point when naming the ray:

\(\overrightarrow{CB}\;\;\left(\text{or}\;\;\overrightarrow{CA}\right)\)

Finally, if we use point B as the endpoint of the ray, we can form two rays. As point B is between points A and C, we have one ray in the direction of point A, and the other ray in the direction of point C:

\(\overrightarrow{BA}\;\;\text{and}\;\;\overrightarrow{BC}\)

Therefore, there are 4 different rays that can be formed from 3 collinear points.

(a) The sum of everyone's utilities is highest when 2,000 people go After and the rest go Before is not a Nash Equilibrium beacuse it doesn’t meet the criteria for Nash Equilibrium.

(b) The Nash equilibrium number of After 7am drivers is 4000.

(c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

a) No, it is not a Nash Equilibrium.

Nash Equilibrium is a set of strategies that make sure that no player can improve their own utility by unilaterally changing their strategy.

Therefore, let’s say that all players choose to follow the strategy of entering After 7 am, given that N>4000 people want to drive into Central London. In this scenario, everyone’s utility would be as follows:

u(After) = 50 – 0.01N

However, if a single person changes his strategy and chooses to enter Before 7 am instead, his utility would be 10 instead of the previous 0 (as he is still affected by the congestion even if he enters after).

Thus, the new utility for the person who switched would be greater than what they would have gotten before.

Therefore, this scenario doesn’t meet the criteria for Nash Equilibrium.

b) The Nash equilibrium number of drivers entering after 7 am can be found by the following formula:

50-0.01N=10

40=0.01N

N=4000

which means 4000 people should choose to go Before 7 am, and the rest should go After 7 am.

c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b.

Let’s say the congestion charge is C. In this case, the utility of entering After 7 am would be

u(After)

=30-0.01(N-A)+20

= 50-0.01N+20-0.01A-20 50-0.01N-0.01A-20 30-0.01N-0.01A

Thus, the Nash Equilibrium number of drivers entering after 7 am would be as follows:

30-0.01N-0.01A=10

20=0.01A

A=2000

N = 4000+2000

N = 6000

Therefore, a congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

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Answer:

8 weeks

Step-by-step explanation:

433-145=288

288÷36=8

Answer:

-11

Step-by-step explanation:

slope is change in y over change in x

-22/2

-11

Answer:

20 units

Step-by-step explanation:

1) find the side of the first square

side = P / 4 = 12:4 = 3 units

2) find the side of the second square

side = P / 4 = 16 : 4 = 4 units

3) use the Pythagorean theorem to find the hypotenuse of the right triangle

\(\sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5\) units

4)  find the perimeter of the third square

P = side x 4 = 5 x 4 = 20 units

Answer:

20 units

Step-by-step explanation:

The answer is D. x = 32 and x = 0

============================================================

Explanation:

Think of x-16 as y. In other words, let y = x-16

We have (x-16)^2 = 256 become y^2 = 256.

Solve for y to get y = 16 or y = -16. You apply the square root to both sides. Don't forget about the plus/minus. This is because (-16)^2 = (-16)*(-16) = 256. We square the negative as well.

--------

If y = 16, then y = x-16 solves for x to get

y = x-16

16 = x-16

x-16 = 16

x = 16+16

x = 32 is one solution

---------

Plug in y = -16 and isolate x

y = x-16

x-16 = y

x-16 = -16

x = -16+16

x = 0 is the other solution

----------

We can check each answer by plugging them back into the original equation

Let's try x = 0

(x-16)^2 = 256

(0-16)^2 = 256

(-16)^2 = 256

256 = 256 ... works

Now try x = 32

(x-16)^2 = 256

(32-16)^2 = 256

(16)^2 = 256

256 = 256 ... also works; both answers have been confirmed

Answer:

See below

Step-by-step explanation:

\( {5}^{2} - {1}^{2} \times {2}^{2} \\ \\ = 25 - 1 \times 4 \\ \\ = 25 - 4 \\ \\ = 21 \\ \\ \\ {7}^{2} + {4}^{3} \div {2}^{5} \\ \\ = {7}^{2} +( {2}^{2} )^{3} \div {2}^{5} \\ \\ = {7}^{2} + {2}^{2 \times 3} \div {2}^{5} \\ \\ = {7}^{2} + {2}^{6} \div {2}^{5} \\ \\ = {7}^{2} + {2}^{6 - 5} \\ \\ = 49 + {2}\\ \\ = 51\)

The laws of cosine , sine and the Pythagoras theorem can be used to find side length from angles .

The Law of Sines: This law states that the ratio of the sine of an angle to the length of the opposite side is constant for all sides of a triangle.

The Law of Cosines: This law states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the angle between them.

The Pythagorean Theorem: This theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

Therefore, the three stated methods can be used to find side length from angles

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Answer: \(y=\frac{1}{5}x\)

Step-by-step explanation:

\(y-1=\frac{1}{5}(x-5)\\\\y-1=\frac{1}{5}x-1\\\\y=\frac{1}{5}x\)

Answer:

Rs 85

Step-by-step explanation:

Cost of 5kgs of rice = Rs 425

Cost of 1 kg of rice = 425/5

= Rs 85

So, the cost of a kg of rice is Rs 85

The standard deviation of scores for this quiz is 0.

Standard deviation is a measure of how spread out the scores are in a set of data. It is calculated by finding the difference between each score and the mean, squaring those differences, and then finding the average of those squared differences.

In this case, since everyone in the class scored an 80, the mean is also 80. This means that the difference between each score and the mean is 0, and therefore the standard deviation is also 0.

Here is the step-by-step explanation:
1. Find the mean of the scores: (80+80+80+...+80)/40 = 80
2. Find the difference between each score and the mean: 80-80 = 0
3. Square those differences: 0^2 = 0
4. Find the average of those squared differences: (0+0+0+...+0)/40 = 0
5. The standard deviation is the square root of that average: √0 = 0

Therefore, the standard deviation of scores for this quiz is 0.

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Answer:

Corresponding angles

Alternate interior angles

Alternate exterior angles

Vertical angles

Step-by-step explanation:

Answer:

The product is  -81 t² + 16

Step-by-step explanation:

The product of two binomials (ax + b)(cx + d), where a, b, c, and d are constant

Multiply (ax) by (cx) ⇒ 1st × 1st

Multiply (ax) by (d) and (b) by (cx) ⇒ ext-reams and nears

Add the two products ⇒ like terms

Multiply (b) by (d) ⇒ 2nd × 2nd

Let us find the product of (9 t - 4) and (-9 t - 4)

Multiply the 1st two terms

∵ (9 t)(-9 t) = -81 t²

Multiply the ext-reams

∵ (9 t)(-4) = -36 t

Multiply the nears

∵ (-4)(-9 t) = 36 t

Add the like terms

∵ -36 t + 36 t = 0

Multiply the 2nd two terms

∵ (-4)(-4) = 16

Write the answer

∴ (9 t - 4)(-9 t - 4) = -81 t² + 0 + 16

∴ (9 t - 4)(-9 t - 4) = -81 t² + 16

The product is  -81 t² + 16

Answer:

It's C 2x - 4

Step-by-step explanation:

Answer:

The greatest possible time taken by Maria is 97.4 seconds.

Step-by-step explanation:

The greatest possible time taken by Maria occurs when she moves at constant rate and is equal to the length of the road divided by the length of the road. That is to say:

\(t = \frac{\Delta s}{v}\)

Where:

\(\Delta s\) - Length of the road, measured in meters.

\(v\) - Average speed, measured in meters per second.

Given that \(\Delta s = 380\,m\) and \(v = 3.9\,\frac{m}{s}\), the greatest possible time is:

\(t = \frac{380\,m}{3.9\,\frac{m}{s} }\)

\(t = 97.4\,s\)

The greatest possible time taken by Maria is 97.4 seconds.

Answer:

10

Step-by-step explanation:

The value of the account will reach $152,800 in 10 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Interest compounded continuously means there is no limit for the process of compound of interest. It is compounding infinite times.

The formula for calculating the final amount when the interest is compounded continuously is,

A = P e^(r t)

Here, A is the final amount, P is the initial or principal amount, r is the rate of interest and t is the number of years.

Given that,

A = $152,800

P = $79,000

r = 6.8% = 6.8/100 = 0.068

We have to calculate t.

152,800 = 79,000 e^(0.068 t)

152,800 / 79000 = e^(0.068 t)

1.934 = e^(0.068 t)

Taking logarithms on both sides,

㏑ 1.934 = ㏑ e^(0.068 t)

We have ㏑(a)ⁿ = n ㏑(a)

0.65968 = 0.068t ㏑ e

0.65968 = 0.068 t × 1

t = 9.7 ≈ 10 years

Hence the amount is compounded to $152,800 in 10 years.

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30% of students mean 30 students wear contact lenses from a random selection of 100 students studying in a university.

Percentage is a fraction or a ratio of a random sample in which the value of whole is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

Percentage is defined as a certain fraction or number out of a hundred. It is a fraction with the denominator 100, and the sign for it is "%."

Finding the proportion of a whole in terms of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:

Use the unitary approach or try adjusting the fraction's denominator to 100.

How to solve?

30 % = 30/100 of a sample = 0.3 of a sample

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Answer:

40 pages

Step-by-step explanation:

240/12 = 20 = pages read in 1 hour

20 x 2 = 40 = pages read in 2 hours

Answer:

4.5x-25.6

Step-by-step explanation:

Hey there!

4.3x – 8.1 + 0.2x – 17.5

COMBINE your LIKE TERMS

(4.3x + 0.2x) + (–8.1 – 17.5)

4.3x + 0.2x = 4.5x

–8.1 – 17.5 = –25.6

Answer: 4.5x – 25.6 ☑️

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Two buddies want to know how far a creek is across. The creek is (3x² - 3x - 3) feet wide.

We know the distance of Friend A from one end of bank and distance of Friend B from another end of the bank and the distance between Friend A and B which is the distance of the rope and we have to calculate the width of the creek.

Distance of rope = Distance of friend A from the one end of the bank + width of creek + distance of Friend B from another end of the bank

6x²- x + 12 = (2x²+2x-2) + width of the creek + (x²+17)

6x²- x + 12 = width of the creek + (2x²+ 2x - 2 + x² + 17)

6x²- x + 12 = width of the creek + ( 3x² + 2x + 15)

width of the creek = 6x²- x + 12 - ( 3x² + 2x + 15)

=  6x²- x + 12 - 3x² - 2x - 15

= 3x² - 3x - 3

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Given:

89.3%

To convert into decimal:

Hence, the answer is 0.893.

Answer:

The correct answers are:

A.) 110 - 16 = 10h

B.) 110 = 16h + 10

Step-by-step explanation:

Sylvie needs $110 for a concert ticket and already has $16 in her pocket. She can make up the difference by working an additional 10 hours at her job.

To earn the $110 required for the concert ticket, she'll need to work 10 hours in addition to the $16 she already has.

As a result, the following calculation can be used to calculate her hourly rate:

110 = 16 + 10h

110 - 16 = 10h

I hope this helps! ^-^

Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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A unit of measurement is a recognised and accepted standard for calculating other amounts of the same kind. It has already been decided by law or tradition.

One of the two widely used measuring systems in the United States is the metric system, which is frequently employed as the major measurement method in many other nations.

The fundamental units in this system of measurement include:

Meter for length measurements

Kilogram for mass measurement

Second for timekeeping

Liters serve as the standard measurement unit for liquid capacity, which is also known as volume.

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