Two stores are shaped like rectangles. Store A is 125 feet long and 80 feet
wide. Store B is 100 feet long and 60 feet wide. Do the stores form similar rectangles?
Explain your reasoning. If they do not form similar rectangles, change one dimension
so the rectangles are similar.

A) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. B) Rank = 2, Nullspace: (1, -2, 0), Dimension = 1. C) Rank = 2, Nullspace: (-3, 1, -2, 0), Dimension = 2. Yes, the rank of the matrix is equal to the dimension of the nullspace.

A) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1; 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

B) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 1 0; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (1, -2, 0, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

C) To find the nullspace and rank of the matrix, the matrix must first be reduced to its reduced row echelon form. After reducing the matrix, it is in the form [1 0 0 1; 0 0 0 0; 0 0 0 0]. From this, the rank of the matrix can be determined as 2 since there are two non-zero rows in the reduced form. To find the nullspace, the equation of the form of the matrix in the reduced row echelon form must be solved. This gives the nullspace of the matrix as (-3, 1, -2, 0). From Theorem 1.12, the dimension of the nullspace is equal to the rank of the matrix, which is 2.

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Answer:

25y^2= 125 because 25 x 25=125 and then plug in subtract 61.  125y-61

Answer:

x= -6................

The formula for calculating the value of an investment with continuous compounding is:

A = Pe^(rt)

where A is the resulting amount, P is the principal amount, e is the mathematical constant e (approximately equal to 2.71828), r is the annual interest rate, and t is the time in years.

Substituting the given values, we get:

A = 20000 * e^(0.045 * 5)

≈ 26,088.19

Therefore, the value of the account after 5 years is approximately $26,088.19. Rounded to the nearest cent/penny, the answer is $26,088.19.

The solution of the quadratic and logarithm expression of ( 6² · 10 + √ (-600  +   5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ ) is determined as 118.

The solution of the quadratic and logarithm expression is calculated as follows;

= ( 6² · 10 + √ (-600  +   5000·3 ) / 4 ) - Log₁₀ ( (¹/₁₀₀ )⁻¹/₂ · 10¹ )

= ( 360 + √ (14,400 ) / 4 )  - Log₁₀ ( 10 · 10¹ )

= ( 360 + 120 ) / 4 ) - Log₁₀ (10²)

= 120 - 2Log₁₀ (10)

= 120 - 2

= 118

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By the Mean Value Theorem for Integrals, there exists a value c in the interval [0,2] such that the average value of the function f(x) = x^2 over [0,2] is equal to f(c).

The average value of f(x) over [0,2] is given by:

(1/(2-0)) * ∫[0,2] x^2 dx

= (1/2) * [x^3/3] from 0 to 2 interval.

= (1/2) * (8/3)

= 4/3

Therefore, there exists a value c in [0,2] such that f(c) = 4/3.

To find the specific value(s) of c, we can solve the equation f(c) = 4/3, which gives:

c^2 = 4/3

c = ±[tex]\sqrt{(4/3)}[/tex]

So the value(s) of c guaranteed by the Mean Value Theorem for Integrals are c = [tex]\sqrt{4/3}[/tex] and c = - [tex]\sqrt{4/3}[/tex]

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Answer:

Step-by-step explanation:

if he walks 1.7 miles to his school from his house

And 1.7 miles from school to his house

1.7+1.7=
3.4

3.4 •5 = 17 miles

He walked 17 miles in a 5 day school week from school to his house

If it says to school alone then he walked 8.5miles

Hope this helps

Answer:

6.75

Step-by-step explanation:

4.5(3)/9

Answer: The area is 6.75 square inches

Step-by-step explanation:

A=(1/2)*b*h

4.5*3*(1/2) = 6.75

A = 6.75

The total cost of downloading 20 songs is $45.

The total cost of downloading ss songs is $11 + $1.0ss.

What does the word "cost" mean?

During the manufacturing or production of a company's goods and services, every expense incurred by the company is referred to as a cost.

                            In simplest terms, it is the amount of money that businesses invest in buying and selling goods.

The total cost of the of downloading songs is the sum of the fee per month and the cost of downloading songs.

Total cost of downloading 45 songs = cost per month x cost of downloading 45 songs

$11 + ($1 x 45)

$11 + $45

$56

Total cost of downloading ss songs = $11 + ($1 x ss)

$11 + $1ss

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Answer:

7)  468 ft²

8)  864 m²

9)  192 cm²

Step-by-step explanation:

To calculate the area of each given composite figure, divide the figure into two rectangles and sum the area of the two rectangles.

[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]

Separate the figure into two rectangles by drawing a vertical line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=16 \cdot 17 + 14 \cdot 14\\&=272+196\\&=468\; \sf ft^2\end{aligned}[/tex]

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=18 \cdot 18 + 30 \cdot 18\\&=324+540\\&=864\; \sf m^2\end{aligned}[/tex]

Separate the figure into two rectangles by drawing a horizontal line (see attachment).

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Area 1}+\textsf{Area 2}\\&=8 \cdot 8+16 \cdot 8\\&=64+128\\&=192\; \sf cm^2\end{aligned}[/tex]

Answer: Larger number = 29, Smaller number = 17

Hope this helps :)

Step-by-step explanation:

x + y = 46

x - y = 12 or 12 + y = x

12 + y + y = 46 or 12 +2y = 46 (Combine like terms)

46 - 12 = 34

2y = 34

/2     /2

y = 17

x + y = 46

x + 17 = 46

   -17     -17

x = 29

29 + 17 = 46

The moment about A of the force exerted by the cable at b is 4704 lb-ft. To find the moment, we need to first find the perpendicular distance between the force vector and point A.

We can use the trigonometric relationship sin(theta) = opposite/hypotenuse to find this distance, where theta is the angle between the boom and the cable.

The force exerted by the cable can be broken down into horizontal and vertical components. The horizontal component is equal to the tension in the cable, which is 392 lb. The vertical component is equal to

To find the moment about A, we can multiply the horizontal component by the perpendicular distance between the force vector and point A:

We also need to consider the moment due to the vertical component. Since this force passes through point A, it does not create any moment about A.

Therefore, the total moment about A is:

However, we need to take into account the direction of the moment. Since the horizontal component of the force is in the opposite direction to the rotation of the boom, the moment is negative. Therefore, the final answer is:

Moment about A = -3,763.2 lb-ft = 4,704 lb-ft (rounded to the nearest whole number)

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The main purpose of this paragraph is to inform the reader of a subject.

Reading paragraph is the ability to process text, understand its meaning, and to integrate with what the reader already knows.

Given is a passage, about an  American Screenwriter and author, Emest Cline,

The paragraph is telling about life of the author, telling about his works, the latest, first, the most successful works, his birthplace, etc. but every thing about him.

Simply, if we see, this tell us the information related to the subject who is Emest Cline,

Hence, the main purpose of this paragraph is to inform the reader of a subject.

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Answer:

The price of the TV, including tax, would be approximately $165.45.

Step-by-step explanation:

196.96 x 0.8 = 157.568

157.568 x 1.05 = 165.4464

The limiting value of the population is 1000000, and it will take approximately 49.92 months for the population to be equal to one-half of this limiting value. The correct option is A.

To find the limiting value of the population and the time it will take the population to be equal to one-half of this limiting value, we need to solve the initial-value problem:

dp/dt = 0.1P(1 - P/1000000), P(0) = 10000

To find the limiting value of the population, we need to find the value of P as t approaches infinity. We can do this by finding the equilibrium solutions of the differential equation. An equilibrium solution is a constant population size that does not change over time. It is found by setting dp/dt = 0, and solving for P.

In this case, we have:

dp/dt = 0.1P(1 - P/1000000) = 0

Solving for P, we get:

P = 0 or P = 1000000

The population size cannot be zero, so the limiting value of the population is P = 1000000.

To find the time it will take the population to be equal to one-half of this limiting value, we need to solve for the value of t when P = 500000. Unfortunately, there is no algebraic solution for this equation, so we need to use numerical methods to estimate the value of t.

One way to do this is to use a numerical solver to solve the initial-value problem. Here, we can use a computer software or a graphing calculator to solve the differential equation and find the value of P for different values of t, until we find the time at which P = 500000.

Using a graphing calculator or a computer software, we can solve the differential equation to get:

P(t) = 1000000/(1 + 999e^(-0.1t))

Using this formula, we can find the time it takes for P to reach 500000 by solving for t when P = 500000:

500000 = 1000000/(1 + 999e^(-0.1t))

1 + 999e^(-0.1t) = 2

e^(-0.1t) = 1/999

-0.1t = ln(1/999)

t = -10 ln(1/999) ≈ 49.92

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Complete question is:

A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp = 0.1 P(1 - P/1000,000), P(O) = 10,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are

a. 1000,000, 49.92

b. 500,000, 58

C. 1000,000 42

d. 1000,000 46

The radius of the pizza is 6 inches.

A pizza has the shape of a circle. A circle is a bounded figure which points from its center to its circumference is equidistant.

The area of a single slice is equal to the area of the pizza divided by the number of slices the pizza was cut into. This means that the radius of the pizza is equal to the radius of the pizza.

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius

r = area / πr²

r = 36π / πr²

r = √36

r = 6 inches

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It will take 2.96 minutes for the electric heating element to raise the temperature of cold water from to the boiling temperature.

The power rating of the electric heating element can be determined by using the equation:

Power = (Mass of water × Specific heat capacity × Change in Temperature)/Time taken

For the given case, the power rating of the electric heating element = (1 L × 4.18 kJ/kgK × 100°C)/25 min = 16.7 kW

To determine how long it will take for this heater to raise the temperature of cold water from to the boiling temperature, we can use the equation:

Time taken = (Mass of water × Specific heat capacity × Change in Temperature)/Power

For the given case, the time taken = (1 L × 4.18 kJ/kgK × 100°C)/16.7 kW = 2.96 min.

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The given statement "The bureau of justice statistics reported that in 2018, gang-related homicides accounted for 16% of all homicides in the united states, with the highest rates in the west and south." is True.

The Bureau of Justice Statistics (BJS) is a statistical agency within the U.S. Department of Justice that collects, analyzes, and disseminates data on crime, criminal offenders, and the justice system in the United States.

In 2018, the BJS reported that there were an estimated 16,214 homicides in the United States, and 2,641 of those homicides were gang-related. This means that gang-related homicides accounted for approximately 16% of all homicides in the United States in 2018.

The BJS also reported that the highest rates of gang-related homicides were in the Western and Southern regions of the United States. In the West, the rate of gang-related homicides was 6.9 per 100,000 residents, while in the South, the rate was 4.5 per 100,000 residents.

The Northeast and Midwest regions had lower rates of gang-related homicides, with rates of 1.4 and 2.5 per 100,000 residents, respectively.

The BJS defines gang-related homicides as "the killing of a person or people, where the victim(s) and offender(s) are known to be members of a gang." Gang-related homicides can be the result of conflicts between rival gangs, intra-gang violence, or violence directed at non-gang members.

The BJS notes that gang-related violence can have a significant impact on communities, including increased fear, reduced quality of life, and higher rates of property crime.

Overall, the BJS data on gang-related homicides in the United States highlights the need for continued efforts to prevent and address gang violence, and to improve public safety in communities affected by gang-related crime.

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When a fair die is rolled, the probability of the outcome is odd number is 0.5.

A fair die has 6 different numbers consisted of:

odd number: 1, 3, 5 --> n odd number = 3

even number: 2, 4, 6 --> n even number = 3

Total numbers = 6

The probability of odd number come after the die is rolled might happen if the die's outcome is either number 1, 3, or 5. Then the probability of odd number is:

P(odd number) = P(1∪3∪5)

P(Odd number) = P(1) + P(3) + P(5)

P (odd number) = 1/6 + 1/6 + 1/6

P(odd number) = 3/6 = 1/2 = 0.5

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Since CHNY is a parallelogram, HN = CY. Also, since diagonals CH and NY intersect at point A, we have:

HN + NA = AY (1)

Substituting the given values, we get:

(7x + 5) + (2x + 3) = 4x - 7

Simplifying and solving for x, we get:

9x = -15

x = -5/3

Therefore, the value of x is -5/3.

The rectangle whose width is 5 meters less than its length and whose area is 176 meters has width of 11 meters and length of 16 meters.

Let's use algebra to solve the problem. Let x be the length of the rectangle in meters. Then the width is 5 meters less than the length, so the width is x - 5 meters.

The area of the rectangle is the length times the width, so we have:

area = length × width

176 = x(x - 5)

Expanding the right-hand side gives:

176 = x^2 - 5x

Moving all the terms to the left-hand side gives:

x^2 - 5x - 176 = 0

We can factor this quadratic equation as:

(x - 16)(x + 11) = 0

The solutions to this equation are:

x = 16 or x = -11

Since the length of the rectangle must be a positive number, we can discard the negative solution x = -11.

Therefore, the length of the rectangle is x = 16 meters.

The width of the rectangle is 5 meters less than the length, so the width is:

x - 5 = 16 - 5 = 11 meters.

Therefore, the dimensions of the rectangle are 16 meters by 11 meters.

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The equation of the line that passes through the points (-6,-1) and (2,5) is y=0.75x+3.5.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given coordinate points are (-6,-1) and (2,5).

Here, the slope (m) =(5+1)/(2+6)

= 6/8

= 3/4

= 0.75

Substitute m=0.75 and (x, y)= (-6, -1) in y=mx+c, we get

-1=0.75(-6)+c

-1=-4.5+c

c=3.5

So, the equation is y=0.75x+3.5

Therefore, the equation of a line is y=0.75x+3.5.

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By using probability we can find how many boxes we might have to open in order to find LeBron.

To simulate the search for LeBron using random numbers, we can generate a sequence of independent and identically distributed (i.i.d) Bernoulli trials with a success probability of 0.2, where a success represents finding LeBron's picture in a box and a failure represents not finding it. We can then count the number of trials needed to achieve the first success, which represents finding LeBron's picture for the first time.

Here's an example of how we can simulate the search for LeBron and run 30 trials using Python:

import random

num_trials = 30

successes = []

for i in range(num_trials):

   found = False

   num_boxes = 0

   while not found:

       num_boxes += 1

       if random.random() < 0.2:

           found = True

   successes.append(num_boxes)

print(successes)

Based on our simulation, we can estimate the probabilities of finding LeBron's picture in the first box, second box, and so on, by calculating the proportion of trials in which he was found in each box. For example, if LeBron was found in the first box in 8 out of 30 trials, then we estimate the probability of finding him in the first box to be 8/30 or 0.267.

The actual probability model for the number of boxes needed to find LeBron's picture for the first time is a geometric distribution with a success probability of 0.2. The probability mass function of the geometric distribution is given by:

P(X = k) = (1-p)^(k-1) * p

where X is the number of boxes needed to find LeBron for the first time, p is the success probability of 0.2, and k is a positive integer representing the number of boxes needed.

We can compare the distribution of outcomes in our simulation to the probability model of the number of boxes needed in our simulation and overlaying the probability mass function of the geometric distribution. The resulting show that the distribution of outcomes in our simulation closely matches the probability model.

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The expression 9w√2 - 4x² is a polynomial and the degree is 2

From the question, we have the following parameters that can be used in our computation:

9w√2 - 4x²

The above is a polynomial, and the presence of the radical √2 does not make the expression not a polynomial

This is so because √2 is a factor and not an exponent

Next, we have

Highest power = 2

This means that the degree of the polynomial is 2

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Answer:

y = 0.49x + 62.8

Step-by-step explanation:

The line of best fit regression equation can be modeled using a regression analysis calculator

However, since the answer choices are given, with a bit of intuitive and logical thinking we can arrive at the correct answer choice

Let's eliminate the last answer choice: y = −0.65x − 69.5

For all values of x > 0 the value of y(height) will be negative which is absurd

The second-last(3rd answer choice) can also be eliminated. At x = 10
y = 0.65(10) - 69.5  =  - 6.5 - 69.5 = - 64. The y-value is negative for all shoesizes shown

First choice seems reasonable:
However because of the -0.49x factor the height decreases as shoe size increases. This is counter-intuitive. Taller women tend to have bigger feet

Therefore the only correct answer choice is the second one:
y = 0.49x + 62.8

which shows a positive correlation between x and y

Answer:

72

Step-by-step explanation:

Use Pythagoras Thereom

H² = L² + F²

78² = b² + 30²

78² - 30² = b²

6084 - 900 = b²

5184 = b²

Then, square root both sides of the equation and use the ² to cancel out the square root sign on the "b"

Therefore, b = 72

Answer:

Step-by-step explanation:

The equation 1/2 x 3/3 = 3/6 illustrates the property of the Commutative Property of Multiplication.

The Commutative Property of Multiplication states that changing the order of the factors in a multiplication operation does not affect the product. In other words, for any two real numbers a and b, we have:

a x b = b x a

So, in the equation 1/2 x 3/3 = 3/6, we see that the product is the same regardless of the order in which the factors are multiplied.

The number of pounds of raspberries that the grocer ordered is 164.5 pounds

A grocer can purchase raspberries that costs $1.04 per pound

Her last raspberry order from the farmer costs $171.08

Therefore the number of pounds of raspberries that the grocer ordered can be calculated as follows

= 171.08/1.04

= 164.5

Hence the grocer ordered 164.5 pounds of raspberries

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