If the constant of variation is 1150 and each student is paying $230 in rent, then the number of students renting the house can be determined by dividing the constant of variation by the rent paid per student. In this case, there are 5 students renting the house.
In an inverse variation, the relationship between two variables is such that the product of the variables remains constant. In this scenario, the rent paid by each student is inversely proportional to the number of students sharing the house. The constant of variation is given as 1150.
To find the number of students renting the house, we divide the constant of variation by the rent paid per student. Given that each student pays $230 in rent, we can calculate the number of students as follows:
1150 / 230 = 5
Therefore, there are 5 students renting the house. As the number of students increases, the rent paid by each student decreases, and vice versa, maintaining the inverse proportionality between the number of students and the rent.
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In 2 and 3 wrote each number in standard form 4x100+7x10+6x1+6x(1/10)+3x(1/100)+7x(1/1000) four and sixty eight thousandths
The number 476.637 written in standard form is four hundred seventy-six and six hundred thirty-seven thousandths.
To write each number in standard form, let's start with the given expression:
4x100 + 7x10 + 6x1 + 6x(1/10) + 3x(1/100) + 7x(1/1000)
Simplifying each term, we get:
400 + 70 + 6 + 0.6 + 0.03 + 0.007
Adding all the terms together, we have:
400 + 70 + 6 + 0.6 + 0.03 + 0.007 = 476.637
Therefore, the number 476.637 written in standard form is four hundred seventy-six and six hundred thirty-seven thousandths.
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The ratio of the side lengths of the smaller box to the side lengths of the larger box is lowest term is to
The calculted ratio of the side lengths is 2 : 3
How to determine the ratio of the side lengthsFrom the question, we have the following parameters that can be used in our computation:
Smaller box = 12 inchesLarger box = 18 inchesUsing the above as a guide, we have the following:
Ratio = Smaller box : Larger box
So, we have
Ratio = 12 inches : 18 inches
Simplify the ratio
Ratio = 2 : 3
Hence, the ratio is 2 : 3
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Question
A company is experimenting with two new boxes for packaging merchandise. Each box is a cube with the side lengths shown. (smaller box is 12 in, larger box is 18 in.)
What is the ratio of the side lengths of the smaller box to the side lengths of the larger box in lowest terms?
Roll dice 1000 times every time it lands on 6 take one away. Write exponential function.
he exponential function for the given problem is
f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]
Let Y denote the number of sixes subtracted in rolling a dice 1000 times.
Here, the probability that one die shows a 6 is equal to p = 1/6, and the number of trials, n = 1000.
So, the number of times a die does not show a 6 is (1 - p) = (5/6) per trial.
Thus, the number of sixes subtracted from the sum after 1000 trials is given by the exponential distribution function.
Mathematically, this function is defined as follows:
f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]
Therefore, the exponential function for the given problem is
f(y) = ((5/6) ^ y) × ((1/6) ^ (1000 - y)) × [1000! / y! (1000 - y)!]
where y = number of times a six is rolled and subtracted.
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We can define a function h(n) which gives us the expected value of the number of 6’s we’ll get in n throws of the dice if we take one away every time we roll a 6. The exponential equation is [tex]h(n) = f(n) - g(n) = \frac{n}{6} - 6 + (5/6)^n[/tex]
Let us define a function f(n) which gives us the expected value of the number of 6’s we’ll get in n throws of a fair dice. For one roll, f(1) = 1/6. Let’s say we make n throws of the dice.
Then we can calculate the probability that none of them are 6’s: (5/6)ⁿ.
Therefore the expected number of 6’s we get is just n times the probability that a single throw is a 6, which is 1/6. Therefore f(n) = n/6.
If every time the dice lands on a 6, one is taken away, then the probability that a roll results in a 6 changes to 1/5. Therefore we can define a new function g(n) which gives us the expected value of the number of times we’ll have to throw the dice until we get a 6:
g(1) = 1/6
g(n) = (5/6)
g(n-1) + 1/6
So, we can rewrite it in a more general way as,
[tex]g(n) = \frac{1}{6} + \frac{5}{6}g(n-1)[/tex]
This is a linear recursive relation with constant coefficients. We can write out the first few terms of the sequence:
[tex]g(1) &= 1/6\\g(2) &= 1/6 + 5/6 \cdot 1/6 = 11/36\\g(3) &= 1/6 + 5/6 \cdot 11/36 = 91/216\\[/tex]
In general,
[tex]\[g(n) = \frac{1 - (5/6)^n}{1 - 5/6} = 6 - (5/6)^n\][/tex]
Therefore we can define a function h(n) which gives us the expected value of the number of 6’s we’ll get in n throws of the dice if we take one away every time we roll a 6:
[tex]h(n) = f(n) - g(n) = \frac{n}{6} - 6 + (5/6)^n[/tex]
This is the exponential function you asked for.
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To determine if the brain can smell fear, scientists compared the saliva and sweat when people did which two activities?
The scientists compared the saliva and sweat when people did two activities to determine if the brain can smell fear. These activities are skydiving and lying.
The question is about the experiment conducted by scientists to determine if the brain can smell fear. The study was conducted by scientists who measured the saliva and sweat of people who were skydiving and lying to determine if the brain can smell fear. The human brain reacts differently to fear, and scientists wanted to study this reaction by monitoring the reactions of people who were afraid. They discovered that the brain can smell fear by analyzing the chemical changes in the sweat and saliva of people who were afraid. Sweat and saliva are two of the primary ways that the human body releases chemicals, including hormones. The sweat and saliva of people who were skydiving and lying were analyzed to determine if there was a chemical reaction to fear. The scientists discovered that the chemical composition of sweat and saliva changes when a person is scared. This discovery led them to conclude that the brain can smell fear.
The results of this study will help scientists better understand how the human brain reacts to fear and how it can help us to protect ourselves.
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Four candidates participated in a school election. Bianca received 1/2 of the votes, Chelsea received 0.28 of the votes, Darnell received 20% of the votes, and Francisco received the rest of the votes. What percent of the votes did Francisco receive?
The percentage of the votes did Francisco receive is = 2%
Given that:
Four candidates participated in a school election.
Bianca received 1/2 of the votes
Chelsea received 0.28 of the votes
Darnell received 20% of the votes
Francisco received the rest of the votes.
Solution:
We know that the sum of all the votes received by the candidates is 100%.
Bianca received 1/2 of the votes
Chelsea received 0.28 of the votes
Darnell received 20% of the votes
Francisco received the rest of the votes.
Therefore, the sum of the votes received by Bianca, Chelsea, Darnell, and Francisco is:
Bianca + Chelsea + Darnell + Francisco = 1/2 + 0.28 + 20% + Francisco%
We know that the sum of all the votes received by the candidates is 100%.
Bianca + Chelsea + Darnell + Francisco = 100%
Converting Bianca's fraction to percent, we get:
Bianca = 1/2 × 100%
Bianca = 50%
Now substituting the values in the expression we get:
50% + 28% + 20% + Francisco% = 100%
Simplify the expression by adding 50%, 28% and 20%
50% + 48% + Francisco% = 100%
98% + Francisco% = 100%
Now we can solve for Francisco by subtracting 98% from each side.
100% - 98% = Francisco%
2% = Francisco%
Hence, Francisco received 2% of the votes.
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fraction numerator x squared plus 7 x plus 6 over denominator x squared minus 3 x minus 4 end fraction
The fraction you provided can be expressed as (x^2 + 7x + 6) / (x^2 - 3x - 4).
Let's break down the fraction and analyze the numerator and denominator separately.
The numerator, x^2 + 7x + 6, is a quadratic expression. It represents a polynomial of degree 2. This expression can be factored as (x + 1)(x + 6). Therefore, the numerator can be written as (x + 1)(x + 6).
The denominator, x^2 - 3x - 4, is also a quadratic expression. It can be factored as (x - 4)(x + 1). Thus, the denominator can be expressed as (x - 4)(x + 1).
Combining the factored forms, the fraction simplifies to [(x + 1)(x + 6)] / [(x - 4)(x + 1)].
Now, we notice that the term (x + 1) appears both in the numerator and the denominator. These terms cancel each other out, leaving us with (x + 6) / (x - 4).
In conclusion, the given fraction (x^2 + 7x + 6) / (x^2 - 3x - 4) simplifies to (x + 6) / (x - 4).
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slove the linear equation x+4+3x=72.state the property that justiflies your first step and why you chose it
\
The solution to the equation is x = 9.71 (rounded to two decimal places). To solve the equation x + 4 + 3x = 72, we will combine like terms and then isolate the variable x.
To solve the linear equation x + 4 + 3x = 72, we'll combine like terms on the left side of the equation. The property that justifies this step is the distributive property. We distribute the coefficient 3 to both x terms, which results in 4x + 3x = 7x.
So, rewriting the equation with the combined like terms, we have 4x + 3x + 4 = 72.
The reason we chose to apply the distributive property is to simplify the equation by adding the coefficients of the x terms together. This allows us to work with a simpler equation and proceed with solving for x.
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In a circle with radius 6.5, an angle measuring 5.5 radians intercepts an arc. Find the length of the arc to the nearest 10th.
L ≈ 35.8 ,the length of the arc to the nearest tenth is 35.8 units
The formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length, is the circle's radius, and is the central angle in radians. The length of the arc to the nearest tenth is 35.8 units. Given, In a circle with radius r = 6.5, an angle measuring = 5.5 radians intercepts an arc. We know that the formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length, is the circle's radius, and is the central angle in radians. Substituting the values in the formula, we get:
L = rL = 6.5(5.5)L = 35.75 ≈ 35.8 (to the nearest 10th)
Therefore, the length of the arc to the nearest tenth is 35.8 units.
In a circle, the length of an arc intercepted by a central angle is determined by the central angle's size and the circle's radius. This is known as the arc's length formula. L=where L is the arc length, is the radius of the circle, and is the central angle in radians. We can use this formula to find the length of an arc intercepted by a central angle in a circle. Let's consider the following illustration to understand the concept better. In a circle with a radius of 6.5, an angle of 5.5 radians intercepts an arc. We'll use the arc length formula to find the arc's length, L.L= (Length of arc formula)Substitute the given value of r and in the formula. L = 6.5 × 5.5L = 35.75The length of the arc is 35.75 units. We'll round this answer to the nearest tenth to get the final answer. L ≈ 35.8Therefore, the length of the arc to the nearest tenth is 35.8 units.
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B. Directions: Make a real-life situation to represent the given integer.
Example: -25----- Joe owes Martin Php25
1. -18
2. +5
3. -38
4. 90
5. +7
3. -38: Sarah's bank account balance is -$38, indicating that she has overdrafted and owes the bank money.
The integer -38 can be represented in a real-life situation where Sarah's bank account balance is negative, indicating an overdraft.
In this scenario, the negative integer -38 represents a negative bank account balance. When Sarah checks her bank account, she sees that her balance is -$38. This means that she has overdrafted her account and owes the bank $38. The negative sign indicates a deficit or debt in this real-life situation. Sarah will need to deposit funds into her account to bring her balance back to positive and clear her debt to the bank.
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Devi bought 7 skits at $x each, n skirts at $12 each, (2n+1) skirts at $15 each and 4 skirts at $3x each. find the total costs of the skirts she bought.
(pls give step by step answers!!)
The total cost of the skirts Devi bought is $19x + $42n + $15. The cost can be calculated by multiplying the number of skirts (4) by the cost per skirt ($3x).
To find the total cost of the skirts Devi bought, we need to calculate the sum of the costs of each type of skirt.
Let's break down the cost of each type of skirt:
Cost of 7 skirts at $x each: The cost can be calculated by multiplying the number of skirts (7) by the cost per skirt ($x).
Cost = 7 * $x = $7x
Cost of n skirts at $12 each: The cost can be calculated by multiplying the number of skirts (n) by the cost per skirt ($12).
Cost = n * $12 = $12n
Cost of (2n+1) skirts at $15 each: The cost can be calculated by multiplying the number of skirts (2n+1) by the cost per skirt ($15).
Cost = (2n+1) * $15 = $15(2n+1) = $30n + $15
Cost of 4 skirts at $3x each: The cost can be calculated by multiplying the number of skirts (4) by the cost per skirt ($3x).
Cost = 4 * $3x = $12x
Now, let's calculate the total cost by summing up the costs of each type of skirt:
Total Cost = Cost of 7 skirts + Cost of n skirts + Cost of (2n+1) skirts + Cost of 4 skirts
Total Cost = $7x + $12n + $30n + $15 + $12x
Total Cost = $7x + $12x + $12n + $30n + $15
Total Cost = $19x + $42n + $15
Therefore, the total cost of the skirts Devi bought is $19x + $42n + $15.
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What are software development methodologies? Question 3 options: Methods to divide tasks related to software creation and deployment up into tasks targeted at building better products with stronger product management guidelines and techniques. An expansion of the scope of a project. Developing work continually and iteratively, with a goal of more frequent prod
Software development methodologies are methods and approaches used to plan, organize, and manage the process of creating software.
They provide a framework for dividing tasks, setting guidelines, and implementing techniques to enhance the development process and improve the quality of software products.
Software development methodologies encompass a range of approaches and practices that guide the development lifecycle. They help teams structure their work, allocate resources, and establish communication channels to efficiently deliver software projects.
Common software development methodologies include:
Waterfall: A sequential approach where each phase of the development cycle is completed before moving on to the next.
Agile: Emphasizes flexibility and adaptability by breaking the project into iterative and incremental cycles, allowing for frequent product releases and continuous feedback.
Scrum: An Agile framework that focuses on collaboration, self-organization, and delivering value in short iterations called sprints.
Kanban: A visual system that tracks the flow of work and limits work in progress to improve efficiency and throughput.
Lean: A methodology that aims to eliminate waste, optimize resources, and continuously improve the software development process.
These methodologies, among others, provide guidelines, tools, and techniques to manage the software development process effectively, ensuring better product outcomes, stronger project management, and more frequent product deliveries when appropriate.
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What is the solution to the equation? a 5 and two-thirds = 9 a 5 and two-thirds = 9. A 5 and two-thirds 5 and two-thirds = 9 minus 5 and two-thirds. A = 3 and one-third. A 5 and two-thirds = 9. A 5 and two-thirds 5 and two-thirds = 9 5 and two-thirds. A = 14 and two-thirds. A 5 and two-thirds minus 5 and two-thirds = 9 5 and two-thirds. A = 14 and two-thirds. A 5 and two-thirds minus 5 and two-thirds = 9 minus 5 and two-thirds. A = 3 and one-third.
The solution to the equation a 5 and two-thirds = 9 is A = 3 and one-third.
To solve this equation, we can subtract 5 and two-thirds from both sides of the equation.
Starting with the equation a 5 and two-thirds = 9, we can subtract 5 and two-thirds from both sides:
a 5 and two-thirds - 5 and two-thirds = 9 - 5 and two-thirds.
Simplifying the equation, we get:
a = 9 - 5 and two-thirds.
To subtract 5 and two-thirds from 9, we need to convert both numbers to the same format. 9 can be written as 8 and two-thirds, so the equation becomes:
a = 8 and two-thirds - 5 and two-thirds.
Subtracting the fractions, we have:
a = 3 and one-third.
Therefore, the solution to the equation a 5 and two-thirds = 9 is A = 3 and one-third.
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To convert a Celsius temperature c to a Fahrenheit temperature, Fthe formula F=9/5c+32is used. Water boils at 100°c. What Fahrenheit temperature is this
The Fahrenheit temperature of 100°C is 212°F. So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.
Given, Celsius temperature c = 100°FTo find Fahrenheit temperature, we can use the formula:F = 9/5C + 32Put the given Celsius temperature into the formula:F = 9/5(100) + 32F = 180 + 32F = 212°F. Therefore, the Fahrenheit temperature of 100°C is 212°F.
We know that the formula for converting Celsius to Fahrenheit is given by:F = 9/5C + 32Where, F is the temperature in Fahrenheit and C is the temperature in Celsius.Water boils at 100°C. So, we need to find the Fahrenheit temperature when Celsius temperature is 100°F.So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.
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The half-life of a radioactive kind of europium is 15 years. If you start with 90,624 grams of it, how much will be left after 75 years?
Answer: To determine how much of the radioactive europium will be left after 75 years, we can use the half-life formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Given that the half-life of the radioactive europium is 15 years and the initial amount is 90,624 grams, we can substitute these values into the formula:
Amount remaining = 90,624 * (1/2)^(75 / 15)
Calculating the exponent first:
(75 / 15) = 5
Substituting this back into the formula:
Amount remaining = 90,624 * (1/2)^5
Simplifying the exponent:
(1/2)^5 = 1/32
Substituting this back into the formula:
Amount remaining = 90,624 * 1/32
Simplifying the calculation:
Amount remaining = 2,832 grams
Therefore, after 75 years, there will be approximately 2,832 grams of the radioactive europium left.
Karen drove 387 miles using 18 gallons of gas. At this rate, how many miles would she drive using 11 gallons of gas?
Karen would be able to drive approximately 241.83 miles using 11 gallons of gas, based on her previous rate of driving 387 miles with 18 gallons of gas.
To find out how many miles Karen would drive using 11 gallons of gas, we can set up a proportion based on the given information. We know that she drove 387 miles with 18 gallons of gas. Let's represent the unknown distance she would drive with 11 gallons of gas as 'x.' The proportion can be set up as follows:
387 miles / 18 gallons = x miles / 11 gallons
To solve for 'x,' we can cross-multiply and then divide:
18 * x = 387 * 11
18x = 4,257
x = 4,257 / 18
x ≈ 236.5
Therefore, Karen would be able to drive approximately 241.83 miles using 11 gallons of gas, assuming she maintains the same rate of fuel consumption.
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The stability of fats is influenced by their degree of unsaturation. Which fats are most susceptible to rancidity
Fats that are highly unsaturated, such as polyunsaturated fats, are most susceptible to rancidity.
Rancidity refers to the deterioration of fats and oils, resulting in undesirable odors and flavors. The stability of fats, or their resistance to rancidity, is influenced by their degree of unsaturation.
1. Fats are composed of fatty acids, which can be classified as saturated, monounsaturated, or polyunsaturated based on the presence of double bonds between carbon atoms in their chemical structure.
2. Saturated fats have no double bonds and are the most stable, as the absence of double bonds makes them less susceptible to oxidation and rancidity.
3. Monounsaturated fats have one double bond, which introduces some susceptibility to rancidity but to a lesser extent than polyunsaturated fats.
4. Polyunsaturated fats have multiple double bonds, making them the most susceptible to rancidity. The presence of multiple double bonds provides more sites for oxidation, leading to increased chemical reactivity and the potential for rancid flavors and odors to develop.
5. Common examples of polyunsaturated fats include vegetable oils such as soybean oil, corn oil, and sunflower oil. These oils are often stored in dark bottles and refrigerated to slow down the oxidation process and extend their shelf life.
In summary, fats that are highly unsaturated, particularly polyunsaturated fats, are the most susceptible to rancidity due to the presence of multiple double bonds, which increase their susceptibility to oxidation and degradation.
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Draw a visual model to show how many tiles she will use. Then explain how you can use your visual model to find the area of the enterway
A grid representing the floor plan of the entryway with tiles arranged in a square pattern. Each square represents one tile.Visual model
By counting the number of squares in the grid, we can determine the total number of tiles used. To find the area of the entryway, we multiply the number of tiles by the area covered by each tile. The area covered by each tile can be determined by measuring the length and width of a single tile and multiplying them together.
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A number cube, labeled 1-6, is rolled 4
times. What is the probability that cube
will land on an even number three out of
four rolls?
When rolling a number cube four times, the probability of obtaining an even number in three of the four rolls is 1/4.
To calculate the probability that a number cube will land on an even number three out of four rolls, we need to consider the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes when rolling a number cube four times is 6^4, which is equal to 1,296. This is because each roll has six possible outcomes (numbers 1 to 6), and the rolls are independent events, so we multiply the number of outcomes for each roll.
Now, let's consider the favorable outcomes. We want the cube to land on an even number three out of four times. There are two cases that satisfy this condition: either the first, second, and third rolls are even, or the second, third, and fourth rolls are even.
Case 1: First, second, and third rolls are even.
The probability of rolling an even number on a single roll is 3/6, or 1/2 since there are three even numbers (2, 4, and 6) out of six total numbers on the cube.
So, the probability of the first, second, and third rolls being even is (1/2) * (1/2) * (1/2) = 1/8.
Case 2: Second, third, and fourth rolls are even.
Again, the probability of rolling an even number on a single roll is 1/2.
So, the probability of the second, third, and fourth rolls being even is (1/2) * (1/2) * (1/2) = 1/8.
Now, we need to add the probabilities from both cases because we are interested in the probability of either of these events occurring:
1/8 + 1/8 = 2/8 = 1/4.
Therefore, the probability that the cube will land on an even number three out of four rolls is 1/4.
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Drag the tiles to the correct boxes to complete the pairs.
Consider the functions below.
Match the expressions to the correct function combinations.
The correct function combinations for the given expressions are: Expression 1 with Function D, Expression 2 with Function A, Expression 3 with Function C, and Expression 4 with Function B.
To determine the correct function combinations for the given expressions, let's analyze each expression and its corresponding function.
Expression 1: 2x + 5
Function D: Linear function
Expression 1 is a linear function with a coefficient of 2 and a constant term of 5. Therefore, the correct function combination for Expression 1 is Function D.
Expression 2: x^2 + 3x + 2
Function A: Quadratic function
Expression 2 is a quadratic function with a squared term, a linear term, and a constant term. Thus, the correct function combination for Expression 2 is Function A.
Expression 3: √x
Function C: Square root function
Expression 3 represents a square root function, denoted by the radical symbol (√). Therefore, the correct function combination for Expression 3 is Function C.
Expression 4: |x|
Function B: Absolute value function
Expression 4 represents an absolute value function, indicated by the vertical bars surrounding the variable x. Hence, the correct function combination for Expression 4 is Function B.
In conclusion, the correct function combinations for the given expressions are Expression 1 with Function D, Expression 2 with Function A, Expression 3 with Function C, and Expression 4 with Function B.
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The number of crimes that occurred in a certain city per 1000 people had decreased from 45.3 in 1920 to 44.3 in 1970. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1970.
The average rate of change in the number of crimes per 1000 people in a certain city from 1920 to 1970 was a decrease of 0.1 crimes per 1000 people per year.
To find the average rate of change, we can use the formula:
Average rate of change = (final value - initial value) / (final year - initial year)
In this case, the initial value is 45.3 crimes per 1000 people in 1920, and the final value is 44.3 crimes per 1000 people in 1970. The initial year is 1920, and the final year is 1970.
Substituting the values into the formula, we get:
Average rate of change = (44.3 - 45.3) / (1970 - 1920)
= (-1) / 50
= -0.02 crimes per 1000 people per year
Therefore, the average rate of change in the number of crimes per 1000 people from 1920 to 1970 is a decrease of 0.02 crimes per 1000 people per year. This means that, on average, the number of crimes per 1000 people decreased by 0.02 every year during that period.
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Calculate the reciprocal of -0. 06, correct to 1 decimal place
The reciprocal of -0.06 is 1666.7.
To calculate the reciprocal of -0.06, we can use the definition of a reciprocal, which states that the reciprocal of a number is 1 divided by that number.
Reciprocal = 1 / Number
In this case, the number is -0.06. Therefore, we have:
Reciprocal = 1 / (-0.06)
To simplify, we can multiply both the numerator and the denominator by -100 to remove the decimal point:
Reciprocal = -100 / (-0.06)
Simplifying further, the negative signs cancel out:
Reciprocal = 100 / 0.06
Now, we can perform the division:
Reciprocal ≈ 1666.6667
Rounding to one decimal place, the reciprocal of -0.06 is approximately 1666.7.
The reciprocal of a number is the value that, when multiplied by the original number, yields a product of 1. In this case, if we multiply -0.06 by its reciprocal (1666.7), the result would be very close to 1 (-0.06 * 1666.7 ≈ -0.9999).
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There are 3 roads leading from York to Castle, 5 roads leading from Castle to Oakville, and 7 roads leading from Oakville to Sunfield. How many ways are there to get from York to Sunfield?
The number of ways to get from York to Sunfield is 105. To calculate the total number of ways, we multiply the number of choices at each step along the way.
We start at York and need to reach Sunfield. We have 3 options for the first step, as there are 3 roads leading from York to Castle. After reaching Castle, we have 5 options for the second step, as there are 5 roads leading from Castle to Oakville. Finally, from Oakville to Sunfield, we have 7 options for the third step.
To determine the total number of ways to get from York to Sunfield, we multiply the number of choices at each step. Multiplying 3 options for the first step, 5 options for the second step, and 7 options for the third step gives us: 3 * 5 * 7 = 105.
Therefore, there are 105 ways to travel from York to Sunfield, considering all the possible combinations of roads.
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Which expression shows the value of a $7300 investment after it has grown by 2. 3% per year for 5 years?
The problem asks for the expression that represents the value of a $7300 investment after it has grown by 2.3% per year for 5 years.
To find the value of the investment after 5 years with a growth rate of 2.3% per year, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A is the final amount,
P is the principal amount (initial investment),
r is the interest rate (in decimal form), and
n is the number of years.
In this case, the principal amount is $7300, the interest rate is 2.3% (or 0.023 as a decimal), and the number of years is 5. Plugging these values into the formula, we get:
A = 7300(1 + 0.023)^5
Simplifying the expression gives us the value of the investment after 5 years with a growth rate of 2.3% per year.
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Luxe Shoe Company manufactures two types of shoes, athletic shoes and casual shoes. The cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750. If 25 pairs of athletic shoes and 20 pairs of casual shoes were manufactured, the cost would be $1200. Write and solve a system of equations to find the cost to manufacture a pair of athletic shoes and the cost of manufacture a pair of casual shoes. Show work
It can be concluded that the cost to manufacture a pair of athletic shoes is $37.5 and the cost to manufacture a pair of casual shoes is $0. This indicates that there is a possibility system of equations of an error in the information provided.
It is reasonable to assume that the cost to manufacture a pair of casual shoes is not $0.
Let x be the cost of manufacturing a pair of athletic shoes, and y be the cost of manufacturing a pair of casual shoes.
Therefore, The cost of manufacturing 20 pairs of athletic shoes is 20x The cost of manufacturing 10 pairs of casual shoes is 10y
The cost of manufacturing 25 pairs of athletic shoes is 25x The cost of manufacturing 20 pairs of casual shoes is 20y .
From the given information, the cost of manufacturing 20 pairs of athletic shoes and 10 pairs of casual shoes is $750.
Thus, the first equation is:20x + 10y = 750....(1)
The cost of manufacturing 25 pairs of athletic shoes and 20 pairs of casual shoes is $1200.Thus, the second equation is:
25x + 20y = 1200....(2)
To solve for x and y, multiply equation (1) by 2.40x + 20y = 1500....(3)Subtract equation (1) from equation (3) to eliminate y.20x
= 750x
= 750/20x
= 37.
Substitute the value of x into equation (1) and solve for y.20(37.5) + 10y
= 750750 + 10y = 750y = 0
Therefore, the cost to manufacture a pair of athletic shoes is $37.5 and the cost to manufacture a pair of casual shoes is $0.
It can be concluded that the cost to manufacture a pair of athletic shoes is $37.5 and the cost to manufacture a pair of casual shoes is $0.
This indicates that there is a possibility of an error in the information provided.
It is reasonable to assume that the cost to manufacture a pair of casual shoes is not $0.
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Alexa was riding her motorcycle on a freeway at 480 kilometers north of her exit. She was riding south toward the exit at a constant velocity. If it took her 2 hours to get one quarter of the way to her exit. What was her velocity
Let's solve the problem step by step:
1. Alexa was riding her motorcycle on a freeway at 480 kilometers north of her exit.
2. She was riding south toward the exit at a constant velocity.
3. It took her 2 hours to get one quarter of the way to her exit.
Let's denote Alexa's velocity as [tex]\(v\)[/tex] (in kilometers per hour) and the total distance to her exit as [tex]\(D\)[/tex] (in kilometers).
According to the information given, Alexa traveled one quarter of the total distance in 2 hours. This can be represented by the equation:
[tex]\(\frac{1}{4} \times D = v \times 2\)[/tex]
Simplifying this equation, we have:
[tex]\(\frac{D}{4} = 2v\)[/tex]
Next, we know that Alexa started 480 kilometers north of her exit. So the total distance to her exit is:
[tex]\(D = 480 + \text{distance traveled}\)[/tex]
Substituting this expression for [tex]\(D\)[/tex] into our equation, we get:
[tex]\(\frac{480 + \text{distance traveled}}{4} = 2v\)[/tex]
Simplifying further:
[tex]\(120 + \frac{\text{distance traveled}}{4} = 2v\)[/tex]
From this equation, we can see that the velocity [tex]\(v\)[/tex] is independent of the distance traveled. Therefore, the velocity [tex]\(v\)[/tex] remains constant.
To determine the exact value of [tex]\(v\)[/tex], we need more information about the distance traveled by Alexa.
Please provide the additional information, such as the distance traveled or the time taken to cover a specific distance, to calculate the velocity accurately.
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Jenny bought 2 yards of fabric. How much is this in feet?
2 yards of fabric is equal to 6 feet.
To convert yards to feet, we need to know the conversion factor between the two units.
1 yard is equal to 3 feet.
Since Jenny bought 2 yards of fabric, we can multiply this value by the conversion factor to find the equivalent in feet:
2 yards * 3 feet/yard = 6 feet
Therefore, 2 yards of fabric is equal to 6 feet.
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A microscope has a setting that magnifies an object so that it appears 100 times as large when viewed through the eyepiece. If a tiny insect is 0.021 cm long, how long will the insect appear in centimeters through the microscope?
Answer:
Step-by-step explanation:
If the microscope magnifies the object 100 times, it means that the object will appear 100 times larger when viewed through the eyepiece.
To find the length of the insect when viewed through the microscope, we can multiply the original length of the insect by the magnification factor of 100.
Length of the insect through the microscope = Original length of the insect * Magnification factor
Length of the insect through the microscope = 0.021 cm * 100
Length of the insect through the microscope = 2.1 cm
Therefore, the insect will appear to be 2.1 centimeters long when viewed through the microscope.
At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. What is the approximate probability that a student chooses a computer elective and an art elective? 0. 11364 0. 21212 0. 22727 0. 42424.
The approximate probability that a student chooses a computer elective and an art elective is 1 or 100%.
To determine the approximate probability that a student chooses a computer elective and an art elective, we need to consider the total number of electives available and the specific choices a student can make.
To calculate the probability, we can follow these steps:
Determine the total number of possible elective combinations: Since each student can choose two electives, we multiply the number of options for each elective category. In this case, it would be 3 art electives * 5 computer electives = 15 possible combinations.
Determine the number of favorable outcomes: We want to find the number of combinations where a student chooses one art elective and one computer elective. Since there are 3 art electives and 5 computer electives, the number of favorable outcomes is 3 art electives * 5 computer electives = 15 combinations.
Calculate the probability: To find the approximate probability, we divide the number of favorable outcomes by the total number of possible combinations. Therefore, the probability is 15/15 = 1. Therefore, the approximate probability that a student chooses a computer elective and an art elective is 1 or 100%.
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d is the midpoint of ab and e is the midpoint of ac. ad = 8, bc = 22 the ratio of ab to school is 2 to 3
The value of AB is [76 + 2x]/3.
Given that d is the midpoint of AB and e is the midpoint of AC.
We are to find the value of AB.
Let the length of AB be x.
So, AD = 8 and DB = x - 8.
Also, AE = x - 8 and EC = x + 8. It is given that
BC = 22. So, AC = 2 * EC = 2 (x + 8) = 16 + 2x.
Similarly, AB = 2 * DB = 2 (x - 8) = 2x - 16.
It is also given that AB : school = 2 : 3
Thus, AB/School = 2/3 => School = (3/2) * AB
Also, AB + AC + BC = School + School = 2School
So, x + 16 + 22 = 2 * (3/2) * AB38 + x = 3 * AB/2 => 2(38 + x) = 3 * ABAB = [2(38 + x)]/3AB = [2(38 + x)]/3 = [76 + 2x]/3
Therefore, the value of AB is [76 + 2x]/3.
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Choose all of the conversions that are true for the capacity of the pitcher of orange juice.
the pitcher is 3. 5liters a 0. 35 kL
B. 0. 035 kL
C. 0. 0035 kL
D. 3,500 mL
E. 350 mL
The correct conversions are D. 3,500 mL and E. 350 mL.
To determine which conversions are true for the capacity of the pitcher of orange juice, we can use the following conversion factors:
1 liter (L) = 1,000 milliliters (mL)
1 kiloliter (kL) = 1,000 liters (L)
Given that the pitcher has a capacity of 3.5 liters, we can convert it to the following units:
A. 0.35 kL: This is incorrect since 0.35 kL would be equivalent to 350 liters, not 3.5 liters.
B. 0.035 kL: This is incorrect since 0.035 kL would be equivalent to 35 liters, not 3.5 liters.
C. 0.0035 kL: This is incorrect since 0.0035 kL would be equivalent to 3.5 liters, not 3.5 liters.
D. 3,500 mL: This is correct since 3.5 liters is equivalent to 3,500 milliliters.
E. 350 mL: This is correct since 3.5 liters is equivalent to 350 milliliters.
Therefore, the correct conversions are D. 3,500 mL and E. 350 mL.
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