The circle in the equation p<-18 is open. In mathematical notation, the symbol "<" represents "less than." Therefore, the inequality p<-18 means that the value of p is less than -18.
When graphing this inequality on a number line, we use an open circle to represent the endpoint, which in this case is -18. An open circle indicates that the value of p cannot equal -18.
To understand this concept, consider the inequality p<5. In this case, the graph would show an open circle at 5, indicating that p can be any value less than 5 but not equal to 5. Similarly, in p<-18, the open circle at -18 signifies that p can take on any value less than -18 but cannot be equal to -18. This distinction is crucial when interpreting inequalities and their graphs.
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W,x,y,z are the sizes of four angles of a quadrilateral. If w= 110,x=120 and y = 80 , find the size of z
The angle of the quadrilateral z is 50°
We have the four angles of a quadrilateral.
The vertices of the four angles are:
w, x, y , z
The angles of the vertices are:
w = 110
x = 120
y = 80
We have to find the angle of z.
Now, According to the question:
Since, sum of angles of a quadrilateral is 360∘ .
Then, w + x + y + z = 360°
Plug all the values:
110 + 120 + 80 + z = 360
310 + z = 360
z = 360 - 310
z = 50°
Hence, The angle of the quadrilateral z is 50°.
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Tom’s house is 65 miles from the beach. A map uses a scale factor of ½ inch : 3 miles. Approximately how far is Tom’s house from the beach on the map?
Tom's house is approximately 1.08 inches away from the beach on the map. Tom's house is approximately 1.08 inches away from the beach on the map.
Let x represent the distance on the map. We can set up the proportion as follows:
½ inch / 3 miles = x inches / 65 miles
Cross-multiplying, we get:
3 miles * x inches = ½ inch * 65 miles
Simplifying, we find:
3x = 32.5
Dividing both sides by 3, we get:
x = 10.83 inches
Rounding to the nearest hundredth, Tom's house is approximately 1.08 inches away from the beach on the map. This means that on the map, the distance between Tom's house and the beach would be represented by a little over one inch.
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Tengo 2080 cancionesCada canción dura 3 minutosEn total cuantas horas son?
If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
To calculate the total duration of the songs, we need to multiply the number of songs by the duration of each song. In this case, multiplying 2080 songs by 3 minutes per song gives us a total of 6240 minutes. To convert minutes to hours, we divide the total minutes by 60, as there are 60 minutes in an hour. So, 6240 minutes divided by 60 equals 104 hours. Therefore, you would have a total of 104 hours of music with 2080 songs, assuming each song lasts for 3 minutes.
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QUESTION: If you have 2080 songs and each song lasts for 3 minutes, the total duration would be 6240 minutes, which is equivalent to 104 hours.
Customers at an ice cream shop took a survey. The results showed that 144 customers rated the shop as being ""very satisfactory."" This number represented 50% of the total number of customers who took the survey. What was the total number of customers who took the survey?
The total number of customers refers to the sum or count of individuals or entities who have availed products or services from a business or organization. It represents the overall customer base of a company.
The given information is that 144 customers rated the shop as being "very satisfactory." This number represented 50% of the total number of customers who took the survey.
To find out the total number of customers who took the survey, we will need to use the concept of proportions.The proportion can be set up as follows:
[tex]\frac{x}{100} = \frac{144}{50}[/tex]
Here, x represents the total number of customers who took the survey.Cross-multiplying,
50x = 14400
[tex]x = \frac{14400}{50}[/tex]
x = 288
Therefore, the total number of customers who took the survey is 288.
Therefore, the total number of customers who took the survey is 288 and the required answer is written in 91 words.
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Paul had a job during his summer vacation. He earned $8.55 per hour. He worked 20 hours per week for 8 weeks. How much money did Paul earn? *
Paul earned a total of $1,368 during his summer vacation. To calculate how much money Paul earned during his summer vacation, we need to determine his hourly rate and the total number of hours he worked.
Given that Paul earned $8.55 per hour and worked 20 hours per week for 8 weeks, we can calculate his total earnings.
First, let's find the total number of hours Paul worked:
20 hours/week * 8 weeks = 160 hours.
Next, we multiply the total number of hours by his hourly rate to find his total earnings:
160 hours * $8.55/hour = $1,368.
Therefore, Paul earned a total of $1,368 during his summer vacation.
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Solve |x| = - 15 I need help with this one
Answer:
Option C
Step-by-step explanation:
Absolute value of an expression can never be a negative integer. So, no solution.
Absolute value of an expression can be zero or positive.
The answer is:
⇨ c)Work/explanation:
We must recall that |x| means the absolute value of x.
Absolute value means the distance from zero. Distance cannot be negative, so neither can absolute value.
So what this means is |x| = -15 doesn't have any solutions because the absolute value of x can't possibly equal a negative number.
Hence, the correct answer is c).
On a nut and bolt production line, all the nuts weighed the same and all the bolts weighed the same. An order of 50 nuts and 60 bolts weighed 10.6kg. An order of 40 nuts and 30 bolts weighed 6.5kg. How much would 60 nuts and 50 bolts weigh ?
The weight of 60 nuts and 50 bolts would be 9.25 kg.
We have to given that,
An order of 50 nuts and 60 bolts weighed 10.6kg.
And, An order of 40 nuts and 30 bolts weighed 6.5kg.
Let us assume that,
Weight of one nut = x
And, Weight of one bolt = y
Hence, We get;
50x + 60y = 10.6 .. (i)
And, 40x + 30y = 6.5 .. (ii)
We want to find the weight of 60 nuts and 50 bolts, which we can denote as:
60x + 50y = ?
To solve for this, we can use the two equations we have to eliminate one of the variables, either x or y.
Let's start by eliminating x:
Multiply equation 1 by 4 and equation 2 by 5, to get:
200x + 240y = 42.4 (equation 3)
200x + 150y = 32.5 (equation 4)
Subtract equation 4 from equation 3:
90y = 9.9
y = 0.11
Now we can substitute y = 0.11 into equation 2 to solve for x:
40x + 30(0.11) = 6.5
40x = 2.5 x = 0.0625
Therefore, the weight of 60 nuts and 50 bolts would be:
60(0.0625) + 50(0.11) = 3.75 + 5.5 = 9.25 kg
So 60 nuts and 50 bolts would weigh 9.25 kg.
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New Orleans averages 77% humidity in the mornings, but it decreases by 20% in the afternoon. What is the average relative humidity in the afternoon in New Orleans? (enter a percent rounded to the tenths place)
I would like the step by step as well
The average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.The problem states that New Orleans has 77% humidity in the mornings and it decreases by 20% in the afternoon.
To determine the average relative humidity in the afternoon in New Orleans, we can follow these steps:
Step 1: Find the decrease in humidity from morning to afternoon.
In the afternoon, the humidity decreases by 20%. To find out what 20% of 77 is, we can use the formula:
decrease = percent decrease × original value decrease = 20% × 77 decrease = 0.2 × 77 decrease = 15.4
Step 2: Subtract the decrease from the original value.To find the average relative humidity in the afternoon, we need to subtract the decrease from the original value (morning humidity):
afternoon humidity = morning humidity − decrease afternoon humidity = 77 − 15.4 afternoon humidity = 61.6.Therefore, the average relative humidity in the afternoon in New Orleans is 61.6%, rounded to the tenths place.
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If the Cable Company offers cable for $110 a month but gives a 10% discount for new customers. Find the cost for the new customers.
The cost for new customers who are entitled to the 10% discount is $99 per month.
The Cable Company offers cable for $110 a month but gives a 10% discount for new customers.
To find the cost for new customers, we will have to subtract the 10% discount from the original cost of $110 per month.
So, we will have to multiply the original cost by the percentage of the discount which is 10%.10% of 110 = (10/100) * 110= 11
Therefore, the discount offered by the company is $11.
Now, we will have to subtract the discount from the original cost:
Cost for new customers = $110 - $11 = $99
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Josephine solved a quadratic equation: (2+6)2 = 49. Her work is shown below.
Step 1: V(x+6)2 = V49
Step 2: x + 6 = 7
Step 3: x = 7-6
Step 4: x=1
In which step did Josephine make an error?
(1 point)
O Step 4
O Step 3
Step 1
Step 2
Josephine made an error in Step 1 of solving the quadratic equation (2+6)^2 = 49. The mistake occurred when she took the square root of both sides and incorrectly simplified the square root of 49 as V49.
The correct simplification should be 7. The error in Step 1 led to subsequent incorrect steps and an incorrect final answer.
Josephine's error can be identified in Step 1, where she attempted to take the square root of both sides of the equation. The square root of (2+6)^2 is correctly simplified as |2+6|, which equals 8. However, Josephine incorrectly wrote it as V(2+6)^2 or V49.
The square root of 49 is actually 7, not V49. This mistake carried forward into Step 2, where Josephine incorrectly equated V(2+6)^2 to 7, resulting in the equation x + 6 = 7. Consequently, the subsequent steps (Step 3 and Step 4) were performed based on this incorrect equation, leading to an incorrect solution of x = 1.
Therefore, Josephine's error occurred in Step 1 of the solution process for the quadratic equation.
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Select the correct answer. Julian’s brother is performing some calculations on his calculator. Julian sees that the result in the display is 4. 1.30E+08. How can this number be expressed in standard notation? A. 4. 13 × 107 B. 4. 13 × 10-7 C. 41,300,000 D. 413,000,000.
The correct answer to express the number "4.1.30E+08" in standard notation is option D: 413,000,000.
In scientific notation, the number "4.1.30E+08" represents a value multiplied by 10 raised to the power of 8. The "E+08" notation indicates that we move the decimal point 8 places to the right. Therefore, the number can be expressed as 413,000,000 in standard notation.
Options A and B are incorrect because they involve multiplying by a factor of 10 raised to a different power. Option C, 41,300,000, does not account for the correct number of zeros. The correct representation is option D, 413,000,000, which reflects the value indicated in scientific notation.
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When Lorretta was 18 years old, she deposited $100 into a 20-year certificate of deposit (CD) account that earns interest at a better rate than her standard savings account. She must leave the money in the account for 20 years, without making any withdrawals or deposits. Six years later, she had $132 in the account. Write an equation that will represent this situation, and use the equation to determine how much money.
this has to be in y=ab^x form and we have to solve using logarithm rules but I wasn't there for that lesson
Therefore, the amount of money in the CD after 6 years is $200.76.
Given that Loretta was 18 years old when she deposited $100 into a 20-year certificate of deposit (CD) account that earns interest at a better rate than her standard savings account and she must leave the money in the account for 20 years, without making any withdrawals or deposits.
Six years later, she had $132 in the account.The formula for the growth of money at a compounded rate is given by
y =[tex]a (1 + r/n)^_(nt)[/tex]
Where
y = the amount of money at the end of the period.
a = the initial amount of money.
r = the annual interest rate in decimal form.
n = the number of times compounded per year.
t = the number of years.
The initial deposit was $100, and the total amount after 20 years would be $132. So, we have
$132 =[tex]$100(1 + r/n)^_(nt)[/tex]
Taking the natural logarithm of both sides,ln 132
= [tex]ln(100) + ln(1 + r/n)^{(nt)}ln 132 - ln 100[/tex]
= nt ln (1 + r/n)ln (132/100)
= nt ln (1 + r/n)ln (1.32)
= nt ln (1 + r/n)ln (1.32)
= t ln (1 + r/n)ln (1 + r/n)
= ln (1.32)ln (1 + r/n)
= 0.2877
Since the number of times compounded per year is not given, it can be assumed that it is compounded annually.i.e., n = 1
Therefore,ln (1 + r/1)
= 0.2877ln (1 + r)
= 0.2877r
= [tex]e^{(0.2877)} - 1r[/tex]
= 0.3338
So, the rate of interest is 33.38%.
Therefore, the equation for the amount of money in the CD after t years is
y = [tex]100(1 + 0.3338)^t[/tex]
Thus, the amount of money at the end of 6 years is
y = [tex]100(1 + 0.3338)^6[/tex]
= $200.76
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How many sheets of paper can be made from a tree that is 50 centimeters in diameter and 25 meters tall
Approximately 80,500 sheets of paper can be made from a tree that is 50 centimeters in diameter and 25 meters tall.
To find the number of sheets of paper that can be made from a tree, the formula is used:Number of sheets of paper = (Volume of wood in cubic meters) × (Density of paper in grams per cubic meter) × (1,000,000 grams per metric tonne) ÷ (Weight in grams per sheet)Where volume of the wood in cubic meters is calculated as:Volume of wood = π × (Diameter/2)^2 × HeightVolume of wood = π × (50/2)^2 × 25Volume of wood = 24,414.86 cubic metersThe density of paper is usually around 400 kg per cubic meter.
Converting the density to grams per cubic meter gives: Density = 400,000 g/m3Weight of an average sheet of A4 paper is 5 grams.To make 1 metric ton (1,000 kg) of paper, 2.5 to 3 tons of wood is needed, so an average of 2.5 tons. This means that:1 tonne of paper = 2.5 tonnes of woodWeight in grams per sheet = Weight of 1 tonne of paper / (number of sheets in 1 tonne of paper)Weight in grams per sheet = (1,000,000 grams) / (200,000 sheets)Weight in grams per sheet = 5 gramsNow, we can use the formula:Number of sheets of paper = (Volume of wood in cubic meters) × (Density of paper in grams per cubic meter) × (1,000,000 grams per metric tonne) ÷ (Weight in grams per sheet)Number of sheets of paper = 24,414.86 × 400,000 × 1,000,000 ÷ 5Number of sheets of paper = 1,232,743,000 ÷ 5Number of sheets of paper ≈ 80,500 sheetsTherefore, approximately 80,500 sheets of paper can be made from a tree that is 50 centimeters in diameter and 25 meters tall.
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Devon bought a new suit that was discounted 40% off the original price. If the original price of the suit was $280, what was the discounted price?
The discounted price of the suit is $168.
Explanation: To calculate the discounted price, we need to subtract the discount percentage from 100% and then multiply it by the original price. In this case, the original price of the suit is $280, and it was discounted by 40%.
First, we calculate the discount amount:
Discount amount = Original price * (Discount percentage / 100)
Discount amount = $280 * (40 / 100)
Discount amount = $280 * 0.4
Discount amount = $112
Next, we will subtract the discount amount from the original price to find the discount price:
Discounted price = Original price - Discount amount.
Discounted price = $280 - $112
Discounted price = $168
Therefore, the discounted price of the suit is $168 after applying a 40% discount to the original price of $280.
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Showing results for a rectangular brick has a length of 5 centimeters a width of 9 centimeters and a height of 20 centimeters what is the surface area of that brick
The surface area of the rectangular brick can be calculated by adding up the areas of all its faces. The surface area of the rectangular brick is 650 square centimeters.
The given dimensions of the brick are:
Length = 5 centimeters
Width = 9 centimeters
Height = 20 centimeters
To find the surface area, we need to calculate the areas of the six faces of the brick. The rectangular brick has three pairs of equal faces: top and bottom, front and back, and left and right sides.
The area of each face can be found by multiplying the length by the width.
The top and bottom faces have the same dimensions, so each face has an area of 5 cm * 9 cm = 45 square centimeters.
The front and back faces also have the same dimensions, so each face has an area of 5 cm * 20 cm = 100 square centimeters.
The left and right side faces also have the same dimensions, so each face has an area of 9 cm * 20 cm = 180 square centimeters.
To find the total surface area, we add up the areas of all the faces:
Total Surface Area = 2 * (45 + 100 + 180) = 2 * 325 = 650 square centimeters.
Therefore, the surface area of the rectangular brick is 650 square centimeters.
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Explain how you can break apart one of the addenda to make a ten to find the number of points Jeannie Kevin scored.
Jeannie Kevin scored 9 points , The method of breaking an addend to make a ten is a technique to help children learn mental math when they are working on addition problems that are not convenient to do with the traditional algorithm. Children can apply this method to breaking down numbers that are near ten, such as 8 and 9.
The breaking addends method works by breaking one of the addends into two parts, one that can be combined with the other addend to make ten and the remaining part can be added to the answer.
For example, to break apart the addend 8 to make ten when solving the problem 8 + 7, we can break 8 into two parts: 2 and 6. Then we can add the 2 to 7 to get 9 and add the remaining 6 to the 9 to get 15. Therefore, 8 + 7 = 15. In this problem, we do not need to break apart any addends because we have a ten in the problem.
If we separate the ten and the 1, we can see that Jeannie scored 9 points.
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The function f(x) = 467(5)x represents the growth of a ladybug population every year in a wooded area. Adrianne wants to manipulate the formula to an equivalent form that calculates every 3 months, not every year. Which function is correct for Adrianne's purposes? f(x) = 67(5)x f of x equals 467 times 5 to the 12 power to the x over 12 power f(x) = 467(5 to the one fourth power)4x f(x) = 4672(5)x.
The correct function for Adrianne's purpose, where the growth is calculated every 3 months instead of every year, is f(x) = 467(5^(x/4)).
To calculate the growth every 3 months instead of every year, we need to modify the original function by adjusting the exponent of 5.
Step 1: The original function is f(x) = 467(5)^x, where x represents the number of years.
Step 2: To calculate the growth every 3 months, we divide x by 4, as there are 12 three-month periods in a year.
Step 3: Adjust the exponent of 5 to (x/4), representing the growth over each three-month period.
Step 4: The modified function becomes f(x) = 467(5^(x/4)), which calculates the growth every 3 months.
Therefore, the correct function for Adrianne's purpose is f(x) = 467(5^(x/4)).
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Type the correct answer in each box. Use numerals instead of words. What is the inverse of this function? f -1(x) = x2 − , for x ≤.
The values for each blank is:
1. x
2. y
3. 4
4. 4
1. Change f(x) to y the the result will be
y = √(x-4)
2. switch x and y, then solve for y
then, x = √y-4
x² = y-4
x² + 4 = y
3. Now change y to [tex]f^{-1}[/tex](x)
then [tex]f^{-1}[/tex](x) = x² + 4
4. Since, the original function is defined only for x - 4 ≥ 0, you solve for x and get x ≥ 4.
Hence, the final blank is 4.
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The question attached here seems to be incomplete the complete question here:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
consider the given function: f(x)= √x-4
To determine the inverse of the given function, change f(x) to y, switch______ and y, and solve for ______.
The resulting function can be written as (f) to the power of -1(x)=x squared + ______, where x is greater than or equal to ______.
A farmer sells 7. 3 kilograms of pears and apples at the farmer's market. 3/4
of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market? Please help me with this I need it for a Zearn answer im stuck on it
The farmer sold 2.42 kilograms of apples at the farmer's market.
To solve the problem, first, we need to find out how much weight the farmer sold in pears.
We are given that 3/4 of the weight is pears and 1/4 of the weight is apples.
We can use this information to set up an equation that represents the weight of the pears sold.
Let the weight of pears sold be "x":
Weight of pears sold + Weight of apples sold = Total weight of fruit sold
3/4x + 1/4x = 7.3 kg
Simplifying this equation, we get:
x = 4.88 kg
This means that the farmer sold 4.88 kg of pears.
To find out how many kilograms of apples she sold, we can subtract this weight from the total weight of fruit sold:
Weight of apples sold = Total weight of fruit sold - Weight of pears sold
Weight of apples sold = 7.3 kg - 4.88 kg
Weight of apples sold = 2.42 kg
Therefore, the farmer sold 2.42 kilograms of apples at the farmer's market.
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write this percentage as a fraction in its simplist form
To write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
Step 1: Write the percentage as a fraction by dividing it by 100.For example, let's say we want to write 25% as a fraction in its simplest form.
25% is equivalent to 25/100 or 0.25 as a decimal.
Step 2: Simplify the fraction by finding a common factor between the numerator and denominator.
For example, let's simplify 25/100.
Both the numerator and denominator can be divided by 25, giving us 1/4.
Therefore, 25% as a fraction in its simplest form is 1/4.
Another example: let's write 60% as a fraction in its simplest form.
60% is equivalent to 60/100 or 0.6 as a decimal.
The numerator and denominator can both be divided by 20, giving us 3/5.
Therefore, 60% as a fraction in its simplest form is 3/5.
In summary, to write a percentage as a fraction in its simplest form, divide it by 100 and simplify the resulting fraction by finding a common factor between the numerator and denominator.
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What are the x-intercepts for the function f(x) = x2 2x – 15?.
The x-intercepts for the function f(x) = x^2 + 2x - 15 are x = -5 and x = 3.
To find the x-intercepts, we set the function equal to zero and solve for x. In this case, we have the equation:
x^2 + 2x - 15 = 0
To factor this quadratic equation, we look for two numbers that multiply to -15 and add up to 2. The numbers that satisfy this condition are -5 and 3.
Therefore, the factored form of the equation is:
(x - 3)(x + 5) = 0
Setting each factor equal to zero, we find the x-intercepts:
x - 3 = 0 --> x = 3
x + 5 = 0 --> x = -5
Hence, the x-intercepts for the function f(x) = x^2 + 2x - 15 are x = -5 and x = 3.
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A fair die is rolled 3 times. The first 2 rolls resulted in 2 threes. What is the probability of not rolling a 3 on the next roll?
a. 1
b.(1/6)^2 x (5/6)
c. (3!/2!5!) x (1/6)^2 x (5/6)
d. 5/6
e. 0
The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).
Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).
Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).
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Which representation of a transformation on a coordinate grid does not preserve congruence?
F. (x,y)→(x+7,y+7)
G. (x,y)→(17x,17y)
H. (x,y)→(y,−x)
J. (x,y)→(x,−y)
We know that congruence is a geometric transformation that preserves angles and lengths.
A representation of a transformation on a coordinate grid that does not preserve congruence is option G, which is (x,y) → (17x,17y).
This transformation enlarges the shape by a scale factor of 17 and changes the distance between each pair of points in the transformed shape.
Option F represents a translation of a shape on a coordinate grid, which means that it preserves congruence because the distance and angles between each pair of points remain the same.
Option H represents a rotation of a shape on a coordinate grid, and option J represents a reflection of a shape across the x-axis.
These transformations also preserve congruence because they do not change the length or angles between each pair of points in the transformed shape.
Therefore, the correct answer is G, (x,y) → (17x,17y).
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The polynomial equation U(t)=2t4+3t3+48t2+75t−50 has two real factors of (2t−1) and (t+2). Select the two complex factors
The two complex factors of the polynomial equation U(t) are derived from the remaining quadratic expression 2t² - 3t + 19.
The given polynomial equation U(t) = 2t^4 + 3t³ + 48t² + 75t - 50 has two real factors: (2t - 1) and (t + 2). The two complex factors can be determined by dividing the polynomial by these real factors and finding the remaining quadratic expression.
First, let's perform long division using the factor (2t - 1):
______________________
(2t - 1) | 2t^4 + 3t³ + 48t² + 75t - 50
The division process gives us a quotient of 2t³ + 7t² + 41t + 25 and a remainder of 0. Now, we can factorize the quotient expression: 2t³ + 7t² + 41t + 25.
Next, let's perform long division using the factor (t + 2):
________________________
(t + 2) | 2t³ + 7t² + 41t + 25
The division process gives us a quotient of 2t² - 3t + 19 and a remainder of 0. Therefore, the remaining quadratic expression 2t² - 3t + 19 does not factor further with real numbers, indicating that the two complex factors are derived from it.
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Match each radical expression with the equivalent exponential expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 3√4 3√ 2√3 2√5
Matching each radical expression with the equivalent exponential expression: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2) To match each radical expression with its equivalent exponential expression, we need to convert the radicals into exponent form.
3√4: The cube root (√3) of 4 is equivalent to raising 4 to the power of 1/3. Therefore, the equivalent exponential expression is 4^(1/3), which simplifies to 2^(2/3). 3√2:The cube root (√3) of 2 is equivalent to raising 2 to the power of 1/3. Therefore, the equivalent exponential expression is 2^(1/3). 2√3: The square root (√2) of 3 is equivalent to raising 3 to the power of 1/2. Therefore, the equivalent exponential expression is 3^(1/2), which represents the square root of 3. 2√5: The square root (√2) of 5 is equivalent to raising 5 to the power of 1/2. Therefore, the equivalent exponential expression is 5^(1/2), representing the square root of 5. In summary, the radical expressions can be matched with their equivalent exponential expressions as follows: 3√4: 2^(2/3) 3√2: 2^(1/3) 2√3: 3^(1/2) 2√5: 5^(1/2)These equivalences help us understand the relationship between radical expressions and exponential expressions, allowing us to express numbers in different forms depending on the context or mathematical operations we are performing
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How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%
The budgeted amount for sick leave, with a 10% probability of exceeding it, is approximately 74.4 hours.
To determine the amount of time that should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%, we need to find the z-score corresponding to a cumulative probability of 0.10 from the standard normal distribution table.
Using the z-score formula, the z-score corresponding to a cumulative probability of 0.10 is approximately -1.28.
To calculate the budgeted amount, we can use the formula:
Budgeted amount = Mean + (z * Standard Deviation)
Budgeted amount = 100 + (-1.28 * 20)
Budgeted amount = 100 - 25.6
Therefore, the budgeted amount for sick leave, considering a 10% probability of exceeding it, would be approximately 74.4 hours.
Complete Question:
The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours. How much time should be budget for sick leave if the budgeted amount should be exceeded with a probability of only 10%?
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When calculating the effective rate of a loan, which statement or statements must be true if n is equal to 1? I. The nominal rate equals the effective rate. II. The length of the loan is exactly one year. III. The interest is compounded annually. A. I and III b. II and III c. I only d. III only Please select the best answer from the choices provided A B C D.
The statement that must be true when calculating the effective rate of a loan with n = 1 is: III. The interest is compounded annually. Therefore, the answer is d. III only.
When n equals 1, it means that the interest is compounded once per year. In this case, the effective rate of the loan is equal to the nominal rate since there are no additional compounding periods within the year.
This is because when n equals 1, there is no need to consider the length of the loan (statement II) since it is already implied that the loan is for one year.
However, statement I, which states that the nominal rate equals the effective rate, may not necessarily be true for loans with other values of n. Hence, only statement III is required to be true when n equals 1 to calculate the effective rate of a loan.
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brian buys a computer for £1600
it depreciates at a rate of 4% per year
how much will it be worth in 3 years
Brian's computer will be worth £1408 in 3 years if it depreciates at a rate of 4% per year. Depreciation is a measure of how much the asset has lost in value over a period of time.
Depreciation refers to a decrease in the value of an asset over time due to its wear and tear or obsolescence. When an asset is purchased, it has an original value that is its initial worth. After some time, the asset will lose its value and become less valuable. Depreciation is a measure of how much the asset has lost in value over a period of time.
In this problem, Brian bought a computer for £1600, and it depreciates at a rate of 4% per year. To find out how much it will be worth in 3 years, we need to use the formula for depreciation which is:
Depreciation = Original value × rate of depreciation (as a decimal) × time (in years)
To calculate the depreciation, we have:
Depreciation = 1600 × 0.04 × 3= £192.
The depreciation value is what the computer will be worth in 3 years. Therefore, we can find the current value of the computer by subtracting the depreciation value from the original value. Hence, we have:
Current value = Original value - Depreciation= £1600 - £192= £1408.
Therefore, the computer will be worth £1408 in 3 years.
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The swimming pool is open when the high temperature is higher than 20 c. Lainey tried to swim on Monday and Thursday (which was 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30 c.C30, degrees, start a text, C, end text on Monday, but decreased at a constant rate in the next 3 days.
Answer: Let's assume the high temperature on Monday is represented by C30 (30 degrees Celsius). Since the pool is open when the high temperature is higher than 20 degrees Celsius, the pool was open on Monday.
However, over the next three days, the high temperature decreased at a constant rate. Let's denote the rate of decrease as "r" (in degrees Celsius per day).
Since the high temperature on Monday was C30, we can calculate the high temperature on Thursday by subtracting the decrease in temperature over three days:
High temperature on Thursday = C30 - 3r
We know that the pool was closed on Thursday, so the high temperature on Thursday must have been lower than or equal to 20 degrees Celsius.
Therefore, we can set up the inequality:
C30 - 3r ≤ 20
Now, we can solve this inequality to find the range of values for the rate of decrease (r) that would satisfy the condition:
C30 - 3r ≤ 20
Substituting C30 = 30, we have:
30 - 3r ≤ 20
Subtracting 30 from both sides:
-3r ≤ -10
Dividing by -3 (and reversing the inequality since we are dividing by a negative number):
r ≥ 10/3
Therefore, for the pool to be closed on Thursday, the rate of decrease in temperature (r) must be greater than or equal to 10/3 degrees Celsius per day.
Would the function describing the relationship between the denomination of U.s. currency and the weight of one million dollars be a discrete function or a continuous function
The relationship between the denomination of U.S. currency and the weight of one million dollars can be categorized as a discrete function. A discrete function is one where the input values are distinct and separate, with no intermediate values between them.
In the context of U.S. currency, the denominations are well-defined and specific, such as $1, $5, $10, $20, and so on. Each denomination corresponds to a specific weight when considering one million dollars.
For example, if we consider $1 bills, the weight of one million dollars would be significantly different from the weight of $5 bills or $10 bills. The weight is directly associated with the discrete values of the denominations.
On the other hand, a continuous function would involve a relationship where the input values vary continuously within a range. In this case, there is no continuous range of values for the denomination of U.S. currency. Each denomination has a specific weight, and there are no intermediate values between them.
Therefore, the relationship between the denomination of U.S. currency and the weight of one million dollars can be categorized as a discrete function, where the specific denominations correspond to distinct and separate weights.
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