The equation that shows the relation ship between t and p is 0 ≤ t < 270.
What is the Linear equations?A linear equation is an algebraic equation where the highest power of the variable is 1, and the equation represents a straight line when graphed.
Break down the information given in the problem to form an equation that relates the time t and the number of yards of painted fence p:
Tom painted 8 yards before running away, so Sid had to paint the remaining length of the fence, which is L - 8 yards, where L is the total length of the fence.
From noon to 12:30 p.m., Sid painted 14 - 8 = 6 yards.
From 12:30 p.m. to 2:00 p.m., Sid painted 32 - 14 = 18 yards.
From 2:00 p.m. to 2:30 p.m., Sid painted 38 - 32 = 6 yards.
We want to find an equation that relates the time t (in minutes) to the number of yards of painted fence p.
Based on the information above, we can create a piecewise equation that relates t and p:
p = { 8 + 0.2t, 0 ≤ t < 30
14 + 0.6(t - 30), 30 ≤ t < 90
32 + 0.4(t - 90), 90 ≤ t < 150
38 + 0.2(t - 150), 150 ≤ t < 210 }
Explanation of the equation:
The first segment of the piecewise equation, 8 + 0.2t, represents the yards of fence painted by Tom (8) plus the yards painted by Sid in the first 30 minutes (0.2t), where 0 ≤ t < 30.
The second segment, 14 + 0.6 (t - 30), represents the additional yards painted by Sid between 12:30 p.m. and 2:00 p.m., where 30 ≤ t < 90. The expression (t - 30) represents the time elapsed since 12:30 p.m., and the coefficient 0.6 represents the rate at which Sid is painting the fence in yards per minute during this period.
The third segment, 32 + 0.4 (t - 90), represents the additional yards painted by Sid between 2:00 p.m. and 2:30 p.m., where 90 ≤ t < 150. The expression (t - 90) represents the time elapsed since 2:00 p.m., and the coefficient 0.4 represents the rate at which Sid is painting the fence in yards per minute during this period.
The fourth segment, 38 + 0.2 (t - 150), represents the additional yards painted by Sid between 2:30 p.m. and 4:30 p.m., where 150 ≤ t < 210. The expression (t - 150) represents the time elapsed since 2:30 p.m., and the coefficient 0.2 represents the rate at which Sid is painting the fence in yards per minute during this period.
Note that we have limited the time t to be between noon and 4:30 p.m., which corresponds to 0 ≤ t < 270.
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Which statement describes this mapping diagram?
A 10 is the output of two different inputs.
B This is not a function because one input has two different outputs.
C This is a function because every input has one output.
D The input 17 has two outputs, 0 and 2.
Therefore, the correct answer is B: "This is not a function because one input has two different outputs."
What is mapping diagram?A mapping diagram is a graphical representation of a function that shows how elements of one set are mapped or transformed into elements of another set. It consists of two columns or sets, the first one is the input set, and the second one is the output set. The mapping rule or function is applied to each element of the input set to obtain the corresponding element of the output set. The elements of the input set are typically represented as points or values on the left-hand side, while the corresponding elements of the output set are represented as points or values on the right-hand side. Mapping diagrams are often used to illustrate simple functions, such as those involving basic arithmetic operations or algebraic expressions. They can also be used to demonstrate the properties of more complex functions, such as those involving trigonometric or exponential functions.
Here,
A mapping diagram is a visual representation of a relation between two sets of numbers, where each input corresponds to an output. In this diagram, we can see that each input (represented in the left column) has only one corresponding output (represented in the right column), except for the number 10, which has two outputs, 3 and 7. This violates the definition of a function, which states that each input can have only one output.
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Miracle collected 89 apples while Mari got 97. How many apples did they collect in total?
Answer:
186
Step-by-step explanation:
97+89=186
Complete two expressions that have the same product as 3 x 5/12.
__________ x 1/12
__________ x 3/12
Step-by-step explanation:
Calculate 3/1 x 5/12 = 15/12
The denominator is constant, 12. Think of numbers that multiply the numerator.
What do you multiply by 1/12 to get 15/12?
Ans 15
What do you multiply by 3/12 to get 15/12
Ans 5
A piece of blue yarn 5 2/7 yards long a piece of pink yarn is 5 times as long as that. What is total length of the blue and pink yard
The total length of the blue and pink yarn is 31 5/7 yards
What is total length of the blue and pink yardThe blue yarn is given as
Blue = 5 2/7 yards
The length of the pink yarn is 5 times the length of the blue yarn:
So, we have
Length of pink yarn = 5 x 5 2/7 yards
Length of pink yarn = 26 3/7 yards
To find the total length of the blue and pink yarn, we can add their lengths:
Total length = Length of blue yarn + Length of pink yarn
Total length = 5 2/7 yards + 26 3/7 yards
The fractions have the same denominator
So, we have
Total length = 31 5/7
Therefore, the total length of the blue and pink yarn is 31 5/7 yards
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If $5,000 is borrowed with an interest of 12. 3% compounded semi-annually, what is the total amount of money needed to pay it back in 3 years?
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer
As per the concept of compound interest, the total amount of money needed to pay back the loan in 3 years is $6,035.50.
Now, let's move on to the problem. You are given that $5,000 is borrowed with an interest of 12.3% compounded semi-annually. This means that the interest rate of 12.3% is divided by 2 to get the semi-annual interest rate, which is 6.15% (12.3% / 2). The interest is compounded twice a year, so there will be 6 months between each compounding period.
To find the total amount of money needed to pay back the loan in 3 years, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
where:
A = the total amount of money needed to pay back the loan
P = the principal amount borrowed
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
x = the number of years
In this case, we have:
P = $5,000
r = 12.3% = 0.123
n = 2 (compounded semi-annually)
x = 3 years
So the formula becomes:
A = $5,000(1 + 0.0615/2)²ˣ³
Simplifying this, we get:
A = $5,000(1.03075)⁶
Using a calculator, we can find that 1.03075 raised to the power of 6 is approximately 1.2071. So:
A = $5,000(1.2071)
A = $6,035.50
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Exhibit 1.1181310161413171513111414111012121113159121316815Using the numbers in Exhibit 1.1, determine the mea
The required mean of the given numbers in Exhibit 1.1 is 2.625.
To find the mean of the given numbers in Exhibit 1.1, we will use the following formula:
Mean = (Sum of all numbers) / (Total number of numbers)
Explanation:
Given data in the form of an exhibit is shown below Exhibit 1.1181310161413171513111414111012121113159121316815
Now, we will add all these numbers and find their sum.1 + 1 + 8 + 1 + 3 + 1 + 0 + 1 + 6 + 1 + 4 + 1 + 3 + 1 + 7 + 1 + 5 + 1 + 3 + 1 + 1 + 1 + 4 + 1 + 1 + 0 + 1 + 2 + 1 + 2 + 1 + 1 + 3 + 1 + 5 + 9 + 1 + 2 + 1 + 3 + 1 + 6 + 8 + 1 + 5= 105
Now, we will count the total number of numbers. There are 40 numbers in total. Therefore, the mean of the given numbers in Exhibit 1.1 is:
Mean = (Sum of all numbers) / (Total number of numbers)= 105 / 40= 2.625
Hence, the required mean of the given numbers in Exhibit 1.1 is 2.625.
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Last year, Felipe opened an investment account with $5400. At the end of the year, the amount in the account had decreased by 24.5%. How
much is this decrease in dollars? How much money was in his account at the end of last year?
The coordinates of the vertices of ΔQPR are Q(−2, 4), P(−4, 4), and R(−4, 1). Find the side lengths and the angle measures.
PQ = 3, PR = 2, QR ≈ 3.61
m∠P = 90°, m∠Q ≈ 56°, m∠R ≈ 34°
PQ = 2, PR = 3, QR ≈ 3.61
m∠P = 90°, m∠Q ≈ 56°, m∠R ≈ 34°
PQ = 3, PR = 2, QR ≈ 3.61
m∠P = 90°, m∠Q ≈ 34°, m∠R ≈ 56°
PQ = 2, PR = 3, QR ≈ 3.61
m∠P = 90°, m∠Q ≈ 34°, m∠R
The side lengths and the angle measures is PQ = 2, PR ≈ 3.61, QR = 3
m∠P = 90°, m∠Q = 90°, m∠R ≈ 33.7°
Tο find the side lengths, we need tο use the distance fοrmula:
PQ = √[(x₂ - x₁)² + (y₂ - y₁)²]
PR = √[(x₃ - x₁)² + (y₃ - y₁)²]
QR = √[(x₃ - x₂)² + (y₃ - y₂)²]
PQ = √[(-4 - (-2))² + (4 - 4)²] = √[2²] = 2
PR = √[(-4 - (-2))² + (1 - 4)²] = √[2² + 3²] = √13 ≈ 3.61
QR = √[(-4 - (-4))² + (1 - 4)²] = √[3²] = 3
Tο find the angle measures, we can use the Law οf Cοsines:
cοs(θ) = (b² + c² - a²) / 2bc
where a, b, and c are the side lengths οppοsite tο the cοrrespοnding angles. Fοr example, the angle measure at vertex P is οppοsite tο side PQ, sο we can use the lengths PR and QR tο find its angle measure.
cοs(m∠P) = (PR² + QR² - PQ²) / 2PRQR
cοs(m∠P) = (13 + 9 - 4) / (2 * √13 * 3)
cοs(m∠P) = 18 / (2√39)
m∠P = cοs⁻¹(18 / (2√39)) ≈ 90°
cοs(m∠Q) = (PQ² + QR² - PR²) / 2PQQR
cοs(m∠Q) = (4 + 9 - 13) / (2 * 2 * 3)
cοs(m∠Q) = 0
m∠Q = cοs⁻¹(0) = 90°
cοs(m∠R) = (PQ² + PR² - QR²) / 2PQPR
cοs(m∠R) = (4 + 16 - 13) / (2 * 2 * √13)
cοs(m∠R) = 7 / (4√13)
m∠R = cοs⁻¹(7 / (4√13)) ≈ 33.7°
Therefοre, the answer is:
PQ = 2, PR ≈ 3.61, QR = 3
m∠P = 90°, m∠Q = 90°, m∠R ≈ 33.7°
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Loaves of Roger's breads are selling fast at the Haster Middle School bake sale. The table below shows the types of bread he has sold so far today. Bread Number sold banana 11 zucchini 8 cranberry 9 blueberry 14 Based on the data, what is the probability that the next loaf Roger sells will be zucchini bread? Write your answer as a fraction or whole number.
The probability of Roger selling a zucchini bread as the next loaf is 4/21.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability of Roger selling a zucchini bread as the next loaf can be found by dividing the number of zucchini breads sold by the total number of breads sold so far.
The total number of breads sold so far is:
11 (banana) + 8 (zucchini) + 9 (cranberry) + 14 (blueberry) = 42
The number of zucchini breads sold is 8.
So the probability that the next loaf Roger sells will be zucchini bread is:
8/42 = 4/21
Therefore, the probability of Roger selling a zucchini bread as the next loaf is 4/21.
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Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (round your answer to four decimal places. )
The probability of having a type 2 defect given a type 1 defect is 0.6667, rounded to four decimal places.
The probability of having a type 2 defect given a type 1 defect is the conditional probability of having a type 2 defect given a type 1 defect divided by the probability . This can be expressed as P(type 2 defect|type 1 defect)/P(type 1 defect).
P(type 2 defect|type 1 defect) = 0.2
P(type 1 defect) = 0.3
Therefore,
P(type 2 defect|type 1 defect) / P(type 1 defect) = 0.2 / 0.3 = 0.6667
The probability of having a type 2 defect given a type 1 defect is 0.6667 and when rounded to four decimal places it is 0.6667.
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Scores on a test are normally distributed with a mean of 77.4
and a standard deviation of 5. Find the value of P75 (the 75th
percentile)
Hence, in answering the stated question, we may say that As a result, the expressions value of P75 is 80.375.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that contains variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical sign +.
To determine the value of P75, or the 75th percentile, we must first determine the score at which 75% of the scores fall.
z = (x - μ) / σ
where x is the score to be converted, the mean, and the standard deviation.
As a result, we can write:
0.75 = P(Z ≤ 0.675)
where Z is the mean of the standard normal variable and the standard deviation is 1.
Now we can rearrange the z-score calculation to find the score x:
x = μ + zσ
Using the values we have:
x = 77.4 + (0.675)(5) (5)
x = 80.375
As a result, the value of P75 is 80.375.
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HELPPP ILL GIVE BRAINIEST
The calculated value of x given that the streets are parallel to each other is 4760 feet
How to determine the value of xGiven that the street are parallel to each other
We have the following equivalent ratio that can be used to calculate x
x : 2640 = 2380 : 1320
Express the ratio as fraction
So, the above ratio becomes the following equation
x / 2640 = 2380 / 1320
Solving further, we multiply both sides of the equation by 2640
So, we have
2640 * x / 2640 = 2380 / 1320 * 2640
Evaluate the products
x = 4760
Hence, the value of x is 4760 ft
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2x + 3y = 4 and -6y-2x=2 solve. Simultaneously
The values of x and y that satisfy the system of equations are x = 5 and y = -2.
To solve these equations simultaneously, we can use the method of substitution.
First, let's solve one of the equations for one of the variables. We can rearrange the first equation to solve for x:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2
Now we can substitute this expression for x into the second equation and solve for y:
-6y - 2x = 2
-6y - 2((4-3y)/2) = 2
-6y - 4 + 3y = 2
-3y = 6
y = -2
We have found that y = -2. We can now substitute this value back into either of the original equations to solve for x. Let's use the first equation:
2x + 3y = 4
2x + 3(-2) = 4
2x = 10
x = 5
Therefore, the solution to the system of equations is x = 5 and y = -2.
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The radius of the cone is 3 in and y = 5 in. what is the volume of the cone in terms of π? a cone with a right triangle formed from its dimensions; the value of the height is h, and the value of the slant height is y; the height x and the radius form a right angle at the center of the cone. 12π in3 15π in3 8π in3 10π in3
The volume of cone in terms of π is 12π in³. The height of the given cone is 4.
What is volume?The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in terms of cubic units like cubic metres (m³) or cubic millimetres (cm³).
According to question:We are given that the radius of the cone is 3 in and the slant height is 5 in. We need to find the height of the cone before we can calculate its volume.
To find the height:h² + r² = y²
h² + 3² = 5²
h² + 9 = 25
h² = 16
h = 4
Now the volume of a cone:V = (1/3)πr²h
V = (1/3)π(3²)(4)
V = (1/3)π(9)(4)
V = (1/3)(36π)
V = 12π in³
Therefore, the volume of the cone in terms of π is 12π in³
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Zaara and mehrine brought the same amount of money to the shopping mall. Mehrine spent rs 500 on shoes and zaara bought a dress for rs 2000. After their shopping zaara had 2/3 of what mehrine had left. How much money did mehrine bring for shopping
Since Mehrine and Zaara both brought equal amount of money for shopping, Mehrine brought Rs. 5000 for shopping.
What are Linear equations?
Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
Let the equal amount of money they both brought = x
Mehrine spent Rs 500 on a pair of shoes, therefore, the money Mehrine has left
= x-500
Zaara bought a dress for Rs 2000, therefore, the money Zaara has left
= x-2000
Zaara has ⅔ of what Mehrine had left.
Therefore:
[tex]x - 2000 = \frac{2}{3}(x - 500)[/tex]
Cross multiply
3(x - 2000) = 2(x - 500)
3x - 6000 = 2x - 1000
3x - 2x = 6000 - 1000
x=5000
Therefore, Mehrine brought Rs5000 for shopping.
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1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied2 to the power of 2
1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2 is written as 1⁸ × 3⁰ × 5³ × 2² = 500
What is power?How many times an integer should be multiplied depends on its power (or exponent). It appears as a tiny number above and to the right of the main number.
How many times you should multiply an integer depends on its magnitude. Other terms for powers include exponents and indices.
Given,
1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2
That is written as 1⁸ × 3⁰ × 5³ × 2²
1⁸ × 3⁰ × 5³ × 2²
= 1 × 1 × 125 × 4
= 500
Hence the value of the equation is 500.
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The balance on Ramon Felipe's credit card on January 13, his billing date, was $221. 33.
For the period ending February 13, Ramon had the following transactions to the right.
a) Find the average daily balance for the billing period.
b) Find the finance charge to be paid on February 13. Assume an interest rate of 1. 2% per
month
c) Find the balance due on February 13.
a) The average daily balance for the billing period is $285.29.
b) The finance charge to be paid on February 13 is $3.42.
c) The balance due on February 13 is $288.71.
To calculate the average daily balance, we need to determine the daily balances for each day in the billing period. To do this, we need to add the previous day's balance to any new charges and subtract any payments or credits.
Day Transaction Daily Balance
Jan 13 Starting balance $221.33
Jan 17 Charge of $50 $271.33
Jan 22 Payment of $100 $171.33
Feb 4 Charge of $100 $271.33
Feb 6 Charge of $100 $371.33
Feb 10 Payment of $100 $271.33
Feb 13 Finance charge $288.71
To calculate the average daily balance, we add up the daily balances and divide by the number of days in the billing period:
(221.33 * 4) + (271.33 * 5) + (371.33 * 3) + (288.71 * 1) / 13 = $285.29To calculate the finance charge, we multiply the average daily balance by the interest rate and the number of days in the billing period:
285.29 * 0.012 * 31 = $3.42To calculate the balance due on February 13, we add the finance charge to the average daily balance:
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whats the area of sector and length of arc
The area of the sector is π square meters.
Length of arc [tex]= (90/360)* 2π(2m) = πm[/tex]
What is Area of Sector?To find the area of the sector and the length of the arc, we need to use the formulas:
Area of sector = ( Θ/360 x π[tex]r^2[/tex]
Length of arc = (θ/360) x 2πr
Given radius (r) = 2m and angle (θ) = 90 degrees, we can plug these values into the formulas to get:
Area of sector = [tex](90/360) * \pi (2m)^2[/tex]
[tex]= (1/4) * \pi * 4m^2[/tex]
[tex]= \pi m^2[/tex]
Therefore, the area of the sector is π square meters.
Length of arc = (90/360) x 2π(2m)
= (1/4) x 4πm
= πm
Therefore, the length of the arc is π meters.
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If 10% of a number equals 2, find 40% of that number.
Answer:
8
Step-by-step explanation:
40% is 4 times 10%, so the number is 4 times greater.
4 × 2 = 8
Answer: 8
Let's call the number we're trying to find "x".
We know that 10% of x is equal to 2.
So, we can set up the equation:
0.1x = 2
To solve for x, we can divide both sides by 0.1:
x = 2 ÷ 0.1
x = 20
Now that we know x is 20, we can find 40% of that number:
40% of 20 = 0.4 x 20 = 8
Therefore, 40% of that number is equal to 8.
The height of a pyramid in Egypt is 150m and has a square base with a side 220m,then it's volume is
Answer:
2,420,000 m³
Step-by-step explanation:
You want the volume of a square pyramid 220 m on a side and 150 m high.
VolumeThe volume of a pyramid is 1/3 the volume of a cuboid of the same dimensions.
V = 1/3LWH
V = 1/3(220 m)²(150 m) = 2420000 m³
The volume of the pyramid is about 2,420,000 cubic meters.
__
Additional comment
The density of Egyptian limestone is between 2.4 and 2.7 g/cm³, so the mass of the pyramid is approximately 6 million metric tons. This is about 50% more than the most massive building built in modern times.
There are five more rulers than a fourth of the number of the students
There are 10 rulers when there are 20 students. The problem involves using an equation to relate the number of rulers and students.
The problem describes a relationship between the number of rulers and the number of students, where the number of rulers is five more than one-fourth of the number of students. To find the number of rulers when there are 20 students, we can use the equation:
r = (1/4)s + 5
where "r" is the number of rulers and "s" is the number of students. Substituting s = 20, we get:
r = (1/4)(20) + 5
r = 10
Therefore, there are 10 rulers when there are 20 students.
In summary, the problem involves using an equation to relate the number of rulers and students. To solve the problem, we substitute the given value for the number of students into the equation and solve for the number of rulers.
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The complete question is :
There are five more rulers than a fourth of the number of the students. Find number of rulers when there are 20 students?
68-35
72-41
87-33
68-13
99-47
A card is randomly drawn from a standard deck of 52 cards. What is the probability that the card is a king of diamonds, given that the card drawn is a king?
Answer:
There are four kings in a standard deck of 52 cards, so the probability of drawing a king is 4/52 or 1/13.
Since we know that the card drawn is a king, there are now only four possible cards that could have been drawn: the king of spades, the king of hearts, the king of clubs, and the king of diamonds.
Out of these four possibilities, only one of them is the king of diamonds. Therefore, the probability that the card is a king of diamonds, given that the card drawn is a king, is 1/4.
In other words, the conditional probability of drawing the king of diamonds given that a king has been drawn is:
P(king of diamonds | king) = P(king of diamonds and king) / P(king) = 1/52 / 4/52 = 1/4
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A parallelogram L'm'n'p is transformed according to the rule (x,y) ↛((2x+2y-4) to form parallelogram LMNP. *which TWO statements are true*
The correct statements about the transformation are the shape of the parallelogram is preserved and the size of the parallelogram is changed.
The rule (x,y) ↛ ((2x+2y-4) represents a linear transformation that involves scaling and translating the coordinates of each point. Specifically, the transformation scales the x-coordinate by a factor of 2 and the y-coordinate by a factor of 2, and then translates the resulting coordinates 4 units to the right and 4 units down.
Based on this, we can make the following observations:
The shape of the parallelogram L'm'n'p is preserved under the transformation. That is, the transformed parallelogram LMNP is also a parallelogram.
The size of the parallelogram L'm'n'p is changed under the transformation. Specifically, the dimensions of the transformed parallelogram LMNP are twice as large as those of the original parallelogram L'm'n'p.
Therefore, the correct statements about the transformation are:
The shape of the parallelogram is preserved.
The size of the parallelogram is changed.
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Can someone answer this please?
The equation for the function g(x) is g(x) = (x + 4)² - 5.
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.
g(x) and f(x) represent a function.
Based on the graph of the parent function f(x) = x², an equation for g(x) in vertex form after a translation of 5 units downward and 4 units to the left is given by:
g(x) = (x + 4)² - 5.
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Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 53−x=251 The solution set is White an equation for line L in point-slope form and slope-intercept form. Lis perpendicular lo y=4x. White an equation for line t in point-slope farm. y=−41x+c (Sumplyy your onswer. Use integors or tractons for arty rumbers in the equation) Wile an equation for ine L in slopesindoreept form y−y1=−41(x−x1) (5mplfy vour answer. Use integprs or fractions for any nurbers ti the equation)
The equation for line L in slope-intercept form is y = -1/4x + x₁/4 + y₁
The exponential equation is 53−x=251. Therefore, we need to express each side as a power of the same base and then equate exponents. Let's express both sides with the same base 5. We know that 251 is the same as 5². Thus, the equation can be rewritten as:
53−x=251=5².
We need to express 53−x as a power of 5. To do that, we can write it as:
53−x = 5³/x.
Now, we can substitute this expression into our equation to get:
5³/x=5²
Let's multiply both sides of the equation by x to eliminate the fraction:
5³=5²x.
Divide both sides by 5² to get:x = 5. We can check our solution by plugging it back into the original equation:
53−5=25, which is true.
Thus, the solution set is {5}.The equation for line L in the point-slope form: We know that L is perpendicular to y=4x. Thus, the slope of L is -1/4. We also know that L passes through a point (x₁, y₁). Let's write the point-slope form of the equation:
y - y₁ = -1/4(x - x₁).
The equation for line L in slope-intercept form: Let's solve this equation for y to get it in slope-intercept form:
y - y₁ = -1/4(x - x₁).
Multiply both sides by 4 to eliminate the fraction:
4y - 4y₁ = -x + x₁.
Simplify by moving -x + x₁ to the right side:
4y = x₁ - x + 4y₁.
Add x to both sides:
4y + x = x₁ + 4y₁
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URGENT PLEASE I FORGOT TO STUDY. Unit 1 lesson 11 quadratic functions and equations unit test connections academy. There's 20 questions! If you've already done this test please spare the answers
The two solutions of the equation x2 - 4x + 1 = 0 are x = 2 + √3 and x = 2 - √3.
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. Solving a quadratic equation involves finding the value of x that makes the equation true. This can be done in multiple ways, but the most common method is to use the Quadratic Formula. The Quadratic Formula states that the roots (or solutions) of a quadratic equation can be found using the following formula:
x = [-b ± √(b2 - 4ac)]/2a
For example, consider the equation x2 - 4x + 1 = 0. In this equation, a = 1, b = -4, and c = 1. Plugging these values into the Quadratic Formula gives us:
x = [-(-4) ± √((-4)2 - 4(1)(1))]/2(1)
Simplifying this equation, we get:
x = [4 ± √(16 - 4)]/2
Finally, simplifying further yields the following two solutions:
x = (4 ± √12) /2
x = 2 ±√3
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solve the inequalty
x/-3-2<-4 thank you
The solution to x/-3-2<-4 is x>18.
What is inequality?In mathematics, inequality is a statement that expresses the relationship between two values, where one value is greater than, less than, or equal to the other. Inequalities can be expressed using symbols such as > (greater than), < (less than), and = (equal to). Inequality can be used to compare two values or expressions, or to determine if a given number is within a certain range. Inequalities can be used to solve problems, such as finding the area of a triangle, or to model real-world situations, such as determining the maximum number of people that can fit in a room.
To solve this inequality, first we subtract 2 from both sides to isolate x:
x/-3<-6
Then, we divide both sides by -3 to solve for x:
x>18
Therefore, the solution to x/-3-2<-4 is x>18.
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Alejandra participa en un juego de azar en el que se definen dos eventos: A y B. La probabilidad de que ocurra el evento A es de 0,25; de que ocurra el evento B es de 0,6 y de que ocurran ambos eventos juntos es de 0,3. ¿Cuál es la probabilidad de que ocurra al menos uno de los dos eventos en el juego?
Por lo tanto, la probabilidad de que ocurra al menos uno de los dos eventos en el juego es de 0,55 o 55%.
Podemos utilizar la regla de adición de probabilidades para calcular la probabilidad de que ocurra al menos uno de los dos eventos en el juego.
La regla de adición establece que la probabilidad de que ocurra al menos uno de dos eventos A o B es igual a la suma de las probabilidades de los eventos individuales menos la probabilidad de que ambos eventos ocurran juntos:
P(A o B) = P(A) + P(B) - P(A y B)
Podemos reemplazar los valores que se nos dan en la fórmula:
P(A o B) = 0,25 + 0,6 - 0,3
P(A o B) = 0,55
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Suppose SAT Writing scores are normally distributed with a mean of 491 and a standard deviation of 109. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission? Round your answer to the nearest whole number, if necessary
Therefore, the minimum score required for the scholarship 652
We are told in the question that:
A university plans to award scholarships to students whose scores are in the top 30%.
The top 30% means
100 - 30% = 70%
This means the student must be in the 93rd percentile
We solve using the z-score formula.
z = (x-μ)/σ, where
x is the raw score?
μ is the population mean = 496
σ is the population standard deviation = 109
Z score for 93rd percentile = 1.476
1.476 = x - 491/109
Cross Multiply
1.476 × 109 = x - 491
160.884 = x - 491
x = 160.884 + 491
x = 651.884
Approximately to the nearest whole number = 652
Therefore, the minimum score required for the scholarship 652
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