The set of all real numbers between 1 and 3, including 1 can be represented using set-builder notation as: { x ∈ R | 1 ≤ x ≤ 3 }
set-builder notation:
{ x ∈ R | 1 ≤ x ≤ 3 }
"The set of all x in the set of real numbers such that x is bigger than or equal to 1 and less than or equal to 3" can be understood from this notation. The word "such that" is denoted by the vertical bar "|," and the condition that follows lists the requirements that each element of the set must meet.
When the criteria is "more than or equal to 1" in this instance, the set contains 1. As they also meet the requirement of being "less than or equal to 3," the set also includes all real numbers between 1 and 3. Observe that no numbers outside of the range [1,3] are included in the collection.
In conclusion, the set of all real numbers between 1 and 3, including 1, may be written as x R | 1 x 3 in set-builder notation.
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Americas shelled out60 billion for 196 million barrels of cola in 1998,generating 29 billion retail profit. Discriptive or inferential
Answer:
Step-by-step explanation:
Descriptive as the information provided is factual and there is no inferences made using the data provided.
The sample space of 2 coins consists of how many outcomes
Answer:
4 Outcomes.
Step-by-step explanation:
Both land tails.
Both land heads.
First coin lands Tails while the Second lands Heads.
First lands Heads while the Second lands Tails.
Monique wants to have $500,000 in 30 years by investing in an account that earns 7.8%
interest compounded half-yearly. Use the TVM calculator to find how much she needs to
invest today.
O $52,529.97
O $34,987
O $45,546
O $50,354.37
Monique needs to invest $50,354.37 today to have $500,000 in 30 years at an annual interest rate of 7.8% compounded half-yearly. Option D
How to calculate how much Monique needs to investWe can use the formula for future value of an annuity to solve this problem:
FV = P * [(1 + r/n)^(n*t) - 1]/(r/n)
Where:
FV = future value (desired amount) = $500,000
P = the amount invested today
r = annual interest rate = 7.8%
n = number of compounding periods per year = 2 (half-yearly)
t = number of years = 30
Substituting the values:
$500,000 = P * [(1 + 0.078/2)^(2*30) - 1]/(0.078/2)
Solving for P using a financial calculator or an online TVM calculator, we get:
P = $50,354.37
Therefore, Monique needs to invest $50,354.37 today to have $500,000 in 30 years at an annual interest rate of 7.8% compounded half-yearly.
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A club Ordered two same sized vegetable pizzas cut into different numbers of pieces
what fraction of a whole pizza is left? PLEASE HELP IM GETTING GROUNDED IF YOU DONT HELP IN THE NEXT 24 HOURS!!!!
Answer:
Without knowing the number of pieces that the pizzas were cut into, it is not possible to determine the fraction of a whole pizza that is left.
Step-by-step explanation:
Part IV: According to the tax table below, how much would Melvin and Sylvia
pay in federal income taxes if filing jointly?
Based on the information in the graph, we can infer that the tax that Melvin and Sylvia must pay if they pay federal income taxes when filling it out together would be 11,631.
How to identify the value of federal income taxes for Melvin and Sylvia?To identify the value of the federal income taxes we must take into account how much money the income of the two of them is. In this case, on the left side, they indicate that they are $77,000.
So, once we know the income we must look at the right side of the graph. In this case we must look for the value that matches the row that says "Married filling jointly" and the value of income (77,000). According to the above, these values coincide in the box that says 11,631.
From the above, we can infer that the tax they must pay would be 11,631
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Let r(x) = f(g(h(x))), where h(1) = 3, g(3) = 4, h'(1) = 3, g'(3) = 4, and f '(4) = 5. Find r'(1).
The value of r'(1) = 60 for the given function, using the chain rule.
What are derivatives of composite function?By adding the derivatives of f(x) with regard to g(x) and g(x) with respect to the variable x, one may get the derivative of the composite function h(x) = f(g(x)). The chain rule of differentiation can be used to derive derivatives of composite functions. Now, let's go over what composite functions are. When a function is expressed in terms of another function, it is said to have a composite function. This suggests that a function can be changed into another function in a composite function.
Using the chain rule of derivatives we have:
r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)
Substituting the values we have:
r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1)
r'(1) = f'(g(3)) * g'(3) * 3
r'(1) = f'(4) * 4 * 3
r'(1) = 5 * 4 * 3
r'(1) = 60
Hence, the value of r'(1) = 60 for the given function, using the chain rule.
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i’ve been struggling for hours and i still can’t figure it out!!! someone please help
Answer:
Step-by-step explanation:
We can use SOH, CAH, TOA to solve this.
sin(55) = 23/x
x = 23/sin(55)
x = 28.08 cm
4. Choose one other career to compare with your original choice. Then complete one table for each career.
Expenses wοuld be same and in bοth cases there expenses wοuld exceed, but in career 1 the οver expense wοuld be $500 while in career 2 the οver expense wοuld be $1000.
Define prοfit and lοss?Tο determine whether a cοntract is lucrative οr nοt, the phrases prοfit and lοss are utilised. These wοrds are frequently used in οrdinary cοnversatiοn. If the selling price exceeds the cοst price, the difference between the twο amοunts is knοwn as the prοfit. The difference between the cοst price and the selling price, if the selling price is less than the cοst price, is referred tο as a lοss. A prοduct's cοst price is the cοst at which it is purchased. The selling price οf a thing is the cοst at which it is sοld. In this essay, let's study mοre abοut prοfit and lοss.
Expenses Career Choice 1 Career Choice 2
Monthly income $10,000 $20,000
Rent: 30%* $3,000 $6,000
Utilities: 10%* $1,000 $2,000
Car Insurance: 5%* $500 $1,000
Cell Phone: 10%* $1,000 $2,000
Occasional Spending: 10%* $1,000 $2,000
Savings: 10%* $1,000 $2,000
Food: 15%* $1,500 $3,000
Car Loan: 10% $1,000 $2,000
Entertainment: 5% $500 $1,000
Total: $10,500 $21,000
Thus, after comparing both the careers, we have come to find that expenses would be same and in both cases there expenses would exceed, but in career 1 the over expense would be $500 while in career 2 the over expense would be $1000.
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What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
______________________________________
(reporting wrong/spam answers)
(giving brainliest to the correct answer)
______________________________________
The cuboidal prism has a volume of 40.625 cubic centimeters
How is area of a cuboid determined?Multiplying the cuboidal prism's length, width, and height yields its volume. Assuming that the width b and height h are both 2.5 cm and the length l is 6.5 cm. The volume of the cuboidal prism is given by multiplying these dimensions:
V = l b h = 6.5cm x 2.5cm x 2.5cm
= [tex]40.625cm^3.[/tex]
As a result, the cuboidal prism has a volume of 40.625 cubic centimeters. As a result, the prism can be utilized for a variety of purposes, including packaging, storage, and transportation, and it can accommodate 40.625 cubic centimeters of material inside its boundaries.
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C. Use Patterns and Structure What do you notice about the relationship between the combined lengths of the two shorter sides and the length of the longest side? 2 cm 4 cm 10 cm 7 cm 3 cm , 6 cm
Based on the information provided, it can be concluded that the length of the two shorter sides combined is half the length of the longest side.
How long are the longest and the shortest?The longest side, which is the green bar is 10 centimeters long. On the other hand, by adding the two shortest sides (orange bar 3 centimeters + blue bar 2 centimeters) the total length would be 5 centimeters.
What can be concluded about this?Considering the longest side is 10 centimeters and the shortest side is 5 centimeters then the length of the two shorter sides combined is half the length of the longest side.
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Please help!! Correct answer gets brainliest!!
Answer:
C) 260 square inches.
Step-by-step explanation:
To find the surface area of a pyramid, we can use the formula.
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
where l is the length of one side of the square base, s is the slant height, and Base Area is the area of the square base.
In this case, the base of the pyramid is a square with side length l = 10 inches, so its area is
Base Area = l^2 = 10^2 = 100 square inches
To find the perimeter of the base, we can simply multiply the length of one side by 4
Perimeter of Base = 4l = 4 x 10 = 40 inches
We are also given that the slant height of the pyramid is s = 8 inches.
Now we can substitute the values into the formula.
Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area
Surface Area = (1/2) x 40 x 8 + 100
Surface Area = 160 + 100
Surface Area = 260 square inches
Therefore, the surface area of the pyramid is 260 square inches.
Answer:360 in
Step-by-step explanation:
What is the range of y= x/8-x
Therefore, the range of the function is all real numbers except for 0. In interval notation, this can be written as (-∞, 0) U (0, ∞).
What is function?In mathematics, a function is a relation between two sets, where each element in the first set (called the domain) is associated with exactly one element in the second set (called the range). Formally, a function f from a set A to a set B is a rule that assigns to each element a in A a unique element b in B, denoted by f(a). The set A is called the domain of the function, and the set B is called the range.
Here,
The given function is y = x/(8-x).
To find the range of this function, we need to determine the possible values of y for all possible values of x.
First, we note that the function is undefined when the denominator (8-x) equals zero. Therefore, x cannot be equal to 8.
Next, we consider the behavior of the function as x approaches positive infinity and negative infinity.
As x approaches positive infinity, the value of y approaches zero. This is because the x term in the numerator grows much more slowly than the 8-x term in the denominator, causing the overall value of the function to approach zero.
As x approaches negative infinity, the value of y approaches negative infinity. This is because the x term in the numerator becomes very negative while the 8-x term in the denominator approaches 8, causing the overall value of the function to become very negative.
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Mason made a cardboard house at school. The lower part of the house is a rectangular prism and the upper part a triangular prism. Find the volume of the house.
Answer: 275,400
Step-by-step explanation:
- First we do 18 multiplied by 20 which would get us the answer of 360
- Next we do 45 multiplied by 17 which would get us the answer of 765
- Now we multiply both 360 and 765 and get the answer of 275,400
Review the information given based on a principal balance of $12,650.00 to answer the question:
FICO Score Simple Interest Rate Total of Payments Total Amount Paid
800-850
12%
29
740-799 15%
33
670-739 18%
38
580-669 21%
300-579 28%
40.0%
48
60
Calculate the percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score. Round the final answer to the nearest tenth. (4 points)
O 46.1%
39.9%
40.1%
$14,168.00
$14,547.50
$14,927.00
$15,306.50
$16,192.00
The percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score is approximately 0.8%, which is closest to option B, 0.8% or 39.9%.
Finding the entire amount paid by each family and comparing the difference in total amount paid will allow us to determine the percentage rise in the amount of interest paid between a household with a credit score of 780 and one with a score of 589.
The overall cost for a FICO score of 780 is:
$12,650 for the principal balance and all installments plus (33 x $60) to get $14,930.
With a 589 FICO score, the total cost is:
Total payments plus principal balance equal $12,650 plus (40 x $60) = $15,050.
The two households' combined total outlays differ in the following ways:
$15,050 - $14,930 = $120
We multiply by 100 and divide the difference by the initial sum to determine the percent increase:
($120 / $14,930) x 100% = 0.802% ≈ 0.8%
In light of this, the difference in interest rates between a family with a 780 credit score and one with a 589 credit score is roughly 0.8%, which is closest to option B, 0.8% or 39.9%.
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If x is the average of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m
Answer: To find the average of x, y, and z in terms of m, we first need to find expressions for x, y, and z in terms of m:
x = (m + 9)/2
y = (2m + 15)/2
z = (3m + 18)/3 = (m + 6)
To find the average of x, y, and z, we add them up and divide by the number of terms:
average = (x + y + z)/3
Substituting the expressions for x, y, and z, we get:
average = [(m + 9)/2 + (2m + 15)/2 + (m + 6)]/3
Simplifying the expression by combining like terms, we get:
average = (4m + 30)/6
Simplifying further by dividing both the numerator and denominator by 2, we get:
average = (2m + 15)/3
Therefore, the average of x, y, and z in terms of m is (2m + 15)/3.
Step-by-step explanation:
A carpet is to be laid in a room with length 7.5 m and breadth 3cm less than the lenght. Find the area of the carpet
The area of the carpet for a room with length 7.5 m and breadth 3 cm less than the length is 562.275m².
What is the area?The area refers to the two-dimensional space of occupied by an object.
The area is computed as the number of unit squares that cover the surface of a closed figure or object.
We measure area in square units like cm² and m².
The area is the squared product of the length and breadth or width.
1m = 100cm
Length = 7.5m
Breadth = 7.5m - 3 cm
= 7.5m - 0.03m
=74.97m
Area = Length x Breadth
= 7.5 x 74.97
= 562.275m²
Thus, the carpet should be 562.275m² in area.
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Find the slope of the following line:
x = 5
Answer:
The equation x = 5 represents a vertical line passing through the point (5, 0) on the x-axis. A vertical line has an undefined slope because the rise (change in y) is undefined when the run (change in x) is zero. Therefore, the slope of the line x = 5 is undefined.
The equation, A=6,000(1+0.029t) represents the amount of money eamed on a savings account with 2.9% annual simple interest. At the end of the investment period, the account balance is $7,392. How many years is the investment period?
A) 1 year
B) 3 years
C) 7 years
D) 8 years
Using the equation, A = 6,000(1+0.029t) The number of years that is the investment period is: D 8 years.
How to Calculate Investment Period?Investment period refers to the length of time during which an individual or organization invests money in a particular investment vehicle or asset. It can also be referred to as the holding period, and it is the duration for which an investment is held or maintained before it is sold or liquidated.
We can start by setting the equation for the final account balance, A, to $7,392:
7,392 = 6,000(1 + 0.029t)
Divide both sides by 6,000:
1.232 = 1 + 0.029t
Subtract 1 from both sides:
0.232 = 0.029t
Divide both sides by 0.029:
t ≈ 8
Therefore, the investment period is approximately 8 years.
So the answer is option D) 8 years.
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Find s I need help with this IXL question
Answer:
s = 8 mi
Step-by-step explanation:
We know that the ratio of side lengths of a 30-60-90 triangle is:
short leg : long leg : hypotenuse
x : x√3 : 2x
We can apply this information to the given triangle. We know that the length of the short leg is 4 mi. This can be substituted for x:
x = 4 mi
We are trying to solve for s, which is the triangle's hypotenuse. So, we can apply the ratio to x.
s = 2x = 2(4 mi) = 8 mi
A jar of dimes and quarters contains $2.55. There are 15 coins in all. How many of each coin are there? (Show Steps)
In linear equation, $38.25 are each coin are there .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
A jar of dimes and quarters = $2.55
There are 15 coins in all.
total coins = $2.55 * 15
= $38.25
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Step By Step 2 of 2
Keyboard Shortcuts
You were asked to solve the following word problem.
To host an event at a popular convention center, it costs $300
plus $55
per person attending.
Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x
be the number of attendees.
In the previous step you determined that for x
number of people, the total cost for hosting the event is 300+55x
. Now, adjust the expression to represent what each attendee would need to be charged to cover the total cost.
1. The rational expression representing the charge each attendee will have to pay is 300 + 55x.
2. Each attendee will have to pay $65 in order to cover the total cost.
The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
All real numbers are thought to be adequately explained by the four basic operations, sometimes known as "arithmetic operations." The mathematical operations quotient, product, sum, and difference come after division, multiplication, addition, and subtraction.
1. We are given that it costs $300 plus $55 per person attending to host an event.
Let the number of attendees be x.
We get the expression as 300 + 55x.
2. We are given that 30 people are attending the event.
So, substituting x = 30 in the expression, we get
⇒ Total cost = 300 + (55 * 30)
⇒ Total cost = 300 + 1650
⇒ Total cost = $1950
Now, using the division operation, we get
⇒ Per person charge = 1950 ÷ 30
⇒ Per person charge = $65
Hence, the required solutions have been obtained.
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Question: To host an event at a popular convention center, it costs $300 plus $55 per person attending.
1. Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.
2. In the previous step you determined that for x number of people, the total cost for hosting the event is 300+55x. Now, adjust the expression to represent what each attendee would need to be charged to cover the total cost if 30 people were attending.
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Two-way communication
Flexible, few rules
Generalized shared tasks
Question 3
Organizational design has two factors-mechanistic and organic Which of the following characteristics fits with the mechanistic factor?
Formal rules
Question 3 of 5
2 points
4
After answering the presented question, we can conclude that Yes, equation formal rules is a characteristic that fits with the mechanistic factor in organizational design.
What is equation?In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.
Yes, formal rules is a characteristic that fits with the mechanistic factor in organizational design.
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Find the equation of the line shown.
Answer:
y = x + 6
Step-by-step explanation:
We can put the equation of the line in slope intercept form [tex]y=mx+b[/tex] where m is the slope and b is the y intercept.
The line passes through (0,6) which means that is our y intercept. Now we have to count the slope. To do this, we can either evaluate the slope given 2 points or count it if given a graph. We have a graph, so the convenient thing to do is to count it. If we count, we see that our slope is [tex]\frac{1}{1}[/tex] or simply 1. All we have to do now is write it in slope intercept form.
[tex]y=x+6[/tex]
Can you solve these please?
The answers are:
3 a). 02:25 is time when aircraft arrives
b). The lower bound of the distance is 3150 km
4). The bottle weight is 200 g
Time when aircraft arrive?3 a). Aircraft leaves at 22:35
As per the given,
From 22:35 and takes 3h 50min is 02:25 will time when aircraft arrive
b). Because the distance is corrected to the nearest 100 km
The lower bound of the distance is = 3200 - 100/2
= 3150 km
4). Assume that the container weighs "x" and the honey weighs "y."
We are aware that a 1000 g container of honey weighs in total.
So Equation 1 is x + y = 1000 g
We can calculate the overall weight to be 600g by using half of the honey.
Equation 2: x + (y/2) = 600 g
y/2=600 - x
y= 2 (600 - x)
y= 1200 - 2x
We can replace “y” with 1200 - 2x in Equation 1:
x + 1200 - 2x = 1000
x = 200 g
The container weighs 200 grammes.
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Write an equation that expresses the following relationship.
d varies directly with the square of w
In your equation, use k as the constant of proportionality.
The relationship "d varies directly with the square of w" can be expressed mathematically as: d = k w² where k is the constant of proportionality.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
This equation states that d is directly proportional to the square of w, meaning that if we double w, d will be four times larger (2² = 4). The constant of proportionality, k, depends on the specific situation and values of d and w. It can be determined by measuring d and w for a given situation, and then solving for k using the equation above.
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Hector deposits $150,000 into an account earning 3.6% simple interest annually. Find the maturation value (final amount) of the account after 5 years.
simple interest
1 year: [tex]3.6\% \cdot 150,000 = \dfrac{3.6}{100} \cdot 150,000 = 5,400[/tex]
5 years: [tex]5,400(5) = 27,000[/tex]
the maturation value:
[tex]150,000 + 27,000 = \$ 177,000[/tex]
Write an equation parallel to each of the following:
Please help!!!!
or Edward opened a savings account and deposited $200.00 as principal. The account earns 9% interest, compounded annually. What is the balance after 5 years?
The final amount after 5 years is $ 49521.98.
Compound interest:Compound interest refers to the interest that is earned on the initial amount of money deposited or borrowed and also on the accumulated interest from previous periods.
The formula for calculating compound interest is:
A = P(1 + r/n)^(nt)Where
Where:
A = Final amount
P = Principal amount
r = Annual interest rate
n = Number of times the interest is compounded per year
t = Time period
Here we have
The deposited amount, P= $200.00
Rate of interest, r = 9% = 9/100 = 0.09%
Number of compounds per year, n = 1
Time period, t = 5 years
Using the formula,
A = 2000(1 + 0.09/1)⁽¹⁽⁵⁾⁾
A = 2000(1.09)⁵
A = 49521.98
Therefore,
The final amount after 5 years is $ 49521.98.
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Write the statement “Given any two numbers x, y, there is a third number w between them” using symbolic logic form and quantifiers.
The statement "Given any two numbers x, y, there is a third number w between them" can be expressed using symbolic logic and quantifiers as follows:
∀x∀y∃w (w is between x and y)
Here, the universal quantifier ∀x∀y indicates that the statement is true for any two numbers x and y. The existential quantifier ∃w indicates that there exists a third number w that is between x and y.
What other names exist for symbolic logic?the examination of the links between statements that are used to express precise mathematical concepts. Formal logic is another name for symbolic logic.
Given any two digits x, y, there exists a third integer w between them. This proposition can be expressed in symbolic logic as follows:
∀x∀y(x<y → ∃w(x<w<y))
Where ∀x means "for all x", ∀y means "for all y", → means "implies", ∃w means "there exists a w", and (x<y → ∃w(x<w<y)) means "if x is less than y, then there exists a w such that w is between x and y".
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The statement can be expressed using symbοlic lοgic and quantifiers as in ∀x∀y∃w (w is between x and y)
What οther names exist fοr symbοlic lοgic?The examinatiοn οf the links between statements that are used tο express precise mathematical cοncepts. Fοrmal lοgic is anοther name fοr symbοlic lοgic.
Given any twο digits x, y, there exists a third integer w between them. This prοpοsitiοn can be expressed in symbοlic lοgic as fοllοws:
∀x∀y(x<y → ∃w(x<w<y))
Where ∀x means "fοr all x", ∀y means "fοr all y", → means "implies", ∃w means "there exists a w", and (x<y → ∃w(x<w<y)) means "if x is less than y, then there exists a w such that w is between x and y".
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Look at the coordinate plane below. T A I N R P K B M O –6 –4 –2 –2 0 –4 2 2 4 4 6 y x Write down the coordinates of the points Write down the letters of the circled points and order them by their second coordinate values, from least to greatest. You will spell a word that describes a way to compare quantities.
Hence, in response to the provided question, we can say that We discard the t = 0.003 solution since time cannot be negative. As a result, the discus takes around 2.375 seconds to strike the ground.
what is function?Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.
The specified function appears to have a typo. I believe it should be:
[tex]h = -16t^2 + 38t + 5[/tex]
a) The discus's initial height can be calculated by entering t = 0 into the function:
[tex]h = -16(0)^2 + 38(0) + 5 = 5[/tex]
As a result, the discus's starting height is 5 feet.
[tex]-16t^2 + 38t + 5 = 0[/tex]
[tex]t = (-b \sqrt(b2 - 4ac)) /[/tex]
t = 0.003 or 2.375
We discard the t = 0.003 solution since time cannot be negative. As a result, the discus takes around 2.375 seconds to strike the ground.
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