Answer: The height of the ball (in meters) after t seconds is given by the equation h = 2 + 5t - 5t^2. We can use this equation to find the values of t for which the ball's height is 3 meters.
We need to find the values of t that make h = 3, so we can substitute 3 for h in the equation:
3 = 2 + 5t - 5t^2
Then we can solve for t by moving all the terms to one side of the equation and factoring it:
-5t^2 + 5t - 1 = 0
And we can use the quadratic formula to find the solutions of this equation:
t = (5 +/- sqrt(5^2 - 4*(-1)(-1)))/ 2(-1)
t = (5 +/- sqrt(25 + 4))/ -2
t = (5 +/- sqrt(29))/ -2
The solutions of this equation are t = (5 +/- sqrt(29))/ -2
Since the time, t, is a real value the square root of 29 should be positive.
The values of t for which the ball's height is 3 meters are not real values, so there's no time when the ball's height is 3 meters.
Step-by-step explanation:
(Score for Question 3:___ of 4 points)
3. Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of APQR after a rotation of 180° about the origin. Label the image AP'Q'R'.
(b) Draw the image of APQR after a reflection across the x-axis. Label the image AP"Q"R".
Answer:
(a) A 180° rotation about the origin would involve rotating the shape by 180° clockwise around the point (0,0).
(b) A reflection across the x-axis would involve reflecting the shape over the x-axis.
What is coordinate plane?
Each point is identified by an ordered pair of numbers: an x-coordinate on the x-axis and a y-coordinate on the y-axis. The starting point is at (0,0).
(a) A 180° rotation about the origin would involve rotating the shape by 180° clockwise around the point (0,0). This would result in the image of APQR being upside down, with A' being located at the point (0,-2), P' being located at the point (-1,-1), Q' being located at the point (1,-1), and R' being located at the point (0,-2)
(b) A reflection across the x-axis would involve reflecting the shape over the x-axis. This would result in the image of APQR being a mirror image of the original shape, with A" being located at the point (0,2), P" being located at the point (-1,1), Q" being located at the point (1,1), and R" being located at the point (0,2)
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Let f(t) be the population (in thousands of people) of Math City, as a function the time t (in years), where t = 0 corresponds to the year 2020. In 2020, the population was 34000, and each year the population increases by 3000 people.
(a) Model the population by finding a formula for f(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof.
(b) Evaluate the expression f(6), and write a sentence explaining what this means.
(c) Solve the equation f(t) = 64, and write a sentence explaining what this means
The f(t) formula is f(t) = 34 + 3t. The expression f(6) = 52; this means that in 2026, the population was 52000 people, and Setting 34 + 3t = 64 leads to t = 10, which means in 2030, the population was 64000 people.
(a) Each year, the population increases by 3000 people; this means that the population is a linear function of time, and its slope is 3 thousand people per year. The population in 2020 was 34000, and so (0, 34) is the vertical intercept, and we have
f (t) = 34 + 3t.
(b) f(6) = 34 + 3×6
f(6) = 34 + 18
f(6) = 52
This means in 2026, the population was 52000 people.
(c) f(t) = 64
34 + 3t = 64
3t = 64 - 34
3t = 30
t = 10
This means in 2030, the population was 64000 people.
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Select the equivalent expression to 4^-3/4^-1
The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The fundamentals of algebra taught us a way to express an unknown price using letters which includes x, y, z, and so on. these letters are referred to as here as variables. An algebraic expression can be a combination of both variables and constants. Any value this is located earlier than and accelerated with the aid of a variable is a coefficient.
Given
expression ,
4^-3 / 4^-1
= 4 ^ (-3-(-1))
= 4^ (-3+1)
= 4^(-2)
= 1/4^2
= 1/16 .
Therefore , The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
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Can someone help me thank you
These mathematical operations can be solved in the given manners.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given some fractions to solve for understanding, I will solve two questions with the same denominator and two with different denominators one with a whole number and one fraction.
6/10 ÷ 4/10Since the base is the same
=> 6/4
=> 1.5
6/10 ÷ 2/5We can write 2 /5 as 4/10 since their values are the same
=> 6/10 ÷4/10
=> 6/4
=> 1.5
1/4 ÷4/6we can write 1/4 as 6/24 and 1/6 as 4/24 to make the denominator same.
=> 6/24/4/24
=> 4/4
=> 1.5
2/9 ÷ 5/6We can write 2/9 as 4/18 and 5/6 as 15 / 18 to make the denominator the same
=> 4/18/15/18
=> 4/15
=> 0.266
Therefore, The given Mathematical operations are being solved In the s
same manner
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Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
No, what they said is not fact.
The statement "producing great engineers who benefit science and technology in India is the most important function of IITs" and "IITs are greatly improving the image of India in the West" are both important functions of IITs, and the priority of these functions may depend on individual perspectives and goals.
Some people might argue that producing engineers is more crucial for the development of India's technology and economy, while others might argue that improving the image of India in the West is equally important for increasing its global recognition and competitiveness. Both functions play important roles and it is a matter of perspective which one is considered more important.
Correct Question :
Jai: IITs are producing great engineers, who ultimately end up benefiting science and technology in India, but more important is the fact that they are greatly improving the image of India in the west
Vijay: No, you're mistaken. Producing great engineers who benefit science and technology in India is the most important function of IITs. Without IITs, most of our software industry wouldn't have existed.
What they said is fact or not? Explain.
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Which of the following describe(s) petroleum formation? (Select all that apply.)
*
1 point
a. When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.
b. Petroleum is renewable over human lifetimes.
c. It takes hundreds of millions of years for petroleum to form.
d. Petroleum formed in cold places.
petroleum formation happens When dinosaurs became extinct 65 million years ago, their bodies decayed to become petroleum.
What is decomposition?Dead creatures are broken down into their basic chemicals through the process of decomposition by bacteria and fungus. The cycle can be completed by plants absorbing and using these substances once again. Because of how they decompose dead organic stuff, decomposing bacteria and fungus are referred to be saprophytic.
Oil and gas are created from organic material that has been decomposed and altered over millions of years, mostly as sediments on the seafloor.
Fuels known as petroleum products are created from crude oil and the hydrocarbons found in natural gas. Coal, natural gas, and biomass can also be used to make petroleum products.
Plant and animal remains are used to create petroleum. Animals and plants that pass away sink and land on the seafloor. These extinct animals and plants decayed millions of years ago and mingled with sand and silt.
Therefore, we can say Petroleum is produced. Dinosaurs became extinct 65 million years ago, and when their corpses decomposed, petroleum was created. Petroleum doesn't form until hundreds of millions of years. Oil was created in chilly climates.
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Find the ratio of kaido’s age to hiroshi age to saitama’s age
If Kaido's age is x, Hiroshi's age is y and Saitama's age is z, then ratio value for their ages is x : y : z.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
Let the age of Kaido be represented as x.
Let the age of Hiroshi be represented as y.
Let the age of Saitama be represented as z.
The ratio of Kaido's age to Hiroshi's age can be given as -
Kaido's age : Hiroshi's age
Substituting the values in the expression -
x : y
The ratio of Kaido's age to Saitama's age can be given as -
Kaido's age : Saitama's age
Substituting the values in the expression -
x : z
The ratio of Hiroshi's age to Saitama's age can be given as -
Hiroshi's age : Saitama's age
Substituting the values in the expression -
y : z
The ratio of Kaido's age to Hiroshi's age to Saitama's age can be given as -
Kaido's age : Hiroshi's age : Saitama's age
Substituting the values in the expression -
x : y : z
Therefore, the ratio expression is obtained as x : y : z.
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Lmkkkkkk same question I just don’t know
add and then subtract them m
Jada spends $74 on a hat, shoes, and shorts. If the hat costs $22 and the shoes cost $33, how much were the shorts? Write and solve an equation. Use an unknown to represent the cost of the shorts.
What is the domain of the function in the graph?
Have to look at photo to answer and I got the answer wrong thinking it was 1
Through the given data points the domain of the function is 1 ≤ n ≤ 5.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The domain of a function is the complete set of all possible values of independent variable.
The points associated with the graph is (1,15) and (5,11).
The formula for equation is (y - y1) = (y2-y1)/(x2-x1) (x - x1).
(y2-y1)/(x2-x1) = (11 - 15)/(5 - 1)
m = -4/4
m = -1
Now, the equation can be written as -
y - y1 = m(x - x1)
y - 15 = -1(x - 1)
y - 15 = -x + 1
y = -x + 16
From the graph k = -n + 16
The independent variable 'n', taking the values between 1 and 5, in that interval graph is continuous.
Therefore, the domain is 1 ≤ n ≤ 5.
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Write an equation that passes through these two points.
(1, 2), (5, 10)
Question 7 of 10
If f(x)=-2 and g(x)=2x²+x-3, find (f+g)(x).
OA. x²-6
OB. 2x²+2x+1
OC. 2x² -+1
OD. 2x²+x-5
SUI
The solution of the given functions (f+g)(x) is 2x²+x-5.
What is function?This connection is typically represented as y = f(x), or "f of x," where y and x are coupled so that for any value of x, there is a certain value of y. This means that f(x) can only have one value for a given x. In set theory jargon, a function connects an element x to an element f(x) in another set.
Here, the given functions are,
f(x) = x/2 - 2
g(x) = 2x ^ 2 + x - 3
(f+g) x = f(x) + g(x)
(f+g) x = x/2 - 2 + 2x ^ 2 + x - 3
(f+g) x = (3x)/2 - 5 + 2x ^ 2
(f+g) x = 2x ^ 2 + (3x)/2 - 5.
= 2x²+x-5
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A study was made to males and females about their favorite activities during the weekend.
Therelative frequency for each category is shown in the picture.
a) What is the probability that the person selected will be someone whose response is Sports and who is a woman?
b) What is the probability that the person selected will be someone whose response is TV or who is a man?
c) What is the probability that the person selected will be someone whose response is Sports given that the person is a man?
d) For the people surveyed, are the events of being a person whose response is Sports and being a man independent? Justify your answer.
d) For the people surveyed, are the events of being a person whose response is Sports and being a man independent? Justify your answer.
e) Assume that, in a large population, the probability that a person will respond watching TV is
0.32. If 6 people are selected at random from the population, what is the probability that at least 4 of the people selected will respond watching TV as their favorite activity? Support your answer.
a) The probability of this event is 0.08., b) The probability is 0.3 + 0.6 - 0.06 = 0.84, c) P(Sports | Man) = 0.12 / 0.6 = 0.2
d) For the people surveyed, the events of being a person whose response is Sports and being a man are not independent.
e) The probability that at least 4 of the people selected will respond watching TV as their favorite activity is 1 - 0.2097 = 0.7903
What is the likelihood of the terms given?a) We need to multiply the proportion frequency of women responding with Sports (0.2) by the relative frequency of women to get the likelihood that the individual chosen will be a woman (0.4).
Thus, we obtain: 0.2 * 0.4 = 0.08 Therefore, the likelihood of this occurring is 0.08.
b) We can add the relative frequency of TV for men (0.3) and the relative frequency of men (0.6) and subtract the overlap (the relative frequency of TV for men and men), which is equal to 0.2 * 0.3 = 0.06 to determine the likelihood that the individual chosen would either respond with TV or be a man.
The probability is therefore 0.3 + 0.6 - 0.06 = 0.84
c) Using the algorithm, we can determine the likelihood that the individual chosen will be a guy and that their response to the question will be "Sports." P(Sports and Man) = 0.2 * 0.6 = 0.12 P(A and B) = P(A and B) / P(B) P(Sports and Man) = P(Sports and Man) / P(Man)
P(Sports|Man) = 0.12/0.6=0.2
d) For the respondents, being a man and having selected "Sports" as a response are not separate events. P(Sports and Man) = 0.12 and P(Sports) * P(Man) = 0.2 * 0.6 = 0.12, which are not equivalent, demonstrate this.
e) Using binomial distribution, the probability that at least 4 of the people selected will respond watching TV as their favorite activity is 1 -
P(X < 4) - P(X = 4)
P(X < 4) = (6 C 0) * (0.32)^4 * (0.68)^2
P(X = 4) = (6 C 4) * (0.32)^4 * (0.68)^2
P(X < 4) + P(X = 4) = 0.2097
Therefore the probability that at least 4 of the people selected will respond watching TV as their favorite activity is 1 - 0.2097 = 0.7903
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Help with both of them please! Thank you!
The numbers to 3 significant figures are as follows:
0.0230 ≈ 0.0230
0.035 ≈ 0.0350
0.804 ≈ 0.804
3.150 ≈ 3.15
140 ≈ 140
509 ≈ 509
The eroding rate of the beach in millimetres per day is 0.109 mm per day.
How to represent decimal in three significant figures?Significant figures are the number of digits in a value. In other words, significant figures are the digits of a number that are important in terms of accuracy and precision.
Therefore, let's find the 3 significant figures of the numbers.
0.0230 ≈ 0.0230
0.035 ≈ 0.0350
0.804 ≈ 0.804
3.150 ≈ 3.15
140 ≈ 140
509 ≈ 509
A particular beach is eroding at a rate of 4cm per year. Let's convert to millimetres per day.
Therefore,
4 cm = 40 mm
365 days = 40 mm
1 day = ?
Hence,
eroding rate = 40 / 365 = 0.10958904109 per day
eroding rate = 0.109 mm per day
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What is the five number summery for this set of numbers 34,35,37,38,42,45,49
The five number summary of the set of numbers is :
Minimum: 34First Quartile (Q1): 37Median: 38Third Quartile (Q3): 42Maximum: 49What is the five number summary ?A five number summary is a way to summarize a set of numerical data by providing five key values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.
For the set of numbers 34, 35, 37, 38, 42, 45, and 49, the five number summary would be:
The minimum value is 34, the lowest value in the set.
The first quartile, also known as Q1, is the value that separates the lowest 25% of the data from the rest of the data, which is 37.
The median is the middle value, which is 38.
The third quartile, also known as Q3, is the value that separates the highest 25% of the data from the rest of the data, which is 42.
The maximum value is 49, the highest value in the set.
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Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $9,000, annual interest: 4%, interest periods: 2, number of years: 15
Answer:
Step-by-step explanation:
The investment below is compounded semi-annually, while an investment of the same principal at the same rate compounded annually would have interest compounded once per year.
The formula for compound interest is A = P(1 + r/n)^nt where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year and t is the number of years.
In the case of the semi-annual investment:
A = 9000(1 + 0.04/2)^(2*15) = $21,831.62
In the case of the annual investment:
A = 9000(1 + 0.04)^15 = $21,812.30
As we can see, the semi-annual investment yields a slightly larger return than the annual investment, $19.32 more. Compounding interest more frequently results in a larger return due to the interest earning interest.
consider the expression 4(8x+5)
complete 2 descriptions of parts the expression
1. the entire expression is the product of ____.
2. on its own, (8x+5) is a sum with ___.
the choices are
2 factors
3 factors
2 terms
3 terms
The entire expression is the product of two terms and 8x+5 is the sum of two terms.
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The expression 4(8x+5)
Evaluating the expression we get 4(8x+5)=32x+20
The entire expression is the product of two factors 4&(8x+5)
Also the expression (8x+5) has two terms and therefore its a binomial
Thus it is the sum of two terms.
Hence, The entire expression is the product of two terms and 8x+5 is the sum of two terms.
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write a real word multiplication problem involving whole numbers and decimals in which you would use estimation to solve then estimate to solve the problem show that your answer is reasonable
Answer:
.023
.75 X .33=.2475/11=.0225 rounded to .023
Step-by-step explanation:
Sam Is Building A Table for her gaming setup.The Length of the table is .75x.33 if she doubles the length of it then divides it by 11 then what will be the length of the table?Round to the nearest thousandths to solve your problem.
P.S:Mark Me Branlisist
Which property would you use to simplify this monomial division problem?
a
O Quotient of a Power Property
O Power of a Quotient Property
Power of a Product Property
O Product of a Power Property
There are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
What is a monomial ?
Monomial is polynomial in which it has only one term.
Given ,
To find Which property would you use to simplify this monomial division problem.
For example :
4a^3 - 10a^2 + 5a / 2a
Now the polynomials ( 4a^3 - 10a^2 + 5a) is written as numerator and the monomial (2a) is written as denominator
Therefore,
we get 4a^3 - 10a^2 + 5a / 2a .
Now we observe that there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
4a^3 / 2a - 10a^2 / 2a + 5a/2a
Therefore, there are three terms in the polynomial so each term of the polynomial numerator is separately divided by the same monomial denominator.
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using linear stability analysis, classify the fixed points of the gompertz model of tumor growth n an
The Gompertz model of tumor growth is a mathematical model that describes the growth of a tumor over time. It is characterized by two parameters, the intrinsic growth rate (r) and the carrying capacity (K), and is described by the following differential equation:
dn/dt = rn(1 - n/K).where n is the size of the tumor and t is time.
To classify the fixed points of the Gompertz model of tumor growth using linear stability analysis, we first need to find the fixed points by setting dn/dt = 0 and solving for n. The fixed points are the values of n that make the tumor size constant. In this case, the fixed point is n* = K.
Next, we need to linearize the system around the fixed point by using the Jacobian matrix. The Jacobian matrix for the Gompertz model is:
J = [dr/dn, d(rn(1-n/K))/dn]
[-rn(1-n/K)/K, rn(1-n/K)+(r*n/K^2)]
In the Gompertz model, the fixed point is n* = K, and the eigenvalues are -r and r/K, which are both negative. This means that the fixed point is stable, and the tumor size will converge to the carrying capacity K if perturbed.
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a destroyer simultaneously fires two shells with different initial speeds at two different enemy ships. the shells follow the parabolic trajectories shown.
1. At 4.142s the first shell will hit the first enemy ship.
2. At 3.536s the second shell will hit the second enemy ship.
3. The two shells will be 677.1 meters apart when they hit their respective targets.
To solve this problem, we can use the equations for the horizontal and vertical motion of a projectile.
The horizontal velocity of a projectile can be found using the equation: [tex]v_x = v_0 * cos\theta[/tex] where,
[tex]v_0[/tex] is the initial velocity[tex]v_x[/tex] is the horizontal velocity[tex]\theta[/tex] is the angle at which the projectile is fired.The vertical velocity of a projectile can be found using the equation:
[tex]v_y = v_0 * sin\theta[/tex]
The horizontal displacement of a projectile can be found using the equation:
[tex]x = v_0 * cos\theta * t[/tex]
The vertical displacement of a projectile can be found using the equation:
[tex]y = v_0 * sin\theta * t - (1/2)gt^2[/tex] where,
t is the time g is the acceleration due to gravity (approximately 9.8 m/s^2) x and y are the horizontal and vertical displacements.1. To find the time that the first shell will hit the first enemy ship, we can use the equation for the horizontal displacement:
[tex]t = x / (v_0 * cos\theta)[/tex]
t = 2000m / (800m/s * cos(45))
= 4.142s
2. To find the time that the second shell will hit the second enemy ship, we can use the equation for the horizontal displacement:
[tex]t = x / (v_0 * cos\theta)[/tex]
t = 2000m / (1000m/s * cos(60))
= 3.536s
3. To find the distance between the two shells when they hit their respective targets, we can use the equation for the horizontal displacement:
[tex]x_1 = v_0 * cos\theta * t \\x_2 = v_0 * cos\theta * t[/tex]
x1 = 800m/s * cos(45) * 4.142s
= 2858.9m
x2 = 1000m/s * cos(60) * 3.536s
= 3536m
x2 - x1 = 3536m - 2858.9m
= 677.1m
So the two shells will be 677.1 meters apart when they hit their respective targets.
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The complete question is:
A destroyer simultaneously fires two shells at two different enemy ships. The first shell has an initial speed of 800 m/s and is fired at an angle of 45 degrees. The second shell has an initial speed of 1000 m/s and is fired at an angle of 60 degrees. The distance between the two enemy ships is 2 km.
1. At what time will the first shell hit the first enemy ship?
2. At what time will the second shell hit the second enemy ship?
3. How far apart will the two shells be when they hit their respective targets?
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what is the difference between the two dashes in yards
For these traditional cooking measurements, there are no specific definitions. The majority of sources, however, claim that a dash is roughly 1/8 of a teaspoon, a pinch is 1/16 of a teaspoon, and a smidgen is 1/32 of a teaspoon.
How many teaspoons is two dashes?For these traditional cooking measurements, there are no specific definitions. The majority of sources, however, claim that a dash is roughly 1/8 of a teaspoon, a pinch is 1/16 of a teaspoon, and a smidgen is 1/32 of a teaspoon.One tablespoon or less of a soft food, like whipped cream or sour cream, is typically referred to as a "dollop."Because of the action of adding an ingredient, such bitters, a dash frequently refers to liquid substances, especially when creating cocktails.Furthermore, a pinch is, as its name suggests, the quantity of an ingredient (such as salt or a dry herb) that you can hold between your thumb and fingers. Additionally, there is a "healthier-sized" pinch that involves your thumb, forefinger, and middle finger, known as a "three-finger pinch." It probably equals between a quarter and an eighth of a teaspoon in terms of volume.The Complete Question.
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someone pls help i’m in desperate need!! photo attached
A standard form is a form of writing equations, numbers, or expressions using a certain set of rules.
solve the equation in standard form -2x²+8x=-1 ?
vertex is (2/-7)
opening down
x=h=8/-2(2)=4
INC(∞,-2) DEC(2,-∞)
D(-∞,∞)
R(∞,-7)
Reference yes dilution by 2
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Use the method of successive differences to determine the next number in the given sequence 3,9,20,36,57,83,114
By using the method of successive differences, the next number in the given sequence 3, 9, 20, 36, 57, 83, 114 is 150.
What is a difference table?In Mathematics, a difference table can be defined as a type of table that is constructed by subtracting adjacent elements (entries) in a sequence, and then repeating the process with next those elements (entries).
Number Difference from previous Difference of differences
3
9 6
20 11 5
36 16 5
57 21 5
83 26 5
114 31 5
150 36 5
First column: 9 - 3 = 6; 20 - 9 = 11; ....... 150 - 114 = 36.
Second column: 11 - 6 = 5; 16 - 11 = 5; ...... 36 - 31 = 5.
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The points (3,0),(x,0), (x,1/x^2), and (3,1/x^x)
For {x} = 5, we can write the coordinates as -
(3, 0)
(5, 0)
(5, 1/25)
(3, 625)
What are coordinates?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given are the coordinates as -
(3, 0), (x, 0), (x, 1/x²) and (3, 1/xˣ)
Let {x} = 5. We can write the coordinates as -
(3, 0)
(5, 0)
(5, 1/25)
(3, 625)
Therefore, for {x} = 5, we can write the coordinates as -
(3, 0)
(5, 0)
(5, 1/25)
(3, 625)
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Answer ASAP please
1. A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. Find the volume of the resulting ring.
2. Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the x-axis.
[tex]y=\frac{1}{x}[/tex]
The volume of the metal sphere is 4π/3(R^3 - r^3)
The volume of the solid generated is 2π cubic units.
The volume of the metal sphereThe volume of the ring can be found by subtracting the volumes of two spheres with radii R and r:
V = (4/3) * π * (R^3 - r^3)
So, the volume of the ring is given by:
V = (4/3) * π * (R^3 - r^3) cubic units.
Evaluate
V = 4π/3(R^3 - r^3)
The volume of the solid generatedWe have the equation to be
y = 1/x
The volume of the solid is given by the definite integral:
V = 2π ∫[a,b] x * y dx
where a and b are the lower and upper limits of the interval over which we are integrating.
In this case, a = 1 and b = 2, so the volume of the solid is given by:
V = 2π ∫[1,2] x * 1/x dx = 2π ∫[1,2] dx = 2π (x)|[1,2] = 2π (2 - 1) = 2π.
So, the volume is to 2π cubic units.
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Which is a counterexample of the conditional? Select all that apply. If a number is divisible by 4, then it is divisible by 8. A. 12 B.32
C.36
D.20
So, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."
A counterexample of a conditional statement is a specific case or example that contradicts the statement or goes against its logical implications.
In this case, the conditional statement is "If a number is divisible by 4, then it is divisible by 8."
Option C, 36, is a counterexample of this conditional statement.
This is because 36 is divisible by 4 (9 x 4 = 36), but it is not divisible by 8 (36 / 8 = 4.5). This contradicts the statement that if a number is divisible by 4, it must also be divisible by 8.
Option A, 12, is not a counterexample of the conditional statement because 12 is divisible by 4 (12 / 4 = 3) and also divisible by 8 (12 / 8 = 1.5).
Option B, 32, is not a counterexample of the conditional statement because 32 is divisible by 4 (32 / 4 = 8) and also divisible by 8 (32 / 8 = 4).
Option D, 20, is not a counterexample of the conditional statement because 20 is not divisible by 4 (20 / 4 = 5)
So, in summary, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."
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please show solution.. thank you
196 millilitres of tomato paste for 16 litres of spaghetti sauce.
=======================================================
Explanation:
We're told that 12 litres of sauce goes with 147 millilitres of paste.
Divide the larger value over the smaller: 147/12 = 12.25 exactly.
Do the same thing to each of the answer choices A through D.
(A) 94/8 = 11.75(B) 108/9 = 12(C) 196/16 = 12.25(D) 169/14 = 12.071 approximatelyOptionally we could represent the results in a table like so
[tex]\begin{array}{|c|c|c|c|} \cline{1-4}\text{Choice} & \text{Paste} & \text{Sauce} & \text{Paste/Sauce}\\\cline{1-4}\text{A} & 94 & 8 & 11.75\\\cline{1-4}\text{B} & 108 & 9 & 12\\\cline{1-4}\text{C} & 196 & 16 & 12.25\\\cline{1-4}\text{D} & 169 & 14 & 12.071 \ \text{(approx)}\\\cline{1-4}\end{array}[/tex]
Spreadsheet software is handy if you go this route. You don't have to worry about the units in this case.
Choice C is the only option that yields the ratio 12.25, which means it's the only possible answer.
Mike earns 5.00 per hour overtime is paid at the time and half of his regular rate worked 42 hours last week what is mikes gross pay
The gross pay mike for last week is $210.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Mike earns 5.00 per hour overtime is paid at the time and half of his regular rate worked 42 hours last week.
Since it is not mentioned that mike worked overtime or not so we will consider this a normal work hour for a week is 42 hours.
Thus total he earns = 42*5
total he earns = 210$
If he works overtime,
for every hour he worked overtime he would get = 1.5* 5
for every hour he worked overtime he would get = 7.5
Therefore, For the week mike's gross pay is $210.
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For the given data, construct a frequency distribution and frequency histogram of the data using five classes. Describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right. Data set: ages of 20 cars randomly selected in a student parking lot 12 6 4 9 11 1 7 8 98 9 13 5 15 7 6 8 8 21 A. skewed right B. uniform C. symmetric D. skewed left
To construct a frequency distribution and frequency histogram of the data using five classes, we first need to determine the range of the data and the class interval.
The range is the difference between the highest and lowest values in the data set, in this case, 98 - 1 = 97.
We can divide the range by the number of classes to determine the class interval. In this case, 97/5 = 19.4.
We will round up to 20 to have easily divisible numbers.
The class intervals with the frequency would be:
1-20: 3
21-40: 2
41-60: 0
61-80: 3
81-100: 2
Next, we need to create a frequency histogram by plotting the class intervals on the x-axis and the frequencies on the y-axis, and then drawing a bar for each class interval representing the frequency.
The histogram will be skewed right. A histogram is skewed right when the tail of the histogram extends farther to the right than the left. In this case, the majority of the data falls in the lower class intervals, but there are a few outliers on the higher end, which extends the histogram to the right.
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