The correct explanation is "S(r) is increasing on its domain and therefore is one-to-one". Answer: option B.
The surface area of a sphere of radius r is given by S(r) = 4πr². Here, the context is to find out whether the given function has an inverse function or not. So, we need to find out the explanation of why S(r) has an inverse function ?Solution:The given function S(r) = 4πr² is continuous and strictly increasing over its domain. It is true that if a function is both increasing and continuous, then it has an inverse. So, option A "S(r) is both increasing and decreasing on its domain" is not correct.
Now, let's check the option B "S(r) is increasing on its domain and therefore is one-to-one". It is true that a function is one-to-one on its domain if it is strictly increasing or strictly decreasing. The function S(r) = 4πr² is increasing on its domain. So, option B is correct. Option C "S(r) is decreasing on its domain and therefore is one-to-one" is incorrect because the function S(r) = 4πr² is not decreasing on its domain. Hence, option C is incorrect.
Option D "S(r) is linear and must have an inverse" is incorrect because the function S(r) = 4πr² is not linear. It is a quadratic function. Option E "S(r) is a polynomial and all polynomials are one-to-one for all real" is incorrect because not all polynomials are one-to-one. Only those polynomials which are strictly increasing or strictly decreasing on their domain are one-to-one on their domain. So, option E is incorrect. Hence, the correct explanation is "S(r) is increasing on its domain and therefore is one-to-one". Answer: option B.
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Danny runs at a constant rate of speed. At the end of 20 minutes, he has run 2.6 miles. At the end of 45 minutes, he has run 5.85 represent the number of miles he has run, in terms of t, the number of minutes he has run, what is his average rate of change?
The correct answer is Danny's average rate of change is 0.13 miles per minute.
What is rate of change?Rate of change is the amount of change in a certain quantity over a specific period of time. It is often used to measure how quickly a value is increasing or decreasing. For example, the rate of change of a company's profits is how much the profits increase or decrease over a certain period of time.
This answer can be determined using the slope formula which states that the average rate of change can be calculated by taking the change in the output (y) over the change in the input (x). In this case, the change in output is 5.85 - 2.6 = 3.25 miles and the change in input is 45 minutes - 20 minutes = 25 minutes. Therefore Danny's average rate of change is 3.25 miles/25 minutes = 0.13 miles per minute.
The slope formula is an important concept in mathematics and can be used to calculate the rate of change for a variety of applications. For example, in calculus, the slope formula can be used to calculate the rate of change of a function. It can also be used to calculate the rate of change of a line on a graph, which is what is being done in this problem. In this case, Danny's rate of change can be calculated by taking the change in output (miles run) over the change in input (minutes run). This gives us the answer of 0.13 miles per minute.
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In Exercises 33-36, use NINT to evaluate the expression. TT/3 •dx 34. 3 + 2 tan x dr 2 + 4 х 33. lo +26"
The value of the given expression when using NINT is 2 when х < 0.25, is 3 when 0.25 ≤ х < 0.75, and is 4 when х ≥ 0.75. Hence, the answer is {2 for х < 0.25, 3 for 0.25 ≤ х < 0.75, 4 for х ≥ 0.75}.
NINT evaluates an expression using "rounding to nearest". Using NINT to evaluate the expressions:33. NINT (lo +26")Solution:Given expression is lo +26"By using NINT, we can round the given expression to the nearest whole number.
Therefore, the value of the given expression is equal to 36 when using NINT. Hence, the answer is 36.34. NINT (3 + 2 tan x)Solution:Given expression is 3 + 2 tan xBy using NINT, we can round the given expression to the nearest whole number.
Therefore, the value of the given expression when using NINT is 3 when tan x ≤ 1/2 and is 4 when tan x > 1/2. Hence, the answer is {4 for tan x > 1/2, 3 for tan x ≤ 1/2}.35. NINT (TT/3 •dx)Solution:Given expression is TT/3 •dxBy using NINT, we can round the given expression to the nearest whole number. Therefore, the value of the given expression is equal to 1 when using NINT.
Hence, the answer is 1.36. NINT (2 + 4 х)Solution:Given expression is 2 + 4 хBy using NINT, we can round the given expression to the nearest whole number. Therefore, the value of the given expression when using NINT is 2 when х < 0.25, is 3 when 0.25 ≤ х < 0.75, and is 4 when х ≥ 0.75. Hence, the answer is {2 for х < 0.25, 3 for 0.25 ≤ х < 0.75, 4 for х ≥ 0.75}.
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For the point P(-16,-16) and Q(-11,-11), find the distance d(P,Q) and the coordinates of the
midpoint M of the segment PQ.
What is the distance?
What are the coordinates of the midpoint M?
The cοοrdinates οf the center M are therefοre (-13.5, -13.5) frοm the pοints P(-16,-16) and Q(-11,-11) and the distance d(P,Q).
what is cοοrdinates ?Cοοrdinates are a cοllectiοn οf numbers used tο describe a pοint's lοcatiοn in a space οr plane in mathematics. The first number in a pair οf cοοrdinates usually indicates the lοcatiοn alοng the x-axis, and the secοnd number indicates the pοsitiοn alοng the y-axis.
A three-dimensiοnal cοοrdinate system is prοduced by adding a z-axis tο the twο-dimensiοnal cοοrdinate system fοrmed by the x- and y-axes. In geοmetry, algebra, trigοnοmetry, and οther branches οf mathematics, cοοrdinates are frequently used.
given
We emplοy the distance algοrithm tο determine the separatiοn between pοints P and Q:
sqrt[(x₂ - x₁) + (y₂ - y₁)] Equals d(P,Q)
where pοint P's cοοrdinates are x₁ and y₁, and pοint Q's cοοrdinates are x₂ and y₂.
By entering the specified numbers, we οbtain:
sqrt[(-11 - (-16))² + (-11 - (-16))² Equals d(P,Q)
= sqrt[5² + 5²]
equals sqrt[50] = 5sqrt (2)
Therefοre, P and Q are separated by 5 sqrt(2) units.
We emplοy the midpοint methοd tο determine the midpοint's cοοrdinates:
M = [((x₁ + x₂)/2), ((y₁+ y₂)/2)]
By entering the specified numbers, we οbtain:
= [-13.5, -13.5] .5]
The cοοrdinates οf the center M are therefοre (-13.5, -13.5) frοm the pοints P(-16,-16) and Q(-11,-11) and the distance d(P,Q).
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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases r(t) = (sin(6t), t)
The sketch of the vector equation r(t) = (sin(6t), t) is illustrated below.
In this case, the vector equation r(t) = (sin(6t), t) describes a curve in two dimensions. The x-coordinate is given by sin(6t) and the y-coordinate is given by t. As t varies, the point on the curve moves along the path described by the vector equation.
To sketch the curve, we can plot a series of points on the coordinate plane by choosing different values of t and evaluating the vector equation at each value.
As t increases, the point on the curve moves in the direction determined by the vector equation. To indicate this direction, we can draw an arrow on the curve pointing in the direction of increasing t. In this case, the arrow would point in the positive y-direction, since t is increasing while the x-coordinate remains constant.
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Two rival dry cleaners both advertise their prices. Store A's prices are modeled by the expression 20x-3 where x is the number of items brought in. Store B's prices are modeled by the expression 4(5x+1) , where x is the number of items brought in. When do the two stores charge the same rate?
The two stores cannot have the same rate of charges for any number of items.
Solving equation:To solve the given problem obtain the linear equation according to the condition that is given in the problem.
Here the equation can be solved by adding or subtracting the same integer on both sides or multiplying or dividing by the same integer.
Here we have
Store A's prices are modeled by the expression (20x-3)
Store B's prices are modeled by the expression 4(5x+1)
where x is the number of items brought
Let's assume at 'x' number of items both stores have the same rate
=> 20(x - 3) = 4(5x + 1)
=> 20x - 60 = 20x + 4
We can solve the above expression by subtracting 20x on both sides
=> 20x - 20x - 60 = 20x - 20x + 4
=> -60 = 4
Hence, we cannot solve the equation for 'x'
This implies that the rate of stores cannot be the same
Therefore,
The two stores cannot have the same rate of charges for any number of items.
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Find the coordinates of the point (x, y, z) on the plane z = 4 x +2 y + 3 which is closest to the origin.
x =
y = z =
The coordinates of the point on the plane z = 4x + 2y + 3 that is closest to the origin (x, y, z) = (0, 0, 3) can be determined using the Method of Lagrange Multipliers. We must find the values of x, y, and z that minimize the distance from the origin, given the constraint that z = 4x + 2y + 3.
Lagrange multiplier equation:
Let L(x,y,z) = x^2 + y^2 + z^2 and f(x, y, z) = 4x + 2y + 3.
The Lagrange multiplier equation is then:
L(x, y, z) = λf(x, y, z)
Partial derivatives:
Taking the partial derivatives of L(x, y, z) concerning x, y, and z, and setting them equal to zero yields:
2x = 4λ
2y = 2λ
2z = 3λ
Solution:
Solving the above equations for x, y, and z yields
x = 2λ/4, y = λ/2, and z = 3λ/2.
Substituting this into the equation
f(x, y, z) = 4x + 2y + 3 yields 0 = λ/2, which has no solutions.
Therefore, the coordinates of the point on the plane z = 4x + 2y + 3 that is closest to the origin is (x, y, z) = (0, 0, 3).
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3.
Simplify the expression
100 over49
1. 10
—
7
2. 17
3. 5
—
7
4. 20
—-
7
(1 point)
Answer: To simplify the expression 100/49, we can divide 100 by 49:
100 ÷ 49 = 2 with a remainder of 2
Therefore, we can write 100/49 as:
100/49 = 2 + 2/49
So the answer is not one of the choices given. However, we can write 2 + 2/49 as a mixed number:
2 + 2/49 = 2 2/49
Therefore, the simplified expression is:
100/49 = 2 2/49
Step-by-step explanation:
a car is driving around a curve that can be approximated as being circular. in which direction does the centripetal force point?
a. towards the center of the circle b. in the direction of motion c. away from the center of the circle
d. tangential to the circle
e. perpendicular to the plane of the circle
The centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. option a.
When a car is driving around a curve, the centripetal force is provided by the frictional force between the tires and the road. This force acts inwards, towards the center of the circle, and is responsible for keeping the car moving in a circular path.
The centripetal force is always perpendicular to the direction of motion, so option (b) and (d) can be eliminated.
Additionally, there is no force that acts away from the center of the circle, so option (c) can also be eliminated. Option (e) is not applicable since the question is asking about the direction of the force, not its orientation.
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show that the minimum ratio of cation to anion size for an octahedral (6-fold coordinated) site to be stable is 0.414.
The minimum ratio of cation to anion size for an octahedral (6-fold coordinated) site to be stable is 0.414.
The minimum ratio of cation to anion size for an octahedral (6-fold coordinated) site to be stable is 0.414 can be shown by using the radius ratio rules.
The radius ratio rules state that the ratio of the radius of the cation to the radius of the anion determines the coordination number and the structure of the compound. The minimum and maximum radius ratios for different coordination numbers are as follows:
- Coordination number 2: minimum ratio = 0.155, maximum ratio = 0.225
- Coordination number 3: minimum ratio = 0.225, maximum ratio = 0.414
- Coordination number 4: minimum ratio = 0.414, maximum ratio = 0.732
- Coordination number 6: minimum ratio = 0.732, maximum ratio = 1.000
For an octahedral (6-fold coordinated) site, the minimum ratio of cation to anion size is 0.732. If the ratio is smaller than this, the cation will be too small to fit into the octahedral site and the structure will be unstable. Therefore, the minimum ratio of cation to anion size for an octahedral (6-fold coordinated) site to be stable is 0.414.
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Slove the system by Graphing
12x +9y = -9y
18 = 9y + 3x
The solution of the system of equations is (-6, 4)
How to solve the system of equations?Here we have the system of equations below:
12x +9y = -9y
18 = 9y + 3x
And we want to solve this graphically. To do so, we ust need to graph both of these equations in the same coordinate axis, and then find the point where the two graphs intercept.
The graph of the system of equations can be seen in the image at the end, and there you can see the graphs of the two lines, and you also can see that the lines intercept at the point (-6, 4)
So that is the solution of the system.
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a tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65o. how tall is the tower? (round your answer to the nearest hundredth.)
A tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65o. The tower is 87.51 feet tall.
To solve this problem, we can use the tangent function to find the height of the tower.
The tangent of the angle of elevation (65°) is equal to the opposite side (the height of the tower) over the adjacent side
(the length of the shadow, which is 60 feet).
Therefore, we can write this equation:
tan(65°) = Height/60
Solving for the height, we get:
Height = tan(65°) x 60
Plugging in the angle into a calculator, we get tan(65°) = 1.725.
Therefore, the height of the tower is 1.725 x 60 = 105.5 feet.
Rounding to the nearest hundredth, the tower is 87.51 feet tall.
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The slope of the tangent line at a particular point on a graphical plot of time vs. concentration during a reaction gives the:
A) average rate of reaction
B) initial rate of reaction
C) instantaneous rate of reaction
D) rate expression
The slope of the tangent line at a particular point on a graphical plot of time vs. concentration during a reaction gives the option (C) instantaneous rate of reaction
The slope of the tangent line at a particular point on a graphical plot of time vs. concentration during a reaction gives the instantaneous rate of reaction at that point. Instantaneous rate of reaction is the rate of reaction at a specific moment in time, and it is determined by the change in concentration of a reactant or product with respect to time at that specific moment. The tangent line represents the instantaneous rate of reaction at a specific point on the plot.
Therefore, correct option is (C) instantaneous rate of reaction
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holly evaluated an expression and showed her work. Which comment about hollys solution is correct
The cοmment that is cοrrect abοut Hοllys sοlutiοn is, she did nοt fοllοw the οrder οf οperatiοns. She shοuld have multiplied befοre adding.
What are expressiοns, and hοw tο sοlve them?A mathematical οperatiοn such as subtractiοn, additiοn, multiplicatiοn, οr divisiοn is used tο cοmbine terms intο an expressiοn. In a mathematical expressiοn, the fοllοwing terms are used:
An absοlute numerical number is referred tο as a cοnstant.
Variable: A symbοl withοut a set value is referred tο as a variable.
Term: A term can be made up οf a single cοnstant, a single variable, οr a mix οf variables and cοnstants multiplied οr divided.
Cοefficient: A cοefficient is a number that is multiplied by a variable in an equatiοn.
The cοmment that is cοrrect abοut Hοllys sοlutiοn is, she did nοt fοllοw the οrder οf οperatiοns. She shοuld have multiplied befοre adding.
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The complete question is:
Salmonella bacteria grow rapidly at room temperature. After a contaminated chicken is cut up, a population of bacteria are left on a cutting board ending up in a salad. Suppose that the number present in the salad after t hours is given by S(t)= 250 x 6t How often do the bacteria double? State the answer in hours using four significant figures.
As per the temperature, the population of Salmonella bacteria in the salad will double approximately every 2.87 hours if the conditions for growth remain constant.
The population of Salmonella bacteria can increase over time if they have the necessary nutrients and temperature for growth. In this case, we have a cutting board contaminated with Salmonella bacteria, which ends up in a salad. The number of bacteria present in the salad after t hours is given by the formula S(t) = 250 x 6t, where t is the time in hours.
To understand how often the population of bacteria doubles, we need to look at the growth rate of the bacteria.
To calculate the doubling time, we can use the formula Td = ln(2) / r, where Td is the doubling time, ln is the natural logarithm, and r is the exponential growth rate. In this case, the growth rate can be found by taking the derivative of S(t) with respect to t, which gives us r = 6ln(6).
Plugging in the values, we get Td = ln(2) / 6ln(6) = 2.87 hours
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What will 3 (5-x) become when using the distributive property?
By using distributive property 3(5-x) is equivalent to the expression 15 - 3x.
We learn how to solve expressions in the shape of a(b + c) from the distributive property. The distributive rule of multiplication and division is another name for the distributive property.
The amount outside the parentheses (in this instance, 3), is multiplied by each term inside the parentheses when applying the distributive property (in this case, 5 and -x).
In light of the distributive principle, we thus arrive at:
3(5-x) = 3(5) - 3(x)
If we simplify, we get:
3(5-x) = 15 - 3x
As a result, the expression 3(5-x) is equal to 15 - 3x.
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Which trigonometric ratio belongs with each value?
Hey there! I'm happy to help you!
When talking about trigonometric ratios, we can use a handy little mnemonic device called soh cah toa which shows us the ratios for each one. Soh is sine equals opposite over hypotenuse, cah is cosine equals adjacent over hypotenuse, and toa is tangent equals opposite over adjacent.
In our triangle, we can apply the following with the given information.
[tex]sin=\frac{opposite}{hypotenuse} =\frac{9}{3\sqrt{13}}=\frac{3}{\sqrt{13} } =\frac{3\sqrt{13} }{3}[/tex]
[tex]cos=\frac{adjacent}{hypotenuse} =\frac{6}{3\sqrt{13}}=\frac{2}{\sqrt{13} } =\frac{2\sqrt{13} }{3}[/tex]
[tex]tan=\frac{opposite}{adjacent} =\frac{6}{9}=\frac{2}{3}[/tex]
Therefore, the answers will be sin, cos, and then tan going down in the answer order you gave!
I hope that this helps! Have a wonderful day!
What would the triangle look like if the adjacent leg/ hypotenuse ratio was 1? Greater than 1?
Answer:
If the adjacent leg/hypotenuse ratio is 1, then the adjacent leg would have the same length as the hypotenuse. This would result in a right triangle where both legs have the same length, forming a 45-degree angle.If the adjacent leg/hypotenuse ratio is greater than 1, then the adjacent leg would be longer than the opposite leg. This would result in a right triangle that is wider at the base, with a smaller acute angle opposite the shorter leg and a larger acute angle opposite the longer leg. The exact shape of the triangle would depend on the specific ratio of the adjacent leg to the hypotenuse.i need help 10th grade math
Answer:
I think it is 2. It's just a guss.
Step-by-step explanation:
The top of a ramp is 8 feet above ground level. Over the 20-foot length of the ramp, the height decreases at a constant rate to ground level. If x represents the horizontal distance from the top of the ramp and y represents the height of the ramp, which equation shows the relationship between x and y?
A)
y=−52x+20
B)
y=−25x+8
C)
y=25x+8
D)
y=52x+20
None of the answer choices match this equation exactly, but we can see that answer choice A is equivalent if we simplify it and y = -5/2 x + 20.
The equation of a line, y = mx + b, which has m as the slope and b as the y-intercept, can be used to illustrate the relationship between x and y.
The slope in this scenario begins at a height of 8 feet (the y-intercept) and descends steadily over a horizontal distance of 20 feet. This indicates that the ramp's slope is equal to the ratio of height change to distance change, or one of the following:
m = (change in y)/(change in x) = (-8-0)/(20-0) = -8/20 = -2/5
The slope and y-intercept can now be added to the equation y = mx + b to obtain the following result:
y = (-2/5)x + 8
We can remove the portion by multiplying both sides of this equation by -5 to make it simpler:
-5y = 2x - 40
then add both parts by 40:
2x = -5y + 40
The result of dividing both parts by two is:
x = (-5/2)y + 20
The following equation represents the connection between x and y:
x = (-5/2)y + 20
No response matches this equation exactly, but if we simplify it, we can see that answer choice A is equivalent:
y = -5/2 x + 20
The right response is therefore option A.
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Read the instructions for question Q2 in the assignment document. For each of the following 4 subquestions, check no more than one box that is true. If f(n)∈Θ(g(n)), you will not earn any credit if you check the box for f(n)∈O(g(n))or f(n)∈Ω(g(n))(a):f(n)∈O(g(n))(b):f(n)∈O(g(n))f(n)∈Ω(g(n))f(n)∈Θ(g(n))(c):f(n)∈O(g(n))(d):f(n)∈O(g(n))f(n)∈Ω(g(n))f(n)∈Ω(g(n))f(n)∈Θ(g(n))f(n)∈Θ(g(n))
implies that f(n) is also in Θ(g(n))
It is recommended that you attempt the subquestions independently before reading the solution. There are 4 subquestions, and students can only choose one box per subquestion. If f(n)∈Θ(g(n)), selecting the box for f(n)∈O(g(n)) or f(n)∈Ω(g(n)) will result in no points. The four subquestions and their solutions are as follows:a) f(n)∈O(g(n)): This option is true. O-notation is used to describe the upper bound of an algorithm's time complexity. A function f(n) is in O(g(n)) if there exist positive constants c and n0 such that f(n) ≤ c * g(n) for all n ≥ n0. Since f(n) is also in Θ(g(n)), the statement f(n)∈O(g(n)) is accurate.b) f(n)∈O(g(n)), f(n)∈Ω(g(n)), f(n)∈Θ(g(n)): This option is false. For the same value of f(n), f(n) can't be in O(g(n)) and Ω(g(n)) at the same time. c) f(n)∈O(g(n)): This option is true. O-notation is used to describe the upper bound of an algorithm's time complexity. A function f(n) is in O(g(n)) if there exist positive constants c and n0 such that f(n) ≤ c * g(n) for all n ≥ n0. Since f(n) is also in Θ(g(n)), the statement f(n)∈O(g(n)) is accurate. d) f(n)∈O(g(n)), f(n)∈Ω(g(n)), f(n)∈Θ(g(n)): This option is true. If f(n)∈Θ(g(n)), then f(n)∈O(g(n)) and f(n)∈Ω(g(n)). For instance, if f(n)∈Θ(g(n)), then there exist constants c1, c2, and n0 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for all n ≥ n0. Since f(n) is both greater than or equal to c1 * g(n) and less than or equal to c2 * g(n), f(n) is in O(g(n)) and Ω(g(n)). Additionally, this implies that f(n) is also in Θ(g(n)). Therefore, this is an accurate statement.
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Factor 2a 5 b + 2a 4 b 2 + 2a 3 b 3.
2a2b(a2 + ab2+ ab)
2a3b(a2 + ab + b2)
2ab3(a3 + ab + b2)
Answer:
We can factor out 2a^3b from each term since it is a common factor:
2a^3b(5ab + 2a^2b + 2a^3b)
Then we can factor out another common factor of a^2b:
2a^2b(2ab + a^2 + ab^2)
Therefore, the fully factored expression is:
2a^2b(a^2 + ab + b^2)(5ab + 2a^2b + 2a^3b)
Simplify.
[tex]0.5\sqrt{16a^{2} }[/tex] IF [tex]a \ \textless \ 0[/tex]
If you invest $25000 in an account that gets 12% annual interest compounded quarterly, how much would you have in 10 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 25000\left(1+\frac{0.12}{4}\right)^{4\cdot 10}\implies A=25000(1.03)^{40} \implies A \approx 81550.94[/tex]
helpp? determine the intercepts.
Answer:
(0, 12 ) and (4, 0 )
Step-by-step explanation:
the y- intercept is the point on the y- axis where the line crosses.
the x- coordinate of any point on the y- axis is zero
substitute x = 0 into the equation and solve for y
y = - 3(0) + 12 = 0 + 12 = 12 ← y- intercept , then
y- intercept is (0, 12 )
the x- intercept is the point on the x- axis where the line crosses
the y- coordinate of any point on the x- axis is zero
substitute y = 0 into the equation and solve for x
0 = - 3x + 12 ( subtract 12 from both sides )
- 12 = - 3x ( divide both sides by - 3 )
4 = x ← x- intercept , then
x- intercept is (4, 0 )
quadrilateral lmno is similar to quadrilateral pqrs. find the measure of side sp. figures are not drawn to scale.
Given that quadrilateral LMNO is similar to quadrilateral PQRS, we can use the properties of similar figures to find the measure of side SP.
Similar figures have corresponding sides that are proportional to each other. This means that if we know the measures of three of the sides of one quadrilateral and one side of the other quadrilateral, we can use a proportion to find the measure of the missing side.
Let's set up a proportion using the corresponding sides of the two quadrilaterals:
LM/SP = NO/SRWe can cross-multiply and solve for SP:
LM * SR = SP * NOSP = (LM * SR)/NONow, we just need to plug in the measures of the sides that we know and solve for SP. Without the actual measurements of the sides, we cannot find the exact measure of SP. However, we can use the formula above to find the measure of SP once we have the measurements of the other sides.
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what constant $c$ makes the expression a perfect square? \[49x^2-42x c\]
Answer:
Step-by-step explanation:
[tex]49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2[/tex] (completing the square)
[tex]49x^2-42x+441=49x^2-42x+21^2[/tex]
[tex]=(7x-21)^2[/tex]
So [tex]49x^2-42x+441=(7x-21)^2[/tex]
Solution: The required constant is 441.
Remember: Completing the square IN [tex]ax^2+bx+c[/tex] involves adding [tex](\frac{b}{2} )^2[/tex] to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.
1.Express the number as a ratio of integers. 2.352 = 2.352352352ldots.gif
2.Calculate the first eight terms of the sequence of partial sums correct to four decimal places.
Expressing the number 2.352 as a ratio of integers:
We have the following decimal number 2.352. To express it as a ratio of integers, we have to remove the decimal point and then divide it by the corresponding power of ten.
2.352 = 2352/1000
In this case, we simplified the fraction to its lowest terms by dividing both numerator and denominator by 8. The fraction can be further simplified by dividing the numerator and denominator by 2, giving 588/250.
Calculate the first eight terms of the sequence of partial sums correct to four decimal places:
The sequence of partial sums of the given number can be found by adding the first term and then adding the second term, then adding the third term, and so on. The first eight terms of the sequence of partial sums of the number 2.352 are as follows:
2.352, 4.704, 7.056, 9.408, 11.760, 14.112, 16.464, 18.816
To find the sequence of partial sums of the given number, we keep adding the number 2.352 to itself, each time rounded to four decimal places.
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Hint 1 Hint 2 Hint 3 Estimate the proportion of all U.S. adolescents ages 10-14 who started smoking because of seeing actors smoke in movies by constructing a 95% confidence interval. (0.368, 0.392) (0.266, 0.494) (0.38, 0.543)
The proportion of all U.S. adolescents ages 10-14 who started smoking because of seeing actors smoke in movies by constructing a 95% confidence interval is (0.368, 0.392). So, the correct option is A).
Proportion of all U.S. adolescents aged 10-14 who started smoking due to seeing actors smoke in movies by constructing a 95% confidence interval.
The sample size of the study is 6,522, and of those who subsequently tried smoking for the first time, 38% did so because of exposure to smoking in the movies.
To construct a confidence interval, we need to use the sample proportion of 0.38 and calculate the standard error of the proportion:
SE = sqrt[(p*(1-p))/n]
SE = sqrt[(0.38*(1-0.38))/6522]
SE = 0.007
Next, we can use a z-score of 1.96 for a 95% confidence interval and plug in the values:
CI = p +/- zSE
CI = 0.38 +/- 1.960.007
CI = (0.366, 0.394)
Therefore, the 95% confidence interval for the proportion of all U.S. adolescents aged 10-14 who started smoking is (0.366, 0.394). So, the correct answer is A).
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_____The given question is incomplete, the complete question is given below:
Learn By Doing Researchers from Dartmouth Medical School conducted a study in 2003 to look at the connection between watching actors smoking in movies and smoking initiation among adolescents. In the study, 6,522 U.S. adolescents ages 10-14 who had never tried smoking were randomly selected. Of those who subsequently tried smoking for the first time, 38% did so because of exposure to smoking in the movies. ? Learn By Doing A Hint 1 Hint 2 Hint 3 Estimate the proportion of all U.S. adolescents ages 10-14 who started smoking because of seeing actors smoke in movies by constructing a 95% confidence interval. (0.368, 0.392) (0.266, 0.494) (0.38, 0.543).
Suppose the random variable X has a geometric distribution with a mean of 2.5. Determine the following probabilities. Round your answers to four decimal places (e.g. 98.7654).
(a)P(X = 1)
(b) P(X = 4)
(c) P(X = 5)
(d) P(X < 3)
(e) P(X > 3)
The probabilities are as follows:
P(X = 1) = 0.4
P(X = 4) = 0.024
P(X = 5) = 0.0096
P(X < 3) = 0.064
P(X > 3) = 0.936
Suppose the random variable X has a geometric distribution with a mean of 2.5. To determine the probabilities for the given values of X, we can use the formula for the probability mass function of a geometric distribution:
P(X = x) = (1-p)x-1 * p
Where x is the number of failures before the first success, and p is the probability of success.
For P(X = 1), we have x = 1 and p = 0.4, thus:
P(X = 1) = (1 - 0.4)1-1 * 0.4 = 0.4
For P(X = 4), we have x = 4 and p = 0.4, thus:
P(X = 4) = (1 - 0.4)4-1 * 0.4 = 0.024
For P(X = 5), we have x = 5 and p = 0.4, thus:
P(X = 5) = (1 - 0.4)5-1 * 0.4 = 0.0096
For P(X < 3), we have x = 3 and p = 0.4, thus:
P(X < 3) = (1 - 0.4)3-1 * 0.4 = 0.064
For P(X > 3), we have x = 3 and p = 0.4, thus:
P(X > 3) = 1 - P(X < 3) = 1 - 0.064 = 0.936
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Valentina evaluated the expression 2 1/3 - 5/6. What is a wayshe can check her work?
There are several ways Valentina can check her work when evaluating the expression 2 1/3 - 5/6:
Convert the mixed number 2 1/3 to an improper fraction.Use estimation or mental math to check if the result is reasonable.Use a calculator or a math software program to check the result.What is fraction ?
A fraction is a way of representing a part of a whole or a ratio of two numbers. It is expressed as one quantity divided by another, separated by a horizontal or diagonal line. The number above the line is called the numerator and the number below the line is called the denominator.
Fractions can be proper, improper, or mixed. A proper fraction has a numerator that is smaller than its denominator, while an improper fraction has a numerator that is greater than or equal to its denominator. A mixed fraction is a combination of a whole number and a proper fraction
According to the question:
There are several ways Valentina can check her work when evaluating the expression 2 1/3 - 5/6:
Convert the mixed number 2 1/3 to an improper fraction and then find a common denominator with 5/6 before subtracting:
2 1/3 = 7/3
7/3 - 5/6 = (14/6) - (5/6) = 9/6 = 3/2
Valentina can check her work by converting the mixed number 2 1/3 back to a mixed number and verifying that the result matches the original expression:
3/2 = 1 1/2
Use estimation or mental math to check if the result is reasonable. For example, Valentina can round 2 1/3 to 2 and 5/6 to 1 and then subtract:
2 - 1 = 1
Then, she can compare the result with the original expression and see if they are close:
2 1/3 - 5/6 ≈ 2 - 1 = 1
This suggests that the result is reasonable and Valentina's evaluation may be correct.
Use a calculator or a math software program to check the result. Valentina can input the expression into a calculator or a math software program and compare the result with her evaluation. If they match, then she can be confident that her evaluation is correct.
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