Answer:
f(x) = (x - 3)^2 + 2
Step-by-step explanation:
The function with a graph that has a vertex 5 units horizontally to the right of the vertex of the graph of g(x) = (x + 2)^2 + 2 is f(x) = (x - 3)^2 + 2, which can be obtained by subtracting 5 from x + 2 to get x - 3 inside the parentheses of (x - 3)^2 and translating the vertex horizontally to (3, 2).
The radius of a sphere is increasing at a constant rate of 2 inches per minute. At the instant when the radius of the sphere is 9 9 inches, what is the rate of change of the volume? The volume of a sphere can be found with the equation � = 4 3 � � 3 . V= 3 4 πr 3 . Round your answer to three decimal places.
Answer:
2035.752 in³/min
Step-by-step explanation:
To find the rate of change of the volume of the sphere at the instant its radius is 9 inches, we need to work out dV/dt when r = 9.
The equation for the volume of a sphere is:
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Differentiate the expression for volume with respect to r:
[tex]\begin{aligned}V&=\dfrac{4}{3}\pi r^3\\\\\implies\dfrac{\text{d}V}{\text{d}r}&=3 \cdot \dfrac{4}{3} \pi r^{3-1}\\\\\dfrac{\text{d}V}{\text{d}r}&=4 \pi r^2\end{aligned}[/tex]
We know that that the radius of a sphere is increasing at a constant rate of 2 inches per minute, so the rate of change of the radius of sphere is:
[tex]\dfrac{\text{d}r}{\text{d}t}=2[/tex]
To find an expression for dV/dt, use the chain rule:
[tex]\boxed{\dfrac{\text{d}V}{\text{d}t}=\dfrac{\text{d}V}{\text{d}r} \times \dfrac{\text{d}r}{\text{d}t}}[/tex]
Substitute the expressions for dV/dr and dr/dt to create an expression for dV/dt:
[tex]\begin{aligned}\implies \dfrac{\text{d}V}{\text{d}t}&=4 \pi r^2 \times 2\\&=8 \pi r^2\end{aligned}[/tex]
To find the value of dV/dt when r = 9, substitute r = 9 into the equation for dV/dt:
[tex]\begin{aligned}\dfrac{\text{d}V}{\text{d}t}\;\textsf{at}\;r=9\implies \dfrac{\text{d}V}{\text{d}t}&=8 \pi (9)^2\\&=8\pi (81)\\&=648\pi\\&=2035.752\; \sf in^3/min\;(3\;d.p.)\end{aligned}[/tex]
Therefore, the rate of change of the volume of the sphere at the instant when its radius is 9 inches is 2035.752 in³/min (rounded to three decimal places).
I need help with this algebra 2. If you don’t know please don’t respond .
Required true statements are B, C, D, G, H, I, L, M.
What is factor?
In mathematics, factors refer to the numbers that can be multiplied together to obtain a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Based on the given factors, we can conclude that:
f(x) has a factor of 3, which means that 3 is a root/solution of f(x).
f(x) has a factor of (2x-1), which means that 2x-1=0 or x=1/2 is a root/solution of f(x).
f(x) has a factor of (x+5), which means that x+5=0 or x=-5 is a root/solution of f(x).
Using these facts, we can determine which statements are true:
A) -1/2 is not a root/solution of f(x). (False)
B) We can check if this expression is equivalent to f(x) by factoring it:
6x² - 33x - 15 = 3(2x² - 11x - 5) = 3(x - 5)(2x + 1).
This shows that f(x) has factors of 3, (2x-1) and (x+5), so this statement is true.
C) -5 is a root/solution of f(x). (True)
D) 3 is a root/solution of f(x). (True)
E) We can check if this expression is equivalent to f(x) by factoring it:
2x²+9x-5 = (2x - 1)(x + 5), which is not the same as the factors given for f(x), so this statement is false.
F) 0 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at 0. (False)
G) We can check if this expression is equivalent to f(x) by factoring it:
6x²+27x-15 = 3(2x²+9x-5) = 3(2x-1)(x+5), which shows that f(x) has the same factors as this expression, so this statement is true.
H) 1/2 is a root/solution of f(x). (True)
I) 5 is a root/solution of f(x). (True)
J) We can check if this expression is equivalent to f(x) by factoring it:
2x²-9x-5 = (2x + 1)(x - 5), which is not the same as the factors given for f(x), so this statement is false.
K) -3 is not necessarily a root/solution of f(x), since the factors given do not guarantee that f(x) intersects the x-axis at -3. (False)
L) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:
f(x) = 3(x + 5)(2x - 1) = 0
This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0). So, this statement is true.
M) To find the x-intercepts of f(x), we need to set f(x) equal to zero and solve for x:
f(x) = 3(x + 5)(2x - 1) = 0
This equation has roots of x=-5 and x=1/2, which means that the x-intercepts of f(x) are (-5, 0) and (1/2, 0).
So, this statement is true.
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obsessivex avatar
obsessivex
17 hours ago
Mathematics
High School
Question 2(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
obsessivex
Based on the IQR values, we conclude that Bus 18 is more consistent than Bus 47, as it has smaller IQR. This means the travel times of students on Bus 18 are more tightly clustered around the median, and are fewer outliers in data.
What is line plots?A line plot is a type of graph that displays data as points or dots along a number line. Each dot or point represents a single data value, and the number line shows the range of the data. Line plots are useful for displaying small to moderate-sized data sets and for identifying the central tendency and variability of the data.
To determine which bus is the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the middle 50% of the data.
From the given data, we can calculate the IQR for both buses as follows:
For Bus 18:
Lower quartile (Q1) = 8
Upper quartile (Q3) = 24
IQR = Q3 - Q1 = 24 - 8 = 16
For Bus 47:
Lower quartile (Q1) = 10
Upper quartile (Q3) = 34
IQR = Q3 - Q1 = 34 - 10 = 24
The range, which is the difference between the maximum and minimum values, is not as appropriate a measure of variability for this purpose, as it is heavily influenced by outliers. Therefore, we cannot use the range to determine the consistency of the data for either bus.
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new car owners were asked to evaluate their experiences in buying a new car during the past 12 months. in the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): subaru, honda, and buick. assuming that each set of rankings is equally likely, what is the probability that owners ranked subaru third? question 5 options: 1/3 1/6 1/2 5/6 6/6
The probability that owners ranked Subaru third is 2/6, which reduces to 1/3. Therefore, the correct answer is 1/3.
To find the probability that owners ranked Subaru third, we need to find out the total number of possible rankings for
the three dealers: Subaru, Honda, and Buick.
There are three possible rankings for the first choice, two for the second choice, and one for the third choice.
Therefore, there are 3 x 2 x 1 = 6 possible rankings for the dealers.
Since each of the possible rankings is equally likely, the probability that owners ranked Subaru third is the number of
ways to rank Subaru third divided by the total number of possible rankings.
Subaru can be ranked third in two out of the six possible rankings:
Subaru, Honda, Buick Honda, Buick, Subaru
Therefore, the probability that owners ranked Subaru third is 2/6, which reduces to 1/3.
Therefore, the correct answer is 1/3.
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What is the product of (-a + 3)(a + 4)? Oa²-a +12 Oa2-a-12 O-a²-a-12 O-a ²-a + 12
The product of equation (-a + 3)(a + 4) is -a² - a + 12.
What is product of equation?
Using the distributive property, we can expand the product of (-a + 3)(a + 4) as follows:
(-a + 3)(a + 4) = -a(a) - a(4) + 3(a) + 3(4)
Simplifying, we get:
(-a + 3)(a + 4) = -a² - 4a + 3a + 12
Combining like terms, we get:
(-a + 3)(a + 4) = -a² - a + 12
Therefore, the product of (-a + 3)(a + 4) is -a² - a + 12.
What is distributive property?
The distributive property is a property of arithmetic operations that is used to simplify expressions by distributing one term over another term inside parentheses.
In particular, the distributive property states that:
a × (b + c) = (a × b) + (a × c)
or
(a + b) × c = (a × c) + (b × c)
This property applies to both multiplication and addition, and can be extended to subtraction and division by adding or subtracting the distributive term to both sides of the equation.
For example, using the distributive property, we can simplify the expression:
3 × (4 + 5)
as follows:
3 × (4 + 5) = 3 × 4 + 3 × 5
= 12 + 15
= 27
In this example, we used the distributive property to distribute the term 3 over the sum (4 + 5), resulting in the equivalent expression 3 × 4 + 3 × 5.
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you have a summer job that pays time and a half for overtime. that is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7. what does the slope of a line segment represent in the context of this situation?
The slope of a line segment represent in the context of this situation is the total wages for the week.
We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the
x-coordinate are denoted by y and x, respectively.
Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is
[tex]m=\frac{y}{x} =\frac{change \ in \ y}{change\ in\ x}[/tex]
You are a crew at a Convenience store that pays an hourly wage $ 7 and 1.5 times the hours wage for the extra hours if you work for more than 40 hours a week. Write a piecewise function that gives the weekly pay P in term of the number of hours h your work.
→ wages for 1 hours = $ 7
So,
we can say that, wages for 40 hours, = 7 x 40 = 280 .
Therefore,
→ Total wages of week is = 280.
Piecewise function is :-
P(h) = 280 , where h ≤ 40.
Now, we have given that, store gives 1.5 times the hours wage for the extra hours if you work for more than
40 hours a week.
So,
→ wages per hour now = 1.5 x 7 = 10.5 .
Therefore,
→ Total wages of week
= 280 + 10.5(h - 40)
= 280 + 10.5h - 420
= 10.5h - 140.
and,
Piecewise function that gives the weekly pay P in term of the number of hours h your work is:
P(h) = 280 + 10.5(h - 40), where [h > 40].
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An economist would like to estimate the average household income in Martin county. The mean household
income of a random sample of 227 families in Martin county was found to be $52,939. The standard
deviation of the household incomes of all households in Martin county is known to be $1,227.
Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the average
household income in Martin county. Report the confidence interval using interval notation. Round solutions
to two decimal places, if necessary.
Therefore , the solution of the given problem of average comes out to be 96% confidence interval is ($52,791.38, $53,086.62).
What is average?The result of a collection, also known as the arithmetic mean, is the sum of all values split by all of the values. One of the most commonly used primary trend indicators, it is frequently referred to as "mean." Multiply the total number of numbers in the collection by each value to get the result. Calculations can be performed using either the raw data or data that has been merged into frequency charts.
Here,
The error margin (E) is equal to z* (standard deviation / sqrt(n)).
Interval of confidence equals sample mean E
Where n is the sample size, z* is the critical value for the required confidence level, and s is the population standard deviation.
We can enter the provided values into the margin of error formula as follows:
=> E = 2.05 * (1227 / sqrt(227))
=> E ≈ 147.62
Therefore, the error range is roughly $147.62.
Next, we can create the confidence interval using the group mean and margin of error:
Interval of confidence equals sample mean E
=> Confidence range is between $52,939 and $147.62.
=> Interval of confidence = ($52,791.38, $53,086.62)
Therefore, the range of the typical household income in Martin County within the 96% confidence interval is ($52,791.38, $53,086.62).
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suppose a simple random sample of 150 students is drawn from a population of 3000 college students. among sampled students, the average iq score is 115 with a standard deviation of 10. what is the point estimate? group of answer choices 3000 115 unable to tell. not enough information given. 10
115.
The point estimate for the average IQ score of the population of 3000 college students based on a simple random sample of 150 students with an average IQ score of 115 and a standard deviation of 10 is 115.
Therefore, the correct option is 115.
A point estimate is an estimate of a population parameter based on a single value or point. It is obtained by using statistics collected from a sample to infer population values. It can be a single value or a range of values that best represents the unknown population parameter.
Based on the given information, a simple random sample of 150 students is drawn from a population of 3000 college students.
Among sampled students, the average IQ score is 115 with a standard deviation of 10. The point estimate, in this case, is the average IQ score of the population, which is estimated to be 115 based on the sample data.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer:
Step-by-step explanation:
Refers to the attachment given below!
It is known that the population standard deviation in waiting tim for L.P.G. gas cylinder in Delhi is 15 days. How large a sample should be chosen to be 95% confident, the waiting time should be 7 days of true average.
We should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.
Describe Confidence Interval?In statistics, a confidence interval is a range of values that is used to estimate an unknown population parameter with a certain degree of confidence or probability. It is a statistical measure that indicates the level of uncertainty or variation associated with a particular estimate or sample.
A confidence interval is typically expressed as a range of values, along with a level of confidence, such as 95% or 99%. This means that if the same study were to be repeated many times, the calculated confidence interval would contain the true population parameter for the given confidence level in a specified proportion of the repetitions. For example, a 95% confidence interval means that if the same study were repeated many times, the interval would contain the true population parameter 95% of the time.
We can use the formula for the margin of error of a confidence interval to solve this problem:
Margin of error = z*(sigma/√(n))
where:
z = the z-score associated with the desired level of confidence (in this case, 1.96 for 95% confidence)
sigma = the population standard deviation (15 days)
n = the sample size we want to find
We want the margin of error to be no more than 7 days, so we can set up the following inequality:
7 <= 1.96*(15/√(n))
Solving for n, we get:
n >= (1.96*15/7)²
n >= 12.36²
n >= 152.7
Therefore, we should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.
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I NEED HELP ASAP! The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 71° is changed to 93°, which of the following measures changes the most and what is the new value?
Mean 82.3°
Median 86.5°
Range 48°
IQR 34°
Answer:
The new value of the list after changing 71° to 93° would be:
58, 61, 93, 77, 91, 100, 105, 102, 95, 82, 66, 57
The measure that changes the most would be the median. Without the change, the median was 86.5°, which was the average of the 7th and 8th values in the list (100 + 77) / 2. However, after changing 71° to 93°, the median becomes 91°, which is the average of the 6th and 7th values in the list (91 + 91) / 2.
Therefore, the median has changed by 4.5° (from 86.5° to 91°).
Help asap :(((((((((((((((((((((
Answer:151
Step-by-step explanation:
Addition of 107 and 44
The value of the angle m∠EFG is 151.
We have,
From the figure,
m∠EFG = m∠EFH + m∠HFG
Now,
Substituting the values in the angle.
m∠EFG
= m∠EFH + m∠HFG
= 44 + 107
= 151
Thus,
The value of the angle m∠EFG is 151.
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Find the equation of line containing the origin and has a slope of 2:
We know that the line passes through the origin, which means that the coordinates of the point on the line are (0,0). We also know that the line has a slope of 2. Therefore, we can use the point-slope form of the equation of a line to find its equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Plugging in the values we know, we get:
y - 0 = 2(x - 0)
which simplifies to:
y = 2x
Thus, the equation of the line containing the origin and with a slope of 2 is y = 2x.
Find the missing dimension of the cone. Volume=1/18
r=2/3
Answer:
Step-by-step explanation:
The formula to calculate the volume of a cone is:
v = h * π * r ^ 2/3
Where,
h: height
r: radio
We then clear the value of h:
h = (3 * v) / (π * r ^ 2)
We substitute the values:
h = (3 * (118π)) / (π * ((2/3) / (2)) ^ 2)
h = 3186 ft
Answer:
The height of the cone is:
h = 3186 ft
A tower is composed of a prism with a square base and a pyramid. the base length is 20 meters, and the height of the prism is 40 meters, while the slant height of the pyramid is 10√2 meters. what is the total surface area, including the bottom base? 400√2 3,600 m2 200√2 3,600 m2 400√2 400 m2 4000√2 m2
The total surface area of the tower, including the bottom base, is [tex]3600+400\sqrt{2}[/tex] square meters.
The surface area of the tower can be found by calculating the surface area of the prism and the surface area of the pyramid separately, and then adding them together.
The surface area of the square base of the prism is [tex]20^2 = 400[/tex] square meters.
The lateral surface area of the prism is the product of the perimeter of the base and the height, which is [tex]4*(20)*40 = 3200[/tex] square meters.
The surface area of the pyramid is given by the formula:
base area + 1/2(perimeter of base)(slant height)
The base area of the pyramid is [tex]20^2 = 400[/tex] square meters. The perimeter of the base is 4(20) = 80 meters. Therefore, the surface area of the pyramid is:
[tex]400 + [(\frac{1}{2})*(80)(10\sqrt{2})] = 400 + 400\sqrt{2}[/tex] square meters.
The total surface area of the tower is the sum of the surface area of the prism and the surface area of the pyramid, which is:
[tex]3200 + 400 + 400\sqrt{2} = 3600 + 400\sqrt{2}[/tex] square meters.
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suppose the weight of coal in 43 cars selected at random had an average x of less than 61.5 tons. would that fact make you suspect that the loader had slipped out of adjustment? why?
If the weight of coal in 43 cars selected at random had an average (x) of less than 61.5 tons, it might make you suspect that the loader had slipped out of adjustment.
Here's why:
Compare the average weight with the expected weight
First, you need to know the expected average weight of coal in the cars when the loader is functioning correctly. If the expected average is significantly higher than 61.5 tons, it could indicate an issue with the loader.
Assess the sample size
A sample size of 43 cars is relatively large, which gives you more confidence in the accuracy of the calculated average weight. If the sample size were smaller, it would be more likely that the result is due to random chance.
Evaluate the deviation from the expected weight
If the average weight is much lower than the expected weight, it would be more likely that the loader is out of adjustment. A small deviation could still be due to random chance or other factors, but a large deviation would suggest a potential issue with the loader.
Consider other factors
Before concluding that the loader is out of adjustment, it's essential to consider other factors that may have caused the lower average weight, such as changes in the type of coal, variations in car sizes, or even human error in weighing the coal.
Investigate further
If the deviation from the expected weight is significant and you cannot identify any other factors that might have caused the lower average weight, it would be reasonable to suspect that the loader may have slipped out of adjustment. In this case, you should conduct a thorough investigation, including inspecting the loader and checking its settings to determine if an adjustment is needed.
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an integer is randomly chosen from the integers $1$ through $100$, inclusive. what is the probability that the chosen integer is a perfect square or a perfect cube, but not both? express your answer as a common fraction.
The probability that the chosen integer is a perfect square or a perfect cube but not both is therefore 13/100.
When choosing an integer from 1 to 100, there are 10 perfect squares (1² to 10²) and 4 perfect cubes (1³ to 4³). However, the number 1 is both a perfect square and a perfect cube. To avoid counting it twice, we use the formula for the union of two sets: |A∪B| = |A| + |B| - |A∩B|. In this case, |A∪B| represents the number of integers that are either a perfect square or a perfect cube. Plugging in the values, we get |A∪B| = 10 + 4 - 1 = 13. The probability is therefore 13/100.
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a. There are different
ways to tell whether an equation
represents a proportional
relationship. Is there one way that is
always best?
b.Explain your reasoning.
Which of the equations y = 2x and
y = 2x + 15, if either, represents a
proportional relationship?
A. only y = 2x + 15
B. neither equation
C. both equations
D. only y = 2x
Pls and thx
The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
A. There is no one optimum approach to determine if an equation indicates a proportionate connection. One popular method is to test if the equation can be stated in the form y = kx, where k is a constant. A proportional connection is represented by an equation that may be expressed in this format.
A. Because it can be expressed as y = kx with k = 2, the equation y = 2x represents a proportional connection. As a result, D is the right answer: just y = 2x.
The equation y = 2x + 15, on the other hand, does not illustrate a proportional connection since it cannot be stated in the form y = kx. As x grows, y increases by a factor of two.
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give the required elements of the hyperbola y^2/9-x^2/81=1
The hyperbola opens:
Vertically
Horizontally
By answering the presented question, we may conclude that equation Asymptotes: y = ±(3/9)x and y = ±(-3/9)x, which simplify to y = ±(1/3)x and y = ∓(1/3)x. and The hyperbola opens Vertically.
What is equation?In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" contends that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true. Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation[tex]"x2 + 2x - 3 = 0,[/tex]" the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.
Center: (0,0)
Transverse axis length: 2a = 2*3 = 6
Conjugate axis length: 2b = 2*9 = 18
Vertices: (0,±3)
Foci: (0,±√18)
Asymptotes: y = ±(3/9)x and y = ±(-3/9)x, which simplify to y = ±(1/3)x and y = ∓(1/3)x.
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The length of a rectangle is the sum of the width and 3. The area of the rectangle is 28 square units. What is the length, in units, of the rectangle?
Answer:
Length is 7 units
Step by Step explanation:
Assuming you mean the Area is 28 square units
Then
L = w + 3
A = w(w + 3)
28 = w2 + 3w
We can subtract 28 from both sides of the equation to obtain the Quadratic
w2 + 3w - 28 = 0
Factoring to give
(w + 7)(w - 4) = 0
The width cannot be -7
w = 4
L = w + 3
L = 4 + 3 = 7
The width of the rectangle is 4 units and the length of the rectangle is 7 unites.
Sarah visited a tree nursery. She measured and recorded the heights of some young trees. This line plot shows her results.
How much taller is one of the tallest trees than one of the shortest trees?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
3 and 1/2
Step-by-step explanation:
7 and 1/2 - 4
Find the zeros of the following quadratic function
The zeros of the quadratic function [tex]f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.[/tex]
What is quadratic function?A quadratic function is a mathematical function of the form:
[tex]f(x) = ax^2 + bx + c[/tex]
where a, b, and c are constants, and x is the variable. The highest power of the variable x in a quadratic function is 2, which means it is a second-degree polynomial.
In a quadratic function, the graph is a parabola, which can open up or down depending on the sign of the leading coefficient a. If a > 0, the parabola opens up, and if a < 0, the parabola opens down. The vertex of the parabola represents the minimum or maximum value of the function, depending on the direction of the parabola.
To find the zeros of the quadratic function:
[tex]f(x) = 2x^2 - 5x + 2[/tex]
We need to solve the equation:
[tex]2x^2 - 5x + 2 = 0[/tex]
We can factor this quadratic equation as follows:
[tex]2x^2 - 4x - x + 2 = 02x(x - 2) - 1(x - 2) = 0(2x - 1)(x - 2) = 0[/tex]
So the zeros of the quadratic function are:
x = 1/2 or x = 2.
Therefore, the zeros of the quadratic function is:[tex]f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.[/tex]
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Use what you know about the patterns in area models to determine which two area models correctly represent a factorable polynomial in the form of ax 2 + bx + c where c = 40. The middle “b” term is unknown.
The correct area models are 4e and none of the given models for 4d and 4c.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The area model of 4c is incorrect because the last term of the polynomial, which is 40, is represented by the bottom right box of the area model. However, in the given area model, the box representing 40 is in the upper row.
The area model of 4e is correct because it represents the polynomial as the product of two binomials, where the factors are (x-5) and (x-8).
When multiplied using the distributive property, the resulting polynomial is x² - 13x + 40, which matches the given polynomial form.
The area model of 4d is incorrect because it does not properly represent a factorable polynomial.
It only includes three boxes, representing the three terms of the polynomial, but it does not show how the terms can be factored into binomials.
Therefore, the correct area models are 4e and none of the given models for 4d and 4c.
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Write the phrase as an algebraic expression. Let x represent the unknown number.
Nineteen more than a number
The Translation is_____.
If x is the unknown number and Nineteen more than a number. Thus, Translation is 19 units on the right to get x + 19.
Explain about the Translation:Each point in a figure is moved the same distance in a single direction using a type of transformation known as translation.
In geometry, a function that transfers an object a specific distance is referred to as translation. Nothing else is done to change the object. It is not scaled, reflected, rotated, or refracted.
Give that:
x is the unknown number and Nineteen more than a number.
Then, there is a shift of 19 units on the right of x. add 19 to unknown number x to get the translation.
x + 19
Thus, Translation is 19 units on the right to get x + 19.
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The probability that a student passes mathematics class is 0.85, the probability that he passes history class is 0.70, and the probability that he passes mathematics and history is 0.50. Are the two events
independent of each other? (4 points)
No, they are dependent because P(M)- P(H)=P(MH)
No, they are dependent because P(M)-P(H)=P(MH)
Yes, they are independent because P(M)-P(H)=P(MH)
Yes, they are independent because P(M)-P(H) P(MH)
By answering the presented question, we may conclude that Hence, the probability answer is that they are dependant since P(M) P(H) does not hold.
What is probability?Probability theory is an area of mathematics that determines the likelihood that an event will occur or that a proposition is true. A probability is a number between 0 and 1, where 1 represents certainty and 0 represents how likely an event is to occur. A probability is a numerical expression for the chance or likelihood that a given event will occur. Probabilities may either be stated as percentages ranging from 0% to 100% or as numbers ranging from 0 to 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all conceivable outcomes.
To see if the two occurrences are independent, we may look at whether the likelihood of one event is changed by the occurrence of the other.
Let M represent a passing mathematics class and H represent a passing history class. The probability may therefore be stated as follows:
P(M) = 0.85 P(H) = 0.70 P(M H) = 0.50 (where signifies the "and" or intersection operation)
We may use the following formula to test for independence:
If M and H are independent, then P(M H) = P(M) P(H).
When we substitute the provided probabilities, we get:
0.50 = 0.85 × 0.70
0.50 ≠ 0.595
As a result, the equation is invalid, and the events are interdependent.
Hence, the answer is that they are dependant since P(M) P(H) does not hold.
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What is the angle of elevation from the ground to the top of a 45 -foot tree from 65 feet away?
Answer: The angle elevation is 34.6 9 degree.
Step-by-step explanation:
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For a certain value of k, the system,
x+y=3z=10,
4x+2y+5z=7,
kx+z=3,
has no solutions. What is the value of k? (the answer is not 2,6,2/7,or 7/2)
The value of k given the system of equations is 2
Calculating the value of kGiven that
x + y + 3z = 10
4x + 2y + 5z = 7
kx + z = 3
Eliminate y in the first two equations
So, we have
2x + 2y - 6z = 20
4x + 2y + 5z = 7
kx + z = 3
Subtract the first two equations
So, we have
2x + z = -13
kx + z = 3
When it has no solution, we have
kx + z = 2x + z
Evaluate
k = 2
Hence, the value of k is 2
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Hue is arranging chair. She can form 6 rowsof a given lengtj with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs. Write and solve an equation to find how many chairs are in that row length.
Hue is arranging chair, She can form 6 rows of a given length with 3 chairs left over, or 8 rows of that same length if she gets 11 more chairs. There are 7 chairs in that row length.
What is row?A row is anything that is arranged in a series, such as a sequence of figures on a worksheet or stitches on a knitting needle. A row is anything that is arranged in a straight line, such as a line of penguins at the zoo, tulips in a yard, or tuba players moving in your town's Fourth of July procession.
Suppose the number of chairs in a row is 'x' and total number of chairs are 'y'.
Given:
Hue can form 6 rows of a given length with 3 chairs left over.
From that we get
y=6x+3 ………… (1)
Or she can form 8 rows of that same length if she gets 11 more chairs.
We get
y=8x-11 …………(2)
We can put the value of y from the equation 1 in equation 2
6x+3=8x-11
Or, 2x=14
Or, x=7
X is the number of chairs present in a row length. So that is 7.
Hence there are 7 chairs in that row length
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Find measure of angle 14. (Just enter the number, no symbols)
A
The measure of angle 14 is 83° in the parallel line t and s and transversal n.
What is parallel line?Parallel lines are a pair of lines in a two-dimensional plane that never intersect or cross each other, regardless of how far they are extended in either direction. Parallel lines have the same slope, which determines their steepness or inclination, and they maintain the same slope throughout their length.
What is transversal?A transversal is a line that intersects two or more other lines in a plane at distinct points. Specifically, if two or more lines in a plane are intersected by a third line, that third line is called a transversal. The lines being intersected are referred to as the "transversed lines".
According to the given information:
Given the parallel lines are t and s, the transversal are line m and n
the given angles are ∠2 = 97° and ∠6 = 83°
In the parallel lines t and s , line n is transversal
By the property that "corresponding angles are equal"
we can say that ∠5 =∠13, ∠7 =∠15, ∠6= ∠14, ∠8=∠16
given ∠6 = 83°, We know that ∠6= ∠14
∠14 = 83° (Corresponding angles are equal)
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using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected. group startstrue or false
The given statement "Using p-value rule for a population proportion or mean, if the level of significance is less than p-value, null hypothesis is rejected." is True because the hypothesis is rejected in this case.
In hypothesis testing, the p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, assuming that the null hypothesis is true. The level of significance, denoted by alpha, is the maximum probability of rejecting the null hypothesis when it is actually true.
If the p-value is less than the level of significance, it means that the observed test statistic is unlikely to have occurred by chance alone, assuming the null hypothesis is true. Therefore, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.
For example, suppose we are testing the hypothesis that the population mean is equal to a certain value. If the p-value is 0.02 and the level of significance is 0.05, we would reject the null hypothesis because the p-value is less than the level of significance.
This means that there is strong evidence against the null hypothesis and we can conclude that the population mean is likely different from the hypothesized value.
In summary, if the level of significance is less than the p-value, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.
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