On a certain marathon course a runner reaches a big hill that is at least 10 miles into the race. If a total marathon is 26.2 miles, how can u find the number of miles the runner still has to go?
this would have to be an inequality equation.
Marathon is 26.2 miles
they get to a hill that is at least 10 miles into the race
26.2-10=16.2
so they have at most 16.2 miles to go
the equation is X<=16.2
How many arrangements of the letters in the word o l i v e can you make if each arrangement must use three letters?
A. 60
B. 5 · 4 · 3 · 2 · 1
C. 20
D. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1
(HELP ME PLEASE) In the drawing, g > h. Which statement about the volumes of the two cylinders is true?
Answer:
The answer on Imagine Math is...
-The volume of the left-hand cylinder is less than the volume of the right-hand cylinder.
Step-by-step explanation:
I got the answer correct on Imagine Math. Hope my answer helps those who need it :)
God bless you all day every day!
The solution is, The ratio of the volumes is the cube of this: 27 : 1.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
here, we have,
given that,
The ratio of the lengths is 75 : 25 or 3 : 1
The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2
(In working out the area the radius is squared)
and, we have,
The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3
(In working out the volume the radius is cubed)
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Describe how the graph of y=|x| – 4 is like the graph of y= |x| – 4 and how it is different.
The graphs of y = |x| and y = |x| - 4 are similar in their overall V-shape and slope behavior, but differ in their vertical position due to the constant term difference in the equations. The second graph is essentially a downward translation of the first by 4 units.
Similarities:
Both represent absolute value functions.
Both graphs pass through the origin (0, 0)
Both graphs have a slope of 1 for positive values of x and a slope of -1 for negative values of x.
Differences:
The graph of y = |x| - 4 is shifted downwards by 4 units
The y-intercept is different for both graphs.
In mathematics, the nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/n. so, the first harmonic number is 1, the second is 1.5, the third is 1.83333... and so on. write an expression whose value is the 8th harmonic number.
The nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/n. the first harmonic number is 1.5 , the second is 1.5 the third is 1.83333... and soon, the harmonic expression will be written as follows
Given:
a1 = first term = 1
a2 = second term = 1.5
a3 = third term = 1.83333...
We will write expression in Harmonic term, as
= [tex]\rm 1.0 + \dfrac{1.0}{2.0} + \dfrac{1.0}{3.0} + \dfrac{1.0}{4.0} + \dfrac{1.0}{5.0} + \dfrac{1.0}{6.0} + \dfrac{1.0}{7.0} +\dfrac{ 1.0}{8.0}[/tex]
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Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.
-When f(x) becomes f(x) + 2
-When f(x) becomes −(1 / 2) * f(x)
Answer:
f(x) + 2 is translated 2 units up and -(1/2)*f(x) is reflected across x-axis.
Step-by-step explanation:
We have f(x) becomes f(x) + 2.
The y-intercept of f(x) is f(0), implies that y-intercept of f(x) + 2 is f(0) + 2. This means that the graph of f(x) is translated 2 units upwards.
Moreover, the region where f(x) increases will be the same region region where f(x) + 2 increases and there will not any change in the size of the figure.
Now, we have f(x) becomes -(1/2)*f(x).
The y-intercept of -(1/2)*f(x) is -(1/2)*f(0). This means that the graph is dilated by 1/2 units and then reflected across x-axis.
Moreover, the region where f(x) increases will be the opposite region region where -(1/2)*f(x) increases and the size of the figure will change as dilation of 1/2 is applied to f(x)
Answer with Explanation
Let the polynomial function which is an odd function, be
[tex]f(x)=x^5+x^3+x[/tex]
f(-x)= - f(x)
So,it is an odd function.
The function will pass through first and fourth quadrant.
Y intercept =0
Function is increasing in it's domain [-∞, ∞]
1. When f(x) becomes f(x)+2
g(x)=f(x) +2
This function will shift 2 units up, and it will not pass through the origin and has Y intercept equal to 2.
This function will also pass through first and fourth quadrant.
Function is an increasing function in it's domain [-∞, ∞]
Now, when f(x) becomes [tex]\frac{-f(x)}{2}[/tex]
The function will pass through second and fourth Quadrant,due to negative sign before it, and distance from y axis either in second Quadrant or in fourth Quadrant increases by a value of [tex]\frac{1}{2}[/tex].
Here also, Y intercept =0
Function is a decreasing function in it's domain [-∞, ∞]
Now, taking the even function
[tex]f(x)=x^6+x^4+x^2[/tex]
f(-x)= f(x)
So,it is an even function.
The function will pass through first and second quadrant equally spaced on both side of y axis.
Y intercept =0
Function is decreasing in [-∞,0) and increasing in (0, ∞]
1. When f(x) becomes f(x)+2
g(x)=f(x) +2
This function will shift 2 units up, and it will not pass through the origin and has Y intercept equal to 2.
This function will also pass through first and third quadrant.
Function is decreasing from [-∞,2) and increasing in (2, ∞]
Now, when f(x) becomes [tex]\frac{-f(x)}{2}[/tex]
The function will pass through third and fourth Quadrant,due to negative sign before it, and function expands by the value of [tex]\frac{1}{2}[/tex] on both sides of Y axis.
Here also, Y intercept =0
Function is increasing in [-∞,0) and decreasing in (0, ∞].
Karen runs 6 miles in 50 minutes. at the same rate, how many miles would she run in 35 minutes?
Differences between 9/11 and pearl harbor
What is the graph of the function f(x) = the quantity of negative x squared plus 4 x plus 6, all over x plus 4? I am stressing over this question is just confusing for me help me please
Answer:
The graph of the function is given below.
We are given the function, [tex]f(x)=\frac{-x^2+4x+6}{x+4}[/tex]
We see that, when x= 0, the value of the function is,
[tex]f(0)=\frac{-0^2+40+6}{x+0}[/tex] i.e. [tex]f(0)=\frac{6}{4}=\frac{3}{2}[/tex].
So, the y-intercept is [tex](0,\frac{3}{2})[/tex].
Also, the zeroes of the function are given by,
[tex]f(x)=\frac{-x^2+4x+6}{x+4}=0[/tex]
i.e.[tex]-x^2+4x+6=0[/tex]
i.e. (x+1.162)(x-5.162)=0
i.e. x= -1.162 and x= 5.162
Thus, the x-intercept are (0,-1.162) and (0,5.162).
The graph of the function is given below.
What is the discriminant of 3x^2-10x=-2?
the discriminant of the equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex] is [tex]\(76\)[/tex].
To find the discriminant of the quadratic equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex], we first need to rewrite it in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex].
The given equation is [tex]\(3x^2 - 10x + 2 = 0\)[/tex].
Comparing it with the standard form [tex]\(ax^2 + bx + c = 0\)[/tex], we have:
- [tex]\(a = 3\)[/tex],
- [tex]\(b = -10\)[/tex],
- [tex]\(c = 2\).[/tex]
The discriminant [tex](\(D\))[/tex] of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex] is given by the formula:
[tex]\[ D = b^2 - 4ac \][/tex]
Substituting the values of [tex]\(a\), \(b\)[/tex], and [tex]\(c\)[/tex], we get:
[tex]\[ D = (-10)^2 - 4 \cdot 3 \cdot 2 \][/tex]
[tex]\[ D = 100 - 24 \][/tex]
[tex]\[ D = 76 \][/tex]
So, the discriminant of the equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex] is [tex]\(76\)[/tex].
When graphed,a system shows the exact same lines. How many solutions will the system have?
(05.03 MC)
Eva has borrowed 200 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x:
A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 280 at increments of 40. A straight line joins the ordered pairs 0, 200 and 1, 160 and 2, 120 and 3, 80 and 4, 40 and 5, 0.
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points)
Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
A) The rate of change is -40 songs each week, that is because the amount of songs left to be downloaded decrease by 40 each week
B) lets use 2 points of the graph p1(0, 200), p2(1, 160)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200
Part A:
Each week the amount of songs that need to download decreases by 40. So The rate of change is -40 songs each week. The initial value is 200 because that is the number of songs left to download.
Part B:
y = -40x + 200
Solve:The quantity 2 x minus 20 divided by 3= 2x
If the height of Mount Everest is about 8.8×10^3 meters, and the height of the Empire State Building is about 3.8×10^2 meters, which of these statements is true?
A.There is no way to compare these heights
B.Mount Everest is about 40 times as tall as the Empire State Building
C.Mount Everest is about 23 times as tall as the Empire State Building
D.The Empire State Building is about 23 times as tall as Mount Everest
Step-by-step explanation:
Height of Mount Everest = 8.8 x 10³ m = 8800 m
Height of the Empire State Building = 3.8 x 10² m = 380 m
[tex]\frac{\texttt{Height of Mount Everest}}{\texttt{Height of the Empire State Building}}=\frac{8800}{380}\\\\\frac{\texttt{Height of Mount Everest}}{\texttt{Height of the Empire State Building}}=23.16[/tex]
Height of Mount Everest = 23 x Height of the Empire State Building.
So, Mount Everest is about 23 times as tall as the Empire State Building
Option C is the correct answer.
A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 2020 ft of fence? What should the dimensions of the garden be to give this area?
If y=12+ 3.5x ,what is the value of the y when x=10
The Partnership for 21st Century Learning lists core subject areas that all employees need to know about. What are two of those core subjects?
A. Economics and mathematics
B. Technology and citizenship
C. Art and Latin
D. Vocational skills and English
The Partnership for 21st Century Learning identifies Economics and Mathematics as two core subjects necessary for employee knowledge, essential for developing critical thinking and problem-solving skills in the global economy. Hence the correct answer is option A
Explanation:The Partnership for 21st Century Learning lists Economics and Mathematics as two core subject areas that are essential for all employees to have knowledge about. These subjects are foundational to understanding the global economy and are associated with the skills needed by "knowledge workers" such as engineers, scientists, doctors, teachers, financial analysts, and computer programmers. A strong grounding in Economics and Mathematics equips students with valuable skills such as critical thinking, problem-solving, and the ability to analyze complex data, which are highly sought after in the modern workforce.
As per the Partnership for 21st Century Learning, to support the quality of American education, it's crucial to prepare students with a well-rounded understanding of core disciplines, including Economics and Mathematics. This preparation is significant in light of increasing global competition and the need for American students to improve in reading, math, and critical thinking to match or exceed the capabilities of their peers in other industrialized nations.
Hence the correct answer is option A
Solve for x and y:
28x−49y=35
4x−7y=5
Select one:
a. The solution is (0, 0).
b. There are an infinite number of solutions.
c. There is no solution.
d. x=3,y=1
What is the value of y so that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8)?
y = −7
y = 1
y=1/2
y = −2
To make line segment AB parallel to line segment CD, we calculate the slope of CD and ensure AB has the same slope. The slope of CD is −1/4.5, and setting the slope of AB equal to this value leads to the conclusion that y = −2 for point A.
Explanation:To determine the value of y such that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8), we need to ensure that the slope of line AB is equal to the slope of line CD. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 − y1) / (x2 − x1).
For line CD, the slope is (8 − 6) / (−2 − 7) = 2 / (−9) = −1/4.5. To find the value of y for point A so that line AB is parallel to CD, we need to set the slope of AB equal to −1/4.5:
(−4 − y) / (6 − (−3)) = −1/4.5
(−4 − y) / 9 = −1/4.5
−4 − y = −9 / 4.5
y = −4 + 2 = −2
Therefore, the correct value of y that makes line AB parallel to line CD is −2.
Chef Pierre can do something unique. Using a secret process, he can bake a nearly perfectly spherical pie consisting of a vegetable filling inside a thick crust. The radius of the whole pie is 12 cm, and the radius of the filling is 8 cm. What is the volume of the crust alone, to the nearest unit? Use p = 3.14.
The volume of Chef Pierre's pie crust is calculated by subtracting the volume of the vegetable filling from the volume of the entire pie, yielding approximately 5,091 cm³.
Explanation:To determine the volume of the crust of Chef Pierre's spherical pie, we need to calculate the volume of the entire pie and then subtract the volume of the vegetable filling. The formula for the volume of a sphere is V = (4/3)πr³. First, we calculate the volume of the whole pie (including crust) with a radius of 12 cm, and then the volume of the vegetable filling with a radius of 8 cm.
Volume of whole pie: Vwhole = (4/3)π(12 cm)³ = (4/3) * 3.14 * (12 cm)³ ≈ (4/3) * 3.14 * 1,728 cm³ ≈ 7,238.56 cm³
Volume of vegetable filling: Vfilling = (4/3)π(8 cm)³ = (4/3) * 3.14 * (8 cm)³ ≈ (4/3) * 3.14 * 512 cm³ ≈ 2,147.97 cm³
Subtract the volume of the filling from the volume of the whole pie to get the volume of the crust alone:
Volume of crust alone: Vcrust = Vwhole - Vfilling ≈ 7,238.56 cm³ - 2,147.97 cm³ ≈ 5,090.59 cm³
To the nearest unit, the volume of the crust is approximately 5,091 cm³.
the least common multiple of 2/3 5/6 and 9/4
The least common multiple of 2/3 5/6 and 9/4 is 12.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We are given that;
The numbers 2/3 5/6 and 9/4
Now,
To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:
Multiples of 3: 3, 6, 9, 12, 15, 18,
Multiples of 6: 6, 12, 18,
Multiples of 4: 4, 8, 12,
Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:
Factors of 2: 1 and 2
Factors of 5: 1 and 5
Factors of 9: 1,3 and9
The only common factor is 1, so this is the greatest common factor of the numerators.
Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:
12 /1 =12
Therefore, the LCM of given fraction will be 12.
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What is the last thing you do as a check inside the car?
I'm lost can you please tell me how to do this step by step
A shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed. By how many standard deviations does a ball bearing with a diameter of 58.2 mm differ from the mean?
Answer:
By 2 standard deviations a ball does bearing with a diameter of 58.2 mm differ from the mean.
Step-by-step explanation:
It is given that a shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed.
[tex]Mean=60[/tex]
[tex]\text{Standard deviation}=0.9[/tex]
Absolute difference written diameter of 58.2 mm and average diameter is
[tex]|58.2-60|=1.8[/tex]
Divide the difference by standard deviation (i.e.,0.9), to find the by how many standard deviations does a ball bearing with a diameter of 58.2 mm differ from the mean.
[tex]\frac{1.8}{0.9}=2[/tex]
Therefore 2 standard deviations a ball does bearing with a diameter of 58.2 mm differ from the mean.
Consider the quadratic function f(x) = 2x2 – 8x – 10. The x-component of the vertex is . The y-component of the vertex is . The discriminant is b2 – 4ac = (–8)2 – (4)(2)(–10) =
The x-coordinate of the vertex is 2 and the y-coordinate is -10. The discriminant is 144.
Explanation:The quadratic function can be rearranged into the form ax² + bx + c = 0, where a = 2, b = -8, and c = -10. To find the x-coordinate of the vertex, we use the formula x = -b / (2a). Plugging in the values, we get x = -(-8) / (2*2) = 2. The y-coordinate of the vertex can be found by substituting the x-coordinate into the original function. Plugging in x = 2, we get f(2) = 2(2)² - 8(2) - 10 = -10.
The discriminant is calculated as b² - 4ac. Plugging in the values, we get (-8)² - 4(2)(-10) = 64 + 80 = 144.
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Edgar started with 2 poems in his journal. Then he started writing 3 poems each day. Which of the following graphs represents Edgar's poem writing
Answer:
Let x represents the number of the days, and y represents total number of the poem.
According to the question,
Edgar started with 2 poems in his journal. Then he started writing 3 poems each day.
Thus, the line that describes the above situation is,
y = 2 + 3 x
The x -intercept of the line is [tex](-\frac{2}{3} , 0)[/tex] or (-0.667 , 0)
And, the y-intercept of the line is (0,2)
Also, if x = 1 y = 5
if x = 2 y = 8
If x = -1 y = - 1
And, if x = - 2 , y = -4
Thus, the points by which the line will pass are,
(1,5), (2,8) , (-1,-1) and (-2,-4)
Therefore, with the help of the above information we can plot the graph of the line. ( shown below)
What's the difference between 1261⁄4 and 78 2⁄3?
A. 48 1⁄3 B. 47 7⁄12 C. 58 5⁄12 D. 57 7⁄12
Answer: The answer is (B) [tex]47\dfrac{7}{12}[/tex].
Step-by-step explanation: We are given to find the difference between the following two numbers:
[tex]n_1=126\dfrac{1}{4},~~~n_2=78\dfrac{2}{3}.[/tex]
To find the difference, we need to subtract the smaller number from the larger one.
Since, [tex]n_1>n_2[/tex], so the difference is given by
[tex]d\\\\=n_1-n_2\\\\=126\dfrac{1}{4}-78\dfrac{2}{3}\\\\=\dfrac{505}{4}-\dfrac{236}{3}\\\\=\dfrac{505\times3-236\times4}{12}\\\\=\dfrac{1515-944}{12}\\\\=\dfrac{571}{12}\\\\=47\dfrac{7}{12}.[/tex]
Thus, (B) [tex]47\dfrac{7}{12}[/tex] is the correct option.
Candy Crunchers wants to see if their new candy is enjoyed more by high school or middle school students. They decide to visit one middle school and one high school in Miami, FL. After interviewing 100 students at each school, they determine that high school students like their candy more than the middle school students do. What is the sample of the population?
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"? 4x + 8y < 50 4x + 8y ≤ 50 4x + 8y > 50 4x + 8y ≥ 50
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
Step-by-step explanation:On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.
Lorenzo needs at least 50 points on the final to earn a "B" in the class.
Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.
Hence, the inequality that will represent the marks he needs is:
4x+8y≥50
In kahneman and tversky's prospect theory, they hypothesized that people tend to _____ low-probability outcomes and _____ high-probability outcomes.
Answer:
Overweight low probability outcomes
UNderweight High probability outcomes.
Step-by-step explanation:
Amos Tversky and Daniel Kahneman proposed the prospect theory that aimed to explain and understand the behavior of individuals, giving them a sample of choices to take, when put in front to the different decisions that had to be made, people often valued chances that were 99% probable to happen with a 95 to 85% chance, meaning that the didn´t give enough credit to the number and probabilities, and when facing risks of 1% probability of happening, they outweigh them with a 5 to 15 %.