When no more than 110 units are produced, the cost of producing y units is given by c(x). c(x)equals0.2 x cubed minus 24 x squared plus 1524 x plus 31 comma 272 how many units should be produced in order to have the lowest possible average cost?
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Information about the age of participants in a robotics competition is below: A box plot titled "Age of Participants" and labeled "Age" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 31 on the number line. A line in the box is at 16. The whiskers end at 11 and 33. The middle 50% of the data is between what two numbers?
The middle 50% of the age of participants in the robotics competition falls between 13 and 31.
Explanation:The box plot represents the age distribution of participants in a robotics competition. The box extends from the lower quartile (Q1) to the upper quartile (Q3), which in this case are 13 and 31, respectively. The line within the box represents the median, which is 16. The whiskers represent the range of the data, ending at 11 and 33.
To find the middle 50% of the data, we need to determine the values that lie between Q1 and Q3. Therefore, the middle 50% of the age of participants in the robotics competition falls between 13 and 31.
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what is a factor of 4x^2+36x+72
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer: 40 pi
Step-by-step explanation:
Write the quotient as a mixed number. 33 ÷ 5 = 6 R2
A car dealer buys a new car for $24,500. The dealer then marks the car's price up 27%
What is the selling price of the car?
Circle 1 is centered at (-4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimeters. What transformations can be applied to circle 1 to prove that the circles are similar? The circles are similar because you can translate circle 1 using the transformation rule ( x, x) and then dilate it using a scale factor of ( ).
we know that
Figures can be proven similar if one, or more, similarity transformations
(reflections, translations, rotations, dilations) can be found that map one
figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a
translation and a scale factor (from a dilation) will be found to map one
circle onto another.
we have that
step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)--------> (x+6,y-4)
so
(-4,5)------> (-4+6,5-4)-----> (2,1)
so
center circle 1 is now equal to center circle 2
The circles are now concentric (they have the same center)
step 2
A dilation is needed to increase the size of circle 1 to coincide with circle 2
scale factor=radius circle 2/radius circle 1-----> 6/2----> 3
radius circle 1 will be=2*scale factor-----> 2*3-----> 6 cm
radius circle 1 is now equal to radius circle
2
A
translation, followed by a dilation will map one circle onto
the other, thus proving that the circles are similar
the answer is
The circles are similar because you can translate circle 1 using the transformation rule ( x+6,y-4) and then dilate it using a scale factor of (3 )Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the measure of each part?
The measure of the each part of the large circle is 90 degrees.
What is the measue of each part?
A circle is a bounded figure which points from its center to its circumference is equidistant. The sum of angles in a circle is 360 degrees.
Measure of the angle of each part = 1/4 x 360 = 90 degrees
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write a number sentence to compare 7.17 and 7.170
Answer:
They are equal
Step-by-step explanation:
The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. what is the probability that washing dishes tonight will take me between 11 and 13 minutes?
Sally has x books that weigh 2 pounds each and 8 books that weigh 3 pounds each. the total weight of her books is 62 pounds. which equation below could be used to find how many 2-pound books sally has?
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Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.
Final answer:
The appropriate hypotheses to determine if graffiti incidents declined involve a null hypothesis where the mean difference is greater than or equal to zero and an alternative hypothesis where the mean difference is less than zero. The μd represents the mean difference in graffiti incidents before and after the institution of the community watch program.
Explanation:
The appropriate hypotheses to test whether the number of graffiti incidents declined in the suburban communities after the institution of a citizen community watch program are as follows:
H0: μd ≥ 0 (Null hypothesis: The mean difference in graffiti incidents before and after is greater than or equal to 0, indicating no decrease.)Ha: μd < 0 (Alternative hypothesis: The mean difference in graffiti incidents before and after is less than 0, indicating a decrease.)Here, μd (mu-sub-d) represents the mean difference between the number of incidents before the program and after the program was implemented. To test these hypotheses, we would typically conduct a paired t-test if the samples are normally distributed or a Wilcoxon signed-rank test if the distribution is not normal.
Assuming μd is the mean difference in graffiti incidents before and after, the test will determine if there is statistically significant evidence to support that the community watch program resulted in a reduction of graffiti incidents.
What value of y makes the equation true?
Explain how you can use a model to find 4x 3/8
Marcus drew a quadrilateral with only 1 pair of parallel sides. Which quadrilateral did Marcus draw?
Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1
The graph that shows a negative linear relationship that has a correlation coefficient, r, that is closer to -1 is: B. graph B.
What is a Negative Linear Relationship Graph?A graph that shows a negative linear relationship has a trendline that slopes downwards from your left to the right.
The closer the data points are to each other along the trendline in a negative linear graph, the closer the correlation coefficient, r, is to -1.
Therefore, the graph that shows a negative linear relationship and has a correlation coefficient, r, that is closer to -1 is: B. graph B.
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Find the relative rate of change of the function f(x)=150-0.08x^2
Use right triangle DCB to find the trig values for angle D.
sinD =
cosD =
tanD =
Answer: sinD = 0. 9459
cosD =0. 3243 tanD=2. 917
Step-by-step explanation:
From the figure above;
opposite = 35
adjacent = 12
hypotenuse = 37
sin D = opposite/hypotenuse
sinD = 35/37 = 0. 9459
cosD = adjacent/hypotenuse
= 12/37 = 0. 3243
tanD = adjacent/opposite
= 35/12 = 2. 9167
PLZ HELP ASAP TANGENTS OF CIRCLES
For a popular Broadway musical, theater box office all $356 apiece 275, tickets and $60 apiece, and 369 tickets and $45 apiece. How much money did the box office ticket Take in?
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?
We have to find value of the house in 8 years so we will plug t=8 years in given equation.
[tex] y=150000(1.004)^{\left(12t\right)} [/tex]
[tex] y=150000(1.004)^{\left(12*8\right)} [/tex]
[tex] y=150000(1.004)^{96} [/tex]
[tex] y=150000(1.46702133432) [/tex]
[tex] y=220053.200148 [/tex]
Hence house will worth approx $220053.20 in 8 years.
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?
Solution:
Equation of the appreciation of the value of house is given by:-
[tex]y=150000(1.004)^{12t}[/tex]
We need to find the worth of the house after 8 years
So, that means time, t=8
Let us plug t=8 in the equation [tex]y=150000(1.004)^{12t}[/tex]
So, we get,
[tex]y=150000(1.004)^{12*(8)}[/tex]
[tex]y=150000(1.004)^{96}[/tex]
[tex]y=150000(1.467021)[/tex]
y=150000*1.467021
y=220053.20
In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320
Find the area of the parallelogram with vertices at (−2,3),(−2,3), (6,14),(6,14), (−14,1),(−14,1), and (−6,12).(−6,12).
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What is the standard form of the equation of a circle given by x^2 + y^2 - 18x + 8y + 5 = 0
Answer:
x-9,y+4,92
Step-by-step explanation:
A wheel spins at 300 revolutions per minute. What is the angular velocity of the wheel, in radians per second? Round the answer to the nearest hundredth.
Answer:
31.42
Step-by-step explanation:
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Which best describes a triangle with side lengths of 6 inches 8 inches and 9 inches?