A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 3600 ft2 (including the margins).
If x denotes the left-right width (in feet) of the billboard, determine the value of x that maximizes the area of the printed region of the billboard.
Answers
An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,
The total area of the billboard, A= x·y
The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]
Given in problem that the area of the billboard is 3600 ft².
x·y = 3600
y = (3600)/x
Substituting the value of y in the equation of the total printed area of the billboard,
[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]
Now, the value of x is needed to be minimum, therefore, differentiating the given function,
[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]
Equate the differentiated function with 0,
[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]
Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
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Related Questions
Please Hurry !!!!!!!A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? Select two options.
(–2, 0) and (2, 5)
(–4, 5) and (4, –5)
(–3, 4) and (2, 0)
(1, –1) and (6, –5)
(2, –1) and (10, 9)
Answers
Answer:
(–2, 0) and (2, 5)
(2, –1) and (10, 9)
Step-by-step explanation:
1. Find the slope of the what is considered perpendicular to -4/5. To do this, we simply use the reciprocal and multiply it by -1. Therefore, a perpendicular line would have a slope of 5/4.
2. Next, we can plug each of the ordered pairs into [tex]\frac{y2-y1}{x2-x1}[/tex] to see whether or not they have a slope of 5/4. We must do this to all of the ordered pairs until we find 2. Keep in mind that coordinates give you (x, y) in that order, so don't get the x's and y's confused. Additionally, it does not matter which coordinate goes first, just make sure that you get y2 and x2 from the same coordinate, and y1 and x1 from the same coordinate.
[tex]\frac{0-5}{-2-2}=\frac{-5}{-4}=\frac{5}{4}[/tex] The first answer![tex]\frac{5-(-5)}{-4-4}=\frac{0}{-8}[/tex] Not an answer[tex]\frac{4-0}{-3-2}=\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-(-5)}{1-6} =\frac{4}{-5}[/tex] Not an answer[tex]\frac{-1-9}{2-10} =\frac{-10}{-8}= \frac{5}{4}[/tex] The second answer!Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
[tex]\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;[/tex]
it is clear, the required constant is 12 (12 per hour).
Write this number in standard form: 5,000,000 + 200,000+ 8,000 + 400+60+9
Answers
Answer:
5,208,469
Step-by-step explanation:
5,000,000 + 200,000+ 8,000 + 400+60+9
5,000,000
200,000
00,000
8,000
400
60
9
5,208,469
from expanded to standard form
Which expression
is equivalent to 4(x+2)?
Answers
Answer:
[tex]\huge\boxed{\sf 4x + 8}[/tex]
Step-by-step explanation:
Given expression:= 4(x + 2)
Distribute
= 4x + 8
[tex]\rule[225]{225}{2}[/tex]
= 4(x + 2)
= 4 * x + 4 * 2
=> 4x + 8
If 4x + 8 is an Option, then that is the Correct Answer. Since options are not given, I don’t know which option corresponds to this Answer.
On a certain day, the high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F. What was the difference in temperature between city A and city B?
Answers
Answer:
99°F
Step-by-step explanation:
The high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F.
The difference in temperature will be:
= 93 - (-6)
= 93 + 6
= 99
(x^4) (3x^3-2) (4x^2+5x)
Answers
Answer:
12x^7+15x^6
Step-by-step explanation:
Change 3x^3-2 to 3x
(x^4)(3x)(4x^2+5x)
Multiply your single terms
(3x^5)(4x^2+5x)
Then distribute
12x^7+15x^6
consider the graph of y= f(x), shown below
Answers
Answer: The domain is [tex]\boxed{(-4, 4)}[/tex] and the range is [tex]\boxed{[-4, 4]}[/tex].
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Please explain and i need it urgently... One fifth of marked price of a watch is given as discount. What is the discount percent?
Answers
Answer:
1/5 times 100= 20%
Step-by-step explanation:
brainliest????????!!!!!!!
[tex] \bold{(10x - 6x³ + 8x²) - (5x² + 12x³ - 4)}[/tex]
Answers
Answer:
[tex]\boxed{\sf -18x^3+3x^2+10x+4}[/tex]
Explanation:
[tex]\rightarrow \sf (10x - 6x^3 + 8x^2) - (5x^2 + 12x^3 - 4)[/tex]
distribute
[tex]\rightarrow \sf 10x - 6x^3 + 8x^2 - 5x^2 - 12x^3 + 4[/tex]
collect terms
[tex]\rightarrow \sf -6x^3-12x^3+3x^2+10x+4[/tex]
add similar terms
[tex]\rightarrow \sf -18x^3+3x^2+10x+4[/tex]
Answer:
[tex]-18x^3+3x^2+10x+4[/tex]
Step-by-step explanation:
Given:
[tex](10x-6x^3+8x^2)-(5x^2+12x^3-4)[/tex]
Apply the rule (a) = a:
[tex]\implies 10x-6x^3+8x^2-(5x^2+12x^3-4)[/tex]
[tex]\textsf{Use the distributive law} \quad -(a+b)=-a-b:[/tex]
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3-(-4)[/tex]
Apply the rule -(-a) = a:
[tex]\implies 10x-6x^3+8x^2-5x^2-12x^3+4[/tex]
Collect like terms:
[tex]\implies -6x^3-12x^3+8x^2-5x^2+10x+4[/tex]
Combine like terms:
[tex]\implies -18x^3+3x^2+10x+4[/tex]
PLEASEEE HELPPP!!
Using the sheet music example above, please name the parts:
________________________
________________________
What is this LINE of music called? ________________________
When both of these staves are connected with this symbol, what is this called? ________________________
Please name all 3 things inside of the box: ___________________________________
_________________________
Answers
The line of music is refered to as the bracket
What is music?It should be noted that music simply means a vocal or instrumental sounds that are combined to produce beauty of harmony and expression if emotions.
When When both of these staves are connected with this symbol, it's called a brace.
Lastly, the things inside the box are voice, piano, and guitar.
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6. Divide:
6x²+7x-2/3x-1
using Long Division.
Answers
Step-by-step explanation:
3x-1) 6x^2 + 7x -2 ( 2x+3
-6x^2 -2x
+
0 + 9x -2
- 9x -3
+
1
A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.
Answers
Using matrix algebra, the material cost of making one of each product at each location is as follows:
Product X Product Z
Location A birr 38 birr 50
Location B birr 38 birr 49.5
What is matrix algebra?Matrix algebra involves the arrangement of numbers in a rectangular array.
Matrices are arranged in columns and rows to express some mathematical values.
Data and Calculations:Matrix O: Materials Requirement Per UnitSteel Glass Plastic
Product X 3 1 2
Product Z 4 0.5 3
Matrix P: Materials Cost Per UnitSteel Glass Plastic
Location A 10 2 3
Location B 9 3 4
Matrix R: (O x P) Material Cost of Product XSteel Glass Plastic Total
Location A 30 2 6 38
Location B 27 3 8 38
Matrix R: (O x P) Material Cost of Product ZSteel Glass Plastic Total
Location A 40 1 9 50
Location B 36 1.5 12 49.5
Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.
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Select The correct answer.
Segment AB Is tangent to the circle at point B. Which equation describes the relationship between the tangent and secant line segments?
B
D
OA
(AD)² = (AC) (AB)
OB. (AB)2 = (AC)(CD)
OC. (AB)2 = (AC)(AD)
OD. AB=(AC + AD)
Answers
According to the tangent-secant theorem, the relationship of the tangent and secant in the given circle is: C. AB² = (AC)(AD).
What is the Tangent-Secant Theorem?The secant tangent theorem defines the relationship between the lengths of the secant and the tangent line segments when they meet outside a circle.
Based on the tangent-secant theorem, using the image given, the equation that describes the relationship of the tangent and secant in the given circle is:
C. AB² = (AC)(AD)
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Answer: C
Step-by-step explanation:
got it right on my test!!
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.54 and a standard deviation of 0.42. Using the empirical rule, what percentage of the students have grade point averages that are less than 2.96? Please do not round your answer.
Answers
Using the Empirical Rule, it is found that 84% of the students have grade point averages that are less than 2.96.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, 2.96 is one standard deviation above the mean. We have that:
The normal distribution is symmetric.Of the 50% of the measures below the mean, all are below 2.96.Of the 50% of the measures above the mean, 68% are below 2.96.Hence the percentage is given by:
P = 50% + 0.68 x 50% = 50% + 34% = 84%.
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Simplify: √64(6z-7)² (square root over entire equation)
Answers
[tex]\sqrt{64(6z-7)^2}=\sqrt{64}\cdot\sqrt{(6z-7)^2}=8\cdot |6z-7|=8|6z-7|[/tex]
Which of the following staements must be true about this diagram check all that apply
Answers
Answer:Since, according to the Exterior Angle theorem, In a triangle the sum of any two adjacent interior angles is equal to the exterior angle of the triangle.
And, here is the exterior angle of the triangle, while , , and are the interior angles of the triangle.
Thus, according to the theorem,
.
⇒
and
Therefore, options B, C, E are correct.
For a fair coin, suppose you toss the coin 100 times.
What is the probability of getting more than 66 heads?
Answers
Using the normal distribution, it is found that there is a 0.0005 = 0.05% probability of getting more than 66 heads.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].For the binomial distribution, the parameters are given as follows:
n = 100, p = 0.5.
Hence the mean and the standard deviation of the approximation are given as follows:
[tex]\mu = np = 100(0.5) = 50[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{100(0.5)(0.5)} = 5[/tex]Using continuity correction, the probability of getting more than 66 heads is P(X > 66 + 0.5) = P(X > 66.5), which is one subtracted by the p-value of Z when X = 66.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66.5 - 50}{5}[/tex]
Z = 3.3
Z = 3.3 has a p-value of 0.9995.
1 - 0.9995 = 0.0005.
0.0005 = 0.05%
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question is attachment
Answers
The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]
To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.
It is given by the formula:
[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]
We have that the mean of the values is:
at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]
at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]
Using the above definitions we have that
at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]
at 12 AM
[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]
In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.
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Trigonometry problem
Answers
Answer:
Hi! So, I'm pretty sure the answer is 1 (rounded).
However, I'm not sure if you're trying to find the answer to COS pi/10 or "the function in terms of cofunction of a complementary angle" which I'm not too sure about. I've given you the answer to the first part if this was not the right way to read the problem I deeply apologize.
Step-by-step explanation:
Using any calculator with the Cos, Sin, and Tan function, you can input
COS (pi / 10) which equals .9999849678 (which you can round as needed)
So cos(pi/10) = sin(pi/2 - pi/10) = sin (5pi/10 - pi/10) = sin (4pi/10) = sin(2pi/5)
Hope this helps!
a.The product of two integers is -20.Find the largest possible sum of the two integers?b.The product of two integers is -30.Find the largest possible sum of the two integers.c.Can you generalize the result of a and b?
Answers
Step-by-step explanation:
first express the second function in terms of the other and find the critical point(which is the point that makes the graph to have a slope of 0). then you get the first number.
how many ml of 40 percent acid should be added to pure acid to make 70ml of 65 percent acid?
Answers
The amount of the acid will be equal to 113.75 Ml.
What is concentration?Concentration in chemistry is calculated by dividing a constituent's abundance by the mixture's total volume.
In chemistry, to solve this kind of exercise, dilutions, and concentrations are common to use the following equation
C1 x V1 = C2 x V2
V1 refers to volume 1, in this case, is 70mL because is the quantity I have, the solution I can use to obtain another solution. C1 refers to the concentration of the solution I also have, in this case, 65%.
C2 and V2 refer to the volume and concentration of the solution I am looking for. So, if want to know V2, which is the volume I need to add, the only thing to do is find V2 in the equation:
V2 = ( C1 x V1 ) / C2
V2 = ( 65% x 70mL) / 40%
V2 = 113.75 Ml.
Therefore the amount of the acid will be equal to 113.75 Ml.
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Which graph shows the solution to the system of linear inequalities?
y≥ 2x + 1
y≤2x-2
Answers
Answer:
g
Step-by-step explanation:
jjnnkvigific and it's a boy f a horse y
A rectangular garden is 15 ft longer than it is wide. Its area is 450
ft^2
. What are its dimensions?
Width equals =------
Length equals=-----
Answers
Answer:
Width= 15ft and Length= 30 ft
Step-by-step explanation:
Length=15+w
Area=450 ft square
(15+w)(w)=450
w²+15w=450
w²+15w-450=0
(w+30)(w-15)=0
w= -30, 15
width can't be negative so possible answer is 15 ft
Length = 15+15=30 ft
Find the range of the function.
f(x) = 10-x²
a. [5,00)
c. (-∞0, 10]
b. (-∞, -1) U [0, 00)
d.
Please select the best answer from the choices provided
(-∞, -1) U [∞o, 10)
Answers
Answer: hard to tell but I think D is correct (−∞,10],{y| y ≤ 10}
Step-by-step explanation:
Range:
(−∞,10] or {y| y ≤ 10}
because there is a vertex at (0, 10)
(found this by using -b/2a giving us 0 for x coord and plugging in 0 to 10-x² giving us (0, 10)
Then understanding since -x² is negative, the parabola goes down. And we know that the range is anything less or equal to 10
How do you find the median and standard deviation for 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11, 11,11,11
Answers
Answer:
Median is 6
standard deviation is 2.39
Step-by-step explanation:
the median is the mid number in the data set
The median formula is {(n + 1) ÷ 2}th, where “n” is the number of items in the set and “th” just means the (n)th number.
There are 51 data points in this set (n = 51)
so 51 / 2 = 25.5, the. number in the 25th slot is our median
3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11
the standard deviation is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
What is the slope of the line passing through the points (−3, −5) and (−1, −6)?
−4/3
−1/2
1/2
/34
Answers
Answer:
The slope of the line passing through the points (−3, −5) and (−1, −6) is [tex]-\frac{ 1 }{ 2 }[/tex] (-0.5)
Step-by-step explanation:
Equation of a straight line:
y = mx + b where m is the slope and b is the y-intercept
(x1, x2) and (y1, y2) : (−3, −5) and (−1, −6)
Calculating Slope (m).
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
m = [tex]\frac{ (-6) - (-5) }{ (-1) - (-3) }[/tex]
m = [tex]\frac{ -6 + 5 }{ -1 + 3 }[/tex]
m = [tex]-\frac{ 1 }{ 2 }[/tex]
we can take this a step further by finding the equation:
Now putting value of m in equation (i)
y = -0.5x + b
Calculating Y-intercept (b).
Lets choose the first point, (-3,-5) for calculating y-intercept:
y = mx + b
-5 = -0.5(-3) + b
-5 = 1.5 + b
-6.5 = b
b = -6.5
Now putting value of b in equation
y = -0.5x + -6.5
Answer:
-1/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-6-(-5))/(-1-(-3))
m=(-6+5)/(-1+3)
m=-1/2
Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x-y=7.
Answers
We can rewrite the equation of the given line to be in slope-intercept form as follows.
[tex]x-y=7\\x=y+7\\y=x-7[/tex]
Thus, the slope of the given line is 1.
Since parallel lines have equivalent slopes, the slope of the line we want to find is also 1.
Substituting into point-slope form,
[tex]y-0=1(x-1)\\\\\boxed{y=x-1}[/tex]
What system of equations would you use to solve the problem below?
A test is worth 100 points. Multiple-choice questions are worth 3 points and
short-answer questions are worth 5 points. If the test has 28 questions, how
many multiple-choice questions are there?
Answers
Let x be multiple-choice questions
Let y be short-answer questions
x + y = 28
3x + 5y = 100
The scatter plot shows a correlation between the cost of a helmet and the consumer rating.
The line of regression models that correlation.
Enter a number to complete each statement.
Answers
Answer:
1. 65
2. 52
3. 13
Step-by-step explanation:
For these answers, we can look at the graph:
Question 1:
For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.
Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.
Hence, the consumer rating is 65.
Question 2:
For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.
Therefore, 65 - 13 = 52
Question 3:
Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.
Hence, the actual consumer rating was 13 above the predicted rating.
Please please help me with my math
Answers
Answer:
D
Step-by-step explanation:
In functions like this, its best to pay attention to the end points of the rays.
On the lower line:
it ends at x -1
because it is a closed circle, that means x can also equal -1.
x≤-1
On the upper line:
it starts at -1
it is an open circle, meaning x cannot be -1
x>-1
