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.
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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Advise the committee of the minimum number of shade tents that must be set up to hold all the balloons so that they don’t fly away ?
The maximum number of spherical balloons that can be held in the canopy will be 30.
What is a canopy?The canopy is the fabric cover that hangs above a bed. It is a covering that is fastened to or carried over a dignitary or a holy item.
The base layer of spheres in a square pyramidal arrangement has n2 balls, where n is the number of balls that make up a square's side.
n=4 inch
The total number of spheres in the pyramid is;
⇒n(n+1)(2n+1)/6
⇒4(4+1)(2×4+1)/6
⇒(4×5×9)/6
⇒30
Hence, in the canopy, 30 spherical balloons are the most that may be accommodated.
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simplify. evaluate.
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
The best way to solve this problem is to simplify each factorial one by one!
Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.
At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.
To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]
Just simply multiply and then divide, and we are given 1/18
Solve each inequality and graph the solution on a
number line.
a.) -12a +7 ≤31
b.) -9 > 3b +6
The solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have two inequalities:
a.) -12a +7 ≤31
b.) -9 > 3b +6
a) -12a +7 ≤ 31
-12a ≤ 31 - 7
-12a ≤ 24
-a ≤ 2
a ≥ 2 (sign changed because multiplied by a negative number)
a ∈ [2, ∞)
b.) -9 > 3b +6
-15 > 3b
-5 > b
or
b < -5
b ∈ (-∞, -5)
Thus, the solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)
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Find the area of the rectangle.
A rectangle is shown. The left side is labeled with the expression 8 x. The top side is labeled with the expression 7 x plus 1. (1 point)
15x + 1
56x2 + 8x
56x + 8
15x2 + 9x
Answer:
56x² + 8x
(second option listed)
Step-by-step explanation:
area: length × width
length: 7x + 1
width: 8x
(8x)(7x + 1)
{distribute 8x}:
(8x)(7x): 8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²
(8x)(1) = 8x
area = 56x² + 8x
so, the area of this rectangle is 56x² + 8x
Answer:
56x² + 8x
[answer B]
Write down the following sets using set-builder notation:
A set A of all numbers greater than 3
A set B of all numbers less than 4
A set Y of all months of the year with more than 30 days
A set W of all days of a week
Answer:
A = { x:x >3 ,where x --> R}
B = { x:x <4, where x --> R}
Y = { x:x is month of year with more than 30 days}
W = { x:x is all days of a week}
Brainliest to whoever answers :) Highly appreciated
Answer:
the answer is L
Step-by-step explanation:
rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20
In(2e^9) in logarithmic expression
I’m having trouble with all of the “In” section and very confused
In logarithmic form, we get In(2e^9)= ln(2)+9.
LogarithmsWe define the logarithm as the power to which any number must be raised to get few other values.Exponentiation is the reverse process of logarithm.We are given,
ln(2[tex]e^{9}[/tex])
We know that, ln(ab) = ln(a) + ln(b)
So we get,
ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])
Since ln(m^n)=n ln(m)
And ln(e)= 1, we will get,
ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)
= ln(2) +9
Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.
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I am not able to tackle this question. Somebody please help me out
The minimum load at which a certain kind of iron wire breaks can be supposed to define a random variable normally distributed with expected value 80N and standard deviation 3N. Find the probability that such a wire will break when the load is (a) 74N
(b)89N
The wire breaks if the load [tex]X[/tex] exceeds some amount. So what you're asked to do is find [tex]P(X\ge74)[/tex] and [tex]P(X\ge89)[/tex].
In either case, transform [tex]X[/tex] to the random variable [tex]Z[/tex] that's normally distributed with expected value 0 and standard deviation 1.
[tex]P(X\ge74) = P\left(\dfrac{X-80}3 \ge \dfrac{74-80}3\right) \\ = P(Z \ge -2) \\ = 1-P(Z < -2) \approx 0.9773[/tex]
[tex]P(X\ge89) = P\left(\dfrac{X-80}3 \ge \dfrac{89-80}3\right) \\= P(Z \ge 3) \\= 1 - P(Z < 3) \approx 0.0013[/tex]
A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?
The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.
To solve the problem, we must:
Know how many 30-minutes have passed during the time period.
1 day = 24 hours
1 hour = 60 minutes = 2 × (30 minutes)
1 day = 24 hours × 2 × (30 minutes)
1 day = 48 × (30 minutes)
Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.
Friday = 48 × [tex]\frac{1}{2}[/tex] = 24
Saturday = 48
Sunday = 48
Monday = 48 × [tex]\frac{3}{4}[/tex] = 36
TOTAL = 24 + 48 + 48 + 36 = 156
Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.
Divide the number of total seconds late by the number of 30-minutes passed.
That is, the number of total seconds late= 468 seconds ÷ 156
= 3 seconds
Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
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A company decides to offer a monetary incentive for employees who log a specified number of hours spent exercising in an attempt to improve employee health. The average health score (higher = better) of the 75 employees who logged enough hours was 87. The mean health score for all employees (population) was 85, with a population standard deviation of 6.5. Calculate the standard error of the mean
The standard error will be equal to 0.75.
What is the standard error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.
The standard error will be calculated by using the formula:-
SE = [tex]\sigma[/tex] / √n
Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.
SE = 6.5 / √75
SE = 0.75
Therefore the standard error will be equal to 0.75.
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what is the slope of the line through the points (-2,-1) and (8,-3)
Answer:
Step-by-step explanation:
Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.
Point-slope form into y-intercept form.
Answer:
For finding slope
we have the formula
m = y2 - y1/ x2 - x1
x1 = (-2)
x2. = ( 8)
y1. = (-1)
y2 =(-3)
putting the value of this in the formula we get,
m = (-3)-(-1)/8-(-2)
m = (-3+1)/8 + 2.
m = (-2)/10
m = (-1)/5.
m = (-1)/5
Line l has a slope of 2/3 The line through which of the following pair of points is perpendicular to l?
We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
The line through which of the following pair of points is perpendicular to l?Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.
So, if line l has the slope 2/3.
Then the perpendicular lines have a slope equal to -3/2.
Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.
If we define (x₁, y₁) = (0, 0), then the other point must be:
[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]
Then we can write the other point as (2, -3).
So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
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How many degrees does Earth turn in one hour?
Answer:
15 degrees
Step-by-step explanation:
Answer:
The earth turns 15 degrees in one hour. Hope this helps!
Step-by-step explanation:
Evaluate the expression.
Answer:
18
Step-by-step explanation:
Using order of operations:
[tex] \frac{15 - 9}{3} (19 - 10)[/tex]
[tex] \frac{6}{3} (9)[/tex]
[tex]2(9) = 18[/tex]
Find the x- and y-intercepts of the parabola y=x2+10x+4
Answer:
x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4
Step-by-step explanation:
For x-intercepts use the quadratic equation
[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]
Fill in your values:
[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]
And solve
[tex]x=-5 +/- \sqrt{21}[/tex]
For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.
3x² - 2x + 1 = [?]
x=4
Answer:
3x²-2x+1=?
3(4²)-2(4)+1=?
3(16)-8+1=?
48-8+1=?
40+1=41
Which of the following terms describes the measure indicated by the black
arrow below?
4
A. Median
B. Range
C. Mean
D. Minimum
Answer:
the answer is A
Step-by-step explanation:
The line is the middle point of the graph/ the middle number of all therefore it's the median.
Simplify each expression.
10x³y²
5x³y
x = 0, y = 0
Step-by-step explanation:
Very easy the value are given apply the value for X and y
C) Three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. Find the probability that, of the three chosen tubers: a) none is spoilt b) all are spoilt c) exactly one is spoilt d) at least one is spoilt.
[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]
a)
[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]
b)
[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]
c)
[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]
d)
[tex]A[/tex] - at least one is spoilt
[tex]A'[/tex] - none is spoilt
[tex]P(A)=1-P(A')[/tex]
We calculated [tex]P(A')[/tex] in a).
Therefore
[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/tex]
Find a solution to the linear equation 11x−y=−11.Find a solution to the linear equation 11x−y=−11.
Answer:
(0,11)
Step-by-step explanation:
If we let x=0, then -y = -11, and so y=11.
Thus, (0,11) is a solution to the linear equation.
Which of the following equations is equivalent to the formula for velocity
Sarah has a solid wooden cube with a length of 4/5 centimeter. From each of its 8 corners, she cuts out a smaller cube with a length of 1/5 centimeter. What is the volume of the block after cutting out the smaller cubes?
The volume of the block after cutting out the smaller cubes is [tex]\frac{63}{125}[/tex] cubic units.
Given that, Sarah has a solid wooden cube with a length of 4/5 centimetres. From each of its 8 corners, she cuts out a smaller cube with a length of 1/5 centimetre.
We need to find the volume of the block after cutting out the smaller cubes.
What is the volume of a cube?The volume of a cube is defined as the total space enclosed by the cube in a three-dimensional space. The formula to find the volume of a cube is a³, where a=edge of a cube.
Now, the volume of a solid wooden cube with a length of 4/5 centimetre
[tex]=(\frac{4}{5} )^{3} =\frac{4}{5} \times \frac{4}{5}\times \frac{4}{5}=\frac{64}{125}[/tex] cubic units.
The volume of a smaller cube with a length of 1/5 centimetre
[tex]=(\frac{1}{5} )^{3} =\frac{1}{5} \times \frac{1}{5}\times \frac{1}{5}=\frac{1}{125}[/tex] cubic units.
The volume of the block after cutting out the smaller cubes[tex]=\frac{64}{125}-\frac{1}{125}=\frac{63}{125}[/tex]
Therefore, the volume of the block after cutting out the smaller cubes is [tex]\frac{63}{125}[/tex] cubic units.
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Answer:
the answer is 64/125 <3
From this diagram, select the
pair of lines that must be
parallel if 27 and 25 are
supplementary. If there is no
pair of lines, select "none."
Answer:
l
Step-by-step explanation:
Answer:
Lines L and n are parallel
Explanation -
In the question it is given that angle 7 and angle 5 are supplementary.
which means that sum of this angle is 180°
so line L and n are parallel
find the measure of angle S and angle TRS pls help
Answer:
60°
Step-by-step explanation:
since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there
Answer:
Step-by-step explanation:
Plan
7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.
Solution
7y + 5y = 180 degrees Combine the left
12y = 180 degrees Divide by 12
12y/12 = 180/12
y = 15
3y + 5y + x = 180 Combine the left side
8y + x = 180 Substitute 15 for y
8*15 + x = 180 Combine
120 + x = 180 Subtract 120 from both sides
120 -120 +x =180 - 120 Combine
x = 60
Answer
s = 60 degrees
<TRS = 5y = 75
The graph shows f(x) and its transformation g(x).
Enter the equation for g(x) in the box.
The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function f(x) is given below.
f(x) = 2ˣ
Then the function g(x) is given as
[tex]\rm g(x) = 2^{x + 1}[/tex]
The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.
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X= ABC+ AB+ ABC Simplify followings
Answer:
X = ABC+ AB+ ABC
X = AB(C+1+C)
X = AB(2C+1)
four times a number is 48 less than 6 times the number
Answer:
the answer is 24
Step-by-step explanation:
6x - 48 = 4x
6x - 4x - 48 = 0
2x - 48 = 0
2x = 0 + 48
2x = 48
x = 24
Expression Math problem...help and get 15 pts!
When h = 0 , [f(x + h) - f(x)]/h = 2x +2 for the given expression.
The missing expression is f(x) = x² + 2x.
What is formula of difference quotient ?f(x+h)-f(x)/h is called the formula of difference quotient.
When h---> 0 ,
the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line
Here the the expression is
f(x) = x² + 2x
Determining f(x + h) by substituting x = x + h on both sides of the given f(x).
Then f(x + h) = (x + h)² + 2(x + h)
= x² + 2xh + h² + 2x + 2h
the difference f(x + h) - f(x).
f(x + h) - f(x) = [x² + 2xh + h² + 2x + 2h] - [x² + 2x]
= 2xh + h² + 2h
Divide the difference from h as in the formula of difference coefficient
[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h
= 2x + h + 2
So, when h = 0 , [f(x + h) - f(x)]/h = 2x +2
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1. (y + x) = 4; use x = 2 and y = 2
2. x + y = 6; use x = 5 and y = 6
3. y(x + 5); use x = 1 and y = 4
4. q-m+q; use m = 3 and q = 6
