Answer:
To maximize the monthly rental profit, 90 units should be rented out.
The maximum monthly profit realizable is $38,200.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
In this question:
Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]
To maximize the monthly rental profit, how many units should be rented out?
This is the x-value of the vertex, so:
[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]
To maximize the monthly rental profit, 90 units should be rented out.
What is the maximum monthly profit realizable?
This is p(90). So
[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]
The maximum monthly profit realizable is $38,200.
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work
Answer:
The answer is 1,000
SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
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Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
Which expression is equivalent to
-32 3/5
-8
-3/325
3/325
1/8
Answer:
[tex]-32^\frac{3}{5} = -8[/tex]
Step-by-step explanation:
Given
[tex]-32^\frac{3}{5}[/tex]
Required
The equivalent expression
We have:
[tex]-32^\frac{3}{5}[/tex]
Rewrite as:
[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]
Expand
[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]
Remove bracket
[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]
[tex]-32^\frac{3}{5} = -2^3[/tex]
[tex]-32^\frac{3}{5} = -8[/tex]
A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.
Answer:
C
Step-by-step explanation:
one line is
y = 3x/7 + 11
its slope is 3/7
the y-intercept is, of course, when x=0. there y=11
the other is
-3x + 7y = 13
7y = 3x + 13
y = 3x/7 + 13/7
its slope is 3/7 (the same as the other line)
the y-intercept (x=0) is y = 13/7 (different to the other line)
Answer:
C. Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
[tex]y=\frac{3}{7} x+11[/tex] and [tex]-3x+7y=13[/tex]
→ Rearrange the second equation to make y the subject
7y = 3x + 13
→ Divide everything by 7
[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]
Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.
Answer:
A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Step-by-step explanation:
Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.
Please show work. The way that you solve for surface area and vol confuse me.
Answer:
search up the formula
Step-by-step explanation:
6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve
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Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
Frazer's speed decreased by 38.1% during the second part.
_____
Additional comment
A negative % change represents a decrease; a positive % change represents an increase.
For the function G defined by G(x) = 5x + 3, find G(2)
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
Simplify this expression.
6 + 8 ÷ 2
3
7
10
12
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
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Answer:
Tn = -4n² +40n +36
Step-by-step explanation:
A graphing calculator readily performs the quadratic regression, yielding the formula ...
Tn = -4n² +40n +36
__
The first and second differences of the given sequence terms are ...
28, 20, 12 and -8, -8
The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:
-4, -16, -36, -64
Subtracting these values from the original sequence gives the linear sequence ...
76, 116, 156, 196
which has first term 76 and common difference 40. The equation for the n-th term of this is ...
an = 76 +40(n -1) = 36 +40n
Adding this linear sequence to the sequence of squared terms, we get ...
Tn = -4n² +40n +36
y you work from 7 a.m. to 4 p.m. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember 30 minutes is equal .5 hours
Answer:
You’ve worked 7 hours and 30 minutes
Step-by-step explanation:
what is factorization of the trinomial below? -x2+2x+48
Answer:
-(x+6) (x-8)
Step-by-step explanation:
-(x^2-2x-48)
two values the multiply to get 48 and the difference of those two numbers gives you -2.
6,-8
6 x -8 =-48
6-8=-2
In this case we factored out the negative so leave it outside
-(x+6) (x-8)
Answer:
-1(x-8)(x+6) is the answer just took the test
Step-by-step explanation:
Express as index form
log 2 64 = 6
Answer:
hsv s deutsche ki bhar ke dekhte hai mera gham na
Write each percent as a fraction in simple form 15 3/5%
Answer:
39/250
Step-by-step explanation:
15 3/5 = 78/5 and percent means per 100, so
(78/5)/100 = (78/5)(1/100)
=78/500 = 39/250
Area of a triangle
A/12 = 12/12bh
solve for b
Step-by-step explanation:
I hope this works for ya.
Question 6 a-c if plz show ALL STEPS like LITERALLY EVERYTHING
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Answer:
a) quadrant III
b) 4π/3, -2π/3
c) (1/2, (√3)/2)
d) ((√3)/2, -1/2
Step-by-step explanation:
a) The attachment shows the point P and the numbering of the quadrants (in Roman numerals). Point P lies in quadrant III.
__
b) Measured counterclockwise, the angle to point P is 240° or 4π/3 radians. Measured clockwise, the angle is -120° or -2π/3 radians. In the diagram, these are shown in green and purple, respectively.
__
c) Adding π/2 to the angle 4π/3 or -2π/3 brings it to 11π/6, or -π/6. This point is marked as P' (blue) on the diagram. The coordinate transformation for π/2 radians CCW rotation is ...
(x, y) ⇒ (-y, x)
P(-1/2, -√3/2) ⇒ P'(√3/2, -1/2)
In terms of trig functions, the coordinates of the rotated point are ...
P'(cos(-π/6), sin(-π/6)) = P'(√3/2, -1/2)
__
d) Adding or subtracting π radians to/from the angle moves it directly opposite the origin. Both coordinates change sign. This point is P'' (red) on the diagram.
i need help ON THIS PLS
Answer:
No, because the ratio of pay to hours is not the same for each pair of value.
find the missing side length in the image below
Answer:
3/6=?/10
Step-by-step explanation:
multiply by together. ?=5
find x on this special right triangle, 45 is not an option!!!!
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
An oil company is going to issue new ID codes to its employees. Each code will have one letter, followed by one digit, followed by three letters. The letters w, x, y, and z will not be used. So, there are 22 letters and 10 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
Answer:
2342560 combos
Step-by-step explanation:
so its 1 letter*1number*1 letter*1 letter*1 letter, or 22x10x22x22x22 which should equate to 2342560 possible ID codes, hope this helps :)
. Using the identity (a + b)² = (a² + 2ab + b²), evaluate 112²
[tex]\\ \sf\longmapsto 112^2[/tex]
[tex]\\ \sf\longmapsto (100+12)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(12)+12^2[/tex]
[tex]\\ \sf\longmapsto 10000+2400+144[/tex]
[tex]\\ \sf\longmapsto 12400+144[/tex]
[tex]\\ \sf\longmapsto 12544[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛112²
⇛(100 + 12)²
⇛(100)² + 2 × 100 × 12 + (12)²
⇛10000 + 2400 + 144
⇛12400 + 144
⇛12544
What is the mean of the following list of extra credit points earned on a statistics test?
10,8,18,17,7
Answer:
12
Step-by-step explanation:
Given the data :
X : 10,8,18,17,7
The mean value of scores obtained can be obtained thus :
Mean = ΣX / n
n = sample size = 5
Mean = ΣX / n = (10+8+18+17+7) / 5
Mean = 60 / 5 = 12
AM and CM
BM and BM
AB and CB
These are variables on your graph
Which equation describes this graph?
Step-by-step explanation:
The graph clearly has a positive slope. So Answer D couldn't be correct. Next: the y-intercept of this line is (0, -2), so b in the formula y = mx÷ b must be -2.
Therefore the correct equation of this line is
y = x - 2 (choice a)
Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0
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Answer:
y was not substituted for every x
Step-by-step explanation:
To find the inverse of ...
y = f(x)
you need to solve ...
x = f(y)
Here, f(x) = x^2 +12x, so f(y) = y^2 +12y
This is not the expression we see on the right of ...
x = y^2 +12x
Apparently y was not properly substituted into f(x).
If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum
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Answer:
d) 10.38%
Step-by-step explanation:
The multiplier for four quarters of quarterly compounding is ...
(1 +10%/4)^4 = 1.025^4 = 1.103812890625
This is about 1 + 10.38%.
The effective rate of interest is about 10.38% per annum.
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
Learn more about slope of a line here
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Bod and coa are _____ angles
Answer:
opposite angles
Step-by-step explanation:
They are formed in the intersection of lines AD and BD.
Answer:
opposite angles
Step-by-step explanation:
they are formed in the intersection of lines AD and BD. two figures are called similar if they have same shape however have different size.
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
