Step-by-step explanation:
8.a.
a function is something that looks like
y = ax + b or similar.
it describes the way to calculate the result for whatever input value you can come up with.
so,
C = 12×d + 8
you could also say
C(d) = 12×d + 8
as, when you rent, you have to pay these $8 in any case, no matter how long you stay, and you need to pay $12 per day you stay.
funny thing is : you understood this perfectly well when doing b.
c.
the constant rate of change is always the factor of the input variable. here : 12
it is the ratio of (y change) / (x change)
or here (C change / d change).
it indicates that for any increase of d by 1 (staying one day longer) the charges C increase by 12.
9.a.
remember, what we just said about the rate of change ?
it is (result change) / (input change).
between 2010 and 2015
the input changed by +5 (from 2010 to 2015).
the result changed by +6.25 (from 37 to 43.25).
the rate of change is therefore
6.25/5 = 1.25 = 1 1/4 = 5/4
the function is therefore
population in millions = (years since 2010)×5/4 + 37
p = y×5/4 + 37
b.
now we want to find the number of years (y) so that the result of that equation is 50.
50 = y×5/4 + 37
13 = y×5/4
52 = 5y
y = 52/5 = 10.4
so, this will be during the 11th year after 2010 = 2021.
10.
be careful and concentrate.
you see that the sequence goes up 20, when n goes up 5 (and not just 1) ? there was your initial mistake.
a.
again, remember the change rate : it is result change / input change.
so, we have here 20/5 = 4.
so,
C(n) = 4×n + 50
b.
n = 12
C(12) = 4×12 + 50 = 98
c.
now we have C(n), and want to find for which n this is true.
C(n) = 78
78 = 4×n + 50
28 = 4×n
n = 7
after 7 visits the costs are 78.
there are the basic costs of 50 (for n = 0 or 0 visits) and then extra 4 for every visit.
d.
the x-axis is for the number of visits, the y-axis for the costs.
so, the line starts at the point (0, 50), and then passes through the points of the original table (5, 70), (10, 90), (15, 110). and if you want you can calculate the points for higher x (or number of visits).
g A pipe of negligible diameter is to be carried horizontally around a corner from a hallway 8 ft wide into a hallway 4 ft wide. What is the longest length that the pipe can be
The length of the longest pipe that can be carried horizontally is given by the minimum value of the function of the length of the pipe.
The longest length that the pipe can be is approximately 16.648 feet.
Reasons:
The length of the pipe, L
Width of the first hallway = 8 ft.
The width of the second hallway = 4 ft.
We have;
(L - a)·sin(θ) = 8
a·cos(θ) = 4
Therefore;
L - a = 8·csc(θ)
a = 4·sec(θ)
L(θ) = 8·csc(θ) + 4·sec(θ)
At the minimum length, we have;
L'(θ) = 4·sec(θ)·tan(θ) - 8·csc(θ)·cot(θ) = 0
4·sec(θ)·tan(θ) = 8·csc(θ)·cot(θ)
Therefore;
[tex]\displaystyle \frac{sec(\theta) \cdot tan(\theta)}{csc(\theta) \cdot cot(\theta)} = \frac{sin(\theta) \cdot tan(\theta) \cdot tan(\theta) }{cos(\theta) } =tan^3(\theta) = \frac{8}{4}[/tex]
[tex]\displaystyle tan(\theta) =\sqrt[3]{\frac{8}{4} } ={\sqrt[3]{2} }[/tex]
θ = arctan([tex]\sqrt[3]{2}[/tex]) ≈ 51.56°
a = 4×sec(arctan([tex]\sqrt[3]{2}[/tex]))
a ≈ 6.434
L = 8·csc(θ) + a = 8 × csc(arctan([tex]\sqrt[3]{2}[/tex])) + 4×sec(arctan([tex]\sqrt[3]{2}[/tex])) ≈ 16.648
The longest length that the pipe can be, L ≈ 16.648 ft.
Learn more here:
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The longest length of the pipe is an illustration of trigonometry functions
The longest length of the pipe is 16.64 ft
The widths of the hallways are given as:
[tex]\mathbf{w_1 = 8}[/tex]
[tex]\mathbf{w_2 = 4}[/tex]
See attachment for the diagram that represents the scenario
From the diagram, we have:
[tex]\mathbf{sin(\theta) = \frac 4x}[/tex]
[tex]\mathbf{cos(\theta) = \frac 8y}[/tex]
Make x and y the subject
[tex]\mathbf{x = \frac 4{sin(\theta)}}[/tex]
[tex]\mathbf{y = \frac 8{cos(\theta)}}[/tex]
Where, the total length (L) of the pipe is:
[tex]\mathbf{L = x + y}[/tex]
So, we have:
[tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]
Differentiate
[tex]\mathbf{L' = -\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]
Set to 0
[tex]\mathbf{-\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)} = 0}[/tex]
Rewrite as:
[tex]\mathbf{\frac{4cos(\theta)}{sin^2(\theta)} = \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]
Divide through by 4
[tex]\mathbf{\frac{cos(\theta)}{sin^2(\theta)} = \frac{2sin(\theta)}{cos^2(\theta)}}[/tex]
Cross multiply
[tex]\mathbf{2sin^3(\theta) = cos^3(\theta)}[/tex]
Divide both sides by [tex]\mathbf{2cos^3(\theta)}[/tex]
[tex]\mathbf{tan^3(\theta) = \frac 12}[/tex]
Take cube roots of both sides
[tex]\mathbf{tan(\theta) = \sqrt[3]{\frac 12}}[/tex]
[tex]\mathbf{tan(\theta) = 0.7937}[/tex]
Take arc tan of both sides
[tex]\mathbf{\theta = tan^{-1}(0.7937)}[/tex]
[tex]\mathbf{\theta = 38.4}[/tex]
Substitute [tex]\mathbf{\theta = 38.4}[/tex] in [tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]
[tex]\mathbf{L = \frac 4{sin(38.4)} + \frac 8{cos(38.4)}}[/tex]
Evaluate
[tex]\mathbf{L = 6.43+ 10.21}}[/tex]
[tex]\mathbf{L = 16.64}}[/tex]
Hence, the longest length of the pipe is 16.64 ft
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3. Sandra earns P62,954 per month. Determine the following Percentage Amount of Deduction Whld Tax 24% SSS 1.4% Philhealth 1.1% SSS 1.4% Pag-ibig 0.2% Total Deduction Net Pay
Sandra's total deductions are $16,808.71, and her net pay is $46,145.29.
Given that Sandra earns $ 62,954 per month, to determine the percentage of deductions the following calculations must be performed:
Withhold Tax 24% 62,954 x 0.24 = 15,108.96 SSS 1.4% 62,954 x 0.014 = 881.35 Philhealth 1.1% 62.954 x 0.011 = 692.49 Pag-ibig 0.2% 62.954 x 0.002 = 125.90 Total Deduction = 15,108.96 + 881.35 + 692.49 + 125.90 = 16,808.71 Net Pay = 62,954 - 16,808.71 = 46,145.29
Therefore, Sandra's total deductions are $16,808.71, and her net pay is $46,145.29.
Learn more about quantities in https://brainly.com/question/25716934
PLZ HElp 24nanjoshua PLZZZZ
Answer: 11/14
Step-by-step explanation:
1/7 = 2/14 (when you time 2 at the top and at the bottom)
2/14 + 9/14 = 11/14
Executives for a company that prints logos on products are expanding the company's services to include souvenirs such as hats, shirts, and foam fingers for sports teams. The data they collected from a sample of 300 adults about their favorite sport to watch and their favorite souvenir to buy are shown in the table.
Answer:
0.01
Step-by-step explanation:
the number of participants that prefer a t-shirt and prefer soccer is 3, since this is out of 300 we have 3/300 or 0.01
Someone pls help me on this! ASAP pls I’ll mark you as a brainliest.
Answer:
almonds are worth 50 cents per ounce
peanuts are worth 25 cents per ounce
almonds are worth more per ounce
Step-by-step explanation:
I just divided 50 cents by 2 to get the cost per ounce of the peanuts, and I plugged 1 into the x in the equation that was given for almonds
Answer:
Almonds=50 cents per ounce
peanuts are 25 cents per ounce
In Phoenix, Arizona, the average number of sunny days is 211 per year. About what percent of the year is Phoenix sunny?
Answer:
57.81
Step-by-step explanation:
Answer:
58%
Step-by-step explanation:
there are 365 days on one year so you need to divide 211 by 365.
211÷365 = 0.578
round: 0.58 or 58%
PLZZZ HELPPP
What are the domain and range of f (x) = 1/2 (x+4)^2 - 11
Domain: All real numbers
Range: f(x) > -11
Domain: 3 > -11
Range: f(x) > -11
Domain: All real numbers
Range: All real numbers
Domain: 2 > -11
Range: All real numbers
Answer:
D. Domain: 2 > -11
Range: All real numbers
Step-by-step explanation:
Correct me if I’m wrong UwU
Answer:
Domain: All real numbers
Range: f(x) ≥ - 11
Step-by-step explanation:
Given the quadratic function in vertex form, f(x) = ½(x + 4)² - 11:
The vertex, (h, k) is (-4, -11).
Range: f(x) ≥ -11.The parabola opens upward (where a = ½, which is greater than 0), and k = -11 is the minimum value for f(x). Hence, the range of the given function must be at least -11, or f(x) ≥ -11.
Domain: all real numbersThere is no restriction for the value of x. Therefore, the domain of the given function is all real numbers.
On the following set of axes, create the graph of a function f (x) with the following characteristics:
Passes through the points,
(-8,0), (5,-2) and (8,3)
Functions can be represented on graphs and graphs can also be represented as functions.
The given parameters are:
Points = (-8,0), (5,-2) and (8,3)
Absolute Maximum = (-4,5)
Absolute Minimum = (2,-6)
Start by plotting the points (including the absolute maximum and the absolute minimum) without connecting the dots (see attachment 1)
The decreasing interval [tex]\mathbf{-4 \le x \le 2}[/tex] implies that the graph decreases from x =-4, to x =-2
See attachment (2) for the rough sketch of the graph that represents the given points and the decreasing interval
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if c is a positive number, how many solutions does vx=c have?
All cases where v and x are both negative or both positive numbers.
URGENT, WILL GIVE BIG BRAIN OR WHATEVER ITS CALLED LOL
For every 1000 hits a YouTub channel gets it makes £2 from ad revenue. a How many hits are required to make £21?
Answer: 10,500 hits
Step-by-step explanation:
I WANT BIG BRAIN! I WANT BIG BRAIN AHAHHHHHHH!!!!!!!
ok there are a number of ways to go about this
it is unclear whether or not the YT content creator will get one pound for 500 hits
i honestly dont know but i am going to assume it will
1000 times 20 (we are plugging in a test variable, 20, here)
so lets say we have 20,000 hits
lets divide that by 1000 and we get 20. 20 times 2 is 40 pounds so obviously thats too much
lets try 1000 times 10
so we have 10 times 2 and thats 20 pounds. we are closer
10,500 hits
(i put in 500 because half of 1000 is 500 and that will give you one pound instead of two)
A simple pendulum is made from a 0.864-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?
Answer:
Step-by-step explanation:
The period of a simple pendulum is
T = 2π√(L/g)
as going from zero velocity to max velocity takes 1/4 of a period
t = ¼(2π)√(L/g)
t = ½π√(L/g)
t = ½π√(0.864/9.81)
t = 0.466 s
Donnel purchased two pairs of jeans. There was a 20% discount on one pair of jeans with an original price of $45.50. There was a 40% discount on the other pair of jeans with an original price of $32.20. How much did he save altogether?
Answer:
$21.98
Step-by-step explanation:
45.50 * .20 = 9.1
32.20 * .40 = 12.88
12.88 + 9.1 = 21.98
Solve the equation for the indicated variable.
8x + y =5, for x
X= [?]
(Simplify your answer.Use integers or fractions for any numbers in the expression.)
Answer:
x = −1/8y + 5/8
Step-by-step explanation:
Step 1: Add -y to both sides.
8x = −y + 5
Step 2: Divide both sides by 8.
8x/8 = −y+5/8
x= −1/8y + 5/8
y= -6x + 1/2
PLEASE I NEED THE ANSWER AND EXPLANATION
Answer:
m = -6 (slope)
b = (1/2)
The Y posistion is (0, 0.5) and the slope of the graph is -6/1 (down 6, right 1).
Some examples of where the line is could be:
(1, -5.5)
(-1, 6.5)
Find the product using formula ...
formula = ( a + b ) ( a - b )
a) 1.2 × 2.8
Step-by-step explanation:
1.2 × 2.8
(2 - 0.8 )(2 + 0.8)
2² - (0.8)²
4 - 0.64
3.36
[tex]\begin{gathered}1.2 \times 2.8 \\ = (2 - 0.8)(2 + 0.8) \\ = {(2)}^{2} - {(0.8)}^{2} \\ = 4 - 0.64 \\ = 3.36\end{gathered}
[/tex]
Answer:3.36
Hope it helps.
Do comment if you have any query.
Help help help help help help help
Answer:
6
Step-by-step explanation:
x coordinate goes left and on 6 line
y coordinate goes up and on 1 line
(x, y)
(6, 1)
x coordinate is 6
The mileage on Ori's car is 73,033 miles. What is the fewest number of miles that Ori needs to drive before the mileage shows three identical digits again?
The fewest number of miles that Ori needs to drive before the mileage shows three identical digits again is 40.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that the mileage on Ori's car is 73,033 miles.
We need to find the fewest number of miles that Ori needs to drive before the mileage shows three identical digits again.
Therefore, the mileage on Ori's car = 73,033 miles.
identical digits = 40
The fewest number of miles that Ori needs to drive before the mileage shows three identical digits again is 40.
To learn more about the unitary method, please visit the link given below;
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#SPJ3
Determine the slope and y-intercept of a line that passes through the points (2, 4) and (–4, 1).
m = [ A. –2.5 , B. –1.5 , C. 0.5 ]
b = [ A. 3, B. 7, C. 9 ]
Answer:
hhhhhhhhhhhhiiiiiiiii
7433654 round to the nearest thousand
Answer:
Already rounded to the nearest thousandth.
7433654.000
Need asapppppppp!!!!!
Answer:
122 degrees-
Step-by-step explanation:
[tex]m\angle {GOC}=m\angle{GOA}+m\angle{AOC}\\=32^\circ + 90^\circ\\=122^\circ[/tex]
Angle GOA is a vertical angle with angle DOE, so it has the same measure (vertical angles are congruent).
Angle AOC is a right angle because angle COE is a right angle.
What’s the common ratio of the geometric sequence?
-4,-8,-16
Hello! :)
A geometric sequence is a sequence where you use multiplication or division to get to the next term.
-4, -8, -16...
Here, we multiply every number by 2. So the common ratio is 2.
Hope it helps, and let me know if you have any queries.
~A smiley teen who adores helping others
[tex]MagicalNature[/tex] here to help
Answer:
The answer is 2.
Step-by-step explanation:
To get the common ratio, simply dividing each number in the sequence from the number preceding it.
-4, -8, -16
-16 ÷ -8 = 2
- 8 ÷ -4 = 2
What is the answer to :
2x (4+3) -5 x [4-(9-7)]
??
Answer:
8×+6×-5×{2}
8×+6×-10×
14×-10×
4×
calculation: 2x(4+3)-5x[4-(9-7)]
2x × 7-5x [4-(9-7)]
14x - 5x [4-(9-7)]
14x - 5x [2]
14x -5x × 2
14x - 10x
4x
Simplifie -4.9(2+6.2v)
Answer:
it's 23over 78 and it can reduce
ZA and B are vertical angles. If mZA = (6x – 11)° and m B = (5x + 4)º,
then find the measure of ZB.
9514 1404 393
Answer:
∠B = 79°
Step-by-step explanation:
Vertical angles are congruent, so you have ...
6x -11 = 5x +4
x = 15 . . . . . . . . . . . add 11 -5x to both sides
5x +4 = 5·15 +4 = 79
The angles measure 79°.
_____
Checkk
∠A = 6x -11 = 6·15 -11 = 90 -11 = 79
Point One = (0, -2) = Point Two = (-3, -5)
write in slope intercept form
Answer: m=1
Step-by-step explanation:
Use the equation y=y2-y1 over x2-x1
1. label your points
0=x1
-2=y1
-3=x2
-5=y2
The first pair is x1 and y1 and the next pair is x2 and y2
plug in the numbers to find your answer
AT WHAT X-VALUE DOES A
RELATIVE MINIMUM
OCCUR?
Answer:
x ≈ 4.239
Step-by-step explanation:
A relative minimum is found at the bottom of any U-shape on the graph. If you expand the graph shown until it has a suitable scale, it can show you the relative minimum occurs at x ≈ 4.239.
__
Additional comment
The relative maximum occurs at the top of any ∩-shape. The graphing calculator can show you that occurs at x ≈ -1.573.
hello I need help please help me
Answer:
1) equation
2) equation
3) expression
4) expression
Step-by-step explanation:
An equation has a result, or something that equals to .
Numbers 1 and 2 have the word "is" which means equaled to, so they are equations. 3 and 4 don't, so they are only expressions.
Hope that helped :)
Step-by-step explanation:
Examples:
[tex]a+4;\ 3b;\ \dfrac{x}{4}-\text{these are the expressions}\\\\x=5;\ c+5=3c;\ p=q-\text{these are the equations}[/tex]
[tex]1.\ n+4=12-\bold{the\ equation}\\\\2.\ 5\cdot n=50-\bold{the\ equation}\\\\3.\ C\cdot 7-\bold{the\ expression}\\\\4.\ 6\cdot(12+t)-\bold{the\ expression}[/tex]
Use the information to complete the Venn diagram. 80 people surveyed on pets they own. 64 people indicated they owned a dog. 34 people indicated they owned a cat and a dog.
Answer:
34 will go in the middle of the two, 80 is everybody who voted, end 64 is the people that own the dog. No people on the cat
Step-by-step explanation:
there
let's substract : (2x + 3y) from (8x + 6y)
[tex]\huge\mathfrak\pink{answer} [/tex]
Kevin buys a bag of cookies that contains 8 chocolate chip cookies, 9 peanut butter cookies, 5 sugar cookies and 4 oatmeal cookies. What is the probability that Kevin randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects an oatmeal cookie
Answer:
4/13 or 30.769%
Step-by-step explanation: