Answer: The reflector's height can be modeled as a function of time. The function will depend on the radius of the wheel, the distance of the reflector from the edge of the tire, and the speed of the bicycle.
Let's call the radius of the wheel r. The radius is half of the diameter, so:
r = 630 / 2 = 315 mm
Also, let's call the distance of the reflector from the edge of the tire d.
d = 79 mm
Given that the reflector is at its lowest height at t = 0, we know that at that time the center of the reflector is at a height of r + d = 315 + 79 = 394 mm.
The height of the center of the red reflector at time t seconds is given by:
h(t) = (r + d) + vt
Where v is the speed of the bicycle in meters per second, and t is the time in seconds.
Substituting the values we have:
h(t) = 394 + (1.6 x t)
So the function for the height of the center of the red reflector at time t seconds is h(t) = 394 + (1.6 x t) (in mm)
It's important to note that this function is based on the assumption that the reflector is at its lowest height at time t = 0 and that the height of the reflector increases linearly with time as the bike moves forward.
Step-by-step explanation:
janet gross salary is 24000 per month her tax free allowances are shown in the table below national insurance 2 1\2 ,personal allowances is 20000 what is her total tax allowances for the year
Janet's total tax allowances for the year are $27,200.
How are the tax allowances determined?The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.
The insurance allowance is computed by applying the rate to the annual gross salary.
The personal and insurance allowances are added to determine the total tax allowances.
Generally, tax allowances reduce the taxpayer's taxable income.
Gross salary per month = $24,000
Annual gross salary = $288,000 ($24,000 x 12)
Personal allowances per year = $20,000
National insurance = 2¹/₂%
= $7,200 ($288,000 x 2¹/₂%)
Total allowances for the year = $27,200 ($20,000 + $7,200)
Thus, Janet is entitled to a total tax allowance of $27,200 for the year.
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Karis ran 3 and 2/3rds miles on Monday. Benita ran 1/2 of the distance that Karis ran. How far did Benita run?
The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.
Karis ran 3 2/3 miles on Monday.
It is said that Benita ran half of the distance ran by Karis.
So, the distance ran by Benita would be,
⇒ 3 2/3 × 1/2
⇒ 11/3 × 1/2
⇒ 11/6 miles
Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
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Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Tony and Sue now have.
There are two phrases for how many sweet Sue and Tony have: 13-x and
How to find the calculation?Equivalent refers to the mathematical notion of equality between several terms and expressions with a comparable value.
Equivalent vs. Equal. Equivalent and equal are distinct terms in mathematics.
Equal means identical in every respect, as opposed to equivalent, which is similar but not the same.
18 + x/ 2 is the equivalent.
Sue has 18 delicious.
Tony has 18 delicious.
Sue gives Tony some candy. Sue Sweet is going to
18 - x Sue consumes 5 candies, thus his sweet will be
18 - 5 - x = 13 - x
Sue gave Tony x candy to take. His sweetness will
18 + x
Tony consumed half of his candy. His final treat will be
18 + x / 2
The phrase for Sue candies is 13 - x.
18 + x / 2 is the equation for Tony Sweets.
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A town has a population of 20000 and grows at 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41600?
If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .
To find out how long it will take for the town's population to reach 41600, we can use the formula :
⇒ A = P(1 + r)ⁿ
Where:
A = final population of town , P = initial population o town
r = percent increase (as a decimal)
let n = number of years for population to reach 41600 .
We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05 and we have to solve for n.
Substituting the values ,
we get ;
⇒ 41600 = 20000(1 + 0.05)ⁿ ;
⇒ 41600 = 20000(1.05)ⁿ ;
⇒ 41600/20000 = (1.05)ⁿ ;
taking "log" on both sides ,
we get ;
⇒ log(41600/20000) = n × log(1.05) ;
⇒ n = log(41600/20000)/log(1.05) ;
⇒ n = 15.0105 ≈ 15
Therefore , it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.
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true or false: if and are mutually exclusive and exhaustive with and , and is an event in , then
If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]
IntersectionThe sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:
A ∩ B = {x | x ∈ A and x ∈ B}
Here's how to determine the separation of two sets:
One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.
The sets are equal if A = B, then A ∩ B = (A = B).
Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.
The sets are not mutually exclusive.
UnionThe union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:
A ∪ B = {x | x ∈ A or x ∈ B}
Here's how to determine the union of two sets:
A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.
The set is equal if A = B then A ∪ B = (A = B).
Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.
The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.
Your question is incomplete but most probably your full question was:
If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False
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Find the slope of a line perpendicular to the line whose equation is 4x+5y=35Fully simplify your answer.
The slope of a line perpendicular to the line is 5/4
What is the slope of a straight line?A straight line of the form
y = mx + c
has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.
If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1
Given;
4x+5y=35
We can write the equation as;
4*x + 5*y - 35 = 0
5*y = - 4*x + 35 or
y = -(4/5)*x + 35
m= -4/5
So, now the slope of this line is -4/5 and line perpendicular slope will be 5/4
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Kate is firing off her homemade rockets for a project in physics class. The
maximum height of any of her rockets can be represented by the equation
h-701-162, where h is the height (in feet) of the rocket after t seconds.
The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;
Domain; 0 ≤ t ≤ 4.375
Range; 0 ≤ h ≤ 39.06
What is a mathematical function?A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.
The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.
The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;
At ground level, h = 0, therefore;
h = 70·t - 16·t² = 0
(70 - 16·t)·t = 0
A possible solution is therefore, t = 0
The other solution is found as follows;
(70 - 16·t) = 0
70 = 16·t
16·t = 70
t = 70/16 = 4.375
The other solution or time at which the rocket is at ground level is t = 4.375
The domain is therefore; 0 ≤ t ≤ 4.375The range is the set of possible h values, which is obtained as follows;
The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;
a = -16
b = 70
c = 0
The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875
The maximum height, [tex]h_{max}[/tex], is therefore;
[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² = 76.5625
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Find the quotient of 6y^4+10y^3-8y^2divided by 2y.
The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:
6y³ + 10y² - 4y.
How to obtain the quotient?The dividend is given as follows:
6y^4 + 10y³ - 8y²
The common factors are given as follows:
Constants 6, 10 and -8: 2, which is the greatest common factor of the three numbers.Exponents 2, 3 and 4: 2, which is the lowest exponent.Hence the dividend can be simplified as follows:
2y²(6y² + 10y - 4).
Simplifying by 2y, the result of the quotient is given as follows:
y(6y² + 10y - 4) = 6y³ + 10y² - 4y.
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20 ft
8 ft
20 ft
12 ft
Find the area
A company manufactures and sells shirts the daily profit. The company makes depends on how many shirts they sell the profit in dollars when the company sells X shirts can be found using the function F (X)equals 6X -90 find the interpret the given function values and determine inappropriate domain for the function f(-9)
profit of
of the problem.
=
f(27)
profit of
of the problem.
=
f(17.5) =
profit of
of the problem.
meaning if the company sells |
dollars. This interpretation
meaning if the company sells
dollars. This interpretation
, meaning if the company sells
dollars. This interpretation
shirts, they would make a
in the context
shirts, they would make a
in the context
shirts, they would make a
in the context
The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).
Explain about the Marginal profit?By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.
Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.
A company that manufactures and sells shirts. Daily profit of...
A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values to determine the appropriate domain for the function.
f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.
f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem
f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.
Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).
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Calculator
During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height
What is the volume of the water that filled one cone?
nter your answer as a decimal in the box. Use 3.14 for pi.
in³
1 2
3
A
4
5
6
7 8 9
10
The volume of One cone held 1.1017.36 inches3 of water when it was full.
A method for determining a cone's volume?A cone's volume is determined using the following formula:
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
A cone's volume is determined using the following ,
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
r = 12/2 = 6in
h =27in
Discover the volume V = 1/3(3.14)(6)2*27
V = 1.1017.36
In light of this, one cone held 1.1017.36 inches of water.
One cone held 1.1017.36 inches of water.
The complete question is,
Construction cones were soaked with water while a project was underway due to a strong downpour. A cone has a 12 inch diameter and a 27 inch height.
How much water was used to fill each cone?
Put a decimal in the box for your response. Pi is equal to 3.14; in3
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joan earns 8% commission on her sales this month Joan had $6000 in sales what was her commission
The amount of commission that Joan earns this month on sales will be $480.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Joan earns an 8% commission on her sales this month Joan had $6000 in sales.
Let 'x' be the commission. Then the equation is given as,
x / $6,000 = 0.08
x = 0.08 · $6,000
x = $480
The amount of commission that Joan earns this month on sales will be $480.
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Average rate of exchange
50 points for answer and brainliest
Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9
Explain about the Average rate?The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.
f (x ) = -2
f (x) = 9/ -2 (-2)-7
= 9 / 4 - 7
=9 / -3
= -3
f (x ) = -4
f (x) = 9/ -2 (4)-7
= 9 / 8 - 7
=9 / 1
= 9
Average rate is -3, 9
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PLEASE HELP!!!!!!! PHOTO BELOW
State the equation of the graphed function.
The equation of the graphed function for this problem is given as follows:
y = x³ - 6x² - 7x - 6.
How to obtain the function?The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function are given as follows:
x = 1.x = 2.x = 3.Hence the linear factors are given as follows:
(x - 1).(x - 2).(x - 3).Then the function is given as follows:
y = a(x - 1)(x - 2)(x - 3).
In which a is the leading coefficient.
The y-intercept is at y = -6, hence the leading coefficient is given as follows:
-6a = -6
a = 1.
Hence the function is:
y = (x² - 3x + 2)(x - 3)
y = x³ - 6x² - 7x - 6.
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Use the ALEKS graphing calculator to find all the zeros of the polynomial function.
g(x) = -2x² - 5x³+2x²+7x+1
Round to the nearest hundredth.
If there is more than one answer, separate them with commas.
zero(s):
The graph of the polynomial function g(x) = -2x² - 5x³ + 2x² + 7x + 1 is plotted and attached
The zeros are (-1.10, 0), (-0.15, 0) and (1.25, 0) to the nearest hundredth)
How to find the zeros of a polynomial function using graphUsing a graph is potted by written the equation on the plotter , the plotter interprets the equation and presents the graph
Zero of polynomial equation is the point where the y is zero this is solved by equating the polynomial function to zero
From the graph, the zeros are identified by the points where the graph cuts the the x axis.
Examining the graph of the function g(x) = -2x² - 5x³ + 2x² + 7x + 1 the zeros are
(-1.104, 0), (-0.145, 0) and (1.249, 0)
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Can someone please help me with this
hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition
[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]
Six friends are going to run a relay race that is 3.12 miles long. Each friend will run an equal distance. How many miles will each friend run? (I WILL GIVE BRAINLIEST!!)
In a relay race each friend run a distance of 0.52 miles.
How to find distance?The distance of the race divided by the runners' times will give you their average velocities.
We are given that
Total distance covered in a race = 3.12 miles
Total number of persons = 6
Each person runs equal parts of the race.
We have to find the miles run by each person.
To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.
Each person runs = Total distance/ Total number of persons
Each person runs= 3.12 / 6 miles
Each person runs = 0.52 miles
Hence, each person runs 0.52 miles.
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Please help just number 10 and 11 thank you.
Answer: 10. 3
Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3
the half-life of radon (rn-222) is 3.82 days. how much (what fraction) of a sample remains after 11.46 days?
Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.
As per the data given in the above question are as bellow,
A material has a half-life when it takes a particular length of time for half of it to disappear or change.
11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.
We thus split the 3 mg sample in half three times.
3 ÷ 2 = 1.5
1.5 ÷ 2 = 0.75
0.75 ÷ 2 = 0.375
After 11.46 days, there will only be 0.375mg of radon-222 left.
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A 50 fluid ounce bottle of laundry detergent washes 32 loads of laundry. A 100 fluid ounce bottle wash is 60 loads of laundry. Are they portional? Do these rates from a proportion? 
Answer:
No, they are not proportional
Step-by-step explanation
50*2=100
32*2=64, not 60
The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of length to width was 8 to 5. This ratio is called the Golden Ratio. If the length of a rectangular painting is 20 inches, determine the width of the painting in order for the length and width of the painting to have the Golden Ratio.
By applying the Golden Ratio rule, the width of the painting is equal to 12.5 inches.
What is a proportion?In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions is a mathematical operation which can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying the Golden Ratio rule, the width of the painting can be calculated as follows;
20/x = 8/5
Cross-multiplying, we have the following:
8x = 20 × 5
8x = 100
x = 100/8
x = 12.5 inches.
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Evaluate the following: −3 − (−8)
Answer: The answer is 5
Step-by-step explanation:
-3-(-8)
-3+8
5
Answer: 5
Step-by-step explanation:
First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5
Find x please help asap
Answer:
68888jours 9999999888
A girl of height 0.9 m is walking away from the base of a lamp-post and covered 4.8 m. If the lamp is 3.6 m above the ground, find the length of her shadow.
If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.
What is proportionality?In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.
Height of the girl = 0.9 m.
Height of the lamp = 3.6 m.
Distance between the lamp and the girl = 4.8 m.
Let the length of her shadow = x m.
From proportionality relation:
3.6 : 4.8 = 0.9 : x
3.6/4.8 = 0.9/x
3.6x = 4.8 × 0.9
x = (4.8 × 0.9) ÷ 3.6
x = 1.2
Hence, the length of her shadow is 1.2 m.
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Pls help me I am stuck on this thanks so much
Answer:
the twelve value will produce -3
Step-by-step explanation:
T(12) = 45 - 4(12)
T(12) = 45 - 48
T(12) = -3
PLEASE PLEASE HELPPP
M is the midpoint of LN. L has coordinates (1,12) and M has coordinates (-10,-4). Find the coordinates of N.
Answer:
N(-21,-20)
Step-by-step explanation:
We can apply midpoint formula to solve for endpoint (N):
[tex]\displaystyle{\text{Midpoint}= \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)}[/tex]
Let [tex]\displaystyle{x_1 = 1}[/tex], [tex]\displaystyle{y_1 = 12}[/tex] and Midpoint = (-10,-4). Therefore:
[tex]\displaystyle{\left(-10,-4\right)= \left(\dfrac{1+x_2}{2}, \dfrac{12+y_2}{2}\right)}[/tex]
Solve x with -10 and y with -4:
[tex]\displaystyle{\text{N}\left(x_2,y_2\right) = \left(\dfrac{1+x_2}{2}=-10, \dfrac{12+y_2}{2}=-4\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(1+x_2=-20, 12+y_2=-8\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-20-1, y_2=-8-12\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right) = \left(x_2=-21, y_2=-20\right)}\\\\\displaystyle{\text{N}\left(x_2,y_2\right)=\left(-21,-20\right)}[/tex]
Therefore, the coordinate of N is (-21,-20)
find the soulotion to this in eqaulity a
> –3
A graph of the solution to this inequality a > -3 is shown on the number line attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.
In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.
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Complete Question:
Find the solution to this inequality a > –3.
in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55
Select the correct answer from the drop-down menu.
What is the author's purpose for including the quote in paragraph 5 in the article?
The author includes the quote to give the reader
were at Mauna Loa.
F
a contrasting view
a first-hand account
an opinion
an objective summary
of how dangerous the conditions
In the essay “A Modest Proposal”, The author includes the quote to give the reader an objective summary of how dangerous the conditions were at Mauna Loa.
What is “A Modest Proposal”?Jonathan Swift, a satirist, suggested jokingly in an essay titled "A Modest Proposal" from 1729 that the people of Ireland sell their children as food. A radical or shocking notion is frequently introduced in an ironic way using the term a modest suggestion.
Swift's essay, which is hailed as a masterwork of irony, is officially titled "A Modest Proposal for Preventing the Children of the Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to Their Public."
When a proposal takes the form of an essay, it typically proposes a fix for a social or political issue. The adjective "modest" denotes reason or modesty. Because the idea is genuinely absurd, it is humorously used in the title of "A Modest Proposal."
A modest proposal is frequently used in jest to make a point by taking something to its logical conclusion, which highlights a problem. Swift's article, which at the time caused controversy, has since become a satirical mainstay and has influenced a lot of authors.
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