There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5 The three digit number 514 is one way the dials can be set as shown in the diagram.
a) Work out the number of different three digit numbers that can be set for the combination lock.
b) How many of the possible three digit numbers have three different digits?
Answer:
a) 125 different numbers
b) 60 numbers with different digits
Step-by-step explanation:
You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.
a) CombinationsAny of the three dials may be set to any of the five digits, so there are ...
5 × 5 × 5 = 125
possible three digit combinations.
The number of different 3-digit numbers is 125.
b) Different digitsIf the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...
5 × 4 × 3 = 60
possible combinations with different digits.
The number of 3-digit numbers with different digits is 60.
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Rashid thought about all the bills that his family needed to pay and wondered what the function would be if the situation changed so that on day 0, they owed $10 and then added a dollar a day.
Write the explicit equation and graph the function that models this situation.
Answer:
y = -x - 10
Step-by-step explanation:
set y as the total money owed
set x as how many days passed
if 0 days are passed, they owed $10, which is "-10" the y-intercept
and owed $1 more everyday which is -1x. We can write it as -x.
30 points!
Graph the system.
y=3x-6
y=2/5x+5
What is the estimated solution of the system?
Enter your answer in the blanks. Round each coordinate to the nearest integer.
The lines intersect closest to the integer coordinates
The estimated solution of the system y=3x-6 and y=(2/5)x+5 is (4, 7)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the linear equation:
y = 3x - 6 (1)
y = (2/5)x + 5 (2)
Subtracting equation 2 from 1 to solve using elimination method gives:
0 = 2.6x - 11
x = 55/13 ≅ 4
put x = 55/13 in eqn 2:
y = (2/5)(55/13) + 5
y = 87/13 ≅ 7
The solution is (4, 7)
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What is the name of the line of reflection for the pair of figures?
Enter your answer in the box.
Line {m} is the line of reflection for the given geometry.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven is a pair of heart shaped geometrical figures as shown.
It can be seen clearly that the line {m} forms the line of reflection for the given figure.
Therefore, line {m} is the line of reflection for the given geometry.
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Suppose that 7 boys and 13 girls line up in a row. Let $S$ be the number of places in the row where a boy and a girl are standing next to each other. For example,for the row $GBBGGGBGBGGGBGBGGBGG$ we have $S=12$. If all possible orders of these $20$ people are considered,what is the average value of $S$?
(a) 9 (b) 10 (c) 11 (d) 12 (e) 13
Answer:
[tex]$\boxed{(c) : 11}$[/tex]
Step-by-step explanation:
We can think of this problem as placing $7$ dividers (representing the boys) in $20$ slots (representing the people). Thus, the number of ways to arrange the boys and girls is the number of ways to place the dividers, which is $\binom{20}{7}$.
To find the average value of $S$, we need to find the total number of arrangements where $S = k$ for each possible value of $k$, then divide by the total number of arrangements.
Let's first consider the case where $k=0$. There is only $1$ way to arrange the boys and girls such that there are no boys and girls standing next to each other: BBBBBBBBBBBBBBBBBBBBB.
Next, let's consider the case where $k=1$. There are $\binom{7}{1}\binom{13}{6}$ ways to arrange the boys and girls such that there is exactly $1$ pair of boys and girls standing next to each other. To see this, consider that there are $\binom{7}{1}$ ways to choose the position of the divider that separates a boy and a girl, and $\binom{13}{6}$ ways to arrange the remaining dividers and slots.
We can continue this process to find the total number of arrangements for each possible value of $k$. When we add up all of these arrangements and divide by the total number of arrangements, we get the average value of $S$.
More specifically, the average value of $S$ is equal to
[\frac{1\cdot1+\binom{7}{1}\binom{13}{6}\cdot1+\binom{7}{2}\binom{13}{5}\cdot2+\binom{7}{3}\binom{13}{4}\cdot3+\binom{7}{4}\binom{13}{3}\cdot4+\binom{7}{5}\binom{13}{2}\cdot5+\binom{7}{6}\binom{13}{1}\cdot6+\binom{7}{7}\binom{13}{0}\cdot7}{\binom{20}{7}}.]
Simplifying this expression gives us $\boxed{(c) : 11}$.
CONSTRUCTION Every 128 fluid ounces of
stain covers about 200 square feet of wood.
About how many fluid ounces of stain
does a homeowner need to stain the beam
shown? (Assume the back of the beam does
not need to be stained.)
Don’t look at 17 nor the pink rectangle pls!! HELPP :(
Answer:
6.08 fluid ounces
Step-by-step explanation:
You want the amount of stain required to cover the surface area of the ends and three sides of a beam 6" square and 6 ft long. 128 floz of stain will cover 200 square feet.
End areaThe two ends of the beam are 1/2 ft square, so the area of each is ...
A = s² = (1/2 ft)² = 1/4 ft²
The two ends have a total area of ...
2 × (1/4 ft²) = 1/2 ft² . . . . end area
Side areaThree of the four sides of the beam are to be stained, so their total area is the area of 3 rectangles, each of which is 1/2 ft by 6 ft.
The area of each rectangle is ...
A = LW
So, the area of the three rectangles is ...
total side area = 3 × (1/2 ft)(6 ft) = 9 ft²
Beam areaThen the area to be stained is the sum of the end area and the side area:
stained area = (1/2 ft²) +(9 ft²) = 9.5 ft²
Stain quantityThe amount of stain required is proportional to the area, so we can write the proportion ...
q/(9.5 ft²) = (128 floz)/(200 ft²)
Multiplying by 9.5 ft² gives ...
q = (128 floz)(9.5/200) = 6.08 floz
The homeowner needs 6.08 fluid ounces of stain to stain the beam.
22. A survey was given to 90 high school students. They were asked if they preferred fiction or non-fiction and if they preferred indoor or outdoor activities. Partial survey results are shown in the table.
What percent of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction?
Enter a number in the box.
P(outdoor | non−fiction)= ______%
Note that the percentage of the students in the survey, to the nearest whole number, that prefer outdoor activities given they prefer non-fiction is: 11%.
What is the rationale for the above response?To get the percentage of those who love outdoor activities as well as non-fiction, we must complete the table.
Given:
Total number of those who love Fiction and Non Fiction but who love indoors = 50
From that list those who love fiction = 24, thus, those who love indoor and non-fiction =
50 - 24 = 26
Total number of those who were served are = 90
If the total number of those who love Fiction and Non-Fiction but who love indoors = 50
Then the total number of those who love Fiction and Non Fiction but who love Outdoors = 90 - 50 = 40
If the total number of those who love outdoor (Fiction and non-fiction) = 40 and those who prefer fiction only from this category is = 30;
Then the total number of those who love Non Fiction but who love Outdoors =
40 -30
= 10
Thus, the percentage of this number against the total number of those surveyed is:
10/90
= 0.1111111111 or 11%
Therefore, the percentage of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction is given as 11%. See the full table attached.
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How do the shapes in group 1 differ from those in group 2
Answer:
Group 1 polygons have sides that are the same length. But group 2 polygons do not.
A fame holds a picture that is 15 inches long and X inches wide. The frame border is
3 inches wide around the picture. What expression represents the area of the frame
border?
Answer:
no
Step-by-step explanation:
Two identical buildings are being constructed by two teams composed of identically skilled workers. The first team has 16 workers and works on the first building, and the second team has 25 workers and works on the second building. They start at the same time, and, after some time has elapsed, 8 workers move from the second team to the first team to help them. Both teams finish their construction at the same time. Find the ratio of the time spent working by the teams after the team change to the time spent working by the original teams as a irreducible fraction p/q . What is p + q?
The answer to this equation using the rule of three is 68.
What is rule of three?Let the time taken by the first team to finish the building be T. Since the teams are identical, the time taken by the second team to finish the building would also be T.
After 8 workers move from the second team to the first team, the first team has 16 + 8 = 24 workers and the second team has 25 - 8 = 17 workers.
Let the time taken by the first team after the worker change be T1 and the time taken by the second team after the worker change be T2.
Since both teams finish the construction at the same time, we can say that T1 = T2.
By the rule of three, we know that T/16 = T1/24 and T/25 = T2/17.
Cross multiplying and equating we get, 16T = 24T1 and 25T = 17T2.
So T1 = (24/16)T = 3/2T and T2 = (25/17)T.
The ratio of the time spent working by the teams after the worker change to the time spent working by the original teams is (3/2T + (25/17)T) / T = (3/2 + 25/17) = (317 + 252)/(2*17) = 51/17.
Therefore, p + q = 51 + 17 = 68.
What is rule of three?The rule of three is a method used to solve problems involving proportionality. It involves expressing the proportion between two values in terms of a third value. It is a mathematical rule used to find the fourth value when three of the values are known. It's also known as proportionality rule, cross-multiplication rule, and inverse proportionality. The rule of three is a simple way to find the value of an unknown quantity in a proportion. The rule of three is used when three of the four values are known and the fourth is unknown.
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Solve 8 sin² (x) - 2 sin(x) - 3 = 0 for all solutions 0 < x < 2π
On solving the provided question we can say that - here in trigonometry [tex]v^2x - 2u - 3 = 0[/tex] = (u-3)(u+1)
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
[tex]sin^2x - 2 sinx - 3 = 0\\u= sinx\\u^2 = sin^2x\\v^2x - 2u - 3 = 0\\\\[/tex]
factors are = -3 and 1
(u-3)(u+1)
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By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is
reduced to 8%, then the selling price will be:
Answer:
Rs.2700
Step-by-step explanation:
14% profit means 100% +14% more=114% profit
then to make into decimal 114% divided by 100 to give 1.14
then divide 2850 by 1.14 to find original selling price of bicycle
which will be Rs.2,500
next, a 8% profit means 100%+8% which equals 108% and then make into decimal which is 1.08
then multiply the original selling price (Rs.2,500) by 1.08 to give your final selling price after the 8% profit of ...
Rs.2,700
Calculations:
The relationship between the slopes
of the parallel sides is...
The relationship between the lengths of
the non-parallel sides is...
The relationship between the slopes of the parallel sides is equal.
The relationship between the lengths of the non-parallel sides is equal.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The parallel sides are DG and EF.
The non-parallel sides are DE and GF.
The slope of DG.
Two points pass through by DG.
(-2, 2) and (1, 2)
Slope = (2 - 2) / (1 + 2) = 0/3 = 0
The slope of EF.
Two points pass through by EF.
(-4, -3) and (3, -3)
Slope = (-3 + 3) / (3 + 4) = 0 / 7 = 0
The length of DE.
D = (-2, 2)
E = (-4, -3)
Length of DE = √(-4 + 2)² + (-3 - 2)² = √(4 + 25) = √29
The length of GF.
G = (1, 2)
F = (3, -3)
Length of GF = √(3 - 1)² + (-3 - 2)² = √(4 + 25) = √29
Thus,
The slope of the parallel sides is equal.
The length of the non-parallel sides is equal.
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Note: This problem MUST be solved using a graphing tool (Desmos, Wolfram
Alpha, graphing calculator). Solutions submitted using logarithms (which is not a
topic taught or assessed in Applied Math) will be given a grade of zero.
Two small towns are adjacent to one another. Town A has a population of 700 people,
while Town B has a population of 1400.
Town A has a population growth rate of 3.5% per year. Town B's annual growth rate is
1.25%.
When will the populations be the same? What will their populations be when they are
the same?
Unless you are instructed differently this assignment is worth 5 marks. Use the
following information to guide your work:
After 31 years the population will be the same. Their populations will be 2072 when they are the same.
What is the growth rate?Growth rates are calculated by dividing the difference between the ending and beginning values for the period under consideration by the starting value. The most common time periods for growth rates are annually, quarterly, monthly, and weekly.
The formula for the growth of the population is:
A = P(1+r)^n
A is the total number population after n years.
P is the initial number of population
r is rate of interest.
For town A,
The initial population is 700. The growth rate is 3.5% = 0.035.
The population of town A after t year is y = 700(1+0.035)^t
For town B,
The initial population is 1400. The growth rate is 1.25% = 0.0125.
The population of town A after t year is y = 1400(1+ 0.0125)^t
The system of equations is:
y = 700(1+0.035)^t
y = 1400(1+ 0.0125)^t
The intersection point is (31.537,2071.432).
After 31 years the populations will be the same.
their populations will be 2072 when they are the same
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A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed but takes a different route. His return trip takes two hours longer and is 30 miles. Find his speed.
Answer: they are ripped
Step-by-step explanation:
i guessed
Answer:
3 mi / hr
Step-by-step explanation:
It takes the cyclist 2 hours to go 6 miles further ( 30 -24 mi)
6 mi / 2 hr = 3 m/hr
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
personally it feels like the best fit
teams , , , and are in the playoffs. in the semifinal matches, plays , and plays . the winners of those two matches will play each other in the final match to determine the champion. when plays , the probability that wins is , and the outcomes of all the matches are independent. the probability that will be the champion is , where and are relatively prime positive integers. find .
The probability that T4 wins is 781.
There are two scenarios in which T4 wins.
The first scenario is where T4 beats T1,73 beats T2, and T4 beats T3, and the second scenario is where T4 beats T1, T2 beats T3, and T4 beats T2.
Considering the first scenario:
The probability of T4 beating t1 is 4/(4+1).
The probability T3 beats T2 is 3/(3+2).
The probability T4 beats T3 is 4/(4+3).
Therefore the first scenario happens with probability 4/(4+1)*3/(3+2)* 4/(4+3)
Considering the second scenario:
The probability of T4 beating t1 is 4/(1+4).
The probability T2 beats T3 is 2/(2+3).
The probability T4 beats T2 is 4/(4+2).
Therefore the second scenario happens with probability 4/(1+4)*2/(2+3)* 4/(4+2)
By summing these two probabilities, the probability that T4 wins is 4/(4+1)*3/(3+2)* 4/(4+3) + 4/(1+4)*2/(2+3)* 4/(4+2) which is equal to 256+525 = 781.
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According to the given sample space the probability that T4 wins is 403/105
Here we have given that there are two scenarios in which T4 wins.
And the first scenario is represents that T4 beats T1, T3 beats T2, and T4 beats T3, then the second scenario is where T4 beats T1, T2 beats T3, and T4 beats T2.
While we considering the first scenario, then we have identified that
T4 beating T1 = 4/5
T3 beats T2 = 3/5.
T4 beats T3 = 4/7.
Then the Probability of first scenario is written as,
=> 4/5 + 3/5 + 4/7
=> 7/5 + 4/7
=> 69/35
Now, we have to take the second scenario, then the probability is written as
T4 beating t1 = 4/5.
T2 beats T3 = 2/5.
T4 beats T2 = 4/6.
Then the probability of the second scenario is calculated as,
=> 4/5 + 2/5 + 4/6
=> 6/5 + 4/6
=> 56/30
When we summing these two probabilities, then the probability that T4 wins is calculated as,
=> 69/35 + 56/30
=> 403/105
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Allison and Aubrey shopped together for art class supplies. Allison bought 3 charcoal pencils and 2 brushes for $17.18. Aubrey purchased the same types of items, but she bought 2 charcoal pencils and 5 brushes for $26.56.
What is the cost of one charcoal pencil ?
Using a system of equations, the unit cost of a charcoal pencil is $3.16.
What is a system of equations?A system of equations involves two or more equations, also known as simultaneous equations, which are solved concurrently or simultaneously.
The cost of one charcoal pencil is the quotient of the total cost of a charcoal pencil divided by the number.
In this situation, after eliminating brushes, we can determine that the total cost of 5.5 charcoal pencils is $17.39. After the division operation, the unit cost is computed to be $3.16.
Allison Aubrey
Charcoal pencils 3 2
Brushes 2 5
Total costs $17.18 $26.56
Let charcoal pencils = c and brushes = b
3c + 2b = 17.18 ... Equation 1
2c + 5b = 25.56 ... Equation 2
Multiply Equation 1 by 2.5:
7.5c + 5b = 42.95 ... Equation 3
Subtract Equation 2 from Equation 3:
7.5c + 5b = 42.95
-
2c + 5b = 25.56
= 5.5c = 17.39
c = 3.16
Thus, after solving the simultaneous equations, we can determine that the cost of one charcoal pencil is $3.16.
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A church window is built in the shape of a semicircle. If the window is to contain three stained glass section of equal size, what is the area of each stained glass section if the length of the diameter is 90cm?
The required area of each stained glass section is 1060.71 square centimeters.
Area of a semicircle.
A semicircle is a part of a circle, gotten from the division of a circle into two equal halves. So that halve of a circle is a semicircle. The area of a semicircle can be determined as;
Area of a semicircle = 1/2 [tex]\pi[/tex] r^2
where r is the radius of the circle.
In the given question, we have;
diameter of the church's window = 90 cm
So that its radius is;
r = 90/ 2
= 45
r = 45 cm
Area of the church's window = 1/2 [tex]\pi[/tex] r^2
= 1/2 * 22/7 * 45^2
= 3182.143
Area of the church's window is 3182.143 square centimeters
Thus, since the semicircle would be divided into three equal parts;
Area of each stained glass section = 3182.143/ 3
= 1060.71 square centimeters
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If f(x) = 3x² - x, Find f( -2)
options
14
10
38
Answer: 14
Step-by-step explanation:
f(-2) means x is -2, so we can solve for when x = -2 by plugging -2 into the equation.
[tex]f(-2) = 3(-2^{2}) - (-2)\\=3(4) + 2\\=12+2\\=14[/tex]
Answer:
Step-by-step explanation:
So what you start with is the variable "x" in 3 different places. When you are changing the x variable, you need to plug it into every variable in the equation. Start by doing that and the problem will look like: f (-2) = 3 (-2)^2 - (-2) Now you can start with either the 3 (-2)^2 or the - (-2), but it is better to go from left to right.
Your Best
Elina
Colton has already earned $45 mowing lawns. He earns $15 per lawn. He needs at least $125 for a new string trimmer. Write and solve an inequality to determine how many more lawns Colton will need to mow to have at least $125.
Answer:
125 = (15x) + 45
(Sorry if I'm wrong!)
Bobby is 3 more than 7 times Jada's age. Bobby is 94 years old. Write and solve an equation to find Jada's age. Pll help due now
Answer:
13 years old.
Step-by-step explanation:
Solution to QuestionLet x be the age of Jada
Given from the question:
Bobby's Age: 7x + 3 years old
Jada's Age: x years old
7x + 3 = 94
7x = 94 - 3
7x = 91
x = [tex]\frac{91}{7}[/tex]
x = 13
Therefore Jada is 13 years old.
please help algebra homework help asap now
Answer:
B
Step-by-step explanation:
$7 for a child X and $13 for a adult Y
Given the following graph, Identify its key features listed below: (USE ESTIMATION)
Y-intercepts
How the graph behaves
End behavior
Possible values of variables
Domain and range
Minimum and maximum values
(BONUS POINTS FOR BEST ANSWER)
The y-intercept of the graph is (0, 10)
The end behaviour is: as x ⇒ +20, y ⇒ 0 and As x ⇒ -∝, y ⇒ +∝The possible values are (0, 10) and (-50, 15)Domain: x < 20 and Range: y > 0The function minimum is (20, 0)How to determine the y-interceptsThis is the point where the graph crosses the y-axis
So, the y-intercept is (0, 10)
How the graph behaves (end behaviour)To do this, we check the values of x in relation to the values of y
From the graph, we can see that the values of y reduces as the values of x increases to 20
This means that the end behaviour is
As x ⇒ +20, y ⇒ 0 and As x ⇒ -∝, y ⇒ +∝
Possible values of variablesTo do this, we again check the values of x in relation to the values of y
From the graph, we can see that the values of y when x = 0 is 10 and also, we have x = -50 and y = 15
So, the possible values are (0, 10) and (-50, 15)
The domain and the rangeHere, we make use of the end behaviours
So, we have
Domain: x < 20Range: y > 0Minimum and maximum valuesThe function has no maximum, but it has a minimum at (20, 0)
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Find the measures of X and Y.
Answer:
m∠X = m∠Y = 100.5°--------------------------------------
Sum of interior angles of a 6-sided polygon is:
180°(6 - 2) = 180°*4 = 720°Both angles ∠X and ∠Y marked as same, let them be x and ∠W is marked as right angle.
The sum is:
2x + 90 + 99 + 171 + 159 = 7202x + 519 = 7202x = 201x = 100.5m∠X = m∠Y = 100.5°.
Answer:
m∠X = 100.5°
m∠Y = 100.5°
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3cm}\underline{Sum of the interior angles of a polygon}\\\\$S=(n-2) \times 180^{\circ}$\\\\where:\\ \phantom{ww}$\bullet$ $n$ is the number of sides. \\ \end{minipage}}[/tex]
The given polygon has 6 sides.
Therefore, the sum of its interior angles is:
[tex]\implies S = (6 - 2) \times 180^{\circ} = 720^{\circ}[/tex]
From inspection of the given polygon:
m∠V = 99°m∠Z = 171°m∠U = 159°m∠W = 90°m∠X = m∠YTherefore:
[tex]\implies m \angle U + m \angle V + m \angle W + m \angle X + m \angle Y + m \angle Z = 720^{\circ}[/tex]
[tex]\implies 159^{\circ} + 99^{\circ} + 90^{\circ} + m \angle X + m∠ \angle Y + 171^{\circ} = 720^{\circ}[/tex]
[tex]\implies m \angle X + m \angle Y + 519^{\circ} = 720^{\circ}[/tex]
[tex]\implies m \angle X + m \angle Y = 201^{\circ}[/tex]
As m∠X is equal to m∠Y:
[tex]\implies m \angle X = m \angle Y = 201^{\circ} \div 2 = 100.5^{\circ}[/tex]
Caleb has a part-time job at an ice skating rink selling hot cocoa. He decided to plot
the number of hot cocoas he sold relative to the day's high temperature and then
draw the line of best fit. Based on the line of best fit, how many hot cocoas would you
predict Caleb to sell if the day's high temperature were 12°F?
Hot Cocoas Sold
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
l + w = 32
The possible widths are 5, 10, 15, 20, and 25.
Now,
[tex]l + 5 = 32\\l = 27\\l + 10 = 32\\l = 22\\l + 15 = 32\\l = 17\\l + 20 = 32\\l = 12\\l + 25 = 32\\l = 7[/tex]
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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2 planes left an airport at 10:30 am.one travelled due south at an average speed of 400km and the second travelled due east at an average speed 300km per hour .how far apart when the two planes at 2:30 pm
Therefore , the solution of the given problem of speed comes out to be average speed of the aeroplane = 200 km/h.
What is speed ?An object's velocity, as opposed to its speed, describes how quickly it goes in both directions. Velocity in physics is the rate of movement in a specific direction. A car's speed is described when we say it goes at 60 km/h.
Here,
Speed of the aeroplane for 400 km = = (400/2) = 200 km/h (due north)
Speed of the aeroplane = 300 km/h (due east)
Speed is a scalar quantity. So no direction is needed. Just for question, direction is given here, for understanding purpose.
Average speed of the aeroplane = (200 + 300)/2
= 250 km/h
Therefore , the solution of the given problem of speed comes out to be average speed of the aeroplane = 200 km/h.
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Answer:
2000km
Step-by-step explanation:
To find the distance between the two planes at 2:30 pm, we need to determine the positions of each plane at that time.
Since the first plane traveled due south at an average speed of 400 km/h for 4 hours (from 10:30 am to 2:30 pm), it would have covered a distance of 400 km/h * 4 h = 1600 km due south.
Similarly, the second plane traveled due east at an average speed of 300 km/h for 4 hours, covering a distance of 300 km/h * 4 h = 1200 km due east.
To find the distance between the two planes, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the distance between the two planes represents the hypotenuse of a right triangle, with the southward distance traveled by the first plane as one side and the eastward distance traveled by the second plane as the other side.
Using the Pythagorean theorem:
Distance^2 = (1600 km)^2 + (1200 km)^2
Distance^2 = 2,560,000 km^2 + 1,440,000 km^2
Distance^2 = 4,000,000 km^2
Taking the square root of both sides to find the distance:
Distance = √4,000,000 km^2
Distance ≈ 2000 km
Therefore, the two planes are approximately 2000 km apart at 2:30 pm.
There are 30 cans of soda in a refrigerator. This table shows how many cans there are of each type. If you reach in and pull out one can of soda, what is the probability that is it not a cola?
The probability of randomly selecting a can that is not a cola is:
P = 0.8
How to find the probability?We know that there are 30 cans of soda on a refrigerator, such that 6 of these are of cola.
We want to find the probability of randomly selecting a can that is not of cola, to get that probability, we need to take the quotient between the number of cans that are not of cola and the total number of cans.
There are:
30 - 6 = 24 cans that are not of cola.
30 cans in total.
Then the probability is:
P = 24/30 = 0.8
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A single die is rolled twice. the 36 equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 3.
Jim is calculating the probability of flipping a coin multiple time. Jim decides to
flip a coin three times.
a. Make a systematic list for the possible outcomes of flipping the coin three times
b. Find the probability of each of the following events occurring. Be sure to show your thinking clearly:
P (all three heads)
il.
P (at least one tail)
a) The list with all the possible outcomes is given as follows:
Heads, Heads, Heads.Heads, Heads, Tails.Heads, Tails, Heads.Heads, Tails, Tails.Tails, Heads, Heads.Tails, Heads, Tails.Tails, Tails, Heads.Tails, Tails, Tails.b) The probabilities are given as follows:
P(all three heads) = 1/8.P(at least one tail) = 7/8.How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Of the 2³ = 8 outcomes, only one result in three heads, hence the probability is given as follows:
p = 1/8.
At least one tail is complementary to three heads, hence it's probability is given as follows:
p = 1 - 1/8 = 8/8 - 1/8 = 7/8.
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