It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.
Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.
To calculate:
How long will it take to triple?
How long will it take to quadruple?
Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)
where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.
So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)
Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)
Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)
Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.
3p_0 = p_0 2^(t/5) 3 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)
Therefore, it will take approximately 8.5 years to triple the population.
Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)
Taking logarithm (with base 2) on both sides,
log_2 4 = log_2 2^(t/5)
log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.
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Someone please help with this? Thank you!
Table values are -3, -1, 3, 5, 13
Define the term function?A function is a mathematical object that maps each element from one set to a unique element in another set. Functions are represented using symbols and can be described using graphs, tables, or equations.
Given function is,
[tex]f(x)=2x +3[/tex]
Solve for x = -3, f(-3) = 2×(-3) + 3 = -6 + 3 = -3
f(-3) = -3
Solve for x = -2, f(-2) = 2×(-2) + 3 = -4 + 3 = -1
f(-2) = -1
Solve for x = 0, f(0) = 2×(0) + 3 = 0 + 3 = +3
f(0) = 3
Solve for x = 1, f(1) = 2×(1) + 3 = 2 + 3 = 5
f(1) = 5
Solve for x = 5, f(5) = 2×(5) + 3 = 10 + 3 = 13
f(5) = 13
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A population of bacteria in culture increases according to the model P=300(2.7)^0.02t, where T is the number of hours and T=0 corresponds to 9:00 AM.
a. Use this model to estimate the number of bacteria at 11 AM.
b. Graph the function and name the p-intercept. Describe what the p-intercept represents and a reasonable domain and range for this situation.
This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.
What is a graph?
A graph is a visual representation of data or mathematical functions. Graphs are used to present data in a clear and concise manner, making it easier for people to understand and interpret the information being presented.
a. To estimate the number of bacteria at 11 AM, we need to plug in t = 2, since 11 AM is two hours after 9:00 AM. Therefore:
P = 300(2.7)^(0.02*2)
P = 300(2.7)^0.04
P ≈ 369.13
So, there are approximately 369.13 bacteria at 11 AM.
b. To graph the function, we can use a graphing calculator or software. The p-intercept is the point where the graph intersects the y-axis, which occurs when t = 0. We can find the p-intercept by setting t = 0 in the equation:
P = 300(2.7)^(0.02t)
P = 300(2.7)^(0.02*0)
P = 300
Therefore, the p-intercept is (0, 300). This means that when the bacteria culture is first created (at 9:00 AM), there are already 300 bacteria present.
The domain of this situation is all non-negative values of t, since time cannot be negative. The range is all positive values of P, since the number of bacteria is always increasing. Therefore, a reasonable domain for this situation would be [0, ∞) and a reasonable range would be (0, ∞).
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Select all numbers that are solutions to the inequality w < 1
-1. 3
5
0. 9
-5
0
The numbers that are solutions to the inequality w < 1 are: -1.3, -5 and 0
Numbers 5 and 0.9 are not solutions to the inequality because they are greater than or equal to 1. An inequality is a statement that compares two quantities or expressions using a mathematical symbol indicating their relative sizes. Inequalities are used to describe a range of values or solutions, rather than a single solution, and are often represented on a number line. Inequalities are commonly used in algebra, calculus, and other areas of mathematics, as well as in science, economics, and engineering. Solving inequalities involves finding all possible values of the variable that satisfy the inequality. This can be done by applying algebraic operations and graphing techniques to isolate the variable and determine the appropriate range of values.
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Find the roots of the polynomial equation.
x^3-x^2+x+39=0
Answer:
-3, 2+3i, and 2-3i.
Step-by-step explanation:
To find the roots of x^3-x^2+x+39=0, we use the Rational Root Theorem and synthetic division to test possible rational roots. We find that -3 is a root, and divide by (x+3) to get the quadratic factor x^2-4x+13=0. Solving this using the quadratic formula gives us the remaining roots of 2+3i and 2-3i. Therefore, the roots of the equation are -3, 2+3i, and 2-3i.
Find the sample space for the experiment. (Enter your answer in set notation) You select two marbles (without replacement) from a bag containing eight red record the color of each marble. three blue martes (denote bye), and eight yellow martie (denote by Y). You
The total number of marbles in the bag is[tex]8 + 3 + 8 = 19[/tex]. We can represent the sample space as follows:
[tex]S = {(R, R), (R, B), (R, Y), (B, R), (B, B), (B, Y), (Y, R), (Y, B), (Y, Y)}[/tex]
Note that the sample space contains 9 elements.
The experiment involves selecting two marbles (without replacement) from a bag containing eight red marbles (denoted by R), three blue marbles (denoted by B), and eight yellow marbles (denoted by Y).
The sample space of the experiment is the set of all possible outcomes.
Each outcome is represented by an ordered pair of the colors of the two marbles selected. Since we are selecting two marbles without replacement, the order in which we select the marbles matters. Hence, we use ordered pairs to represent each outcome.
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The graph below shows petrol prices at two petrol stations, Station X and Station
Y.
Ellie went to one of the petrol stations and bought 20 litres of petrol for £24.
a) Did Ellie go to Station X or Station Y?
b) How much would 15 litres of petrol cost at the same station?
Give your answer in pounds (£).
Cost (£)
Cost against amount of petrol
40
30
20
10-
5
10 15 20 25
Amount of petrol (litres)
Key
Station X
Station Y
At Station Y, 15 litres of gasoline would cost £18.
What is cost in?Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.
b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:
Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20
Cost of 1 litre of petrol = £24 / 20
Cost of 1 litre of petrol = £1.20
Therefore, 15 litres of petrol at Station Y would cost:
Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15
Cost of 15 litres of petrol = £1.20 x 15
Cost of 15 litres of petrol = £18
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Required information M7-20 to 22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual FIFO,LIFO,and Weighted Average Cost [LO 7-S1] In its first month of operations,Literacy for the Iliterate opened a new bookstore and bought merchandise in the following order400 units at $5 on January 1,2600 units at $7 on January 8,and 3830 units at $8 on January 29.Assuming 1.030 units are on hand at the end of the month M7-22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual Weighted Average Cost [LO 7-S1] Calculate the cost of goods available for sale,cost of goods sold,and ending inventory under the weighted average cost flow assumptions.Assume perpetual inventory system and sold 800 units between January 9 and January 28.(Round your intermediate calculations to 2decimal places.) Weighted Average Cost Goods Avallable for Sale Cost of Goods Sold Ending Inventory Aetivate Window
Calculating Cost of Goods Sold and Ending Inventory under Perpetual FIFO, LIFO, and Weighted Average Cost [LO 7-S1] In its first month of operations, Literacy for the Illiterate opened a new bookstore and bought merchandise in the following order 400 units at $5 on January 1, 2600 units at $7 on January 8, and 3830 units at $8 on January 29.
Assuming 1.030 units are on hand at the end of the month M7-22(Supplement 7A) Calculating Cost of Goods Sold and Ending Inventory under Perpetual Weighted Average Cost [LO 7-S1]
In order to calculate the cost of goods available for sale, cost of goods sold and ending inventory under the weighted average cost flow assumptions, you need to first calculate the weighted average cost of the goods.
Weighted Average Cost = (400 units x $5) + (2600 units x $7) + (3830 units x $8) / (400 + 2600 + 3830)
= $6.62
Cost of Goods Available for Sale = Weighted Average Cost x (400 + 2600 + 3830)
= $6.62 x 7,830
= $51,916.60
Cost of Goods Sold = Weighted Average Cost x 800 units
= $6.62 x 800
= $5,296.00
Ending Inventory = Cost of Goods Available for Sale - Cost of Goods Sold
= $51,916.60 - $5,296.00
= $46,620.60
The cost of Goods Available for Sale is $51,916.60
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Find the distance between the points ( – 9, – 7) and ( – 3,1).
Answer:
10 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 9, - 7 ) and (x₂, y₂ ) = (- 3, 1 )
d = [tex]\sqrt{(-3-(-9))^2+(1-(-7)^2}[/tex]
= [tex]\sqrt{(-3+9)^2+(1+7)^2}[/tex]
= [tex]\sqrt{6^2+8^2}[/tex]
= [tex]\sqrt{36+64}[/tex]
= [tex]\sqrt{100}[/tex]
= 10 units
[tex] \: [/tex]
[tex] \textrm{( -3 , 1 )}[/tex][tex] \: [/tex]
To find:-[tex] \textrm{Distance between two points = ?}[/tex][tex] \: [/tex]
By using formula:-[tex] \underline{ \star \small \boxed{{ \rm{ \purple{Distance = \sqrt{( x_2 - x_1 )² + ( y_2 - y_1 )²} }}}}}[/tex][tex] \: [/tex]
Solution:-[tex] \rm \: D =\sqrt{ ( x_2 - x_1 )² + ( y_2 - y_1 )²} [/tex][tex] \: [/tex]
where ,
[tex] \: \: \star \rm \red{x_1 = -9 , x_2 = -3 } \\\star \green {\rm y_1 = -7 , y_2 = 1}[/tex]
[tex] \: [/tex]
[tex] \rm \: D = \sqrt{ ( -3 - ( - 9 ))² + ( 1 - (-7 ))²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{( -3 + 9)² + ( 1 + 7 )²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{( 6 )² + ( 8 )²} [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{36 + 64 } [/tex][tex] \: [/tex]
[tex] \rm \: D = \sqrt{100} [/tex][tex] \: [/tex]
[tex] \boxed{ \textrm{ \color{green}{D = 10 \: }}}[/tex][tex] \: [/tex]
Therefore , the distance between two points is 10 units !
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hope it helps ⸙
At the start of 2014
Mikes car was worth 12000 the value of the car decreased by 30%
Answer:
If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:
New value = Original value - (Percentage decrease × Original value)
Percentage decrease = 30%
Original value = 12000
New value = 12000 - (0.30 × 12000)
New value = 12000 - 3600
New value = 8400
Therefore, at the end of the decrease, the value of Mike's car was 8400.
On January 1,1999 , the average price of gasoline was $1.19 per gallon. If the price of gasoline increased by 0.3% per month, which equation models the future cost of gasoline? y=1.19(1.003)^(x) y=1.19(x)^(1.03) y=1.19(1.03)^(x)
Answer:
first one
Step-by-step explanation:
The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.
In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).
Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:
y = 1.19(1.003)^(24)
y = 1.19(1.08357)
y = 1.288 per gallon
Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.
Miko bought five 2-litre bottles of water. She poured all the water equally into 15 bowls. What was the volume of water in each bowl?
The volume of water in each bowl is approximately 666.67 ml.
Miko bought five 2-liter bottles of water, which means that she had a total of 10 liters of water. She then poured all the water equally into 15 bowls. To find out the volume of water in each bowl, we need to divide the total volume of water by the number of bowls.
We can start by converting the 10 liters of water into milliliters (ml), which will make it easier to work with. To do this, we multiply 10 by 1000, since there are 1000 ml in one liter. This gives us a total of 10,000 ml of water.
Next, we divide the total volume of water (10,000 ml) by the number of bowls (15) to find the volume of water in each bowl. This can be written as:
Volume of water in each bowl = Total volume of water / Number of bowls
Volume of water in each bowl = 10,000 ml / 15
Volume of water in each bowl = 666.67 ml (rounded to two decimal places)
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you're playing a game where you defend your village from an orc invasion. there are 3 33 characters (elf, hobbit, or human) and 5 55 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from. if you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
There is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.
Since, A total of 3 x 5 = 15 outcomes are possible given the presence of 3 characters and 5 defense mechanisms.
There are three scenarios if the character is a hobbit (hobbit with magic, hobbit with sword, and hobbit with shield), three scenarios where the tool is an umbrella (any character with an umbrella), and one scenario where neither.
As a result, there are the following number of possibilities where neither the character nor the tool is a hobbit:
15 - 3 - 1 = 11
One of these 11 outcomes is likely to occur at a rate of:
= 11/15
As a result, there is an 11/15, or around 0.733, chance that you won't be a hobbit or wear an umbrella.
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an equation of a circle is given by (x+3)^2+(y_9)^2=5^2 apply the distributive property to the square binomials and rearrange the equation so that one side is 0.
The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].
Given:
Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]
Expand the equation
[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]
[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]
[tex]5^2 = 25[/tex]
Then, substitute the expanded expressions into the equation
[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]
Simplify and combine like terms
[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]
Rearrange the equation so that one side is 0
[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.
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Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
A rabbit is running with a constant speed of 3m/s. Find out the distance covered by rabbit in 10 seconds
The rabbit covers a distance of 30 meters in 10 seconds at a constant speed of 3m/s.
As we know that distance is equal to speed multiplied by time, we can use this formula to calculate the distance covered by the rabbit in 10 seconds. Given that the speed of the rabbit is constant at 3m/s, we can use this value to calculate the distance it covers in 1 second.
So, distance covered by rabbit in 1 second = Speed of rabbit = 3m/s
Now we can use this value to find the distance covered by the rabbit in 10 seconds, which is equal to 10 times the distance covered by the rabbit in 1 second.
Distance covered by rabbit in 10 seconds = 3m/s x 10 seconds
= 30 meters
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If you run towards a faraway friend at 5 miles per hour and she bikes towards you at 15 miles per hour, how many miles closer are you to each other after 1 hour?
Using the unitary method we calculate that the friend would be 20 miles closer in an hour.
If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:
5 miles / hour - (- 15 miles / hour) = 20 miles / hour
Also, we know that
speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,
20 miles/hour × 1 hour = 20 miles
Therefore, you would be 20 miles closer to each other after 1 hour.
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Anyone know the answer?
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
what is volume ?The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.
given
We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:
[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]
where h is the height of the frustum, r is the small radius, and R is the large radius.
Given the numbers, we can determine:
R = 5 in.
3 centimeters is r.
24 inches tall
With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]
As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.
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Please help, just need H!
Answer:
Step-by-step explanation:
[tex]f(x)=\frac{27}{4} x[/tex]
[tex]p(x)=\sqrt{3x}[/tex]
[tex][p(x)]^6=(3^\frac{1}{2}x^\frac{1}{2})^6= 27x^3[/tex]
[tex][p(x)]^6g(x)=27x^3(\frac{x}{4} )=\frac{27x^4}{4}[/tex]
[tex][p(x)]^6g(x)[t(x)]^3=\frac{27x^4}{4} (\frac{1}{x} )^3=\frac{27x^4}{4x^3} =\frac{27}{4} x[/tex]
Solution: [tex][p(x)]^6g(x)[t(x)]^3=f(x)[/tex]
I think there might be nicer solutions but this works!
Statistics question: (answer and explanation much appreciated)
a) The probability that the player is a non-pitcher not from the Dominican Republic is given as follows: 0.7578 = 75.78%.
b) The probability that a Dominican player is a pitcher is given as follows: 0.8595 = 85.95%.
c) The probability that a non-pitcher is not Dominican is given as follows: 0.4985 = 49.85%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Of the Dominican players, the percentages are given as follows:
5.6% of 42%.x% of 58%.The total percentage of Dominican players is of 10.5%, hence the value of x is given as follows:
0.056 x 0.42 + 0.58x = 0.105
x = (0.105 - 0.056 x 0.42)/0.58
x = 0.1405.
Of the 58% of the batter, 14.05% are from the Dominican Republic, hence the probability of chosen a batter not from the Dominican Republic is of:
p = 1 - 0.1405/0.58
p = 0.7578 = 75.78%.
14.05% of the players from the Dominical Republic are batters, hence the probability of choosing a pitcher is given as follows:
1 - 0.1405 = 0.8595 = 85.95%.
Of the 58% of the batters, 14.05% are Dominican, hence the 85.95% are not Dominican, thus the probability of choosing a non-Dominican batter is given as follows:
0.58 x 0.8595 = 0.4985 = 49.85%.
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The following data was collected from 40 of Mr. O'Block's AP Physics students in 2018.
Listed below are their scores (out of 100) on the second semester final exam:
58
70
63
73
71
68
85
74
66
87
88
91
Intervals Frequency
[0-10)
[10-20)
[20-30)
[30-40)
(40-50)
[50, 60)
[60-70)
[70-80)
[80-90)
[90-100)
2015 no
80
92
O
93
80
84.
61
82
98
85
83
97
88
89
91
77
80
1) Using the data above, create a well labeled histogram on the axes below.
74
62
71
80
0
93
71
99
102
90
99
100
2
HELP ME PLEASE I REALLY NEED IT!
Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.
What is rectangle?
A rectangle is a two-dimensional shape with four sides, where the opposite sides are equal and parallel, and all angles are right angles (90 degrees).
To create a histogram, you need to first group the data into intervals or bins. You can use the intervals given in the table as a guide, or you can create your own intervals.
For this example, I will use the intervals [0-10), [10-20), [20-30), [30-40), [40-50), [50-60), [60-70), [70-80), [80-90), and [90-100).
Next, count the number of scores that fall into each interval. For example, there are no scores between 0 and 10, one score between 10 and 20, two scores between 20 and 30, and so on.
Therefore, plot the intervals on the x-axis and the frequency (or count) on the y-axis. Draw rectangles for each interval with a height equal to the frequency. The rectangles should be adjacent to each other and have equal width.
below is the histogram -
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five program systems are prepared so that they work independently of each other. each system has a 0.3 chance of detecting an error. find the probability that at least one program system will detect an error. use 4 decimal places.
The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
How to find the probabilityGiven information:
five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.
Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.
The probability of a system not detecting an error is 1 - 0.3 = 0.7.
Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.
The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).
Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).
Hence, the correct option is 0.832.
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5. {MCC.6.RP.A.3B} How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes?
*
1 point
Answer:
Step-by-step explanation:
It will take you 8 hours to ski a distance of 24 miles at a speed of 6 miles per 30 minutes. This is because you will have to travel the 24 miles at a rate of 6 miles every 30 minutes, so you will need to travel for 4 hours at this rate to cover the full distance. Thus, it will take you 8 hours to ski the full 24 miles at a rate of 6 miles per 30 minutes.
Answer:
120 minutes / 2 hours
Step-by-step explanation:
time = distance / velocity
[tex]time = \frac{24}{(6/30)} \\time = 120 minutes[/tex]
Solve the triangle PQR (find the measures of ∠P, ∠Q, and side PQ).
(I need help finding both angle measure and side measure, please and thank you!)
Therefore , the solution of the given problem of triangle comes out to be the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
What precisely is a triangle?A polygon is a hexagon if it has over one extra segment. It's shape is a simple rectangle. Only the sides A and B can differentiate something like this arrangement from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a portion of the cube. Three edges and three angles make up a triangle.
Here,
The rule of cosines can be applied to the triangle PQR to determine the length of side PQ:
=> PQ² = PR² + QR² - 2(PR)(QR)cos(∠PQR)
=> PQ² = 9² + 12² - 2(9)(12)cos(62°)
=> PQ² ≈ 110.03
=> PQ ≈ 10.49
As a result, side PQ is roughly 10.49 units long.
The rule of sines can then be used to determine the dimensions of angles P and Q:
=> sin(∠P) / PQ = sin(62°) / PR
=> sin(∠P) / 10.49 = sin(62°) / 9
=> sin(∠P) ≈ 0.6322
=> ∠P ≈ 39.39°
=> sin(∠Q) / PQ = sin(77°) / QR
=> sin(∠Q) / 10.49 = sin(77°) / 12
=> sin(∠Q) ≈ 0.8559
=> ∠Q ≈ 58.10°
As a result, the angles P and Q have measurements of roughly 39.39° and 58.10°, respectively.
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Warren is constructing an open box from a piece of paper that is 8 in wide and 11. 5 in long
The sides of the squares be to obtain a box with the largest volume is 114.20 inch³.
Quadratic functions are used in various fields of engineering and science to obtain the values of various parameters. Graphically, they are represented by parabolas. Determines the direction of the curve based on the highest order coefficient. The word "quadratic" is derived from the word "Quad", which means square. In other words, a quadratic function is a "polynomial function of degree 2.
According to the Question:
Let a be the size of the square to be cut at 4 corners.
The cardboard is folded along the dotted line such that following are the box dimensions
Given that
Length, L= 11.5–2a ; Width. B = 8–2a ; Height, H = a
Volume of box, V = (18–2a )(8–2a) a
V = (11.5-2a)(8-2a)a
⇒ V = 92a -3a²-16+ 4a³
⇒ V = 4a³-3a² +92a -16
Now,
The condition for volume to be maximum is that,
dV/da = 0
⇒ [tex]\frac{dv}{da} (4a^3)- \frac{dv}{da} (3a^2) +\frac{dv}{da}(92a) - \frac{dv}{da} (16)[/tex]
⇒ 12a² -6a + 92
Taking common 2 from the above equation, we get:
⇒ 6a² - 3a + 46
Therefore,
The roots of this quadratic equation are,
a = 6.93 and 1.729
Case 1: If a = 6.93,
then B= -5.87 < 0 which is not a valid dimension.
Case 2: If a =1.729 then,
L = 14.54 ; B= 4.54 ; H=1.729
Therefore,
Volume of the box = 14.54 x 4.54 x 1.729 = 114.20
Therefore, the sides of the squares be to obtain a box with the largest volume is 114.20 inch³
Complete Question:
An open box is to be made from 8 inches by 11.5 inches piece of cardboard by cutting squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume?
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Drag the expression that is the most reasonable measurement for each object.
All the reasonable measurement for each object can be define as given table below.
What is called measurements?Measurements refer to the process of determining the magnitude, quantity, or degree of something using standardized units or instruments. It involves observing and recording data about an object, event, or phenomenon, and then comparing it to a reference standard to obtain a numerical value. They allow us to quantify and compare physical properties accurately and provide a universal language for expressing quantities.
Objects Measurements
Length of a school bus 1.4 × 10¹ metersWidth of an Orange 5 × 10° centimetersDistance from earth to the moon 3.7 × 10⁵ kilometersThickness of a human fingernail 9 × 10² micrometersTo know more about units, visit:
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answer is in the image below:
Five percent of the parts produced by a machine are defective. Fifteen parts are selected at random. Use the binomial probability tables to answer the following questions. (a) What is the probability that exactly 3 parts will be defective? (Round your answer to four decimal places.) (b) What is the probability that the number of defective parts will be more than 2 but fewer than 6? (Round your answer to four decimal places.) (c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.) (d) What is the expected number of defective parts? (e) What is the variance for the number of defective parts?
The variance for the number of defective parts is 0.7125.
(a) What is the probability that exactly 3 parts will be defective? (Round your answer to four decimal places.)In the given question, the probability of a part being defective is 5%, which is represented as p=0.05. The probability of a part being non-defective is (1 - 0.05) = 0.95.The given question represents a binomial experiment, which includes the following conditions:The experiment consists of n identical trials.Each trial has only two possible outcomes, a success, and a failure.Success has probability p and failure has probability 1-p.The trials are independent.To calculate the probability of exactly 3 parts being defective when 15 parts are selected randomly, we use the following formula:P (X = k) = nCk x pk x (1-p) n-kWhere P(X=k) is the probability of getting k defective parts, nCk is the number of ways of getting k defects from n parts, pk is the probability of getting k defective parts, and (1-p) n-k is the probability of getting n-k non-defective parts.p = 0.05q = (1 - 0.05) = 0.95n = 15a. P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508The probability of getting exactly 3 defective parts is 0.2508. Hence, the required probability is 0.2508.(b) What is the probability that the number of defective parts will be more than 2 but fewer than 6? (Round your answer to four decimal places.)b. We need to calculate the probability of getting defective parts more than 2 but less than 6.P (3 < X < 6) = P (X = 3) + P (X = 4) + P (X = 5)P (X = 3) = 15C3 x 0.05³ x 0.95¹² = 0.2508P (X = 4) = 15C4 x 0.05⁴ x 0.95¹¹ = 0.0925P (X = 5) = 15C5 x 0.05⁵ x 0.95¹⁰ = 0.0204P (3 < X < 6) = 0.2508 + 0.0925 + 0.0204 = 0.3637The probability of getting defective parts between 2 and 6 is 0.3637. Hence, the required probability is 0.3637.(c) What is the probability that fewer than 3 parts will be defective? (Round your answer to four decimal places.)c. We need to calculate the probability of getting fewer than 3 parts defective. The probability of getting zero defective parts or getting one defective part is given by:P (X = 0) = 15C0 x 0.05⁰ x 0.95¹⁵ = 0.4630P (X = 1) = 15C1 x 0.05¹ x 0.95¹⁴ = 0.3456P (X < 3) = P (X = 0) + P (X = 1) = 0.4630 + 0.3456 = 0.8086The probability of getting fewer than 3 defective parts is 0.8086. Hence, the required probability is 0.8086.(d) What is the expected number of defective parts?The expected number of defective parts is given by:μ = npμ = 15 × 0.05μ = 0.75The expected number of defective parts is 0.75.(e) What is the variance for the number of defective parts?The variance for the number of defective parts is given by:σ² = npqσ² = 15 × 0.05 × 0.95σ² = 0.7125The variance for the number of defective parts is 0.7125.
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Say my population is USA voters. If I interviewed people in front of a major grocery supermarket. Making sure that I selected supermarkets in high median salary areas. What type of sampling best fits my experiment?
The sampling method that best fits your experiment is convenience sampling.
Describe Sampling?Sampling is the process of selecting a subset of individuals or items from a larger population in order to gather information and draw conclusions about the entire population. Sampling is often used in scientific research, market research, and other fields where it is impractical or impossible to measure the entire population.
There are many different types of sampling methods, including random sampling, stratified sampling, cluster sampling, and convenience sampling. Each method has its own advantages and disadvantages, and the choice of sampling method depends on the specific research question and the resources available.
The sampling method that best fits your experiment is convenience sampling. Convenience sampling is a non-probability sampling method that involves selecting individuals who are readily available and accessible to the researcher. In your case, you are selecting individuals who are present in front of a major grocery supermarket, which is a convenient location. Convenience sampling is often used in situations where it is difficult or impractical to obtain a random sample, and is commonly used in market research and pilot studies.
However, it is important to note that convenience sampling has some limitations. Since the sample is not randomly selected, it may not be representative of the population as a whole. In your case, selecting supermarkets in high median salary areas may introduce bias into the sample, as it may not accurately represent the entire population of USA voters. Additionally, the sample size and characteristics may be affected by factors such as time of day, day of the week, and other factors that may affect who is present in front of the supermarket at a given time. Therefore, the results obtained from this sampling method may not be generalizable to the entire population of USA voters.
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solve( 3x^ 2)+2y +4=0
Answer:
Step-by-step explanation:
You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.
To be honest I don’t know what I’m doing with this question
Answer:
[tex]\sqrt{231}[/tex] cm
Step-by-step explanation:
The Pythagorean theorem is a mathematical principle that relates to the three sides of a right triangle. The formula for this is:
[tex]a^2 + b^2 = c^2[/tex]
In this case, the hypotenuse (c) is 16 cm, and one of the legs (a) is 5 cm. We can plug in the values and solve for the missing value.
[tex]5^2+b^2=16^2[/tex]
[tex]25+b^2=256[/tex]
[tex]b^2=256-25[/tex]
[tex]b^2=231[/tex]
[tex]b = \sqrt{231}[/tex] cm
I need some help please
Given:-
[tex] \texttt{c = 1}[/tex][tex] \: [/tex]
[tex] \texttt{d = 3}[/tex][tex] \: [/tex]
Solution:-
[tex] \texttt{3(2c + d ) -4 ( c - d ) + d² }[/tex][tex] \: [/tex]
put the given values in tha equation
[tex] \texttt{= 3( 2 ( 1 ) + 3 ) -4 ( 1 - 3 ) + ( 3 )² }[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 2 + 3 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 3 ( 5 ) -4 ( -2 ) + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 15 + 8 + 9}[/tex][tex] \: [/tex]
[tex] \texttt{= 23 + 9}[/tex][tex] \: [/tex]
[tex] \boxed{ \texttt{ \purple{= 32}}}[/tex][tex] \: [/tex]
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hope it helps ⸙