The number of bacteria after 5 hours is approximately 1013.8.
We can use the formula for exponential growth to solve this problem. If a population grows at a rate proportional to its size, then we can writ
N(t) = N₀ × e^(rt),
where N(t) is the size of the population at time t, N₀ is the initial size of the population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.
We know that the culture starts with 40 bacteria, so N₀ = 40. We also know that after 2 hours, the size of the population is 180. We can use this information to solve for r:
180 = 40 × e^(2r)
180/40 = e^(2r)
ln(180/40) = 2r
r = ln(180/40)/2
r ≈ 0.6931
Now we can use the formula to find the size of the population after 5 hours:
N(5) = 40 × e^(0.6931×5)
N(5) ≈ 1013.8
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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-4 ≤ x- 4 ≤ 0 graph the conjuntion ?? can someone help
The inequality is simplified as 0 ≤ x ≤ 4
Define inequalityIn mathematics, inequality refers to a mathematical expression that indicates that two values or quantities are unequal. An inequality is represented by the symbols "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
For example, the inequality "x > 5" means that the value of x is greater than 5, and the inequality "y ≤ 10" means that the value of y is less than or equal to 10.
To graph the conjunction, we first need to solve for x:
-4 ≤ x - 4 ≤ 0
Add 4 to all parts of the inequality:
0 ≤ x ≤ 4
Image of graph is attached below.
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The area of LMN is 18 ft2, and the area of FGH is 32 ft². If LMN -FGH, what is the ratio of LM to FG?
A. 3:4
B. 3√2:4
C. √3:2
D. 4:3
Please select the best answer from the choices provided
The ratio of LM to FG is 3:4, so correct option is A.
Describe Triangles?A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.
The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.
Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.
Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.
If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).
So we have:
LMN / FGH = 18 / 32
(x²) = 18 / 32
x² = 9 / 16
x = (3 / 4)
Therefore, the ratio of LM to FG is 3:4, which is option A.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.17. The probability that it will rain and the flight will be delayed is 0.02. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
The probability that the flight will leave on time when it is not raining is approximately 0.83.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).
According to the given information:
To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).
Let:
P(rain) = 0.07 (probability of rain)
P(delayed) = 0.17 (probability of delay)
P(rain and delayed) = 0.02 (probability of rain and delay)
We can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, we want to find P(on time | not raining), which can be expressed as:
P(on time | not raining) = P(on time and not raining) / P(not raining)
Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:
P(on time | not raining) = P(on time) / (1 - P(rain))
We can now substitute the given probabilities to calculate the required probability:
P(on time | not raining) = P(on time) / (1 - P(rain))
P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))
P(on time | not raining) = (1 - 0.17) / (1 - 0.07)
P(on time | not raining) = 0.83
So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).
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Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile? (5 points)
a
fraction 18 over 26
b
fraction 24 over 26
c
fraction 24 over 50
d
fraction 26 over 50
The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].
What is an Experimental Probability?Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).
Given:
[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]
Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.
We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:
The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50
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Does the image below prove ABC = DEF? Explain your answer.
Step-by-step explanation:
yes,because of SAS side angle side are equal.
I need questions 26-31 for 5 STARS
Answer:
26) 1.32
27) 90
28) 0.00845
29) 2.56x10^-1
30) 9.5x10^-3
31) 7.8x10
What is the total surface area of the figure shown?
The total surface area of the given figure is 619.2 in², which is not listed in the provided options.
Give a brief account on total surface area.The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.
The triangular face of the given figure represent an equilateral triangle of sides 12 in.
Area of the triangle = (√3/4) × a²
Area of the triangular face:
= (√3/4) × 12²
= (√3/4) × 144
= 57.6 in²
Area of the rectangle = Length × width
Area of the rectangular face:
= 12 × 14
= 168 in²
Area of the given figure:
= (2 × 57.6) + (3 × 168)
= 115.2 + 504
= 619.2 in²
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What is the range of f? A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
A coordinate plane. The x- and y-axes both scale by one. The graph of the function f starts at negative six, negative two, which is plotted. Then is decreases at a non linear rate to negative five, negative five, where it increases at a non linear rate to negative two, one and one-half. At two, one and one-half the function decreases at a non linear rate through the origin and to the point two, negative one and one-half. Then the function increases at a non linear rate until five, five, which is plotted.
Choose 1 answer:
(Choice A) The f(x)-values -6, -3, 0, 2, and 5
(Choice B) The f(x)-values -5, -2, 0, 2, and 5
(Choice C) -6 ≤ f(x) ≤ 5
(Choice D) − 5 ≤ f(x) ≤ 5
The range of f include the following: D. -5 ≤ f(x) ≤ 5.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-6, 5} or -6 ≤ x ≤ 5.
Range = {-5, 5} or -5 ≤ f(x) ≤ 5.
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Happy birthday Rainbowww :)
Question: What is the pathagorean therom?
Answer: c=a2+b2
Step-by-step explanation:
x^2+3x=0 what is the gcf
Answer:
gcf is 'x'
Step-by-step explanation:
the common factor to the terms 'x²' and '3x' is 'x'
highway accidents: dui the u.s. department of transportation, national highway traffic safety administration, reported that 77% of all fatally injured automobile drivers were intoxicated. a random sample of 27 records of automobile driver fatalities in kit carson county, colorado, showed that section 8.3 testing a proportion p 479 15 involved an intoxicated driver. do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in kit carson county? use a 5 0.01.
The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.
No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.
The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.
The p value for this test is 0.788, which is greater than the alpha level of 0.01.
The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.
This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.
The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.
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The distance between two cities on a map is 17 centimeters. The scale on the map relates 5 centimeters on the map as 30 miles on the road. What is the actual distance, in miles, between the two cities?
Answer: 102 miles.
Step-by-step explanation:
You divide 17 by 5 and then multiply by 30.
how can the power series method be used to solve the nonhomogeneous equation, about the ordinary point ? carry out your idea by solving the equation. you can either attach your work or type in your work.
The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.
The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.
Assuming that the nonhomogeneous differential equation has the form
y''(x) + p(x)y'(x) + q(x)y(x) = f(x)
where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation
y''(x) + p(x)y'(x) + q(x)y(x) = 0
Using the power series method, we can assume a solution of the form:
y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...
where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.
Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.
After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:
y(x) = u(x) + v(x)
where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.
Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.
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Mack's Toy Shop made 600 trains yesterday and found that 30 were defective. They
plan to make 4,500 trains this week.
Using the information given, how many trains are expected to be defective?
225 trains
6,000 trains
15 trains
500 trains
Answer:
225 trains
Step-by-step explanation:
since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :
600 / 30 = 20/1
one out of 20 is defect.
so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :
4500 / 20 = 225
I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?
Find a degrees. a 12 13 5
In the given triangle, α is equal to 67.36°.
What is a triangle's definition?
A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).
Now,
Using Trigonometric functions
We can use the sine function
So,
Sin α=Perpendicular/Hypotenuse
Sin α = 12/13
α=67.36°
Hence,
The value of α will be 67.36°.
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Enrique has 1 gallon of milk and 1 pint of orange juice in his refrigerator how many cups of milk and orange juice does Enrique have in all
The total cups of milk orange juice Enrique has in refrigerator is equal to 18 cups.
Gallons of milk Enrique has in his refrigerator = 1 gallon
Pint of orange juice Enrique has in his refrigerator = 1 pint
Convert gallons to cups and pint to cups .
There are ,
16 cups = 1 gallon of milk
And 2 cups = 1 pint of orange juice
Enrique has 16 cups of milk
and 2 cups of orange juice.
Total cups of milk and orange juice in refrigerator
=16 cups of milk + 2 cups of orange juice
= 18 cups of milk and orange juice
Therefore, in total Enrique has 18 cups of liquid in his refrigerator.
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A ball is dropped from a height of 32 m.
With each bounce, the ball reaches a
height that is half the height of
the previous bounce. After
which bounce will the ball
rebound to a maximum
height of 25 cm?
URGENT!! Will give brainliest :)
What is the equation for the line of best fit for the following data? Round the slope and -intercept of the line to three decimal places.
A. y=-0.580×+ 10.671
B. y=-10.671 x+ 0.580
C. y= 10.671 x-0.580
D. y= 0.580x - 10.671
To find the equation for the line of best fit, we can use linear regression. Based on the given data:
x: 2, 5, 7, 12, 16
y: 9, 10, 5, 3, 2
The equation for the line of best fit would be in the form: y = mx + b, where m is the slope and b is the y-intercept.
Using a calculator or statistical software, we can calculate the slope and y-intercept for the line of best fit.
The result is:
Slope (m): -0.580 (rounded to three decimal places) Y-intercept (b): 10.671 (rounded to three decimal places)
So, the correct answer is:
A. y = -0.580x + 10.671
Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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To the nearest tenth, the solution to the equation
4,300e^0.07x-123=5,000 is
The solution to the equation 4,300e^(0.07x) - 123 = 5,000 for x is 2.5.
Evaluating the equation for xWe can solve the equation 4,300e^(0.07x) - 123 = 5,000 for x by first adding 123 to both sides and then dividing both sides by 4,300 and taking the natural logarithm of both sides:
Using the above as a guide, we have the following:
4,300e^(0.07x) - 123 = 5,000
4,300e^(0.07x) = 5,123
e^(0.07x) = 5,123/4,300
e^(0.07x) = 1.1914
0.07x = ln(1.1914)
x = ln(1.1914)/0.07
Using a calculator, we get:
x ≈ 2.50
Rounding to the nearest tenth, the solution to the equation is approximately 2.5.
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please someone help and give answers !!!
16.) Mean average deviation= option C
17.) Range of a data set = option E.
18.) First quartile = opinion AB
19.) Second quartile = option B
20.) Third quartile = option A
21.) Interquartile range = option D
How to determine the measures of the spread?
To determine the measures of the spread is to match their various definitions to the correct measures given such as follows:
16.) Mean average deviation: The average deviation of data from the mean.
17.) Range of a data set : The difference between the highest value and the lowest value in a numerical data set.
18.) First quartile: The median in the lower half.
19.) Second quartile: The median value in a data set.
20.) Third quartile: The median in the upper half.
21.) Interquartile range: The distance between the first and the third quartile.
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Type the correct answer in each box. Use numerals instead of words for numbers.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is |
| =
.
The minimum possible diameter of a soccer ball is
, and the maximum possible diameter is
.
Reset
The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
What is equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.
This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.
It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.
Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
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Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
Helping in the name of Jesus.
PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST.
Answer:
Step-by-step explanation:
3x + 18 > 54 solve the inequality? pls help?
Answer:
x > 12
Step-by-step explanation:
3x + 18 > 54
flip a coin three times. you will win $2 for each heads. what is the expected winning (expec- tation of your winning)? a
The expected winning is $2.
To calculate the expected winning, we need to find the probability of each outcome and multiply it by the amount we will win in that outcome.
There are 2 possible outcomes for each coin flip: heads or tails. Therefore, there are 2x2x2=8 possible outcomes for flipping a coin three times.
Here are all the possible outcomes with the number of heads in each outcome:
HHH (3 heads)HHT (2 heads)HTH (2 heads)THH (2 heads)HTT (1 head)THT (1 head)TTH (1 head)TTT (0 heads)The probability of each outcome can be calculated using the formula: probability = (number of favorable outcomes) / (total number of possible outcomes)
For example, the probability of getting 3 heads (HHH) is 1/8 because there is only one favorable outcome out of 8 possible outcomes.
Using this formula, we can calculate the probability and expected winning for each outcome:
HHH: probability = 1/8, expected winning = $6HHT: probability = 1/4, expected winning = $4HTH: probability = 1/4, expected winning = $4THH: probability = 1/4, expected winning = $4HTT: probability = 3/8, expected winning = $2THT: probability = 3/8, expected winning = $2TTH: probability = 3/8, expected winning = $2TTT: probability = 1/8, expected winning = $0To calculate the overall expected winning, we need to add up the expected winning for each outcome multiplied by its probability:
(1/8) x $6 + (1/4) x $4 + (1/4) x $4 + (1/4) x $4 + (3/8) x $2 + (3/8) x $2 + (3/8) x $2 + (1/8) x $0 = $2
Therefore, the expected winning is $2.
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A scale drawing of a famous statue uses a scale factor of 230:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
191.7 feet
228.2 feet
231.2 feet
276 feet
The actual height of the statue is option C 231.2 feet.
What is scale factor?A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.
In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.
Given that the scale factor is 230:1.
Thus,
actual height of statue / 230 = height of drawing / 1.2 feet
Now,
actual height of statue = (1.2 feet / 1.2 feet) * 230
actual height of statue = 230 feet
Hence, the actual height of the statue is option C 231.2 feet.
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of the cartons produced by a company, 3% have a puncture, 6% have a smashed corner, and 1.4% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:
P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)
where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.
Substituting the given probabilities into the formula, we get:
P(puncture or smashed corner) = 0.03 + 0.06 - 0.014
P(puncture or smashed corner) = 0.076
Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.
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please help and explain and show your work on how you got the answer. I WILL MARK YOU BRAINLIEST
Answer:
Step-by-step explanation:
it is -2
Answer: -2
Step-by-step explanation:
So this is asking for the cube root of -8.
This is the same as asking what is multiplied by itself 3 times to get -8.
-2 * -2 *-2 = -8
You can also use a calculator.
Another way to solve it is to write -8^(1/3).
Hope this helps!!!