If three bulbs are randomly selected, the probability that a) exactly 2 are 23 watts is 0.136, the probability that b) all are of the same type is 0.542 and c) there will be one bulb of each type is 0.244.
Here we have been given that out of 23 bulbs,
8 are 13 watt
9 are 18 watt
6 are 23 watt
now if three bulbs are randomly selected out of these, it can be done in
²³C₃ ways
a)
There are 6, 23 watts, and 17 bulbs that are not 23 watts.
Hence they can be chosen in
⁶C₂ X ¹⁷C₁ ways
Therefore the probability to get exactly 2 23 watt bulbs is
[⁶C₂ X ¹⁷C₁]/²³C₃
= [6 X 5 X 17 X 3 X 2]/[2 X 23 X 22 X 21]
= [3 X 5 X 17]/[23 X 11 X 7]
= 240/1771
= 0.136
b)
The probability that all three bulbs are of the same type will have three cases. Hence they can be selected in
⁸C₃ + ⁹C₃ + ⁶C₃ ways
Hence the probability will be
[⁸C₃ + ⁹C₃ + ⁶C₃]/²³C₃
= [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)](3 X 2)/[23 X 22 X 21]
= [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)]/[23 X 11 X 7]
= [336 + 504 + 120]/1771
= 960/1771
= 0.542
c)
The probability to select one bulb of each type will be
[8 X 9 X 6]/²³C₃
= [8 X 9 X 6]/[23 X 11 X 7]
= 432/1771
= 0.244
d) Now if at least 6 bulbs need to be examined, hence
the probability will be 1 - probability that we need to check (1, 2, 3, 4, 5)
= 1 - (¹⁷C₀/23 + ¹⁷C₁/²³C₂ + ¹⁷C₂/²³C₃ + ¹⁷C₃/²³C₄ + ¹⁷C₄/²³C₅)
= 1 - (1/23 + 17/253 + 136/1771 + 136/1771 + 340/4807)
= 0.66
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Complete Question
A box in a supply room contains 23 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 6 are rated 23-watt. suppose that three of these bulbs are randomly selected. (round your answers to three decimal places.)
(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?
(b) What is the probability that all three of the bulbs have the same rating?
(c) What is the probability that one bulb of each type is selected?
(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?
If f(x)= 2*, find and simplify (i) f(x²)ƒ(1)
The value of given function is (i) f(x²) = 2*x² and (ii) f(1) = 2*1 = 2.
What does the mathematical term "function" mean?A function is a link or expression that contains one or more variables. There is a collection of inputs and outputs.
A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A function is typically referred to as f(x), where x is the input.
Applications of functions include population, distance traveled, and discovering profit. When using functions, one enters a number into the formula or locates the independent variable on a table or graph before computing the dependent variable that results.
(i) f(x²) = 2*x²
(ii) f(1) = 2*1 = 2
So, f(x²) = 2*x² and f(1) = 2
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The length of a new rectangular playing field is 4 yards longer than triple the width. If the perimeter of the rectangular playing field is 416 yards, what are its dimensions?
Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:
l = 3w + 4 (the length is 4 yards longer than triple the width)
We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:
P = 2l + 2w
We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:
416 = 2(3w + 4) + 2w
Simplifying and solving for w:
16 = 6w + 8
8 = 6w
w = 8/6 = 4/3
We can now substitute that back into the equation for the length:
l = 3w + 4
l = 3(4/3) + 4
l = 4 + 4
l = 8
So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.
Step-by-step explanation:
(x+5)(x-7) expand and simplify
The expansion gives x² - 7x + 5x - 35
It is simplified to x = -5 and x = 7
What is an algebraic expression?An algebraic expression can be described as an expression that is comprised of terms, factors, constants, coefficients and variables.
They are also known to be made up of mathematical operations, such as;
DivisionBracketParenthesesFloor divisionAdditionSubtractionMultiplicationFrom the information given, we have that;
(x+5)(x-7)
Now, expand the bracket
x² - 7x + 5x - 35
factorize in pairs
(x² - 7x) + (5x - 35)
factor the common terms
x(x - 7) + 5(x - 7)
then,
x = -5 and x = 7
Thus, the expansion is x² - 7x + 5x - 35
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Which expression is a factor of -2x2 - 11x - 20
No real Factors
(2x + 10)
(x - 10)
(2x - 5)
The given expression will not have real factors. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the quadratic expression is -2x² - 11x - 20. The expression will be solved as below:-
E = -2x² - 11x - 20
Apply the quadratic factorization formula,
x = [ -b ± √( b² - 4ac ) ] / 2a
x = [ 11 ± √ ( 121 - ( 4 x - 2 x - 20 ) ] / ( 2 x - 2 )
x = [ 11 ± 39i } / -4
The roots of the quadratic equation are not real.
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Answer:
no real factors
Step-by-step explanation:
i took the test
What basic trigonometric identity would you use to verify that ?
Question 20 options:
The identities in verifying the trigonometric expression sinx cosx tanx=1-cos^2x include:
tanx = sinx/cosx
sin^2x+cos^2x = 1
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.
Anytime trigonometric functions are used in an expression or equation, trigonometric ifentities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity holds true. These trigonometric functions (such as sine, cosine, and tangent) of one or more angles are involved geometrically in these identities.
Based on the question, tanx = sinx/cosx and sin²x+cos^²x = 1 are applicable.
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What basic trigonometric identity would you use to verify that sinx cosx tanx=1-cos^2x
Sample Questions Chapters 3, 12, 13, 14. All of the following contribute to the success of incumbent members of Congress n election campaigns EXCEPT Incumbents.
All of the following contribute to the success of incumbent members of Congress n election campaigns EXCEPT Incumbents tend to understand national issues better than do their challengers.
What does the term incumbent mean?The term "incumbent" has several meanings depending on the context, but it generally refers to someone who holds a particular position or office. The most common usage of this term is in the context of politics, where an incumbent is the current holder of a political office, such as a president, governor, or member of Congress. An incumbent candidate is the candidate who is currently holding a political office and is running for re-election.
In other fields, the term incumbent is used to describe someone who holds a particular job, position or role and is responsible for certain tasks or duties, for example an incumbent employee, an incumbent contractor, an incumbent provider, etc.
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Complete question not found
At a family reunion, each of Shamar's aunts and uncles is getting photographed once. The aunts are taking
pictures in groups of 5 and the uncles are taking pictures in groups of 10. If Shamar has the same total number
of aunts and uncles, what is the minimum number of aunts that Shamar must have?
The minimum number of aunts that Shamar must have based on the information provided is 10.
What are the possible number of uncles and aunts?It is known that uncles will take a photograph in groups of 10, while aunts will take a photograph in groups of 5. Based on this, the possible number for each are:
Uncles: 10, 20, 30, 40, 50
Aunts: 5, 10, 15, 20, 25
How to find the minimum number of relatives?In this case, the minimum number is the LCM or Least Common Multiple and based on the previous list, this number is 10.
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wood block pulled along a wooden surface at an angle moving at constant velocity what is tension on teh rope
The work done by the force of friction is μmgd.
The work done by the applied force is equal to the displacement of the block (d) multiplied by the component of the force parallel to the displacement. If the applied force is F and the angle between the force and the displacement is θ, then the component of the force parallel to the displacement is Fcos(θ).
Therefore, the work done by the applied force is given by dFcos(θ). The force of friction will also do work, which is equal to the displacement of the block multiplied by the force of friction. The force of friction is given by μN, where N is the normal force and is equal to the weight of the block (mg). Therefore, the work done by the force of friction is μmgd, where d is the displacement.
Correct Question :
A block of mass m is pulled along a horizontal surface by applying a force at an angle θ with the horizontal. If the block travels with a uniform velocity and has a displacement d and the coefficient of friction is μ, then the work done by the applied force is?
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mathematical models allow researchers to make different predictions by varying assumptions. which of the following parameters was an assumption varied by lima, valone,
Fitness increases with energy intake rate was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying
Now, According to the question:
A parameter is used to describe the entire population being studied. For example, we want to know the average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.
Fitness increases with energy intake rate varied by Lima, Valone and Caraco (1985) in their model of squirrel food carrying.
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The given question is incomplete, complete question is:
Mathematical models allow researchers to make different predictions by varying assumptions. Which of the following parameters was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying?
estimate the distance (in mi) the race car traveled during this time period using the velocities at the beginning of the time intervals
The distance the race car traveled during this time period using the velocities at the beginning of the time intervals is 23.886 mi
Use areas of rectangles to approximate the area under the curve. The width of each rectangle is 10 sec = 1/36 hrs and the lengths are the velocities.
LH = 1/36 ( 183.9 + 167 + 107.6 + 98.8 + 125.5 + 177.1)
LH=1/36(862.9)
LH≈ 23.886 mi
To find the right-hand approximation:
RH = 1/36 (167 + 107.6 + 98.8 +125.5 +177.1 + 176.6)
RH=1/36(852)
RH≈ 23.683 mi
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3) Six of the students in Ms. Collier's class play an
instrument. These six students make up 20% of
the class. How many students are in the class?
the 3x3x3 cube consists of 27 small cube.s some of the small cubes are removed. if you now look at the cube from the right, from above and from the front, you see the following: how many little cubes were removed?
The little cubes can be possible to remove in number of 18 cubes maximum.
What is cube ?
A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids.
The original surface area is (3x3) x 6 = 54 units.
A unit cube has 6 units of area, so we need 9 cubes.
Remove all the cubes except the original eight corners and the center cube.
The 3×3×3 cube has a surface area of 6×3×3 square units. Taking the 27 smaller units and connecting them to form a single entity, the maximum exposed surface area per cube is 6 square units. If nine of these are connected vertex to vertex in any shape then the objective is achieved. So a maximum of 18 of the small cubes can be removed.
Hence , The little cubes can be possible to remove in number of 18 cubes maximum.
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write a division story for 40 divided by 4. draw a bar diagram to represent your story. then solve.
Graphs are used to represent information in bar graphs. Students can solve problems and comprehend relationships between quantities by using bar graphs to show such relationships.
What is bar diagram example?To produce powerful problem-solvers, bar graphs were created!One unknown quantity that students must find is often included in problems that have two known quantities.Students can solve problems and comprehend relationships between quantities by using bar graphs to show such relationships.Graphs are used to represent information in bar graphs.To represent value, it uses bars that reach varying heights.Bar graphs can be produced using stacked, horizontal, grouped, or vertical bars to compare results in many categories (bars containing multiple types of information).Data with just one variable and classifications on a spatial, quantitative, or temporal basis are shown using a straightforward bar chart.
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The World Future Society predicts that by the year 2020, airplanes will be able to carry 1400 passengers. Today’s biggest jets can carry 600 passengers. What will be the percent of increase of airplane passengers? nearest percent
To calculate the percent increase in airplane passenger capacity, we first need to find the difference between the current capacity (600 passengers) and the predicted future capacity (1400 passengers).
1400 - 600 = 800
Then divide this difference by the current capacity, and multiply by 100 to express the answer as a percentage.
(800/600) * 100 = 133.33
So the predicted percent increase in airplane passenger capacity is approximately 133%.
The nearest percent is 133%.
6. How can you be certain that the angles you have created form a square inside the circle? (4
points for a thorough explanation)
To be certain that the angles created form a square inside a circle, it is important to first understand the properties of a square and a circle.
How to sure that Angles created form a Square inside a Circle?A square is a four-sided polygon with all sides of equal length and all angles of 90 degrees. This means that if we draw a square inside a circle, the four corners of the square should be tangent to the circle.
A circle is a shape with all points on the circumference equidistant from the center. This means that if we draw a square inside a circle, the distance from the center of the circle to the midpoint of each side of the square should be equal to the radius of the circle.
By verifying that the above two conditions are met, we can be certain that the angles created form a square inside the circle. Additionally, we can also check that all the four angle of the square is 90 degrees and the opposite sides are parallel.
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different between foreign policy during Tewodros,Menelik,and Yohannes and emperor Haileselassie
During the first eighteen years of his rule, he spent most of his time defending his nation against attacks from Egypt, Italy, and the Mahdists.
What was Ethiopia's foreign policy under Emperor Yohannes? During the first eighteen years of his rule, he spent most of his time defending his nation against attacks from Egypt, Italy, and the Mahdists.Through the use of compromise and power-sharing, Yohannes was largely successful in pacifying the nation and growing his kingdom.In order to strengthen his kingdom and forward his reforms, he devised a daring foreign strategy in 1861.Queen Victoria of Great Britain was offered an alliance by Tewodros in 1862 to eradicate Islam.When the British rejected the plan, Tewodros imprisoned the British envoy and other Europeans. Tewodros waited for an answer but never received one.The Derg dictatorship was able to act in the same way because Haile Selassie's foreign policy for Ethiopia was essentially intended to keep him in power.To learn more about foreign policy refer
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the quotient of ten less than negative four and negative one half
Answer:
Step-by-step explanation:
28
3 less than triple a number results in 42. Find the number.
Answer:
14
Step-by-step explanation:
let the number be x
3x=42
x=42/3
=14
if 348 prospective college students are tested for their iq (assume normal distribution) approximately how many students' iq scores will be within either two standard deviations away from the mean (i.e 2 and -2)
Answer:
330 approximately.
Step-by-step explanation:
The percentage lying between 2 standard deviations is 95%.
So we have 348 * 0.95 = 330 approximately.
let abcd be a regular tetrahedron and m,n distinct points in the planes abc and adc respectively. show that the segments mn,bn,md are the sides of a triangle.
The segments MN, BN, and MD are the sides of a triangle.
Let AM intersect BC at point P and let AN intersect CD at point Q. Spin A about PQ to obtain E where AE = AB. We want to prove that EMN is the required triangle. For that, it is adequate to show that EM = MD and EN = BN.
Let h be the distance of A from the BCD. Then the distance of A from the line PQ is minimum h, so point E exists provided that the side length maximum is 2h. It is √(3/2) h.
We have by construction AD = AE and EP = AP. Also, since P lies on the line BC, then PA = PD. Hence PA = PA, PD = PE, AD = AE, so PAD and PAE are congruent triangles. Hence E can also be acquired by spinning D about AP. Since M lies on AP, it gives EM = DM.
Similarly, with B and D interchanged and M and N interchanged, we get EN = BN.
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The second bus company that Ms. Baudy contacted wanted to charge each student $5.00 for
roundtrip service. If the total price of the trip per student was $7.00, approximately what
percentage of the trip would go towards the price of the bus?
If the total price of the trip per student was $7.00, approximately the percentage of the trip that would go towards the price of the bus is 71.43%.
What is the percentage?The percentage is the ratio of a variable or value to another.
Percentages are fractional values, computed as the quotient of a numerator over a denominator multiplied by 100.
The bus roundtrip charge per student = $5.00
The trip price per student = $7.00
Percentage of the trip going towards the price of the bus = 71.43% ($5/$7 x 100).
Thus, we expect that 71.43% of the trip amount will be consumed for the bus charter.
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Show me 2/4 comparing 5/8 on a number line
Using a number line, the number 5/8 is greater than 2/4
How to compare the numbers on a number lineFrom the question, we have the following parameters that can be used in our computation:
Comparing 2/4 and 5/8 on a number line
Here is a number line that shows the comparison of 2/4 and 5/8:
1/2 2/4 3/4 5/8 3/4 2/4 1/2
--|---------|---------|---------|---------|---------|--
As you can see, 2/4 is located halfway between 1/2 and 3/4, while 5/8 is located halfway between 3/4 and 3/4.
Therefore, 5/8 is larger than 2/4.
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please help will mark BRAINLIEST
Answer:
90
Step-by-step explanation:
the bottom of the picture is cut off but it's 90°
becuase the picture shows you the 2 sides of the triangle r equal
the angles on the top are also equal
so that means the middle line has to be perpendicular to the base.
so Y is 90
terry is post-mastectomy from breast cancer. sadly, she has now found out that the cancer has metastasized to her parietal lobe of her brain. report the brain cancer with code:
The brain cancer with code is secondary malignant neoplasm of brain. So the option 3 is correct.
Some women experience persistent nerve pain (neuropathic pain) in the arm, armpit, or chest wall following breast cancer surgery. Due to the fact that it was originally identified in women who had mastectomies, this is known as post-mastectomy pain syndrome (PMPS), but it can also occur following other forms of breast-conserving surgery.
According to studies, 20% to 30% of women experience PMS symptoms following surgery. It most frequently occurs following procedures that remove tissue from the underarm or upper outer region of the breast.
It is crucial to discuss any pain you are experiencing with your doctor. You might not use your arm as you should because of PMPS, and eventually you might stop being able to use it normally.
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The complete question is:
Terry is post-mastectomy from breast cancer. Sadly, she has now found out that the cancer has metastasized to her parietal lobe of her brain. Report the brain cancer with code:
1. Benign neoplasm of brain, supratentorial
2. Malignant neoplasm of parietal lobe
3. Secondary malignant neoplasm of brain
4. Neoplasm of uncertain behavior of brain, supratentorial
Macmillan Learning
Assume the Pacific Ocean has a surface area of 1.5 x 108 km² and an average depth of 3700 m.
Calculate the volume of water in the ocean in liters:
5.6 x 10¹2 L
5.6 x 10¹7 L
O 5.6 x 10¹¹ L
5.6 x 10^20 L
The volume of water in the ocean in litters, 5.6 x 10¹¹ L.
How do you calculate the size of the Pacific Ocean?In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms. The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.
The area of the final shape, or the height and depth of the prism or cylinder, is the basic formula for prisms' and cylinders' volumes.
In reality, the area of one side multiplied by the depth or height of the design yields the volume of cylinders and prisms.
Volume is calculated as Area x Depth.
1.5 × 108/3700 = 5.6 x 10¹¹ L.
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Solve for x and y.
2x - (5-x) = 3x + 2(x-7)
Answer:
[tex]x= \cfrac{9}{x}[/tex]Step-by-step explanation:
[tex]2x - (5-x) = 3x + 2(x-7)[/tex]
[tex]3x-5=3x+2(x-7)[/tex]
[tex]-5=2(x-7)[/tex]
[tex]-\cfrac{5}{2} =x-7[/tex]
[tex]-\cfrac{5}{2}+7=x[/tex]
[tex]-\cfrac{9}{2}=x[/tex]
[tex]x= \cfrac{9}{x}[/tex]
A cross between a plant with flowers and a plant with white flowers yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plant? Explain
The genotype must be Rr and rr because the outcome is close to the 1:1 ratio of red to white flowering plants.
What is meant by Law of Dominance?According to Mendel's law of dominance, one feature in a heterozygote will mask the existence of another trait for the same attribute. The dominant allele will be exclusively expressed, as opposed to both alleles contributing to a trait.
When parents with distinct, opposing qualities are crossed, only one form of the trait manifests itself in the offspring, according to Mendel's law of dominance. Only the dominant phenotypic characteristic will be present in the hybrid offspring. The first law of inheritance is the dominance principle.
This regulation states that the first generation of offspring from purebred parents shall exhibit solely dominant features.
There will be a 1:1 ratio between the dominant and recessive traits when a heterozygous dominant parent mates with a pure recessive parent.
The cross:
r r
R Rr Rr
r rr rr
The genotype must be Rr and rr since the outcome is close to the ratio of red to white flowering plants.
Therefore, the correct answer is option A. The result is close to the 1:1 ratio of red to white flowering plants, so the genotype must be Rr and rr.
The complete question is:
A cross between a plant with red flowers (R = dominant) and a plant with white flowers (r = recessive) yielded 47 plants with red flowers and 51 plants with white flowers. What are the genotypes of the parent plants? Explain
A. The results are close to a 1:1 ratio of plants with red flowers to plants with white flowers. Therefore, the genotypes of the Rr and ir
B. The results should yield plants with red flowers and plants with white flowers in a 3:1 ratio due, so the genotype of each parent is Rr. The number of offspring was not large enough to produce the expected results
C. The results differ from the predicted values. Therefore, the genotypes of the parents cannot be determined.
D. The results should show a ratio of 3 plants with white flowers to 1 plant with red flowers, so the genotypes of the parent plants are RR and rr.
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20 people fit comfortably in a 10 feet by 10 feet area. Use this value to estimate the size of a
crowd that is 7 feet deep on ONE side of the street along a 1 mile section of a parade route.
The size of the crowd is 7392 people.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
20 people fit comfortably in a 10 feet by 10 feet area.
So,
the ratio of the number of people per unit area = 20/(10 × 10) = 20/100 = 1/5
The area, A, occupied by the crowd = 7 feet × 1 mile × 1
1 mile = 5280 feet
A = 7 feet × 5280 feet × 1 = 36960 feet².
Now, number of people = 36960 x 1/5
= 7392 people.
Therefore, the required value is 7392 people.
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Joe’s garden hose fills the pool in hours. His neighbor has a thinner hose that fills the pool in hours. How long will it
take to fill the pool using both hoses?
The length of time it would have taken for both garden hoses to fill the pool would be 6.67 hours.
How to find the time taken ?To solve this problem, we can use the formula:
1/rate = time
In the case of Joe's hose, the rate is 1/12 of the pool per hour. For his neighbor's hose, the rate is 1/15 of the pool per hour.
So, the combined rate is:
= (1/12) + (1/15)
= (5/60) + (4/60)
= 9/60 of the pool per hour
So, the time it will take to fill the pool using both hoses is:
= 1 / (9/60)
= 60/9 hours
= 6.7 hours
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The full question is:
Joe's garden hose fills the pool in 12 hours. His neighbor has thinner hose that fills the pool in 15 hours. How long will it take to fill the pool using both hoses?
the base of a certain solid is the region r. cross sections through the solid taken perpendicular to the x-axis are squares. an integral that expresses the volume of the solid is:
The integral[tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid, where f(x) is the side length of the square cross sections taken perpendicular to the x-axis in the region r.
The given integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid whose base is the region r. The integral is calculated by taking the cross sections of the solid perpendicular to the x-axis and consider them as squares. The side length of each square is denoted by f(x). The integral is calculated over the region r, which is the base of the solid. This integral is the sum of the areas of all the squares, which is equivalent to the volume of the solid. The integral is calculated by taking the lower limit of integration as[tex]$-\infty$[/tex] and the upper limit of integration as[tex]$\infty$[/tex]. Hence, the integral [tex]$\int_{-\infty}^{\infty} f(x)^2 dx$[/tex] expresses the volume of the solid with the base region r and square cross sections.
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