Using Probability,
The probability that a randomly selected student in the class likes math or English is 11/26.
We have provided the following information,
total number of students in a class = 26
number of students who likes Math = 15
number of students who likes English = 13
number of students who does not likes English or Math = 9
let x be number of students who likes both of subjects .
firstly , we have to find out the value of x i.e total number of students who likes both subjects out of 26 students class .
For this , number of students who likes any one of subjects from both = 26- 9 = 17
but we have total 28 (i.e., 15 + 13 )students who likes Math and English.
so, number of students who likes only Math = 17-15 = 2
number of students who likes only English = 4
then, number of students who likes both subjects
(x) = 26 - 4- 2-9 = 11
randomly one student is selected from the Class,
The probability that a randomly selected student in the class likes math or English = 11/26
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Complete question:
In a class of 26 students: 15 like math, 13 like English, 9 does not like both. What is the probability that a randomly selected student in the class likes math or English?
2^10 times 2^15 is expressed as some integer to the fifth power, what is that integer?
[tex]2^{10}\cdot 2^{15}\implies 2^{10+15}\implies 2^{25}\implies 2^{5\cdot 5}\implies (2^5)^5\implies {\Large \begin{array}{llll} 32^5 \end{array}}[/tex]
For 0 ≤ t ≤ 6 seconds, a screen saver on a computer screen shows two circles that start as dots and expand outwards. 1) At the instant that the first circle has a radius of 9 centimeters, the radius is increasing at a rate of 3/2 cm/sec. Find the rate at which the area of the circle is changing at that instant. 2)The radius of the first circle is modeled by g(t) = 12 - 12e-0.5t for 0 ≤ t ≤ where g(t) is measured in centimeters and t is measured in seconds. At what time t is the radius of the circle increasing at a rate of 3 cm/sec. 3) A model for the radius of the second circle given b the function f for 0 ≤ t ≤ 6, where f(t) is measured in cm and t is measured in seconds. The rate of change of the radius of the second circle is given by f1(t) = t2-4t+4. Based on this model, by how many cm is the radius of the second circle increasing from time t =0 to t = 3?
The rate of change of area is given as 27 π. The time at which radius of circle is increasing is 1.386 sec and change in radius is 3 cm.
What is rate of change?
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another.
a) Given, radius of circle = 9 cm
rate of change of radius = 3/2
We know area of circle = πr^2
change in area =2πrr'
we get 2×π×9×2/3=27π
B) Given,
g(t) = 12 - 12e^0.5t
derivate it
g'(t) =-12×-1/2e^t/2
g'(t)=3
3= 6e^t/2
t = 1.386
c) f1(t) = t2-4t+4.
Integrate it we get
radius =3.
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What is the quotient of x3 1 is divided by x2 x 1?.
The quotient of of x³ + 1 divided by x² - x + 1 is x + 1
Given,
The polynomial function; x³ + 1 and x² - x + 1
We have to find the quotient of x³ + 1 divided by x² - x + 1
Polynomial function;-
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Here,
Divide x³ + 1 by x² - x + 1
x² - x + 1 ) x³ + 1 (x + 1 ⇒ Quotient
x³ - x² + x
0 + 1 + x² - x
0 + 1 + x² - x
0 ⇒ Remainder
That is,
The quotient of of x³ + 1 divided by x² - x + 1 is x + 1
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a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten. what is the probability that the sample contains 1 or more rotten oranges?
The probability that the sample contains 1 or more rotten oranges be, 1/8.
Given, a customer at cavallaro's fruit stand picks a sample of 3 oranges at random from a crate containing 40 oranges, of which 5 are rotten.
we have to find the probability that the sample contains 1 or more rotten oranges,
first we will find the probability that the sample contains no rotten oranges,
P(E) = 35/40
P(E) = 7/8
Now, the probability that the sample contains 1 or more rotten oranges be,
1 - 7/8
P(E) = 1/8
Hence, the probability that the sample contains 1 or more rotten oranges be, 1/8.
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A computer scientist is investigating the usefulness of twodifferent design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are askedto code to code a standard function in both languages, and asked tocode a standard function in both languages, and time (in minutes)is recorded. The data follow:
(a) Is the assumption that the different in coding time isnormally distributed reasonable?
Time
Programmer Design Language 1 Design Language 2
1 17 18
2 16 14
3 21 19
4 14 11
5 18 23
6 24 21
7 16 10
8 14 13
9 21 19
10 23 24
11 13 15
12
18
20
(b) Find a 95% confident interval on the different in meancoding times. Is there any indication that one designlanguages is preferable?
The 95% confidence interval for the mean coding time difference is (-1.2169,2/5502) one design language is better than another.
Given that,
A computer scientist is looking into how two different design languages may make programming chores better. Twelve experienced programmers who are fluent in both languages are given the task of creating a standard function in each language, and the time taken (in minutes) is recorded.
We have to identify the 95% confidence interval for the mean coding time difference. Is there any evidence that one design language is better than another.
We know that,
The attached file's histogram demonstrates that the distribution of differences is roughly normal.
It follows that the distribution must be regular.
The 95% confident level for μ=μ₁-μ₂
We get,
=d±t(S/√n)
=0.666667±2.201(2.964436/√12)
=0.666667±2.201(0.85576)
=0.666667±1.883525474
We get (-1.2169,2.5502)
Therefore, The 95% confidence interval for the mean coding time difference is (-1.2169,2/5502) one design language is better than another.
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What are 4 ways to care for your nervous system?.
The four ways to care for our nervous system are exercise, meditation, proper sleep and healthy food.
There are many ways to care and protect our nervous system. But some of the basics and the most important ways to care for our nervous system are to follow a basic routine which includes regular exercise, practicing meditation daily, having proper sleep for at least seven hours a day and having healthy food mostly.
Now, doing exercise means that we are constantly engaged in some kind of physical activity and healthy food also means to have a balanced lifestyle.
Hence, the four ways to care for our nervous system are exercise, meditation, proper sleep and healthy food.
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Why is ABC congruent to CDA?.
Any two triangles must meet a number of requirements in order for congruence to be established. In order for two triangles to be similar:
The triangles' three corresponding sides must have identical lengths on all three (SSS) The triangles' two matching sides and one corresponding angle must be equal (SAS) The triangles' two comparable angles and one corresponding side must be equal (ASA) Congruence of the right angle and hypotenuse side (RHS)Investigation is required to determine whether the triangles in the preceding diagram, ABC and CDA, are congruent. Considering the diagram
The two triangles share side AC.
Side BC equals Side AD (given)
Angle DAC equals angle ACD (alternate angles as depicted in the diagram)
Therefore, ABC and CDA are congruent because both triangles' two sides and an included angle (SAS) are equivalent.
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The question is incomplete. Completed question is given below;
Based on the given information in the figure at the right, how can you justify that triangle ABC is congruent to triangle CDA?ASA, SSS, AAS, SAS
Figure is attached
the values of the sample mean, sample standard deviation, and (estimated) standard error of the mean are 2.481, 1.611, and 0.294, respectively. does this data suggest that the true average percentage of organic matter in such soil is something other than 3%? carry out a test of the appropriate hypotheses at significance level 0.10. [note: a normal probability plot of the data shows an acceptable pattern in light of the reasonably large sample size.]
True average percentage of organic matter in such soil is different from 3%.
What is Statistics?
Statistics is the study of data collection, analysis, presentation, and interpretation. Much of the early push for the subject of statistics came from government demands for census data as well as information about a range of economic operations.
Solution:
We are given that the values of the sample mean and sample standard deviation are 2.481 and 1.611 respectively.
Suppose we know the population distribution is normal, we have to test the hypothesis that does this data suggest that the true average percentage of organic matter in such soil is something other than 3%.
Let μ = true average percentage of organic matter in such soil
SO, Null Hypothesis : μ = 3% {means that the true average percentage of organic matter in such soil is equal to 3%}
Alternate Hypothesis : μ ≠ 3% {means that the true average percentage of organic matter in such soil is different than 3%}
The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;
TS = (0.02481 - 0.03)/(0.01611)/√30
TS = 4.6% (approx)
Therefore, we conclude that the true average percentage of organic matter in such soil is different from 3%.
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In a recent survey, 78% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 10 of them favor the building of the health center. Use binomial probability distribution formula and write your answer with four decimal places.
The probability that exactly 10 of the citizens favor the building of the health center is;
P(X = 10) = 0.0355
This question is a binomial probability distribution question that takes the formula;
P(X = x) = ⁿCₓ * pˣ * q⁽ⁿ ⁻ ˣ⁾
Where
p = chance of success
q = chance of failure
n = number of trials
We are given;
p = 78% = 0.78
q = 1 - 0.78 = 0.22
n = 14
Thus, probability that exactly 10 of them favor the building of the health center is;
P(X = 10) = ¹⁴C₁₀ × 0.78¹⁰ × 0.22⁽¹⁴ ⁻ ¹⁰⁾
P(X = 10) = 182× 0.78¹⁰ × 0.22⁴
P(X = 10) = 0.0355
Therefore, the probability that exactly 10 of the citizens favor the building of the health center is;
P(X = 10) = 0.0355
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Which graph is not a function?.
The graphs with consist of nonuniform points are not functions.
Given that,
To determine which graph is not a function.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here,
The only graph that cannot be a function, whose expression is not able to be determined, one example is that points are drawn non-uniformly and do not have a relation with each other, that type of relationship is not a function on a graph.
Thus, the graphs with consist of nonuniform points are not functions.
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7.81 for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
The maximum absolute values of the shear and bending moments are
Cy = 1800 lbs
Ay = 4800 lbs
Max absolute BM = 14400 lbs-feet
Given,
Draw the shear and bending moment diagrams for the beam and the indicated loading, and then figure out the highest absolute values of the shear and bending moment.
(a) The shears and bending-moment diagrams,
Ay + Cy = 800 * 9 - 600
Ay + Cy = 6600 lbs
Ay
∑Ma = 0
Cy * 15 + 600 * 9 = 800 * 9²/2
Cy = 1800 lbs
Ay = 4800 lbs
(b) Determine the maximum absolute values of the shear and bending moment,
Map absolute B.M:
Map positive B.M occurs, when SF = 0 is at 'x'
4800 - 800x = 0
x = 6ft
Positive map = 4800 * 6 = 800 * 6²/2
Max absolute BM = 14400 lbs-feet and it developed at 6ft from support A.
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the following for loop calculates the amount of money in a savings account after numberyears given an initial balace of savingsbalance and an annual interest rate of 2.5%. complete the for loop to iterate from 1 to numberyears (inclusive).
The loop will be written in Matlab.
Simply setting the years' range will allow the for loop to run its course and complete the task. To allow the loop to iterate from 1 to the number of years, we add the expression 1:number years.
function savingsBalance = CalculateBalance(numberYears,savingsBalance)
% numberYears: Number of years that interest is applied to savings
% savingsBalance: Initial savings in dollars
interestRate = 0.025;
% 2.5 percent annual interest rate
% Complete the for loop to iterate from 1 to numberYears (inclusive)
for n = 1:numberYears
savingsBalance = savingsBalance + (savingsBalance * interestRate);
end
end
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a bottle of lemonade normally contains 400 ml. special edition bottles have 10 % extra free. how much lemonade is in the special edition bottles?
Answer:360ml
Step-by-step explanation:
400/10=10%=40
400-40=360ml
What are 3 materials that do not conduct electricity?.
Plastic, wood, and rubber are the three materials that do not conduct electricity.
Conductors are materials that conduct heat or electricity. Insulators are the materials that do not allow to conduct heat or electricity.
Electrical insulators are materials that do not allow to pass electricity through them.
Glass, wood, rubber and plastic are examples of these materials. Air also acts as an insulator.
Thus,these non-conductors/insulators are useful in a variety of applications.
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A right-angled triangle and three equations are
shown below.
Give your answer in degrees to 1 d.p.
The correct equation is tan θ = 6 / 13, and the value of angle θ will be 24.775°. Then the correct option is C.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The right-angle triangle is shown below.
The length of the perpendicular is 6 cm and the length of the base is 13 cm. Then the angle θ is written as,
tan θ = P / B
tan θ = 6 / 13
Simplify the equation to get the value of the angle θ will be given as,
tan θ = 6 / 13
tan θ = 0.4615
θ = 24.775°
The correct equation is tan θ = 6 / 13, and the value of angle θ will be 24.775°. Then the correct option is C.
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The length of a certain insect is 7/8 inches. What is length of the tail if it's half the insects total length
The length of the tail if it's half the insects total length as described in the task content is; 7/16 inches.
What is the length of the tail of the insects?It follows from the task content that the length of the tail of the insect whose length is as given is to be determined.
Since the given length of the insect is; 7/8 inches.
Also, the tail of the insect is half the insects to tak length.
Consequently, the expression which holds true for the length of the tail is;
(1/2) × (7/8)
= 7/16.
The length of the insect's tail is therefore; 7/16 feet.
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Maura's driveway has an angle of depression of 40 degrees from the flat roadway. If it levels off to the garage floor, which is 3 meters below the roadway, how long is the driveway and how far into the lot is the garage?
Maura's driveway is 4.7 meters long and the distance from the garage into the lot is 3.6 meters
How to determine the length of the drive wayThe length of Maura's drive way is solved using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The information in the question describes a right angle triangle of
opposite = 3 meters
adjacent = distance into the lot = ?
hypotenuse = Maura's drive way = ?
angle of depression = 40
The length of the drive way
sin 40 = 3 / hypotenuse
hypotenuse = 3 / sin 40
hypotenuse = 4.667 m
The distance from the garage to the lot
tan 40 = 3 / adjacent
adjacent = 3 / tan 40
adjacent = 3.575 m
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(a) Strawberries cost $4.20 per kilogram and cream costs $8.56 per litre. Venus buys 1.2 kg of strawberries and 125 ml of cream. Work out the total cost.
which measure captures the variation in ressponses? multiple choice the frequency distribution the median the mode the standard deviation the mean
the measure that captures the variation in responses is mean and it is the weighted average
What is the meaning of mean in math?
In mathematics and statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean.
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use the distance formula and algebra to show that the set of all points (x, y) that are equidistant from the point (f, k) and the line x
We have proved that the set of all points (x, y) that are equidistant from the point (f, k) and the line x.
What is a parabola?
A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
That’s a parabola in the usual orientation. y=1 is the directrix. (f, k) is the focus. Squared distance, as usual, is the fundamental quantity.
If (x,y) is a point in the set, the squared distance to y=1 is (y−1)². The squared distance to (f, k).
(y - 1)²=(x - f)²+(y - k)²
Hence, we can say that the set of all points (x, y) is equidistant from the point (f, k) and the line x.
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calculate the percentage of 2000 and 50000
The percentage of 2000 from 50000 is 4%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
The percentage of 2000 from 50000 will be:
= 2000/50000 × 100
= 4%
The percentage is 4%.
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aplicarán 6/3 kg de Nitrógeno, 2/5 kg de Fósforo y 6/4 kg de Potasio. ¿Cuál es la cantidad total de fertilizante que se aplicará?
Addition of the fractions showed that the total amount applied is 39/10 kg
Addition of FractionsThe addition of fractions is a little different from the normal addition of numbers since a fraction has a numerator and a denominator which is separated by a bar. The addition of fractions can be easily done if the denominators are equal. While like fractions have common denominators, unlike fractions are converted to like fractions to make addition easier.
In this case, we simply need to add the fraction of nitrogen, phosphorous and potassium.
This becomes;
6/3 + 2/5 + 6/4 = 2 + 2/5 + 3/2 = 39/10 = 3.9kg
The amount added is 39/10kg or 3.9kg
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Translation: 6/3 kg of Nitrogen, 2/5 kg of Phosphorus and 6/4 kg of Potassium will be applied. What is the total amount of fertilizer to be applied?
the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base. find the altitude.
If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch
The area of a triangle is 96 sq. inches
Let base be b
Its altitude is 2 inches greater than five times its base.
a=5b+2
ab/2=A
(5b+2)b/2=96
(5b+2)b=192
5b²+2b=192
5b²2+2b-192=0
On solving the quadrartic equation,
we get
b=6
a=32
Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs
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Solve; round to the nearest hundredth.
a 2x² = 24
b x² - 4 = 14
Answer:
Step-by-step explanation:
a
2/2 x^2 = 24/2
x^2 = 12
x = √12
x = 3.464102 = 3.46
x = -√12 = -3.46
b
x^2 = 14 + 4
x^2 = 18
x = √18
x = 4.242641 = 4.24
x = -√18 = -4.24
What is the rule of obtuse angle?.
The rule of obtuse angle is that one angle measures more than 90° and total sum og angle should be 180°.
How many angles are there in total?Acute, obtuse, right, straight, reflex, and complete rotation are some of the terms used to describe fundamental angles. Two rays are joined at their termini to form the geometric shape known as an angle. The most common way to express an angle is in degrees.
What does the word "angle" mean?A measure of an angle or the amount of turning required to bring one line or plane into coincidence with or parallel to another angled is represented by two lines extending from the same point.
A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.
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Kilometer and inche are ome meaurement ued to meaure length. What are ome other unit ued to meaure length
Some other measurements used to measure length are meter, centimeter millimeter, decameter, decimeter, hectometer, foot, etc
What is length of an object?
Length of an object is the distance between one end point to another end point of the object.
The concept of length is a very important tool in mathematics, especially in geometry and mensuration. Concept of length is very important in physics also
Kilometer and inches are some measurements used to measure length.
Some other measurements used to measure length are meter, centimeter millimeter, decameter, decimeter, hectometer, foot, micrometer, nanometer, angstrom, picometer, Fermi, etc
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yang company sold merchandise for $4,000. the event is subject to a state sales tax of 9%. based on this information, yang would be required to
Sales revenue will be recorded at $4,000 and yang Yang would be required to Recognize sales tax liability of $360.
What is sales revenue?
The terms revenue and sales revenue are sometimes used synonymously. However, the concept of revenue includes income derived from sources other than those directly connected to the primary business, such as interest on savings or money distributed as dividends. Revenue comprises income derived from the sale of goods and services. The classification of this is "non-operating income."Sales = $4,000
State sales tax rate = 9%
State sales tax = Sales x State sales tax rate
= 4,000 x 9%
= $360
Sales revenue will be recorded at $4,000 and sales revenue is not affected by the sales tax amount.
Hence, Yang would be required to Recognize sales tax liability of $360.
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A young woman with normal distant vision has a 10. 0% ability to accommodate (that is, increase) the lens strength (a. K. A, lens power) of her eyes. What is the closest object she can see clearly? assume that the lens-to-retina distance of her eye is 2. 00 cm.
The closest object that she is going to be able to see clearly is going to be situated at a distance of 20 cm from her eyes.
Here, it has been given that the lens-to-retina distance of her eye is = 2.00 cm (i)
The normal power for distant vision is 50.00 Dioptres. This woman has the ability to increase lens strength by 10%. The new power for this is going to be -
= P1 = 50.00 + 10% of 50
= P1 = 55.00 D (ii)
Now, the power of a lens, P = 1/f = 1/u + 1/v where f = focal length of the lens, u = object distance from eye lens, and v = image distance from eye lens.
We are aware of the formula = P1 = 1/u + 1/v
Using the values of (i) and (ii) and the formula, we get -
= 1/u = P'- 1/v
= 1/u = 55.0 D - 1/0.02 m
= 1/u = 5.0 m⁻¹
= u = 1/5.0 m⁻¹
= u = 20 cm
Hence, we have found out that the woman can see objects at a distance of 20 cm.
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The resale value R (in dollars) of a particular type of laser cutting tool t years after its initial purchase is approximated by R(t) = 550,000e^0.22t Find and interpret the rate at which the resale value is changing. a. What is the decay rate of the resale value? -121000e^(-, 22t) b. 10 years after the initial purchase. R'(10) = -13407.18 c. 20 years after the initial purchase. R' (20) = -1485.56
The decay rate for the resale price of laser cutting tool will be -121000[tex]e^{-0.22t}[/tex]
Let R is the resale value of a particular type of laser cutting tool after years
Where, R(t) = 550000[tex]e^{-0.22t}[/tex]
Rate at which the resale value is changing will be dR/dt = 550000[tex]e^{-0.22t}[/tex](-0.22)= -121000[tex]e^{-0.22t}[/tex]
Initial value of the laser cutting tool, at time ‘t’ =0 will be 550000[tex]e^{-0.22t}[/tex]x0 = 550000
At time ‘t’ resale value is 550000 [tex]e^{-0.22t}[/tex]
Therefore, the decay in resale price = 550000 - 550000 [tex]e^{-0.22t}[/tex]
Therefore, the decay rate = (550000 - 550000 [tex]e^{-0.22t}[/tex])/t = 550000(1-[tex]e^{-0.22t}[/tex])/t
As we have dR/dt = R’ = -121000[tex]e^{-0.22t}[/tex]
Therefore, R’(10) = -121000[tex]e^{-2.2}[/tex] = -13407.18
Therefore, after 10 years the resale price will be -13407.18
R’(20) = -121000[tex]e^{-4.4}[/tex]= -1485.55
Therefore, after 20 years the resale price will be -1485.55
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What is the experimental probability of rolling a single die ten times and landing on 6?
The experimental probability of landing on a 6 is 1/10.
What is the probability?Probability is used to calculate the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Result of the experiment:
Face Frequency
1 2
2 1
3 0
4 5
5 1
6 1
Probability of landing on a 6 = 1 /10
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