The first 8 prime numbers that occur are as given below in the lis
2, 3, 5, 7, 11, 13, 17, 19,The prime numbers can be referred to or concentrated as such numbers, which are whole number s but are divisible only by 1 and the number itself. The list given above contains the numbers which are not only prime but are also divisible only by one and the number themselves. The list given above contains such numbers which are divisible as per the conditions of prime numbers. Therefore, the significance regarding prime numbers has been aforementioned in the given list.
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Is rational number are closed under addition True or false?.
The rational numbers are closed under addition. The answer is True.
What is a rational number?Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.
Consider two rational numbers a/b and c/d.
The addition of the two numbers is:
a/b + c/d
= (ad + bc)/bd
Now, (ad +bc) and bd are again an integer, therefore, let p = (ad +bc) and q = bd, then
(ad + bc)/bd
= p/q, Which is again a rational number.
Hence, the rational numbers are closed under addition. The answer is True.
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we have an urn with 10 balls numbered from 1 to 10. we choosea sample of 111 with replacement. approximate the probability of the event thatthe number one appears at most 3 times in the sample. use both the normaland the poisson approximation, and compare the results with the exact probability0:000949681
The exact probability is less than probability using Poisson distribution is less than probability using normal distribution.
Given that,
10 balls, numbered from 1 to 10, are in an urn. We selected a 111-person sample with replacement.
We have to calculate the probability that the number one appears in the sample no more than three times. Compare the outcomes with the precise probability using both the normal and the Poisson approximations. 0:000949681
We know that,
Let
X= number of times that 1 appears in a sample
Probability of getting 1 =1/10=0.1
Then X congruent to Binomial (111,0.1)
Now,
If we approximately X is Poisson distribution with parameter
λ=111 ×0.1=11.1
Then
P(X≤3)=∑x=0 to 3 e⁻¹¹°¹(11.1)ˣ/x!
P(X≤3)= 0.004558534
If we approximate X by Normal distribution with mean
μ=111 ×0.1=11.1
σ=√111 ×0.1×0.9= 3.160696 then
P(X≤3)=0.005192688
Exact probability is
P(X≤3)=0.003275558
Therefore, The exact probability is less than probability using Poisson distribution is less than probability using normal distribution.
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HELP ME PLEASEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
what about this question do you find difficult ?
point P1 (3,-2) in the form (x1,y1)
slope = m = 4
y - y1 = m(x -x1) ( point-slope formula)
y - (-2) = 4(x-3)
y + 2 = 4(x-3)
Two different groups in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The population mean and standard deviation are unknown. The sample from the first group survey has 49 data values. The sample from the second group survey has 81 data values. For each sample, the groups construct a 90% confidence interval to estimate the population mean.Which confidence interval will have greater precision (smaller width) for estimating the population mean?Group of answer choicesThe confidence interval based on the sample of 49 data values will be more precise.Both confidence intervals will have the same precision.The confidence interval based on the sample of 81 data values will be more precise.
The confidence interval for the second group's estimate of the population mean will be more accurate due to the increased sample size.
What is mistake, exactly?
An error is an inaccurate or improper action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake.
Detailed explanation:
margin of a confidence interval's error:
The following format describes the equation for a confidence interval's margin of error:
M=zα/√n
where is the population's standard deviation, n is the sample size, and z is connected to the confidence level.
This suggests that a larger size results in a better degree of interval precision, or a smaller margin of error.
In this instance:
There are 49 data values in the sample from the first group survey and 81 from the second group.
The confidence interval for the second group's estimate of the population mean will be more accurate due to the increased sample size.
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Find b value
3(1.2b − 1) + 3.6 = 4.2
Answer: B = 1
Step-by-step explanation:
You want to get b alone, first, you will subtract 3.6. What you do on one side you do to the other
3(1.2b - 1) + 3.6 = 4.2
3(1.2b - 1) + 3.6 - 3.6 = 4.2 - 3.6
Since the 3 is multiplied, we will do the opposite to eliminate it, Divison. So divide each side by 3.
3(1.2b - 1) = 0.6
3(1.2b - 1)/3 = 0.6/3
Then we will add one to each side.
1.2b - 1 = 0.2
1.2b - 1 + 1 = 0.2 + 1
The last step is to divide each side by 1.2 to find b.
1.2b = 1.2
1.2b/1.2 = 1.2/1.2
b = 1
Calculate the deferred tax liability given the following items incurred in 2020 by company b. Bonuses are tax deductible only in the year in which they are paid.
The deferred tax liability given the following items incurred in 2020 by company b. Bonuses are tax deductible only in the year in which they are paid, is 372.
In the give question, we have to calculate the deferred tax liability given the following items incurred in 2020 by company b.
Bonuses are tax deductible only in the year in which they are paid.
From the given question;
Accounting Income = 86000
Add Depreciation expence = 6500
Less Tax Depreciation = 4000
Less 2019 Bonus Paid in 2020 = 2630
Add 2020 accured Bonus = 3500
Total Taxable Income = 84670
Accounting income is more that the taxable income. Hence defffered tax liability will arise on the temporary taxable difference.
Temporary Taxable Difference = 86000-84670 = 1330
So Deffered Tax Liability = 1330*28% = 372
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how many years after the 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline
According to all Reports of U.S media and other,
approx. 97 years after in 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline.
DDT (dichloro-diphenyl-trichloroethane) has been one of the most commonly used pesticide chemicals in the United States for many years and was first synthesized in 1874. However, its efficacy as an insecticide was not discovered until 1939. Shortly thereafter, especially during World War I, the United States began producing large amounts of DDT abroad to combat vector-borne diseases such as typhoid fever and malaria. It declined sharply, falling from a peak of about $80m that year to just under $12m in the early 1970s. Over 80% of the amount of pesticides used between 1970 and 1972 was on cotton, with the rest mainly on peanuts and soybeans. The decline in DDT use is due to
(1) increased resistance to insects
(2) development of more effective alternative pesticides
(3) Growing public concern about adverse environmental impacts.
(4) Strengthening government restrictions on the use of DDT.
Residues of the pesticide DDT in the food supply, human tissues, and the environment have declined in recent years, especially since the EPA banned the chemical from major uses in 1972.
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in a distribution, a random variable can take any value in a specified range. group of answer choices discrete probability cumulative relative frequency continuous probability
In a continuous probability distribution, a random variable can take any value in a specified range. (Option D)
A probability distribution refers to the mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. Continuous probability distribution refers to a probability distribution with continuous types of data or random variables where the random variable can take on any value and is continuous. As there are infinite values that the variable can assume, the probability of the variable assuming any one specific value is zero. A continuous distribution is characterized by a range of values that are infinite, and therefore uncountable. The normal distribution is one example of a continuous distribution.
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match the integrals with the type of coordinates which make them the easiest to do. put the letter of the coordinate system to the left of the number of the integral. b 1. where e is: c 2. where e is: a 3. b 4. where e is: d 5. where d is: a. polar coordinates b. cartesian coordinates c. spherical coordinates d. cylindrical coordinates
1. C. cylindrical coordinates 2 A. spherical coordinates 3. A. spherical coordinates 4. D. Cartesian coordinates 5 B. polar coordinates
USE THE BOUNDARY INTERVALS TO IDENTIFY
1. ∭E dV where E is:
x^2 + y^2 + z^2<= 4, x>= 0, y>= 0, z>= 0 -- This is A CYLINDRICAL COORDINATES SINCE x>= 0, y>= 0, z>= 0
2. ∭E z^2 dV where E is:
-2 <= z <= 2,1 <= x^ 2 + y^2 <= 2 This is A SPHERICAL COORDINATES
3. ∭E z dV where E is:
1 <= x <= 2, 3<= y <= 4,5 <= z <= 6 -- This is A SPHERICAL COORDINATES
4. ∫10∫y^20 1/x dx ---- This is A CARTESIAN COORDINATES
5. ∬D 1/x^2 + y^2 dA where D is: x^2 + y^2 <=4 This is A POLAR COORDINATES
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Determine the minimum surface area of a rectangular box with a square base, an open-top, and a volume of 500in3. Enter only the minimum surface area, and do not include units in your answer.Major problems that can be simplified by the technique of classical optimization are consist of single or multivariable functions without having constraints. It is also practiced in physics as an energy minimization technique.
The minimum surface area of a rectangular box with a square base is 300 square inches.
What is meant by surface area?Surface area is the amount of space on the outside of a three-dimensional form. The surface area of a solid item is the total area that the object's surface occupies.
The mathematical definition of surface area in the presence of curved surfaces is significantly more involved than the definition of arc length for one-dimensional curves or surface area for polyhedra , where the surface area is the sum of the areas of its faces. Smooth surfaces, such as spheres, are ascribed surface area through their representation as parametric surfaces.
The volume of a rectangular box with a square base, an open-top is 500 cubic inch
So, V=lbh
500 inch³=lbh
Also, given that base is a square, so l=b
h= 500 inch³/lb
h=500 inch³/l²
Now, Surface area(A)= Area of base+ Area of 4 walls
=l²+4lh
=l²+4l(500/l²
=l²+(2000/l)
To minimize the surface area, differentiate it with respect to l.
A'(l)=d/dl(l²+(2000/l))
=2l-(2000/l²)
=(2l³-2000)/l²
Substitute A'(l)=0 to obtain the critical point
(2l³-2000)/l²=0
2l³-2000=0
2l³=2000
l³=1000
l=10
Again differentiating A'(l) to confirm the minimum value at l=10
A"(l)=d/dl((2l³-2000)/l²)
A"(l)=2+(4000/10³)
A"(10)=2+(4000/10³)
A"(10)=6>0
Thus, the required surface area is,
Surface area=l²+(2000/l)
=10²+(2000/l)
=300
Therefore, the minimum surface area of a rectangular box is 300 square inches.
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a. work out the range
b. how many students are in the group
c. work out the mean mark of the group
If a wheel of a bicycle covers 440m in 200 rotations find the diameter of the wheel.
The diameter of the wheel of the bicycle that covers 440m in 200 rotations is 0.7m.
What do we mean by diameter?Any straight line segment that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry.
It is also known as the circle's longest chord.
The diameter of a sphere can be defined using either of the two methods.
The diameter or length of a circle is its circumference.
A straight line connecting a point on one end of the circle to a point on the other end, passing through the center, is the diameter.
So, the diameter of the wheel will be:
Circumference = 440/200
Circumference = 44/20
Circumference = 22/10
Circumference = 2.2/1
2πr = 2.2
Now, calculate the radius:
2πr = 2.2
r = 2.2/2π
r = 7/22 * 2.2/2
r = 0.35
Diameter: 3.5 * 2 = 0.7m
Therefore, the diameter of the wheel of the bicycle that covers 440m in 200 rotations is 0.7m.
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How do you tell if the degree of a polynomial is even or odd from a graph?.
A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function.
How do you tell if a polynomial graph is odd or even?
In general, we can determine whether a polynomial is even, odd, or neither by examining each individual term. A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions
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Ia jogged two-third of the way home from chool. Then he wa tired, o he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, tart text, pace, m, end text. How many kilometer did Ia travel from chool to hi houe?
Based on the jogging and walking distance, Issa travelled 9.6 km from school to his house.
Let us assume the total distance between between school and home be x. So, jogging distance will be = 2/3x
The remaining distance = 3200 m
Now forming the equation from mentioned information -
2/3x + 3200 = x
Rewriting the equation
3200 = x - 2/3x
Taking LCM, we get 3
3200 = (3x - 2x)/3
Performing subtraction on Right Hand Side
3200 = x/3
x = 3200 × 3
Performing multiplication
x = 9600 m
As we know, 1000 m = 1 km
9600 m = 9.6 km
Hence, the distance is 9.6 km.
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The complete question is -
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3200 m. How many kilometers did Issa travel from school to his house?
5.) If b = -2, which equation is true? A 2(b +5) = 6 2(b-4)= 12 B C 2(b + 3) = 10 D 2(b-5) = 14
Answer:
a.) 2(b+5)=6
Step-by-step explanation:
[tex]b=-2\\\\a.)2(b+5)=6\\2[(-2)+5]=6\\2(3)=6\\6=6\\\\b.)2(b-4)=12\\2[(-2)-4]=12\\2(-6)=12\\-12\neq 12\\\\c.)2(b+3)=10\\2[(-2)+3]=10\\2(1)=10\\2\neq10\\\\d.)2(b-5)=14\\2[(-2)-5]=14\\2(-7)=14\\-14\neq14[/tex]
the angles of a triangle are in a ratio of 1:1:2. find the ratio of the sides opposite these angles.
The ratio of opposite sides of given angle is 1 : 1 : [tex]\sqrt{2}[/tex].
We have given that the angles of a triangle are in ratio of 1 : 1 : 2.
Let us consider angle is x°.
We know that the sum of angles of triangle is 180°.
Therefore we can write it as,
1(x) + 1(x) + 2(x) = 180°
4x = 180°
x = 45°
then the angle become 45° ,45°, 90°.
That means triangle is an isosceles triangle.
We know that if triangle is an isosceles right triangle (45-45-90) then the side lengths will follow the ratio 1 : 1 : [tex]\sqrt{2}[/tex].
Hence the sides of the given triangle have a ratio of 1 : 1: [tex]\sqrt{2}[/tex].
A triangle in which at least two sides are equal is called an Isosceles triangle. An Isosceles triangle have both two equal sides and two equal angles.
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instructions: match each term to its definition below by selecting the correct term from each dropdown list. scroll down to see all of the definitions. when you are done, select check.1. ______ means that each individual has a designated supervisor to whom they report to at the scene of the incident. 2. ______ allows agencies with different legal, geographic, and functional authorities and responsibilities to work together effectively without affecting individual agency authority, responsibility, or accountability. 3. ______ refers to the orderly line of authority within the ranks of the incident management organization.chain of commandunity of commandunified of command
Each terminology should be matched to its definition as follows:
Unity of command: means that each individual has a designated supervisor to whom they report to at the scene of the incident. Unified of command: allows agencies with different legal, geographic, and functional authorities and responsibilities to work together effectively without affecting individual agency authority, responsibility, or accountability. Chain of command: refers to the orderly line of authority within the ranks of the incident management organization.What is ICS?ICS is an abbreviation for incident command system and it can be defined as a subset of the National Incident Management System (NIMS) which is typically used for planned events, as well as for emergencies and coordinated responses in various business organizations and/or circumstances.
Generally speaking, there are six (6) fundamental functional areas in an incident command system (ICS) and these including the following;
PlanningCommandIntelligence/InvestigationOperationsFinance/AdministrationLogisticsIn conclusion, chain of command, unity of command, and unified of command are all terminologies that are associated with an incident command system (ICS).
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Set up the linear programming problems in this exercise set. Do not attempt to solve them. The Humidor blends regular coffee, High Mountain coffee, and chocolate to obtain four kinds of coffee: Early Riser, Coffee Time, After Dinner, and Deluxe. The blends and profit for each blend are given in the following chart:The shop has 260 pounds of regular coffee, 90 pounds of High Mountain coffee, and 20 pounds of chocolate. How many pounds of each blend should be produced to maximize profit?
The set of linear programming for this problem is, to maximize [tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex] subject to [tex]80x_{1} + 75x_{1} + 75x_{1} + 50x_{4}\leq 260;[/tex] [tex]20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90;2x_{2} + 5x_{3} + 10x_{4} \leq 20;[/tex] [tex]x_{1} \geq 0,x_{2} \geq 0,x_{1} \geq 0[/tex] [tex], x_{4} \geq 0[/tex].
In the given question,
The Humidor blends regular coffee, High Mountain coffee, and chocolate to obtain four kinds of coffee: Early Riser, Coffee Time, After Dinner, and Deluxe.
The blends and profit for each blend are given below in the following chart:
The shop has 260 pounds of regular coffee, 90 pounds of High Mountain coffee, and 20 pounds of chocolate.
Let [tex]x_{1}, x_{2}, x_{3}[/tex] and [tex]x_{4}[/tex] be the weight in pounds of early riser, Coffee time, after dinner and deluxe respectively.
The maximum available pounds of regular coffee are 260 pounds.
Therefore,
[tex]80x_{1} + 75x_{2} + 75x_{3} + 50x_{4}\leq 260[/tex]
The maximum available pounds of High Mountain are 90 pounds.
Hence,
[tex]20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90[/tex]
The maximum available pounds of chocolate are 20 pounds.
Therefore,
[tex]0x_{1} + 2x_{2} + 5x_{1} + 10x_{4} \leq 20[/tex]
To maximize the profit, the equation will be
[tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex]
So the linear programming model for the situation is
Maximize
[tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex]
Subject to
[tex]80x_{1} + 75x_{1} + 75x_{1} + 50x_{4}\leq 260\\20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90\\2x_{2} + 5x_{3} + 10x_{4} \leq 20\\x_{1} \geq 0,x_{2} \geq 0, x_{1} \geq 0, x_{4} \geq 0[/tex]
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Sara wants to trim a lampshade with braid. the lampshade is shaped like a rectangular prism. the length of the base of the lampshade is 4 inches greater than its width. if the perimeter of the base is 54 inches, find the length of the base.
Answer:
15.5 inches
Step-by-step explanation:
Let the width be [tex]w[/tex] and the length be [tex]w+4[/tex].
Using the formula for the perimeter of a rectangle,
[tex]2(w+w+4)=54 \\ \\ 2w+4=27 \\ \\ 2w=23 \\ \\ w=11.5 \\ \\ \implies w+4=15.5[/tex]
Damon drank 1. 49 L of water. Gavin drank 0. 86 L of water. How many more litre of water did Damon drink?
Damon wants to drink 1.49 L of water and if he has drink 0.86 L of water then he has to drink 0.63 L of water.
What is subtraction in mathematics?
Subtraction in math means to take something away from a group or a number of things. When we subtract, the number of items in the group decreases or becomes smaller. A subtraction problem includes the minuend, subtrahend, and difference.
Damon wants to drink 1.49 L of water and he has drink 0.86 L of water
The required amount of water will be = 1.49 - 0.86 = 0.63 L of water.
Hence, Damon wants to drink 1.49 L of water and if he has drink 0.86 L of water then he has to drink 0.63 L of water.
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A large object with an initial temperature of 150 degrees fahrenheit is dropped into the ocean. the current temperature of the ocean water in the area is 77 degrees. the function f(t)=ce(−kt) 77 represents the situation, where t is time in minutes, c is a constant, and k is a constant. after 10 minutes the object has a temperature of 120 degrees. after how many minutes will the temperature of the object be equal to 80 degrees? round your answer to the nearest whole number, and do not include units.
After t = 60.3 minutes will the temperature of the object be equal to 80 degrees.
The function f(t) = Ce^-kt + 77........ (1)
Now, at t = 0, f(0) = 150 = C + 77
C = 73
So, the function (1) becomes f(t) = 73e^-kt + 77 ......... (2)
Now, it is given that at t = 10 minutes, f(10) = 120 degree.
Consequently, from equation (2), 120 = 73e^-kt + 77
73e^-10k = 43
e^-10k = 0.589
Now, taking logarithm ln both sides we get -10k (ln e) =ln (0.589)
k = 0.0529
Therefore, the equation (2) becomes f(t) = 73e^-( 0.0529)t + 77 ......(3)
Now, putting f(t) = 80 degree, we have from equation (3),
f(t) = 73e^-( 0.589)t + 77
80 = 73e^-( 0.589)t + 77
e^-( 0.0529)t = 0.041
Taking ln both sides we get, -0.0529t = - 3.19, ⇒ t = 60.3 minutes
The object's temperature will reach 80 degrees after t = 60.3 minutes.
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6. PQR and XYZ are similar with m
Answer:
XZ = 22.5 inches
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{XZ}{PR}[/tex] = [tex]\frac{XY}{PQ}[/tex] ( substitute values )
[tex]\frac{XZ}{15}[/tex] = [tex]\frac{9}{6}[/tex] ( cross- multiply )
6 × XZ = 15 × 9 = 135 ( divide both sides by 6 )
XZ = 22.5 inches
How will you differentiate linear inequalities in two variables from systems of linear inequalities in two variables?.
Linear equation and Linear inequality are differentiatable on the sybolically. The symbol used in linear equation is "=" equality sign and the symbols used in linear inequality are ">","<","
"≤", " ≥".
We need to distinguish between linear inequalities in two variables and systems of linear equations in two variables.
We will first discuss linear equations and then linear inequalities.
Linear Equations:
If a equation is written in the form ax + by + c=0, the equation is said to be a linear equation in two variables. where a, b & c are real numbers and coefficients of x and y. , that is, a and b are not equal to zero.
Characterstic :
Variables in a linear equation are not raised to powers or used as denominators of fractionsFind pairs of values that make the linear equation true, and plot those pairs on a coordinate grid so that all points are Lying on the same line. The graph of a linear equation is a straight line.A linear equation in two variables can be written as a linear relationship between x and y.For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
methods for solving linear equations in two variables:
graphical methodsreplacement methodscross-multiplication methodselimination methodsLinear inequality:
Linear inequalities in two variables use the greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤) symbols instead of the equal (=) symbol. Use the.
Features:
You can add, subtract, multiply and divide with the same number to solve inequalitiesMultiply and divide with negative numbers reverse the inequalityOrder outside shaded area Pairs are inequalities that cannot be solved graphically.Example: 8x + 3y ≥ 5 and 2x + 3y < 10 are linear inequalities in two variables.
Method: Graphical
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find two possible functions f, given the second-order derivative. (enter your answers as a comma-separated list.) f ''(x)
The two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x.
The derivative of the first derivative of the given function is known as the second order derivative. We can learn about the slope of the tangent at a particular position or the instantaneous rate of change of a function at that point from the first-order derivative at that point.
F”(x)= x^2+6
F’(x)= \int f"(x) dx
= \int( x^2+6) dx
= \frac{x^3}{3}+6x+c_1 c_1 is the integral constant.
F(x)= \int f\prime(x) dx
= \int f (\frac{x^3}{3}+6x+c_1) dx
= \frac{x^4}{12}+3x^2+c_1x+c_2
(i) if c_1=0 , and c_2=0
F(x)= \frac{x^4}{12}+3x^2
(ii) if c_1=1, and c_2=0
F(x)= \frac{x^4}{12}+3x^2+x
Therefore the two possible functions is F(x)= \frac{x^4}{12}+3x^2 and F(x)= \frac{x^4}{12}+3x^2+x
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sat scores in one state is normally distributed with a mean of 1595 and a standard deviation of 80. suppose we randomly pick 33 sat scores from that state. a) find the probability that one of the scores in the sample is less than 1585. p ( x < 1585 ) p(x<1585)
The probability that one of the scores in the sample is less than 1585 is 4.9%
Given that,
Given that mean u = 1585
standard deviation σ = 80
sample size n = 33
Probability means is the ability to happen. The subject of this area of mathematics is the occurrence of random events.The value is expressed in the range of 0 to 1. Probability has been brought to mathematics to predict the likelihood of events. Probability is essentially defined as the degree to which something is likely to occur.
P(x<1585) = P(X-u/σ < 1585-1595/80)
= P (X-u/σ < -0.125)
P(x<1585) = 0.45026
P(x>1585) = 1 - P(x<1585) = 0.54974
P(1585<x<1595) = 0.5 - P(x<1585) = 0.049738
So, The probability that one of the scores in the sample is less than 1585 is 4.9%
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Abigail has an account that pays 6.92% simple interest per year and wants to accumulate $5,896 in interest from this account over six years. how much money should abigail invest in this account to meet this goal? a. $2,448.02 b. $8,344.10 c. $14,200.39 d. $20,096.67 please select the best answer from the choices provided a b c d
Abigali should invest $14197.97 in this amount to get the goal
From the formula of the simple interest,
S.I = P.r.t/100
Simple interest is the interest amount on the particular amount for the required rate in a given interval of time.
Where S.I = simple interest for the original amount
P = principal amount
t = number of times of period
r =rate interest
In this problem, we have
r = 6.92
S.I = 5896
t = 6 years
Since, Abigali pays 6.92% simple interest per year in her account for the interest of $5896 in the six years
Therefore, as per the question
P = (S.I x 100)/r.t
P = (5895 x 100)/ (6.92 x 6) = $14197.97
Therefore, original money will be $14197.97
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What does the 9 3 3 1 ratio for phenotypes mean?.
The 9 3 3 1 ratio for phenotype mean the classic mendelian ratio for a di-hybrid cross in which the alleles of two different genes assort independently into gametes Independent assortment of genes.
A cross is made between the two parents based on two pairs of characters known as Di-hybrid cross.
A cross is made between homogenous yellow round seed to another homozygous green wrinkled seeds.
At the [tex]F_1[/tex] generation, all plants are heterozygous yellow round. Whenever this plant is subject to self pollination, in the [tex]F_2[/tex] generation, 9 plants are Yellow round, 3 plants are yellow wrinkled, 3 plants are green round and 1 plant is green wrinkled.
This called Di-hybrid phenotype ratio 9:3:3:1. Mendel is expressed this one as "Law of independent assortment".
Therefore the 9 3 3 1 ratio for phenotype mean the classic Mendelian ratio for a di-hybrid cross in which the alleles of two different genes assort independently into gametes Independent assortment of genes.
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g if a distribution is approximately bell shaped with the mean 12 and standard deviation 2 then the percentage of observations between 8 and 10 is approximately:
The percentage of observations between 8 and 10 is 13.59%
Given,
The distribution is bell shaped.
The mean of the distribution, μ = 12
Standard deviation of the distribution, σ = 2
We have to find the percentage of observations between 8 and 10.
Here,
Calculate z score;
z score = (x - μ) / σ
For x = 8
z score = (8 - 12) / 2 = -4/2 = -2
For x = 10
z score = (10 - 12) / 2 = -2/2 = -1
The p value;
P (-2 < z < -1) = P(z < -1) - P(z < -2)
= 0.158655 - 0.02275
= 0.135905 ≈ 0.13.59 x 100 = 13.59%
That is,
The percentage of observations between 8 and 10 is 13.59%
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Can the two triangles be proven congruent by SAS explain?.
The triengle ABC and XZY are proved to be congruent by SAS.
Explain the concept of congruence.Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.
By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)
Here in he given triangle,
BC=YZ
AC=XZ
∠ACB=∠XZY
By SAS ΔABC≅ΔXYZ
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suppose a computer using direct mapped cache has 220 bytes of byte-addressable main memory, and a cache of 32 blocks, where each cache block contains 16 bytes.
The number of blocks will be 2^16 blocks. The address will be tag:11, block:5, offset:4. The memory address will be 0DB63 that will map to 22nd block and 3 byte size of block.
What is memory address?A memory address in computing is a reference to a particular memory region that is utilized at different levels by hardware and software. Memory addresses are unsigned numbers that are often presented and handled as fixed-length digit sequences. A device or CPU uses a memory address as a specific identifier to track data. The CPU can keep track of where each memory byte is in the system by using this binary address, which is defined by an ordered and finite sequence.
Here,
Calculations are given in image.
2^16 blocks will make up the total amount of blocks. Tag:11, block:5, offset:4 will be the address. The memory address will be 0DB63, which corresponds to the 22nd block with a 3 byte block size.
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