By using the well ordering principle we can easily prove that the equation
4a³ + 2b³ = c³ does not have any solution for positive integers.
Let (a, b, c) be a positive integer solution with c the smallest possible.
Then c³ is even as the sum of a factor of 4 and factor of 2 is always even .
hence c itself is even.
Let us consider c = 2c₀ ;
4a³ + 2b³ = (2c₀)³
or, 4a³ + 2b³ = 8c₀³
then 2a³+b³ = 4c₀³
This time, we see that b must be even. using the same principle as above .
Put b = 2b₀ ;
2a³ + 8b₀³ = 4c₀³
then a³ + 4b₀³ = 2c₀³
thus a = 2a₀ must be even,
and 4a₀³+2b₀³=c₀³,
i.e. (a₀, b₀, c₀) is another solution. But c₀ = c/2<c.
And we have taken c to be the smallest of the solutions.
hence we get a contradiction.
Therefore our assumption is not valid.
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Which variable has a binomial distribution?
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution
The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.
The basic presumptions of the binomial distribution are:
each trial has a single possible outcome each trial has an equal chance of success each trial is either independent of the others or mutually exclusive.As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.
The result is then multiplied by the sum of the number of attempts and the number of successes.
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Which ordered pair lies on the graph of the function y = -2x + 1? (0, -2) (2, -2) (3, -5) (5, 2
So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)
We will use the substitution method and check for all the ordered pair which are given
If the ordered pair lies on the graph, then it should satisfy the function.
So,
Given,
y = -2x+1
First check for (0,-2)
x=0, y=-2
Substitute the values,
y = -2x+1
-2=-2(0)+1
-2=1
It is false.
Next check for (2,-2)
x=2, y=-2
Substitute the values,
y = -2x+1
-2=-2(2)+1
-2=-3
It is false.
Next check for (3,-5)
x=3, y=-5
Substitute the values,
y = -2x+1
-5=-2(3)+1
-5=-5
It is true.
Next check for (5,2)
x=5, y=2
Substitute the values,
y = -2x+1
2=-2(5)+1
2=9
It is false.
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A professor wanted to know what proportion of college students believe in ghosts. She polled 200 students and found that 58% said they believe in ghosts. Create a 99% confidence interval for the true proportion of college students believing in ghosts. a. (0.5116, 0.64840 b. (0.2074, 0.3727) c. (0.4901, 0.6699) d. (0.2271,0.3529)
A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c) (0.4901, 0.6699)
According to the question,
A professor wanted to know what proportion of college students believe in ghosts.
For that he drawn a sample from the college.
Sample size : n = 200
Proportion of students that believed in ghosts in sample = 58%
=> p = 0.58
Proportion of students who does not believe in ghost : q = 1 - p
=> q = 0.42
We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts
Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200
=> 0.58 ± 2.576 √0.001218
=> 0.58 ± 2.576 × 0.035
=> 0.58 ± 0.08958
C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)
Hence, Option (c) is correct
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Answer:
41%
Step-by-step explanation:
a school organized three different trips. 50% of the students went on 1st trip, 80% went on the second trip and 90% went on the third trip. a total of 160 students went on all the three trips. how many students are at the school
Answer:m
Step-by-step explanation:
Select the best answer. The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population). (b) if the population is Normally distributed and the sample size is reasonable large. (c) if the population is Normally distributed (for any sample size). (d) if the population is Normally distributed and the population standard deviation is known (for any sample size). (e) if the population size is reasonably large (whether the population distribution is known or not).
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
Given that,
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,
In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.
Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.
The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.
Therefore,
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
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Which expressions are equivalent to 20 divided by 1 plus 4
The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.
What are the rules of PEDMAS?The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.
The given statement for the problem is, " 20 divided by 1 plus 4".
It can be written in the form of expression as follows,
The sign of plus is given as '+'.
And, for divide it is '÷'.
Now, 20 divided by 1 plus 4 can be written as,
20 ÷ 1 + 4
Which is evaluated by BODMAS to give,
20 + 4 = 24.
Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.
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The expression 8x³-1 is a ...
Select all that apply
linear
quadratic
cubic
quartic
quintic
monomial
binomial
trinomial
Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.
What is a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by degree of polynomial?The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.
Expression : [tex]8x^{3}-1[/tex]
Degree of polynomial =3
The expression is a Cubic Expression.
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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.
What is a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by degree of polynomial?The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.
Expression : 8x³ - 1
Degree of polynomial =3
The expression is a Cubic Expression.
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find the value of the expression w2 + 1v for v=3 and w=3
Answer: 12
Step-by-step explanation:
Since we are given what v and w are, we can directly plug them in to solve the expression.
w²+1v [plug in v and w]
(3)²+1(3) [exponent]
9+1(3) [multiply]
9+3 [add]
12
The expression is equal to 12.
This function vertically stretches y = √x by a factor of 3, then translates it 2 units left.
We get 3y= √(x+2) after vertically stretches by 3 and translated 2 unit left.
What means vertically stretches?If a function is multiplied by a positive value that greater than 1, the graph of function is called vertically stretched graph. Here vertically stretches means the factor 3>1 and we need to multiply the y value by 3.
What means by translate 2 unit left?Translation of a graph means move the graph from one position to another position without changing its size, shape or orientation. Here, the graph is translated 2 units left so we need to add 2 with the x value.
We are given a graph, y= √X
Hence, after transformation the graph became 3y= √(x+2)
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Find the measure of one exterior angle in each regular polygon. Round your answer to the
nearest tenth if necessary.
3)
45°
27.7°
51.4°
For rhombus LMNO, m∠LON = 102° and NP = 5 units.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Use the diagram of rhombus LMNO to find the missing measures.
The measure of ∠LPM is
°.
The measure of ∠PMN is
°.
The length of LN is
units.
the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
Define Rhombus.
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.
For a Rhombus, LMNO
∠LON = 102°
NP = 5 units
By the properties of Rhombus, we know that
All sides of a rhombus are congruent (equal)
So, LM = MN = NO = OL
and
Opposite angles are equal and the opposite sides are parallel.
So, ∠LON = 102° = ∠LMN
Since Adjacent angles add up to 180°.
Therefore ∠L + ∠M = 180°
∠M + ∠N = 180°
∠N + ∠O = 180°
∠O + ∠L = 180°
So, ∠N = 180° - ∠O = 180° - 102° =78°
∠L = 180° - ∠O = 180° - 102° =78°
∠M = 180° - ∠L = 180° - 78° =102°
Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.
So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°
Thus, the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
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Answer:
Lpm= 90
PMN=51
LN= 10
Step-by-step explanation:
Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.
The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)
The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.
Here we have given the inequality (x² - 5)/ (x - 36) < 0
And we need to find the solution in inequality notation and in interval notation.
In order to find the inequality notation, we have to solve the given inequality, then we get.
(x² - 5)/ (x - 36) < 0
(x² - 5) < 0
x² < 5
x < √5
While we looking into the inequality we must know that the denominator must not be 0.
So, the interval notation can be written as,
=> (-∞ . -√5]∪[√5,36)
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HELP NEEDED IMMEDIATELY!!!!!!!!!!!!!!!!! Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Robbie, Jennie, Willie, and Kylie played a numbers game. Jennie picked a number but did not tell her friends. Robbie and Willie both picked a number as well, and Jennie described their numbers like this to Kylie.
Robbie picked a number that is nine more than four times Jennie's number.
Willie picked a number that is two less than three times Robbie's number.
Deciding to call her number, n, Jennie asked Kylie to write an expression that describes Willie's number.
Kylie came up with two expressions that equal Willie's number.
Her first expression was
(
n +
) - 2. Simplifying her first expression, her second expression was 12n +
.
The two equations that equal Willie's number are given as follows:
n = 3y - 2.n = 12x + 25.How to obtain the equations?Jennie's number is unknown, hence we use the variable x to refer to her number.
Robbie picked a number that is nine more than four times Jennie's number, hence:
y = 9 + 4x.
(using y to refer to Robbie's number).
Willie picked a number that is two less than three times Robbie's number, hence:
n = 3y - 2.
(using n to refer to Willie's number).
Considering the expression for y, the second expression that describes Willie's number is given as follows:
n = 3(9 + 4x) - 2
n = 12x + 25.
Missing InformationThe problems asks foir the two expressions that equals Willie's number.
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i need help divided 4/7 by 3
Answer:
0.1904
Step-by-step explanation:
4/7 ÷ 3 is = 0.1904
Answer: I hope this helps
Step-by-step explanation:
4/7 divided by 3
Dividing is equivalent to multiplying by the reciprocal
4/7 times 1/3 or 4/7•1/3
Multiply the fractions
And you get
4/21 or 0.190476
expressions equivalent to 9 2/3
The equivalent expression for the given expression is 29/3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given mixed fraction [tex]9\frac{2}{3}[/tex].
There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.
Convert mixed fraction to improper fraction as follows
Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator
[(9×3)+2]/3
=[27+2]/3
= 29/3
Therefore, the equivalent fraction for the given mixed fraction is 29/3.
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Match the correct statement with the given information.
The correct statements regarding the transformations to the volumes are given as follows:
1. A cone's radius increases x 3: -> The cone's volume will increase x 9.
2. A cone's height increases x 3: -> The cone's volume will increase x 3
3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.
4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.
What are the volumes?The volume of a cone of radius r and height h is given as follows:
V = πr²h/3.
Then the scale factors are considered as follows:
If the radius is multiplied by 3, the volume is multiplied by 9, as the volume is squared.If the height is multiplied by 3, the volume is also multiplied by 3, as the power of the variable h is of h.The volume of an sphere of radius r is given as follows:
V = 4πr³/3.
Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.
The volume of a cylinder of radius r and height h is given as follows:
V = πr²h.
Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.
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What is true about machine learning algorithms? A/Model is fitted using training dataset B/Performance of the model is assessed using test data C/Model is validated on validation dataset D/Model is calibrated on test dataset E/Validation dataset is used to minize model overfitting Select all what applies to traditional classification tree model: A/Group of answer choices B/Unsupervised learning method C/Requires categorical output(target) variable D/Does not require any output variables E/None of the above F/Supervised learning method
A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms
The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.
Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.
Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.
According to the question,
Option A and option E are correct about the machine learning algorithms
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Find tan(0), if cot(0) = -2.6
According to Trigonometric Identity , tan(theta) = -5 / 13
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. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.
Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.
According to the given information
We know that
tan(theta) = 1/cot(theta)
= 1 / -2.6
= -1 / 2.6
= -10 / 26
= -5 / 13
According to Trigonometric Identity , tan(theta) = -5 / 13
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Solve ABC using diagram and the given measurement A=64 a=7.4
Answer:
Hope this helps!
To describe the details of the significant result, compare the provided observed and expected frequencies. Which of the following statements best describes the results? a. A greater proportion of the adolescent girls with anorexia nervosa live in the Northeast than live in the other regions when compared to the general US population
b. A greater proportion of the adolescent girls with anorexia nervosa live in the West than live in the other regions when compared to the general US population c. A greater proportion of the adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population
c. A greater proportion of adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population.
Null Hypothesis, [tex]H_{0}[/tex] : All proportions are the same
Alternative Hypothesis, [tex]H_{1}[/tex]: At least two of the proportions are not the same
The alternative and null are both population-based assertions. The reason for this is that the purpose of hypothesis testing is to draw conclusions about a population from a sample.
The null and alternative hypotheses are two competing claims that researchers weigh the evidence for and against using a statistical test:
Null hypothesis: There’s no effect on the population.
Alternative hypothesis: There’s an effect on the population.
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Here is a linear equation: y= 1 4x+2. What is the x-intercept of the graph of the equation?
As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the information given in the question,
The given equation is,
y= -1/4 x + 2
Now, let's take y = 0 for x- intercept,
So, the equation will be,
0 = 1/4x + 2
1/4x = -2
x= -8
The x-intercept is (-8, 0).
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The question sees incomplete, your question may be:
Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?
Write each of these numbers in base five as a sum of multiples of powers of five (5):
(a). 1012⁵
(b). 101⁵
(c). 1.1⁵
(d). 10.21⁵
(e). 210⁵
Answer:
Step-by-step explanation:
a) 1012⁵ can be written as:
1012⁵ = 15¹² + 05¹¹ + 1*5¹º
= 5¹² + 5¹º
= 3125 + 625
= 3750
(b) 101⁵ can be written as:
101⁵ = 15⁴ + 05³ + 1*5²
= 5⁴ + 5²
= 625 + 25
= 650
(c) 1.1⁵ can be written as:
1.1⁵ = 15¹ + 15º
= 5¹ + 5º
= 25 + 5
= 30
(d) 10.21⁵ can be written as:
10.21⁵ = 15² + 05¹ + 25º + 15⁻¹
= 5² + 2*5º + 5⁻¹
= 25 + 10 + 0.2
= 35.2
(e) 210⁵ can be written as:
210⁵ = 25⁴ + 15²
= 2*625 + 25
= 1250 + 25
= 1275
Can someone help me?
Answer:
Y=6x-12
Step-by-step explanation:
whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.
received the new experimental drua. 23 subiects were assigned to the control group and received a standard, well-known treatment. after a suitable period. the reduction in blood pressure for each subiect was recorded. thev are going to conduct a test at a 5% sianificance level to see if the mean reduction in blood pressure is different between the arouos. the resultina statistics are as follows:
To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.
To conduct the t-test, you will need the following information:
The sample size of each group (number of subjects in each group)The mean reduction in blood pressure for each groupThe standard deviation of the reduction in blood pressure for each groupThe level of significance (in this case, 5%)Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.
If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.
If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.
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Evaluate ab−c+d if a=78 , b=−716 , c=0.8 , and d=14 . Write your answer as a mixed number in simplest form.
In the case where a=78, b=716, c=0.8, and d=14, the simplest form of a mixed number is -117/640.
Explain about the simplest form?The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.
The term "reduced form" refers to the fraction's simplest form. As an illustration, the simplest form of a fraction with a common component of 1 is 34 However, while 2/4 can be further condensed and expressed as 12, it is not the most basic form.
When the top and bottom of a fraction cannot be any smaller while remaining whole numbers, it is said to be in its simplest form.
b a + c d
b= -7/16
a= 7/8
c= 08.(4/5)
d= 1/4
It can therefore be calculated as follows.
-7/16×7/8 + 4/5×1/4
-49/128 + 1/5
-246+128/640
= -117/640
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Answer to this required:
Answer:
9
Step-by-step explanation:
3.4^0 = 1
9^1 = 9
1 * 9 = 9
please help and tell me what to put in
Using the two column proof, we have been able to prove that;
ΔPQR ≅ ΔTSR by AAS Congruency Postulate
How to solve two column proof problems?A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.
Thus, the two column proof required is as follows;
Statement 1: PR ≅ TR
Reason 1: Given
Statement 2: ∠PQR ≅ ∠TSR
Reason 2: Given
Statement 3: ∠PRQ ≅ ∠TRS
Reason 3: Opposite angles
Statement 4: ΔPQR ≅ ΔTSR
Reason 4: AAS Congruency postulate
AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles
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Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college. The rate is 4.3%. How much interest accrued in the first four-and-a-half years
The interest accrued in the first four years is $1.69 and a half years is $0.21.
What is interest rate?
The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Given:
Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.
The rate is 4.3%.
We have to find the interest accrued in the first four-and-a-half years.
First to find the interest for first four years.
p = $9.800, r = 4.3% = 0.043, t = 4
⇒ I = P x r x t
I = 9.800 x 0.043 x 4
I = 1.6856
I = $1.69
Now to find the interest for a half years.
p = $9.800 , r = 4.3% = 0.043, t = 1/2
I = p x r x t
I = 9.800 x 0.043 x 1/2
I = 0.2107
I = $0.21
Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.
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Help me!!!
Graph the equation:
y - 2 = 3 (x - 2)
Answer:
See below and attached graph
Step-by-step explanation:
If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.
If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)
Expand the brackets on the right hand side
3(x - 2) = 3x - 6
So the original equation becomes
y - 2 = 3x - 6
Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2
y = 3x - 4 [1]
This form of equation is known as a slope-intercept form of the line
We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points
Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph
Point 2
Choose another value for x, say x = 4
y = 3·4 - 4
y = 12-4
y = 8
So (4, 8) is another point
Draw a line through these two points
A magician's hat contains black rabbits and white rabbits. The magician selects two rabbits without replacement. If the probability of selecting a black rabbit and a white rabbit is 1/4, and the probability of selecting a black rabbit on the first draw is 5/12, find the probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit.
The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.
P(B∩W) = 1/4 getting a black and a white rabbit
P(B) = 5/12 getting a black rabbit
P(W/B)
= P(B∩W) / P(B)
= (1/4) / (5/12)
= 12/20
= 3/5
Therefore, the conditional probability is 3/5.
Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.
The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.
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