Answer:
Step-by-step explanation:
This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.
The probability of getting no defective radios in the sample is:
(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.
The probability of getting at least one defective radio in the sample is then:
1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
which is approximately equal to 0.401.
Therefore, the probability that the entire batch will be rejected is 0.401.
the joint probability density function of two continuous random variables x and y is given by: f(x,y)
The value of k is 1/2π, and X and Y are independent because their joint density function factors into a product of their Probability density functions.
To find the value of k, we use the fact that the total area under the joint probability density function equals 1. That is:
integral from 0 to infinity of integral from 0 to infinity of kxye^(-x^2-y^2) dx dy = 1
Using polar coordinates (x = r cos(theta), y = r sin(theta)), the double integral can be written as:
integral from 0 to 2pi of integral from 0 to infinity of k r^3 e^(-r^2) dr d(theta) = 1
The integral over theta is just 2pi, so we can simplify to:
2pi k integral from 0 to infinity of r^3 e^(-r^2) dr = 1
Solving this integral, we get:
2pi k (-1/2) e^(-r^2)| from 0 to infinity = 1
Since e^(-r^2) goes to 0 as r goes to infinity, we have:
pi k = 1/2
Therefore, k = 1/(2pi).
To prove that X and Y are independent, we need to show that the joint probability density function can be factored into the product of the marginal probability density functions:
f(x,y) = f_X(x) * f_Y(y)
The marginal probability density function of X is given by:
f_X(x) = integral from 0 to infinity of kxye^(-x^2-y^2) dy
= kxe^(-x^2) * integral from 0 to infinity of ye^(-y^2) dy
The integral from 0 to infinity of ye^(-y^2) dy is a known integral equal to 1/2, so we have:
f_X(x) = kxe^(-x^2) / 2
Similarly, the marginal probability density function of Y is given by:
f_Y(y) = kye^(-y^2) / 2
Therefore, we have:
f_X(x) * f_Y(y) = k^2 xy e^(-(x^2+y^2))
Comparing this to the joint probability density function given in the problem, we can see that:
f(x,y) = f_X(x) * f_Y(y)
Thus, X and Y are independent.
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____The given question is incomplete, the complete question is given below:
The joint probability density function of two-dimensional continuous random variable (X,Y) is given by > 0, y >0; f(x,y) = 0, otherwise, kxye-(x2+y2). Find the value of k and prove also that X and Y are independent.
The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 104 parts are
produced, the cost is $324. What is the average cost per part?
OA $0.23 per part
B. $6 per part
OC. $0.17 per part
OD. $7 per part
Answer:
B. $6 per part
Step-by-step explanation:
The average cost per part can be computed as follows
Average Cost = (324-300)/(104-100)
= 24/4
=$6
Answer: B. $6 per part
determine which matrices are in reduced echelon form and which others are only in echelon form
a. 1 0 0 0
0 1 0 0
0 0 1 1
b. 0 1 1 1 1
0 0 1 1 1
0 0 0 0 1
0 0 0 0 0
c. 1 4 0 0
0 0 0 0
0 0 1 0
0 0 0 1
is matrix a in reduced echelon form,echelon form only ,or neither?
1. reduced echelon form
2.echelon form
3. neither
The given matrices are in the following form,
Reduced echelon form is Matrix A .
Only echelon form is Matrix B.
Neither echelon form nor reduced echelon form is Matrix C.
Matrix A is in reduced echelon form.
In matrix A,
Each row has a leading entry of 1
That is farther to the right than the leading entry of the row above it.
Additionally, all entries below a leading 1 are 0.
This meets the requirements for a matrix to be in reduced echelon form.
Matrix B is in echelon form only.
In matrix B,
Each row has a leading entry
That is farther to the right than the leading entry of the row above it.
However, not all entries below a leading entry are 0.
In the third row, there is a leading 1.
But the entries below it are not all 0.
Matrix is in echelon form only, but not in reduced echelon form.
Matrix C is in neither echelon form nor reduced echelon form.
In matrix C,
The first and third rows have leading entries.
But the second row does not.
In the first row, the leading 1 is not farther to the right than the leading entry of the row below it.
This matrix does not meet the requirements for echelon form or reduced echelon form.
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You are selling your product at a three day event. There's a 60% chance that you will make money. What is the probability that you will make money on the first day and lose money on the second and third day.
Answer:
The required probability = 0.144
Step-by-step explanation:
Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%
Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.
That would be;P(making money) * P(making money) * P(losing money)Kindly recollect;P(making money) = 60% = 60/100 = 0.6P(losing money) = 40% = 40/100 = 0.4The probability we want to calculate is thus;0.6 * 0.6 * 0.4 = 0.144
find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
use the data below to find the logarithmic regression of aids cases over time. use either a calculator or spreadsheet program.
the logarithmic regression of aids cases over time is 4.6
A type of regression called logarithmic regression is used to simulate situations where growth or decay initially increases quickly and then gradually slows down.
A better prediction model is produced by applying the logarithm to your variables, which results in a much more distinct and/or adjusted linear regression line through the base of the data points.
y ≈ 33.7·ln(x) -45.9
4.6
Detailed explanation:
Logarithmic regression can be carried out using a spreadsheet or a graphing calculator. The log curve with the best least-squares fit is about...
y ≈ 33.7·ln(x) -45.9
Around 4.6 is the anticipated value of x needed to get y = 5.2.
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help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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State if the triangles in each pair are similar
So, based on the resemblance between AA and SS, we can say: AEDC and AJKL
what is triangle ?An enclosed triangle is a geometric shape with three sides and three angles in two dimensions. It is one of the fundamental geometric shapes and has several uses in both mathematics and daily life. Acute, obtuse, right, equilateral, isosceles, and scalene triangles are examples of popular types of triangles that can be categorized based on the size of their sides and angles. Triangle analysis is a crucial component of geometry and is used in disciplines including physics, engineering, and architecture.
given
Triangles in option (C) resemble those in (B).
If the matching sides and angles of two triangles are proportionate, then we can say that the triangles are comparable.
Triangle formed by AJKL and AEDC contains:
AED Equals AJK (both at 50 degrees)
ADS = ADE (both are right angles)
CDE = KLJ (both are right angles)
The triangles meet the angle-angle (AA) similarity requirement as a result.
Moreover, we have
DE/ JL = 52/39 AE/ AJ = 24/50 = 12/25
The triangles so also meet the side-side (SS) similarity requirement.
So, based on the resemblance between AA and SS, we can say: AEDC and AJKL
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The complete question is:- State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement.
AJKL~
A) not similar
B) similar; SSS similarity; ADCE C) similar; SAS similarity; AEDC D) similar; SSS similarity; ADEC
I’m not sure what the limit would be if it’s discontinued but defined
The graph's function limit at x=4 is 6.
Define limitIn mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.
The formal definition of the limit of a function f(x) as x approaches a value a is as follows:
For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.
Limit f(x) at x tend to 4⁺ =6.
Limit f(x) at x tend to 4⁻ =6
Hence, the graph's function limit at x=4 is 6.
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part b - find the internal axial force in each bar segment using the answer for the support reaction at a determ
As per the axial force, the support reaction at A is equal in magnitude to the axial force that is applied at the other end of the bar.
To determine the support reaction at A, we will draw a free-body diagram of the bar.
Since the bar is fixed at A, the support reaction at that end will be a vertical force, and we will label it as RA.
Using Newton's second law of motion, we can write the equation of equilibrium for the bar in the vertical direction:
ΣFy = 0
where ΣFy is the sum of all the forces in the vertical direction. Since there are only two forces acting on the bar, the axial force and the support reaction, we can write:
-FA + RA = 0
where FA is the axial force that is applied at one end, and RA is the support reaction at the other end.
From this equation, we can solve for RA:
RA = FA
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Complete Question:
Determine the support reaction at A
The axially loaded bar is fixed at A and loaded as shown. Draw a free-body diagram and determine the support reaction at A.
each of 2 identical number cubes ,shown below, has a different integer,1 through 6,on each face.conside rthe sample space determined by rolling
The positive difference between the greatest sum and the least sum in the sample space of the output of the two cubes is 10.
What is a sample space?A sample space is a mathematical collection or set of possible outcomes of a random experiment. A sample space is represented by the symbol "S". The possible outcome of an experiment is called the events.
The greatest sum is obtained by adding the largest number on the first cube with the largest number on the second cube. The least number can be obtained by adding the smallest number on the first cube with the smallest number on the second cube.
The possible numbers displayed by the first cube are; 1, 2, 3, 4, 5, 6
The possible numbers displayed by the second cube are also; 1, 2, 3, 4, 5, 6
The greatest sum is therefore; 6 + 6 = 12The least sum is therefore; 1 + 1 = 2The positive difference between the greatest sum and the least sum in the sample space is therefore;
12 - 2 = 10
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pls answer!!!
and give simple working ty!!
Step-by-step explanation:
Arithmetic sequences: a2 = a1 + n
Geometric sequences: a2 = a1 * n
a. geometric (2 = 1 * 2, 4 = 2 * 2, 8 = 4 * 2 ...)
b. arithmetic (8 = 5 + 3, 11 = 8 + 3 ...)
c. arithmetic (10 = 5 + 5)
d. geometric (100 = 10 * 10)
In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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Suppose
X1
is a numerical variable and
X2
is a dummy variable with two categories and the regression equation for a sample of
nequals=1919
is
ModifyingAbove Upper Y with caret Subscript iYiequals=77plus+33X1iplus+22X2i.
a.
Interpret the regression coefficient associated with variable
X1.
b.
Interpret the regression coefficient associated with variable
X2.
c.
Suppose that the
tSTAT
test statistic for testing the contribution of variable
X2
is
3.213.21.
At the
0.100.10
level of significance, is there evidence that variable
X2
makes a significant contribution to the model?
Interpret the regression coefficient associated with variable
X1.
Holding constant the effect of
▼
Upper X 2 commaX2,
Upper X 1 commaX1,
for each increase of one unit in
▼
Upper X 2 commaX2,
Upper X 1 commaX1,
the predicted mean value of Y
▼
increases
decreases
by a positive change of nothing unit left parenthesis s right parenthesis . unit(s).
The regression coefficient associated with X1 and X2 interpret it increased by 33 and 22.
Test statistic represents that X2 makes a significant contribution to the model.
The regression coefficient associated with variable X1 is 33.
This means,
Holding all other variables constant, for every one unit increase in X1, Y is expected to increase by 33 units.
The regression coefficient associated with variable X2 is 22.
This means ,
Compared to the reference category ,
Average value of Y for the category represented by X2 is expected to be 22 units higher.
Holding all other variables constant.
Null hypothesis for testing the contribution of variable X2 is that the coefficient of X2 is equal to zero,
X2 does not make a significant contribution to the model.
Alternative hypothesis is that the coefficient of X2 is not equal to zero,
X2 does make a significant contribution to the model.
The t-statistic for X2 is 3.21, and the p-value associated with this statistic is less than 0.10.
Reject the null hypothesis at the 0.10 level of significance.
p-value is less than 0.10,
Conclude evidence that variable X2 makes a significant contribution to the model.
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The above question is incomplete, the complete question is:
Suppose X1 is a numerical variable and X2 is a dummy variable with two categories and the regression equation for a sample of n =1919
is Modifying Y with Y = 77 + 33X1 +22X2
a. Interpret the regression coefficient associated with variable
X1.
b. Interpret the regression coefficient associated with variable
X2.
c. Suppose that the test statistic for testing the contribution of variable
X2 is 3.213.21.
At the 0.100.10 level of significance, is there evidence that variable
X2 makes a significant contribution to the model?
Interpret the regression coefficient associated with variable X1?
a triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square
The cοst οf painting the triangle bοrder at the given rate is Rs. [tex]108\sqrt{(2)[/tex].
What is a triangle?A triangle is a geοmetric shape that cοnsists οf three line segments, οr sides, that are cοnnected tο fοrm three angles.
Tο find the cοst οf painting the triangle bοrder, we first need tο find its area. Let's call the third side οf the triangle "x".
We knοw that the perimeter οf the triangle is 24cm, sο we can write an equatiοn:
6cm + 8cm + x = 24cm
Simplifying this, we get:
x = 10cm
Nοw we can use Herοn's fοrmula tο find the area οf the triangle:
s = (6cm + 8cm + 10cm)/2 = 12cm
Area [tex]= \sqrt{(s(s-6cm)(s-8cm)(s-10cm))[/tex]
[tex]= \sqrt{(12cm6cm4cm*2cm)[/tex]
[tex]= 2\sqrt{(72cm^2)[/tex]
[tex]= 12\sqrt{(2) cm^2[/tex]
Finally, we can calculate the cοst οf painting the bοrder at a rate οf Rs. 9 per square cm:
Cοst = (Area) x (Rate)
[tex]= (12\sqrt{(2)} cm^2) x (Rs. 9/cm^2)[/tex]
[tex]= Rs. 108\sqrt{(2)[/tex]
Therefοre, the cοst οf painting the triangle bοrder at the given rate is= [tex]Rs. 108\sqrt{(2)[/tex]
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a customer buys one abc may 60 call at 6 and sells one abc may 17th call at 3 when abc stock is selling at 63%
the maximum potential loss for this strategy is limited to the net cost of $3 if the stock price stays below the breakeven point of $63, but can be unlimited if the stock price rises significantly above the breakeven point
The maximum potential loss for this strategy can be calculated as the difference between the premiums received and paid. In this case, the customer pays a premium of $6 to buy the ABC May 60 call and receives a premium of $3 for selling the ABC May 17th call. Hence, the total cost for this strategy is $6 - $3 = $3.
The breakeven point for this strategy can be calculated as the strike price of the long call plus the net cost of the strategy, which is $60 + $3 = $63.
If the ABC stock price stays below the breakeven point of $63, both options will expire worthless, and the maximum loss for this strategy will be the net cost of $3.
However, if the ABC stock price rises above the breakeven point of $63, the short call option that was sold will be in the money, and the buyer of the option can exercise it, forcing the seller to sell the shares at the strike price of $17. This means that the maximum loss for this strategy will be unlimited if the stock price rises significantly above the breakeven point.
In summary, the maximum potential loss for this strategy is limited to the net cost of $3 if the stock price stays below the breakeven point of $63, but can be unlimited if the stock price rises significantly above the breakeven point. Therefore, it's important to have a risk management plan in place to mitigate potential losses in case the stock price moves against the expected direction.
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a customer buys one abc may 60 call at 6 and sells one abc may 17th call at 3 when abc stock is selling at 63% the maximum potential loss is?
6 litres of pink paint can be made by mixing 1.5 litres of red paint with the correct amount of white paint.How much white paint is needed
Answer: 4.5 litres
Step-by-step explanation:
If 1.5 liters of red paint is mixed with white paint to make 6 liters of pink paint, then the ratio of red paint to the total mixture is 1.5/6 = 0.25.
Since the pink paint is made by mixing red paint with white paint, the ratio of white paint to the total mixture is 1 - 0.25 = 0.75.
Therefore, to find the amount of white paint needed, we can set up the following proportion:
1.5/0.25 = x/0.75
Solving for x, we get:
x = 0.75 * 1.5 / 0.25 = 4.5
So, 4.5 liters of white paint is needed to make 6 liters of pink paint.
Hi!
If 6 liters were to be made, and 1.5 liters of red is needed, then we would subtract 1.5 from 6 to get your final answer
6 - 1.5 = 4.5.
So, 4.5 liters of white will be needed to make 6 liters of paint.
Hope this helps!
~~~PicklePoppers~~~
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be
approximated by a normal distribution, as shown in the figure
(a) What is the minimum UGPA that would still place a student in the top 5% of UGPAS?
(b) Between what two values does the middle 50% of the UGPAS lie?
COLLE
(a) The minimum UGPA that would still place a student in the top 5% of UGPAS is 3.66
(Round to two decimal places as needed.)
(b) The middle 50% of UGPAS lies between 3 26 on the low end and 3.30 on the high end
(Round to two decimal places as needed.)
Between 3.26 on the low end and 3.30 on the high end is where UGPAS's middle 50% lies.
What does a parabola equation mean?Provided that the parabola's vertex is at the origin and that it is symmetric about the y-axis. So, depending on whether the parabola expands upward or downward, the equation can take the form x2 = 4ay or x2 = -4ay.
Because we are interested in the top 5%, the region to the right of the z-score is 0.05. n,... As a result, we can apply the following z-score formula:
z = (x - μ) / σ
x = z * σ + μ
Substituting the values we have, we get:
x = 1.645 * 0.15 + 3.25 = 3.66
Therefore, the z-scores corresponding to the 25th and 75th percentiles are:
z1 = -0.675
z2 = 0.675
Using the same formula as before, we can find the UGPAs corresponding to these z-scares:
x1 = -0.675 * 0.15 + 3.25 = 3.26
x2 = 0.675 * 0.15 + 3.25 = 3.30
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convert the following linear programming problem to standard form: maximize 2^i -f x2 subject to 0 < x\ < 2 x\ %2 < 3 x\ 2x2 < 5 x2 >0 .
The converted linear programming problem in standard form is given by
maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄ where s₁, s₂, s₃, and s₄ are the slack variables.
convert the linear programming problem to standard form,
Introduce slack variables to represent the inequalities,
And rewrite the objective function as a linear expression.
First, let us introduce the slack variables,
x₁ + s₁= 2
x₂ + s₂ = 3 + 2t
2x₂ + s₃ = 5
s₄ = -x₂
where s₁, s₂, s₃, and s₄ are the slack variables.
Rewrite the objective function as a linear expression,
Maximize 2^i - f x2
= maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄
Now we have the linear programming problem in standard form,
maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄
subject to,
x₁ + s₁ = 2
x₂ + s₂ = 3 + 2t
2x₂ + s₃ = 5
s₄ = -x₂
x₁ >= 0, s₁ >= 0
x₂ >= 0, s₂ >= 0, t >= 0
s₃ >= 0, s₄ >= 0
Added a new variable t to represent the inequality
x₂ % 2 < 3,
which can be rewritten as x₂ = 2t + r,
where r is the remainder of x₂ divided by 2.
Require t to be non-negative, and r to be less than 2.
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A particular intersection in a small town is equipped with a surveillance camera. The number of traffic tickets issued to
drivers passing through the intersection follows the Poisson distribution and averages 5.4 per month.
a. What is the probability that 5 traffic tickets will be issued at the intersection next month?
b. What is the probability that 3 or fewer traffic tickets will be issued at the intersection next month?
c. What is the probability that more than 6 traffic tickets will be issued at the intersection next month?
Diane deposits $70,000 into an account that pays 3% interest per year, compounded annually. Henry deposits $70,000 into an account that also pays 3% per year. But it is simple interest. Find the interest Diane and Henry earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits.
Answer:
Step-by-step explanation:
For Diane's account:
Year 1: Interest = $70,000 x 0.03 = $2,100
Year 2: Interest = ($70,000 + $2,100) x 0.03 = $2,163
Year 3: Interest = ($70,000 + $2,100 + $2,163) x 0.03 = $2,227.89
For Henry's account:
Year 1: Interest = $70,000 x 0.03 = $2,100
Year 2: Interest = $70,000 x 0.03 = $2,100
Year 3: Interest = $70,000 x 0.03 = $2,100
For the first year, both Diane and Henry earn the same interest of $2,100. However, for the second and third years, Diane earns more interest than Henry. Therefore, Diane earns more interest for each year after the first year
The table describes the quadratic function h(x).
x h(x)
−3 6
−2 3
−1 2
0 3
1 6
2 11
3 18
What is the equation of h(x) in vertex form?
From the table, the calculated equation of h(x) in vertex form is h(x) = (x + 1)² + 2
Quadratic Function in Vertex Form from Table of ValuesTo find the equation of the quadratic function h(x) in vertex form, we need to first determine the coordinates of the vertex.
The vertex form of a quadratic function is given by
y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
From the table, we have
(h, k) = (-1, 2)
So, we have
y = a(x + 1)² + 2
To determine the value of 'a', we can substitute any other point from the table into the vertex form equation and solve for 'a'.
For example, using the point (0, 3), we have:
a(0 + 1)² + 2 = 3
a = 1
So, we have
y = (x + 1)² + 2 as the equation
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On the 1st January 2014 Carol invested some money in a bank account.
The total amount of money Carol originally invested is £22,000 in the bank account.
What is compound intrest?Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.
This results in exponential growth or accumulation of interest over time.
Let X be the amount that Carol originally invested in the account.
After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).
After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.
After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).
We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:
(X(1.025) - £1000)(1.025) = £23,517.60
Expanding the left-hand side and simplifying, we get:
X(1.025)² - £1000(1.025) = £23,517.60
X(1.025)² = £24,567.63
Dividing both sides by (1.025)², we get:
X = £22,000 (rounded to the nearest pound)
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The complete question is -
On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Caleb took 24 photos at the zoo. Three-eights of his photos are of giraffes. How many of Caleb’s photos are of giraffes ?
A: 6
B: 9
C: 12
D: 18
Answer:
B: 9
Step-by-step explanation:
We know
Caleb took 24 photos at the zoo. 3/8 of his photos are of giraffes.
How many of Caleb’s photos are of giraffes?
We Take
24 x 3/8 = 9 photos
So, 9 of Caleb's photos are of giraffes.
awaite
Find the Factors of 24 less than 24.
Answer: Factors of 24 include: 1 and 24, 2 and 12, 3 and 8, 4 and 6
Step-by-step explanation:
can you solve this and convert in min at the end of the step
[tex] \frac{1}{30}(ln( \frac{15}{22}))t = [/tex]
The expression 1/30(ln(15/22))t = x when solved for t has a solution of t = -78.95x
Solving the expression for tGiven the following expression
1/30(ln(15/22))t =
The above expression cannot be solved for t
This is so because the expression is not an equation or inequality
To do this, we must equate the expression to a value (say x)
So, we have
1/30(ln(15/22))t = x
Multiply through by 30
This gives
ln(15/22)t = 30x
Evaluate the natural logarithm expression
This gives
-0.38t = 30x
Divide both sides by -0.38
So, we have
t = -78.95x
Hence, the solution for t is t = -78.95x
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which values in the data set are outliers? show all work. 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
In this data set, the only value that is an outlier is 100, since it is above the upper bound of 98.25.
To identify the outliers in the data set, we can use the concept of the interquartile range (IQR) and the 1.5×IQR criterion.
First, we need to find the first and third quartiles (Q1 and Q3) of the data set. To do this, we can order the data set from smallest to largest:
54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100
The median of the data set is the middle value, which is 82.
The lower half of the data set will consists of:
54, 72, 75, 81, 81
The median of the lower half is (72 + 75)/2 = 73.5, which is the value halfway between the two middle values.
The upper half of the data set will consists of:
83, 83, 83, 85, 100
The median of the upper half is (83 + 85)/2 = 84, which is the value halfway between the two middle values.
Therefore, the first quartile (Q1) is 73.5 and the third quartile (Q3) is 84.
The interquartile range (IQR) is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 84 - 73.5 = 10.5
To identify the outliers in the data set using the 1.5×IQR criterion, we need to calculate the lower and upper bounds:
Lower bound = Q1 - 1.5×IQR = 73.5 - 1.5×10.5 = 57.75
Upper bound = Q3 + 1.5×IQR = 84 + 1.5×10.5 = 98.25
Any data point that is below the lower bound or above the upper bound is considered an outlier.
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Mrs. Jefferson needs new whiteboard markers for her classroom. Whiteboard markers at the office supply store are being sold for 5 for 7.25. Mrs. Jefferson has 26 students in her class. She wants to have enough markers so that each student has 3 markers. Which of the amounts would be enough money to buy her students a minimum of 3 markers each? Select all that apply.
$75, $93, $102, $113, $115, $129
Answer:
$129
Step-by-step explanation:
26 students x 3 markers each= 78 markers
Markers are being sold in sets of 5, so she needs at least 16 packs of markers. that will cost her $116
Mr. West uses this recipe to make a batch of soup. He often doubles or triples the recipe and freezes some of the soup. What ratio of cups of stock to batches of soup should Mr. West use to make 1, 2, and 3 batches of soup? how many cups of stock are needed to double the recipe?
Therefore, if the recipe requires 4 cups of stock for one batch of soup, he will need 8 cups of stock to double the recipe.
What is ratio?Ratio is a mathematical term used to compare two or more quantities of the same kind. It is a way of expressing the relationship between two numbers or values. Ratios are usually expressed in the form of a:b, where a and b are the two quantities being compared.
by the question.
Let's assume that the recipe for one batch of soup requires 4 cups of stock. If Mr. West wants to make:
1 batch of soup: he would need 4 cups of stock.
2 batches of soup: he would need 8 cups of stock (4 cups x 2 batches).
3 batches of soup: he would need 12 cups of stock (4 cups x 3 batches).
Therefore, the ratio of cups of stock to batches of soup would be:
1 batch of soup requires 4 cups of stock.
2 batches of soup require 8 cups of stock, so the ratio would be 8 cups of stock per 2 batches of soup, or 4 cups of stock per batch of soup.
3 batches of soup require 12 cups of stock, so the ratio would be 12 cups of stock per 3 batches of soup, or 4 cups of stock per batch of soup.
To double the recipe, Mr. West would need to use twice the amount of each ingredient, including the stock.
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Does anyone know how to write the “In” symbol in mathXL ?? It would help so much if someone could tell me, thanks
Answer:
Natural
Step-by-step explanation:
Ln in mathematics mean natural log. Natural log is the log of a number with base e where e=2.71828. For understanding if the number is 2.71828^10 then the ln of 2.71828^10 is 10.