Answer:
Mark's salary after 25 years is $52,499.39
Step-by-step explanation:
This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:
[tex]S(25) = 32000(1.02)^{(25)}[/tex]
[tex]S(25) = 52499.39[/tex]
assuming no employees are subject to ceilings for their earnings, calculate salaries payable and employer payroll tax expense.
Assuming no employees are subject to ceilings for their earnings IS $7,450
The computation of Salaries Payable is shown below:-
Gross Payroll $10,000
Less:
Federal income tax withheld $1,800
Social security rate at 6% -$600
Medicare rate at 1.5% -$150
Total deduction -$2,550
Salary Payable $7,450
We simply deduct three above taxes from the gross payroll so that we get to know for the salary payable amount
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First use appropriate properties of logarithms to rewrite f(x) and then find f’(x)
Answer:
f(x) = 6ln(8) -6ln(x)f'(x) = -6/xStep-by-step explanation:
You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).
Rules of logarithmsThe log of a ratio is the difference of logs:
ln(a/b) = ln(a) -ln(b)
ApplicationUsing this to rewrite f(x), we have ...
f(x) = 6ln(8/x) = 6(ln(8) -ln(x))
f(x) = 6·ln(8) -6·ln(x)
DerivativeThe derivative of the constant is zero, so ...
f'(x) = -6/x
Universal Electric manufactures sell two models of lamps X and Whose profit being $ 15 and $ 10 respectively. The Process involves two workers A and B who are available for this kind of work with 100 and 80 hours per month respectively. A assembles X in 20 minutes and Y in 30 minutes. B paints X in 20 minutes and Y in 10 minutes. Assuming that all lamps made can be sold without difficulty, determine production figures that maximize profit.
y
The production figure to maximize the profit is is Z = 15x + 10y subject to
2x + 3y ≤ 600 ; 2x + y ≤ 480 ; x,y≥ 0 .
In the question ,
it is given that ,
a company named Universal Electric manufactures sell two models of lamps that is Lamp X and Lamp Y and
Whose profit is $ 15 and $ 10 respectively.
let the number units the company manufactures of lamp X be = x units
let the number units the company manufactures of lamp Y be = y units
let the total profit be = Z ,
So , the profit to maximize be Z = 15x + 10y
worker A assembles Lamp X in 20/60 hours and Lamp Y in 20/60 hours ; and that he is available for 100 hours per month;
So , the inequality is
(20/60)x + (30/60)y ≤ 100.
20x + 30y ≤ 6000
2x + 3y ≤ 600
Similarly , worker B assembles Lamp X in 20/60 hours and Lamp Y in 10/60 hours ; and that he is available for 80 hours per month;
the inequality will be ,
(20/60)x + (10/60)y ≤ 80.
20x + 10y ≤ 4800
2x + y ≤ 480 .
Therefore , the LPP to maximize the profit is Z = 15x + 10y subject to
2x + 3y ≤ 600 ; 2x + y ≤ 480 ; x,y≥ 0 .
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LetVbe the vector space of continuous functions defined on the interval[0,1]. Define an inner product onVby the following rule:⟨f,g⟩=∫01f(x)g(x)dx.Use the Gram-Schmidt orthonormalization procedure to produce an orthonormal basis for the subspace spanned by1,x,x2. Use the results to find the closest-point projection ofx3into this subspace.
The closest projection will have a value of -29/360.
we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,
Set u₁ = 1, a unit vector.
Set v₂ = x and u₂ = v₂ / ||v₂||.
Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.
Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.
Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,
proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃
The inner products will be calculated as follows:
(x³, u₁) = ∫x³ X 1 dx = 1/4
(x³, u₂) = ∫ x³ X x dx = 1/5
(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx
Here all the integrals will have limits of 0 and 1.
Hence we get
= 1/9 - 1/4 X 1/2 - 1/5 X 1/3
= 1/9 - 1/8 - 1/15
= (40 - 45 - 24)/360
= -29/360
Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:
proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃
This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.
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2) If you wish to save up $220,000 using an annuity, what monthly payment is required into the
annuity if the annuity has an APR of 8.0% compounded annually and you wish to reach your
savings goal in 30 years?
The monthly payment required into the annuity with an APR of 8.0% compounded annually and you wish to reach your savings goal in 30 years is $156.19.
How the monthly payment is determined?The monthly payment is required for 360 months (30 years x 12).
We can compute this periodic payment using an online finance calculator by inputting the parameters below:
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 8%
PV (Present Value) = $0
FV (Future Value) = $220,000
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 1
Results:
Monthly Payments (PMT) = $156.19
Sum of all periodic payments = $56,228.40
Total Interest = $163,771.60
Thus, to reach a future value of $220,000, the monthly annuity deposit should be $156.19 for 30 years at 8%.
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The following age structure diagrams were created for various counties in the United States from 2000 census data. Which of the following statements best describes the pattern seen in age structure diagram C?
There is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
Which age structure diagram represents a population's ages the best?
However, it is generally agreed that using a population pyramid is the most effective technique to graphically depict the age and sex distribution of a certain population. A population pyramid displays the numbers or percentages of men and women in each age group using a paired bar chart-style image.Age structure diagrams in nations with high population increase have a sharp pyramid shape.Age structure diagrams in nations with rapid growth have a pyramidal shape, indicating a majority of younger people, many of whom are of reproductive age.Hence, there is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
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The angle θ lies in Quadrant III.
cosθ=−16
What is tanθ?
Responses
35−−√
square root of 35
−35√6
negative fraction numerator square root of 36 end root over denominator 6 end fraction
−35−−√
negative square root of 35
35√6
The tanθ for the angle θ that lies in Quadrant III is √35
How to determine tanθ?Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Given: The angle θ lies in Quadrant III
cosθ= −1/6 (adjacent/hypotenuse)
adjacent = -1 and hypotenuse = 6
We can draw the position of the angle as shown in the image attached.
Using Pythagoras' theorem:
opposite = √6²-(-1)² = √35
tanθ = (-√35) / (-1) = √35 (tanθ = opposite/adjacent)
Note: opposite in Quadrant III is negative
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onvert the integral below to polar coordinates and evaluate the integral. instructions: please enter the integrand in the first answer box, typing theta for . depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. then, enter the limits of integration and evaluate the integral to find the volume. a
Evaluation of the integral is [tex]\frac{81}{16}[/tex]
In mathematics, an integral is either a definite value representing the region under a function's graph for a certain interval or a new function whose derivative represents the original function (indefinite integral). The fact that a definite integral of any function that can be integrated may be found using the indefinite integral and a corollary to the calculus fundamental theorem connects these two interpretations.
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According to the graph of H(w) below, what happens when the width
approaches zero?
Height
25-
(4,25)
(5,20)
(10,10)
(20,5)
25
Width
50
OA. The height gets very large.
OB. The height equals zero.
OC. The height approaches a horizontal asymptote.
OD. The height gets very small.
As per the graph of H(w) when w draws near to no the worth of H(w) gets extremely high.
Explain bit about graph of the function?The graph of a function f is the arrangement of all places in the plane of the structure (x, f(x)). We could likewise characterize the diagram of f to be the chart of the situation y = f(x). In this way, the chart of a capability if an exceptional instance of the diagram of a situation.
According to question:Think about the gave diagram of H(w)
If we observer the diagram of the function H(w) we reasoned that as the worth of w pushes toward 0 the worth of H(w) increments quickly.
The worth of H(W) is getting increasingly high when we are moving towards 0.
So, we can say that
When W → 0, H(w) → ∞
Thus, As per the chart of H(w) when w draws near to no the worth of H(w) gets extremely enormous.
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what is the slope of a equation 2y = 3x + 4
Answer:
[tex]\textsf{Slope}=\dfrac{3}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]2y=3x+4[/tex]
Rearrange the equation to make y the subject by dividing both sides by 2:
[tex]\implies \dfrac{2y}{2}=\dfrac{3x+4}{2}[/tex]
[tex]\implies y=\dfrac{3x}{2}+\dfrac{4}{2}[/tex]
[tex]\implies y=\dfrac{3}{2}x+2[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Compare the rearranged equation with the slope-intercept formula.
Therefore:
[tex]\textsf{Slope}=\dfrac{3}{2}[/tex][tex]\textsf{$y$-intercept}=2[/tex]- GIVING 50 POINTS - !!!PLEASE I BEG OF YOU HELP ME!!! What is the probability that a given student is on financial aid, given that he or she is a graduate? P(Financial Aid | Graduate)=[?]
The probability that a given student is on financial aid, given that he or she is a graduate is 0.72
How to determine the probability that a graduate student is on financial aid?Probability is the measure of the likelihood of an event occurring. In other words, it is a numerical representation of the chance that a particular event will happen.
Probability (graduate student is on financial aid) = number of (graduate student is on financial aid / total number of graduate students
Tota number of graduate students = 1879+ 731 = 2610
P(Financial Aid | Graduate) = 1879 / 2610 = 0.72
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2) If you wish to save up $220,000 using an annuity, what monthly payment is required into the
annuity if the annuity has an APR of 8.0% compounded annually and you wish to reach your
savings goal in 30 years?
Answer:
$936.91
Step-by-step explanation:
To find the monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years, we can use the following formula:
payment = (goal * rate) / (1 - (1 + rate) ^-n)
In this formula, "goal" is the savings goal, "rate" is the monthly interest rate, and "n" is the number of payments.
To find the monthly payment, we need to first convert the annual interest rate to a monthly rate by dividing it by 12:
rate = 8.0% / 12 = 0.0067
Next, we need to find the number of payments by multiplying the number of years by the number of payments per year:
n = 30 years * 12 payments/year = 360 payments
Substituting these values into the formula, we get:
payment = (goal * rate) / (1 - (1 + rate)^-n)
= (220,000 * 0.0067) / (1 - (1 + 0.0067)^-360)
= $936.91
The monthly payment required to save up $220,000 using an annuity with an APR of 8.0% compounded annually over 30 years is $936.91.
Which of the following is not a solution for x < 8?
O x = -3
OX= 7.95
Ox=9
OX= 4.3
Answer:
x=9
Step-by-step explanation:
x=9
To find out what is a solution for x<8 you have to plug in all the answer choices for x.
When you plug in -3, you get -3<8 and 8 is bigger than -3, so then that makes it a solution because -3 is less than 8 and when you plug it in it sets the equation right.
When you plug in 7.95, you get 7.95<8 and 8 is bigger than 7.95 by a few but it still is bigger so then it's a solution because 7.95 is less than 8 making it a solution.
When you plug in 4.3, you get 4.3<8 and 8 is bigger than 4.3 so then it's a solution because it sets the equation right.
When you plug in 9, you get 9<8 and that's not right because 8 isn't bigger than 9, setting this answer choice as a non-solution to the inequality.
(Hope you understand this..)
Consider the dot plots which show the distribution of data collected on two high school basketball players. Which statement BEST describes the center of the data collected for the two players? Responses A mean score for player 1 is greatermean score for player 1 is greater B range is greater for player 1range is greater for player 1 C median score for player 2 is greatermedian score for player 2 is greater D mean score for player 2 is greatermean score for player 2 is greater E mean scores are the same for both players
The best description of the dot plot is; median scores are the same for both players
How to interpret dot plots?A dot plot is defined as a simple plot that displays data values as dots above a number line. Now, dot plots show the frequency with which a specific item appears in a data set. Dot plots shows the distribution of the data.
The median of a data set is simply defined as the value in the middle of that same data set when arranged in ascending order.
From player 1, the data set when arranged in ascending order are;
8, 10, 10, 10, 12, 12, 14, 16, 16
In this case, the exact middle term is 12 which will be the median
For player 2, the data set when arranged in ascending order are;
0, 2, 6, 10, 12, 16, 18, 22, 22
In this case, the exact middle term is 12 which will be the median.
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The length of a rectangle is twice its width.
If the perimeter of the rectangle is 48 cm, find its length and width.
If the perimeter of the rectangle is 48 cm, its length and width is equal to 16 cm and 8 cm respectively.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this equation;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the length is twice the width, we have;
L = 2W
Substituting the given parameters into the perimeter formula, we have;
48 = 2(2W + W)
48 = 6W
W = 48/6
Width, W = 8 cm.
For the length of this rectangle, we have;
L = 2W
L = 2(8)
L = 16 cm.
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match the following descriptions with the method. group of answer choices a model is an automatic, flexible, non-linear regression model, not interpretable, and retains all predictor variables although it may limit the effects of some. [ choose ] a model handles outliers well, handles many potential predictor variables easily, and sorts through predictor variables repeatedly to divide the data into groups to best determine the response variable.
decision tree and neutral network
What is decision tree?
The most effective and well-liked technique for categorization and prediction is the decision tree. A decision tree is a type of tree structure that resembles a flowchart, where each internal node represents a test on an attribute, each branch a test result, and each leaf node (terminal node) a class label.
A model is an automatic flexible non linear regression model not interpretable and retains all predictor variables although it may limit the effect of some decision tree
A model is handles outliers well handle many potential predictor variable easy and short through predictor variables repeatedly to divide the data into group to best determine the response variable is neutral network
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-5xy² + 7x²y+3y³ - 8x³
11
According to question
-5xy²+7x²y+3y³-8x³
putting x=2 and y=3
⇒ -5(2)(3)²+7(2)²(3)+3(3)³-8(2)³
⇒-5(18)+7(12)+3(27)-8(8)
⇒-90+84+81-64
∴ 11
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The correct question is find the value of equation if x=2 and y=3 , -5xy² + 7x²y+3y³ - 8x³
Which expression is equivalent to 8x-2y+x+x
A) 4x
B 8x
c) 6x-2y
D) 10x - 2y
Please help will give brainlest!!!
Answer: D
8x + 1x + 1 x - 2y
The multiple instruments on the spacecraft-Cassini observed a giant storm erupted in December 2010 on Saturn. Which one of the following descriptions is NOT correct for the giant storm?
A. The storm developed in the northern hemisphere.
B. Lightning was not detected in the giant storm.
C. The storm generated very bright clouds on Saturn.
D. The storm affected the radiant energy budget of Saturn
The correct answer is option B.
The observation of a giant storm on Saturn from spacecraft Cassini indicates that lightning was not detected in the giant storm.
Usually Mega storms on Saturn happen on every 20 to 30 years.
Through the Cassini spacecraft, scientists could see a massive storm in December 2010. They saw that the storm waves were spreading from the planet's centre and that it was seen as a ringed globe.
The storm waves covered the whole surface of Saturn and had a diameter of around 190,000 miles or 300,000 kilometres.
Simply said, this enormous storm is also known as the Great Northern Storm or the Great White Spot.
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Community center sells a total of 297 tickets
Adult tickets are $3
Student tickets are $1
They collect $479 in ticket sales
How many of each type of ticket were sold ?
They sold $479 in ticket sales and they had a total of 297 tickets sold, so they must have sold $479/297 = $<<479/297=1.61>>1.61 per ticket.
There are two types of tickets, adult tickets and student tickets, and adult tickets are $3, so the student tickets are $1.61 - $3 = $<<1.61-3=-1.39>>-1.39.
However, a ticket cannot be negative so we know that all of the tickets must have been adult tickets and they sold 297 tickets for $479, so they sold 297 tickets * $3/ticket = $<<297*3=891>>891 worth of adult tickets. Answer: \boxed{891}.
NEED HELP ASAP ALSO I’M GIVING A TON OF POINTS AND THANKS! :)
Answer:
Compounded Semiannually: [tex](1.03454)^t[/tex] and APR = 3.454%
Compounded Quarterly: [tex](1.03469)^t[/tex] and APR = 3.469%
Step-by-step explanation:
Compound Interest Formula:The Compound Interest Formula is as follows: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], which can also be written as: [tex]A = P((1 + \frac{r}{n})^n)^t[/tex], using properties of exponents. This is crucial since we want one value inside the parenthesis to calculate the APR (Annual Percentage Rate). Since we want the APR, the only thing we really care about is the [tex](1 + \frac{r}{n})^n[/tex], but this is going to be our APR + 1.
In the question, it's formatted as: [tex]b^t[/tex], and this inside part is going to be our b, so: [tex]b = (1 + \frac{r}{n})^n[/tex], and to calculate the APR we simply subtract 1.
Calculating APR:Compounded semiannually means the interest is compounded twice a year, so n = 2. We are also given the interest to be 3.425% which in decimal form is 0.03425
Plugging this into the formula stated above we get: [tex]b = (1 + \frac{0.03425}{2})^2 \approx 1.03454[/tex]
So we have the form:
[tex](1.03454)^t[/tex]
With our APR simply being the base - 1:
[tex]APR \approx 0.03454[/tex]
We multiply this by 100 to get it in percentage form:
[tex]APR\approx 3.454\%[/tex]
Compounded quarterly means the interest is compounded four times a year, so n = 4. Plugging in known values we get:
[tex]b = (1 + \frac{0.03425}{4})^4 \approx 1.03469[/tex]
So we have the form:
[tex](1.03469)^t[/tex]
With our APR simply being the base - 1
[tex]APR \approx 0.03469[/tex]
Multiply this by 100 to get it in percentage form:
[tex]APR \approx 3.469\%[/tex]
Answer:
[tex]\begin{array}{|c|c|c|}\cline{1-3} \vphantom{\dfrac12} \sf koooAccount& b^t& \sf Annual\;Percentage\;rate \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;annually& (1.03425)^t& 3.425\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;semiannually & \left(1.03454\right)^t &3.454\% \\\cline{1-3} \vphantom{\dfrac12} \sf compounded\;quarterly & \left(1.03469\right)^t& 3.469\%\\\cline{1-3} \vphantom{\dfrac12} \sf compounded\; daily& \left(1.03484\right)^t& 3.484\%\\\cline{1-3} \end{array}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
From inspection of the compound interest formula:
[tex]\implies b^t=\left[\left(1+\dfrac{r}{n}\right)^n\right]^t[/tex]
To find the annual percentage rate:
[tex]\implies APR=(b-1)\times 100[/tex]
Compounded annuallyGiven:
r = 3.425% = 0.03425n = 1Substitute the values into the formula for [tex]b^t[/tex]:
[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{1}\right)^1\right]^t[/tex]
[tex]\implies b^t=\left(1.03425\right)^t[/tex]
Therefore, the annual percentage rate is:
[tex]\implies APR=(1-1.03425) \times 100[/tex]
[tex]\implies APR=0.03425 \times 100[/tex]
[tex]\implies APR=3.425\%[/tex]
Compounded semi-annuallyGiven:
r = 3.425% = 0.03425n = 2Substitute the values into the formula for [tex]b^t[/tex]:
[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{2}\right)^2\right]^t[/tex]
[tex]\implies b^t=\left(1.03454326...\right)^t[/tex]
[tex]\implies b^t=\left(1.03454\right)^t[/tex]
Therefore, the annual percentage rate is:
[tex]\implies APR=(1-1.03454) \times 100[/tex]
[tex]\implies APR=0.03454 \times 100[/tex]
[tex]\implies APR=3.454\%[/tex]
Compounded quarterlyGiven:
r = 3.425% = 0.03425n = 4Substitute the values into the formula for [tex]b^t[/tex]:
[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{4}\right)^4\right]^t[/tex]
[tex]\implies b^t=\left(1.03469241...\right)^t[/tex]
[tex]\implies b^t=\left(1.03469\right)^t[/tex]
Therefore, the annual percentage rate is:
[tex]\implies APR=(1-1.03469) \times 100[/tex]
[tex]\implies APR=0.03469 \times 100[/tex]
[tex]\implies APR=3.469\%[/tex]
Compounded dailyGiven:
r = 3.425% = 0.03425n = 365Substitute the values into the formula for [tex]b^t[/tex]:
[tex]\implies b^t=\left[\left(1+\dfrac{0.03425}{365}\right)^{365}\right]^t[/tex]
[tex]\implies b^t=\left(1.03484162...\right)^t[/tex]
[tex]\implies b^t=\left(1.03484\right)^t[/tex]
Therefore, the annual percentage rate is:
[tex]\implies APR=(1-1.03484) \times 100[/tex]
[tex]\implies APR=0.03484 \times 100[/tex]
[tex]\implies APR=3.484\%[/tex]
Note: There is an error in the given table: the given "compounded daily" rate is incorrect.
What is the role of galaxies, planets, satellites, comets, and asteroids in shaping the universe?
We can say that the role of galaxies, planets, satellites, comets and asteroids, in the conformation of the universe, is based on being elements to structure it.
¿What is the universe and what are its components?In physics, it is mentioned that the universe is all physical existence that exists, this goes from our planet to what is found abroad.
Within the universe, as an entity, how to find different elements that structure it, for example, we have:
GalaxiesPlanetsSatellitesKitesAsteroids¡Hope this helped!
Find the critical values, to, to test the claim that H, H2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that of to. Use a = 0,05 ny = 25, n = 30, X = 23, X2 = 21,5 = 1.5,82 = 1.9 OA 2064 OB 2.797 Oct2492 OD 1.711
The critical values for the following sample are ±2.0064.
Here it is given that α = 0.05,
To calculate the critical values we will use the t-statistic.
Here n₁ = 25 and n₂ = 30
Hence, the degrees of freedom
d.f = n₁ + n₂ - 2 [Since it's a 2-sample test]
= 25 + 30 - 2
= 53
Now our significance level is α = 0.05,
To know the critical value we will make use of a t-distribution table and look up the value corresponding to a 0.05 significance level and 53 degrees of freedom.
Here we will get the critical values ±2.0064
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Maya spent 40% of her savings to pay for a bicycle
How much
money does she have left in her savings after buying the bicycle?
Answer:
60% because the total should be 100% and if you take 40% away you should be left with 60%
Describe a real-life representation of the following.
12/49 =0.24
A real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
In this case, the real-life representation of the following fraction 12/49 =0.24 is that 12kg or rice is to be shared among 49 friends. How many kg will each person get?
This is illustrated as 12/49.
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A distribution of values is normal with a mean of 120 and astandard deviation of 21. From this distribution, you are drawingsamples of size 13. Find the interval containing the middle-most76% of sample means:Enter your answer using interval notation. In this context,either inclusive or exclusive intervals would be acceptable. Roundyour numbers to one decimal place. Answers obtained using exactz-scores or z-scores rounded to 3 decimal places are accepted.
The interval containing the middle-most76% of sample means [tex]102.836 < \mathrm{x} < 137.164[/tex].
As per the data given in the above question,
A distribution of values is normal with a mean of [tex]\mu=120[/tex].
A standard deviation of [tex]\sigma=21[/tex].
Drawing samples of size n=13.
The middle-most76% of sample means.
Find the interval containing the middle-most76% of sample means?
[tex]\mathrm{P}(-\mathrm{z} < \mathrm{x} < \mathrm{z})=0.76\\\mathrm{P}(\mathrm{x} < \mathrm{z})-\mathrm{P}(\mathrm{x} < -\mathrm{z})=0.76\\[/tex]
Further
[tex]\mathrm{P}(\mathrm{x} < -\mathrm{z})=\mathrm{P}(\mathrm{x} > \mathrm{z})[/tex]
[tex]\mathrm{P}(\mathrm{X} < \mathrm{Z})-\mathrm{P}(\mathrm{X} > \mathrm{Z})=0.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})-1+\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.46\\2 \mathrm{P}(\mathrm{X} < \mathrm{Z})=1.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.88[/tex]
[tex]= NORMSINV (0.73)\\\mathrm{Z}=0.613[/tex]
[tex]& \mathrm{X}=\mathrm{z} \sigma+\mu \\& \mathrm{X}=0.613 \times 28+120 \\& \mathrm{X}=137.164-\mathrm{x} & =\mu-\mathrm{z} \sigma \\-\mathrm{x} & =120-0.613 \times 28 \\-\mathrm{x} & =102.836[/tex]
Now the interval sample is as follow,
[tex]102.836 < \mathrm{x} < 137.164[/tex]
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assuming the roc to be lzl < 113, use long division to determine the values of x[o], x[ -1], and x[ -2].
Long division can be used to determine the absolute value of x[0], x[-1], and x[-2] when the roc is known. To do this, divide the roc (113) by the coefficient of the highest power in the polynomial (x2). Then, divide the remainder (3) by the coefficient of the next highest power (x), which gives x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives x[-2] = 8.
To use long division to determine the values of x[0], x[-1], and x[-2], begin by dividing the roc (113) by the coefficient of the highest power in the polynomial (x2). This gives a result of 113/x2 = 10. This means that x[0] = 10. This number is then used as the divisor for the next step, which is to divide the remainder (3) by the coefficient of the next highest power (x). This gives a result of 3/x = 3, so x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives 8/1 = 8, so x[-2] = 8. This process can be repeated to determine the values of x[n] for any polynomial.
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1/2% of b is 50 find the quantity b ,if
Answer: 100
Step-by-step explanation:
You can set up the equation:
50 / (1/2)
Dividing by 1/2 is thhe same as multiplying by 2.
50 / (1/2) = 100
50(2) = 100
How to find the length of a line segment in a circle?
Additional Topics in Math
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Circle Geometry
The semicircle above has a radius of r inches, and chord CD is parallel to the diameter AB. If the length of CD is 2/3 of the length of AB, what is the distance between the chord and the diameter in terms of r?
The semicircle above has a radius of r inches, The distance between the chord and the diameter in terms of r is √5 r/3 inches.
What is chord of Circle ?A chord of a circle can be defined as a line segment connecting any two points on the circumference. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.
To find the distance required one can use either the Pythagorean theorem or the trigonometric ratios. Let the semicircle have center O. The diameter AB has length 2r. Because chord CD is 2/3 of the length of the diameter,
CD=2/3(2r) = 4r/3
let the distance between diameter AB and chord CD be x inches. To find x draw a right triangle connecting center O, the midpoint, E of chord CD, and point C . Using Pythagorean theorem here,
r² = x² + (CD/2)²
=> r² = x² + (2r/3)²
=> r² = x² + 4r²/9
=> x² = r² - 4r²/9 = 5r²/9
=> x = √5 r/3
Hence, the distance between the chord and the diameter in terms of r is √5r/3..
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The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?
The value of each company's product sold price is given as follows:
Company x: $22,000,500.Company y: $21,999,500.How to obtain the values?The values of each company's product sold price is obtained using a system of equations, for which the variables are defined as follows:
Variable x: Company's x sold price.Variable y: Company's y sold price.The sold sum of both the two companies salaries are $44,000,000, hence:
x + y = 44000000.
The sold price of company x is 1000 more than the other, hence:
x = 1000 + y.
Then the sold price of company y can be found replacing the second equation into the first, as follows:
1000 + y + y = 44000000
2y = 44000000 - 1000
y = (44000000 - 1000)/2
y = $21,999,500.
The sold price for company x is then calculated as follows:
x = 1000 + y = 1000 + 21999500 = $22,000,500.
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