Step-by-step explanation:
Maping is the weak point in fixed point method.
Problem 2 Consider three functions f, g, and h, whose domain and target are Z. Let fx)x2 g(x)=2x (a) Evaluate fo g(0) (b) Give a mathematical expression for f o g
Answer:
a) 0; b) 4[tex]x^{2}[/tex]
Step-by-step explanation:
a) To compute f o g (0), first evaluate g(x) for x=0 and then evaluate f for x=g(0).
[tex]f \circ g (0)=f(2 \cdot 0)=f(0)=0^2[/tex]
b) To compute a mathematical expression for f o g do the same but instead of 0 use x,
[tex]f \circ g (x) = f( 2 \cdot x)= (2 \cdot x )^2[/tex]
In the question, f(x) = x², g(x) = 2x. We need to determine the value of function f composed with function g at 0 (f o g(0)), and the general expression for f o g(x). f o g(0) = 0 and (f o g)(x) = 4x².
Explanation:To solve this problem, we first need to understand that 'f o g' denotes the composition of function f and function g, defined as (f o g)(x) = f(g(x)). In this case, function f(x) = x^2 and function g(x) = 2x.
(a) To evaluate f o g at 0, we substitute x = 0 into g(x), giving us g(0) = 2*0 = 0. Substituting g(0) into f(x), we get f(g(0)) = f(0) = 0. So, f o g(0) = 0.
(b) For a general form of f o g, we substitute g(x) = 2x into f(x), resulting in (f o g)(x) = f(2x) = (2x)^2 = 4x^2.
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Soles the differential equations using the substitution u=y’; u’=y”
y’y”=2
Answer with explanation:
The given differential equation
y'y''=2--------(1)
We have to apply the following substitution
u=y'
u'=y"
Applying these substitution in equation (1)
u u'=2
[tex]u \frac{du}{dx}=2\\\\ u du=2 dx\\\\ \int u du=\int 2 dx\\\\\frac{u^2}{2}=2 x+K\\\\\frac{y'^2}{2}=2 x+K\\\\y'^2=4 x+2 K\\\\y'=(4 x+2 K)^{\frac{1}{2}}\\\\ dy=(4 x+2 K)^{\frac{1}{2}} d x\\\\\int dy=\int(4 x+2 K)^{\frac{1}{2}} d x\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{4 \times \frac{3}{2}}+J\\\\y=\frac{(4 x+2 K)^{\frac{3}{2}}}{6}+J[/tex]
Where , J and K are constant of Integration.
Suppose the lifetime of a computer memory chip may be modeled by a Gamma distribution. The average lifetime is 4 years and the variance is 16/3 years squared. What is the probability that such a chip will have a lifetime of less than 8 years?
Final answer:
To find the probability that a computer memory chip will have a lifetime of less than 8 years, we can use the properties of the Gamma distribution.
Explanation:
To find the probability that a computer memory chip will have a lifetime of less than 8 years, we can use the properties of the Gamma distribution. The average lifetime of the chip is given as 4 years, which corresponds to the mean. The variance is given as 16/3 years squared, which is equal to the mean squared.
Using these values, we can determine the shape and rate parameters of the Gamma distribution. The shape (α) is equal to the mean squared divided by the variance, which in this case is 16/3. The rate (β) is equal to the mean divided by the variance, which in this case is 4/(16/3).
To find the probability that the chip will have a lifetime of less than 8 years, we can calculate the cumulative distribution function (CDF) of the Gamma distribution with the shape and rate parameters we obtained.
The principal at Apple Blossom High School decided to take her students on a field trip to the movie theater. A total of 250 people went on the trip. Adults paid $4.50 for a ticket and students paid $2.50 for a ticket. How many students and how many adults went to the movies if they paid a total of $805 at the movie theater?
Answer:
90 adults; 160 students
Step-by-step explanation:
Let "a" represent the number of adults who went. The number of students can be represented by (250-a). Then the total cost of tickets is ...
4.50a +2.50(250-a) = 805
2a + 625 = 805 . . . . . . simplify
2a = 180 . . . . . . . . . . . . subtract 625
a = 90 . . . . . . . . . . . . . . divide by 2
# of students = 250 -90 = 160
160 students and 90 adults went to the movies.
Answer:
the answer is 90 adults , and 160 students
A sample of 81 calculus students at a large college had a mean mathematics ACT score of 26 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all calculus students at this college.
Final answer:
The 95% confidence interval for the mean mathematics ACT score for all calculus students at this college is calculated to be between 24.693 and 27.307.
Explanation:
To calculate a 95% confidence interval for the mean mathematics ACT score for all calculus students at the college, we use the sample mean and standard deviation along with the z-score for a 95% confidence level. Since the sample size is large (n=81), we can use the z-distribution as an approximation for the t-distribution.
The formula for a confidence interval is:
Mean ± (z-score * (Standard Deviation / √n))
Here, the sample mean (μ) is 26, the standard deviation (s) is 6, and the sample size (n) is 81. For a 95% confidence level, the z-score is approximately 1.96.
Now we calculate the margin of error (ME):
ME = 1.96 * (6 / √81) = 1.96 * (6 / 9) = 1.96 * 0.6667 = 1.307
Therefore, the 95% confidence interval is
26 ± 1.307
Lower Limit = 26 - 1.307 = 24.693
Upper Limit = 26 + 1.307 = 27.307
The confidence interval is (24.693, 27.307).
We estimate with 95 percent confidence that the true population mean for the mathematics ACT score for all calculus students at the college is between 24.693 and 27.307.
Please help me with this
Answer:
Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU
Step-by-step explanation:
You can observe the sides of both triangles to see if this property holds
Lets check the length of AB
A(0,3) and B(0,-1)
[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\\\AB=\sqrt{(0-0)^2+(-1-3)^2} \\\\\\\\AB=\sqrt{0^2+-4^2} \\\\\\AB=\sqrt{16} =4units[/tex]
Now check the length of the corresponding side DE
D(1,2) and E(1,-2)
[tex]DE=\sqrt{(1-1)^2+(-2-2)^2} \\\\\\DE=\sqrt{0^2+-4^2} \\\\\\DE=\sqrt{16} =4units[/tex]
The side AB has the same length as side DE.This is also true for the remaining corresponding sides.
You have just won $150,000 from a lottery. If you invest all this amount in a tax-free money market fund earning 8% compounded weekly, how long do you have to wait to become a millionaire? (Round your answer to two decimal places.)
Answer:
1234.08 weeks.
Step-by-step explanation:
Since, the amount formula in compound interest is,
[tex]A=P(1+r)^t[/tex]
Where, P is the principal amount,
r is the rate per period,
t is the number of periods,
Given,
P = $ 150,000,
Annual rate = 8 % = 0.08,
So, the weekly rate, r = [tex]\frac{0.08}{52}[/tex] ( 1 year = 52 weeks )
A = 1,000,000
By substituting the values,
[tex]1000000=150000(1+\frac{0.08}{52})^t[/tex]
[tex]\frac{1000000}{150000}=(\frac{52+0.08}{52})^t[/tex]
[tex]\frac{20}{3}=(\frac{52.08}{52})^t[/tex]
Taking log both sides,
[tex]log(\frac{20}{3})=t log(\frac{52.08}{52})[/tex]
[tex]\implies t = \frac{log(\frac{20}{3})}{ log(\frac{52.08}{52})}=1234.07630713\approx 1234.08[/tex]
Hence, for become a millionaire we should wait 1234.08 weeks.
2)Whitney is shopping for party supplies. She finds a package of 10 plates, 16 napkins, and a package of 8 cups. What is the least number of packages of plates, napkins, and cups so that she has the same number of each? Write answer in sentence form.
Final answer:
To have the same number of plates, napkins, and cups, Whitney will need at least 80 of each.
Explanation:
To find the least number of packages of plates, napkins, and cups so that Whitney has the same number of each, we need to find the least common multiple (LCM) of 10, 16, and 8. The LCM is the smallest multiple that all three numbers have in common.
10 = 2 x 5, 16 = 2 x 2 x 2 x 2, and 8 = 2 x 2 x 2
We can identify the prime factors of each number and then multiply the highest factor from each number. In this case, the LCM is 2 x 2 x 2 x 2 x 5 = 80.
Therefore, Whitney will need at least 80 plates, 80 napkins, and 80 cups to have the same number of each.
What is another name for validity in qualitative research? a. objectivity b. bias c. trustworthiness d. reliability
Answer:
(d) reliability
Step-by-step explanation:
mostly we see that validity and reliability is the key aspects of all research they help in differentiation between good and bad research so both are very necessary aspects of any research so the another name for validity in quantity research is reliability.
so the reliability will be the correct answer
so option (d) will be correct option
Express the answers to the following calculations in scientific notation, using the correct number of significant figures. (a) 145.75 + (2.3 × 10−1) × 10 (b) 79,500 / (2.5 × 102) × 10 (c) (7.0 × 10−3) − (8.0 × 10−4) × 10 (d) (1.0 × 104) × (9.9 × 106) × 10
Each calculation has been evaluated, taken all significant figures into consideration, and results have been presented in scientific notation. Special attention was given to rules related to multiplying numbers in scientific notation.
Explanation:The given calculations require us to use scientific notation and proper treatment of significant figures. We are using the fundamentals of arithmetic with scientific notation, which is based on the rules of exponents. Each calculation is treated as follows:
(a) For the expression 145.75 + (2.3 × 10−1) × 10 = 147.05. This result has five significant figures, but to write numbers in scientific notation, we should round off to two significant figures as the lowest number of significant figures is 2 (in 2.3). Therefore, 147.05 becomes 1.47 × 10² in scientific notation. (b) For the expression 79,500 / (2.5 × 10²) × 10 = 3180. This is in turn expressed in scientific notation with three significant figures (since 2.5 has 3 significant figures) as 3.18 × 10³. (c) For the expression (7.0 × 10−3) − (8.0 × 10−4) × 10 = 6.2 × 10-3. Converting to scientific notation using two significant figures (based on original values), get 6.2 × 10⁻³. (d) For the expression (1.0 × 10⁴) × (9.9 × 10⁶) × 10 = 9.9 × 10¹¹ based on the rule of multiplying the numbers out front and adding up the exponents. Learn more about Scientific Notation and Significant Figures here:
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For each of the squences below, find a formula that generates the sequence.
(a) 10,20,10,20,10,20,10...
Answer:
[tex]a_{n}=15 + (-1)^n * 5[/tex]
Step-by-step explanation:
First, we notice that the when n is odd, [tex]a_{n}[/tex] = 10. And when n is even, [tex]a_{n}[/tex] = 20.
The average of 10 and 20 is [tex](10+20)/2 = 15[/tex]. So, the distance between 15 and 10 is the same that between 15 and 20.
That distance is 5.
From 15, we need to subtract 5 to get 10 when n is odd and we need to add 5 to get 20 when n is even.
The easiest way to express that oscilation is using [tex](-1)^n[/tex], because it is (-1) when n is odd and 1 when is even. And when multiplied by 5, it will add or subtract 5 as we wanted.
From a standard 52-card deck, how many eight-card hands consists of three cards of one denomination, three cards of another denomination, and two cards of a third denomination?
Answer:82,368
Step-by-step explanation:
Final answer:
The total number of eight-card hands formed from a standard 52-card deck where the hand consists of three cards of one denomination, three cards of another, and two cards of a third is 27,456. This is calculated by finding combinations of denominations and the specific cards within those denominations.
Explanation:
To answer the question of how many eight-card hands can be formed from a standard 52-card deck, where the hand consists of three cards of one denomination, three cards of another denomination, and two cards of a third denomination, we have to use combinations. This is a problem of combinatorics in which we are finding the number of ways to select items from a group without regard to order.
First, we choose the denominations. There are 13 denominations and we want to choose 3 of them for our hand. Using the combination formula, this can be done in C(13, 3) ways:
C(13, 3) = 13! / (3! × (13-3)!) = 286
After choosing the denominations, we need to select the specific cards. For each of the first two denominations, we select 3 out of the 4 available suits, and for the third denomination, we select 2 out of the 4 suits. This can be done as follows:
C(4, 3) for the first denomination: C(4, 3) = 4 ways
C(4, 3) for the second denomination: C(4, 3) = 4 ways
C(4, 2) for the third denomination: C(4, 2) = 6 ways
Multiplying the ways to choose the denominations by the ways to choose the cards for each denomination gives us the total number of distinct hands.
Total hands = C(13, 3) × C(4, 3) × C(4, 3) × C(4, 2) = 286 × 4 × 4 × 6 = 27,456
Therefore, there are 27,456 different eight-card hands that meet the given criteria.
An experimental drug is administered to 80 randomly selected individuals, with the number of individuals responding favorably recorded.Does the probability experiment represent a binomial experiment?
Answer:
Yes, because the experiment satisfies all the criteria for a binomial experiment.
Step-by-step explanation:
A binomial experiment has the following criterias,
1. There must be a fixed number of trials
2. Each trial is independent of the others
3. There must be only two outcomes ( success and failure )
4. The probability of each outcome is same.
Given,
An experimental drug is administered to 80 randomly selected individuals, with the number of individuals responding favorably recorded,
The number of trials = 80 ( fixed )
Each individuals is independent,
Total outcomes = 2 ( yes or no ),
Also, the probability of each individual is same,
Hence, the given probability experiment represent a binomial experiment.
I NEED THIS DONE IN AN EXCEL SPREADSHEET WITH SOLUTIONS
The following probabilities for grades in management science have been determined based on past records:
Grade Probability
A 0.1
B 0.2
C 0.4
D 0.2
F 0.10
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on.
Determine the expected grade and variance for the course.
Answer:
Expected Grade=2 i.e., C
Variance=1.2
Step-by-step explanation:
[tex]Expected\ value=E\left [ x \right ]=\sum _{i=1}^{k} x_{i}p_{i}[/tex]
The x values are
A = 4
B = 3
C = 2
D = 1
F = 0
Probability of each of the events
P(4)=0.1
P(3)=0.2
P(2)=0.4
P(1)=0.2
P(0)=0.1
[tex]E\left [ x \right ]=4\times 0.1+3\times 0.2+2\times 0.4+1\times 0.2+0\times 0.1\\\therefore E\left [ x \right ]=2[/tex]
Variance
[tex]Var\left ( x\right)=E\left [ x^2 \right ]-E\left [ x \right ]^2[/tex]
[tex]E\left [ x^2 \right ]=4^2 \times 0.1+3^2 \times 0.2+2^2 \times 0.4+1^2 \times 0.2+0^2 \times 0.1\\\Rightarrow E\left [ x^2 \right ]=5.2\\E\left [ x \right ]^2=2^2=4\\\therefore Var\left ( x\right)=5.2-4=1.2\\[/tex]
PLEASE HELP TRIG SEE ATTACHMENT WILL MARK BRAINLIEST
Answer:
sin Ф=3/√13
Cos Ф=2/√13
Tan Ф=3/2
Step-by-step explanation:
Let x=2
Let y=3
Let r be the length of line segment drawn from origin to the point
[tex]r=\sqrt{x^2+y^2}[/tex]
Find r
[tex]r=\sqrt{2^2+3^2} =\sqrt{4+9} =\sqrt{13}[/tex]
Apply the relationship for sine, cosine and tan of Ф where
r=hypotenuse
Sine Ф=length of opposite side÷hypotenuse
Sin Ф=O/H where o=3, hypotenuse =√13
sin Ф=3/√13
CosineФ=length of adjacent side÷hypotenuse
Cos Ф=A/H
Cos Ф=2/√13
Tan Ф=opposite length÷adjacent length
TanФ=O/A
Tan Ф=3/2
Installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. If the interest rate is 1.25% per month on the unpaid balance, find (a) the cost of the TV (b) the total amount of interest paid
Answer:
a) $ 1465.418
b) $ 214.582
Step-by-step explanation:
Since, the monthly payment formula of a loan is,
[tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]
Where, PV is the principal amount of the loan,
r is the monthly rate,
n is the total number of months,
Here, P = $ 30, r = 1.25 % = 0.0125, n = 36 ( since, time is 3 years also 1 year = 12 months )
Substituting the values,
[tex]30=\frac{PV(0.0125)}{1-(1+0.0125)^{-36}}[/tex]
By the graphing calculator,
[tex]PV=865.418[/tex]
a) Thus, the cost of the TV = Down Payment + Principal value of the loan
= $ 600 + $ 865.418
= $ 1465.418
b) Now, the total payment = Monthly payment × total months
= 30 × 36
= $ 1080
Hence, the total amount of interest paid = total payment - principal value of the loan
= $ 1080 - 865.418
= $ 214.582.
help please? even if someone gave me the steps to figure the answer myself, that'd be great
Answer:
The height is 28.57 cm.
The surface area is 9,628 cm^2.
Step-by-step explanation:
I assume the cooler is shaped like a rectangular prism with length and width of the base given, and with an unknown height.
volume = length * width * height
First, we convert the volume from liters to cubic centimeters.
60 liters * 1000 mL/L * 1 cm^3/mL = 60,000 cm^3
Now we substitute every dimension we have in the formula and solve for height, h.
60,000 cm^3 = 60 cm * 35 cm * h
60,000 cm^3 = 2,100 cm^2 * h
h = (60,000 cm^3)/(2,100 cm^2)
h = 28.57 cm
The height is 28.57 cm.
Now we calculate the internal surface area.
total surface area = area of the bases + area of the 4 sides
SA = 2 * 60 cm * 35 cm + (60 cm + 35 cm + 60 cm + 35 cm) * 28.57 cm
SA = 9,628 cm^2
The surface area is 9,628 cm^2.
Find an equation for the line that passes through the points (-6, -1) and (4, 5)
Answer:
y=3/5x+13/5
Step-by-step explanation:
Finding the slope:
m=6/10
m=3/5
The y intercept is 13/5
Thus, the equation is y=3/5x+13/5
Answer:
Equation of the given line is, y = (3/5)x +13/5
Step-by-step explanation:
Points to remember
Equation of the line passing through the poits (x1, y1) and (x2, y2) and slope m is given by
(y - y1)/(x - x1) = m where slope m = (y2 - y1)/(x2 - x1)
To find the slope of line
Here (x1, y1) = (-6, -1) and (x2, y2) = (4, 5)
Slope = (y2 - y1)/(x2 - x1)
= (5 - -1)/(4 - -6)
= 6/10 = 3/5
To find the equation
(y - y1)/(x - x1) = m
(y - -1)/(x - -6) = 3/5
(y + 1)/(x + 6) = 3/5
5(y + 1) = 3(x + 6)
5y + 5 = 3x + 18
5y = 3x + 13
y = (3/5)x +13/5
Explain why a positive times a negative is a negative number.
Explanation:
This can be explained by thinking numbers on the number line as:
Lets take we have to multiply a positive number (say, 2) with a negative number say (-3)
2×(-3)
Suppose someone is standing at 0 on the number line and to go to cover -3 , the person moves 3 units in the left hand side. Since, we have to compute for 2×(-3), The person has to cover the same distance twice. At last, he will be standing at -6, which is a negative number.
A image is shown below to represent the same.
Thus, a positive times a negative is a negative number.
What is the converse of the following: "If n is prime then n is odd or n is 2." A. If n is prime then n is odd or n is 2 B. If n is odd or n is 2 then n is composite. C. If n is even but not 2 then n is composite. D. If n is odd or n is 2 thenn is prime. E. If n is composite then n is even but not 2. F. If n is prime then n is even but not
Answer:
Option D "If n is odd or n is 2 then n is prime"
Step-by-step explanation:
we know that
To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
In this problem
the conditional statement is "If n is prime then n is odd or n is 2."
The hypothesis is "If n is prime"
The conclusion is "n is odd or n is 2."
therefore
interchange the hypothesis and the conclusion
The converse is "If n is odd or n is 2 then n is prime"
Final answer:
The converse of 'If n is prime then n is odd or n is 2' is 'If n is odd or n is 2 then n is prime', therefore, the correct answer from the given options is D.
Explanation:
The converse of the statement 'If n is prime then n is odd or n is 2' is constructed by reversing the hypothesis and the conclusion. The converse would state 'If n is odd or n is 2 then n is prime'. Hence, the correct answer is D. We establish the converse by suggesting that the given properties (being odd or being the number 2) necessarily imply that a number is prime; however, it's important to note that while all prime numbers other than 2 are indeed odd, not all odd numbers are prime. Therefore, the converse is not logically equivalent to the original statement.
Question 1
A county reports 250 deaths with a population of 500,000. What is the mortality rate?
For the same month last year, the mortality rate was .42 Have deaths increased, decreased, or stayed the same?
Possible answers:
Mortality rate is 0.5 per 1000
The death rates have increased.
Answer:
Mortality rate is 0.5 per 1000 habitant
the number of deaths have increased (from 210 to 250)
Step-by-step explanation:
Hello
Mortality rate is the number of deaths in a specific population,usually expressed in units of deaths per 1,000 individuals per year
[tex]Mortality\ rate\ (S)= \frac{(D)}{(P)} *10^{n} \\\\\\\\[/tex]
where
S=Mortality rate
D=deaths
P= population
n= is a conversion form ,such as multiplying by 10^{3}=1000, to get mortality rate per 1,000 individuals( we will use n=3)
step 1
asign
S=unknown
D=250
P=500000
n=3, (for each 1000 people)
step 2
Replace
[tex]S=\frac{250}{500000}*1000\\S=\ 0.5\ per\ 1000[/tex]
Mortality rate is 0.5 per 1000 habitant
step 3
what if S=0.42
S=0.42(assuming it is 0.42 per 1000,n=3)
D=unknown
P=500000
[tex](S)= \frac{(D)}{(P)} *10^{n}\\\\isolatin D\\\\S*P=D*10^{n}\\ D=\frac{S*P}{10^{n} } \\\\and\ replacing\\\\D=\frac{(0.42)*(500000)}{10^{3} }\\\\ Deaths=210\\[/tex]
the number of deaths have increased (from 210 to 250)
Have a great day
Convert 141 to base seven.
Answer:
(141)₁₀→(241)₇
Step-by-step explanation:
(141)₁₀→(?)₇
for conversion of number from decimal to base 7 value we have to
factor 141 by 7
which is shown in the figure attached below.
from the attached figure we can clearly see that the colored digit will
give the conversion
we will write the digit from the bottom as shown in figure
(141)₁₀→(241)₇
Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang. Find the height and width of the door.NOTE: 1 zhang = 10 chi = 100 cun. Give your answers inunits of chi and cun.
Answer:
height: 9 chi 6 cunwidth: 2 chi 8 cunStep-by-step explanation:
The factor-of-ten relationship between the different units means we can combine the numbers in decimal fashion. If 1 unit is 1 zhang, then 1 chi is 0.1 zhang and 1 cun is 0.01 zhang. Hence 6 chi 8 cun is 0.68 zhang.
Let x and y represent the width and height, respectively. In terms of zhang, we have ...
y - x = 0.68
x^2 +y^2 = 1^2
Substituting y = 0.68 +x into the second equation gives ...
x^2 + (x +0.68)^2 = 1
2x^2 +1.36x - 0.5376 = 0 . . . . . eliminate parentheses, subtract 1
Using the quadratic formula, we have ...
x = (-1.36 ±√(1.36^2 -4(2)(-0.5376)))/(2·2) = (-1.36 ±√6.1504)/4
x = 0.28 . . . . . the negative root is of no interest
y = 0.28 +0.68 = 0.96
In units of chi and cun, the dimensions are ...
height: 9 chi 6 cun
width: 2 chi 8 cun
Answer:
Height: 9 chi 6 cun
Width: 2 chi 8 cun
Step-by-step explanation:
Now there is a door whose height is more than its width by 6 chi 8 cun. The distance between the [opposite] corners is 1 zhang. The height of the door is 9 chi 6 cun and the width of the door is 2 chi 8 cun.
1 zhang = 10 chi = 100 cun
For a lottery game, a player must match a sequence of three repeatable numbers, ranging from 0 to 9, in exact order. With a single ticket, what is the probability of matching the three winning numbers?
Answer:[tex]\frac{1}{1000}[/tex]
Step-by-step explanation:
For the lottery game three numbers must match in exact order
From 0 to 9 total 10 numbers are there
Therefore selecting exactly same numbers as of winner is
=[tex]^{10}C_1\times ^{10}C_1\times ^{10}C_1 [/tex]
Since numbers are repeatable therefore each time we have a choice of choosing 1 number out o 10
=[tex]10\times 10\times 10[/tex]
Probability of winning=[tex]\frac{1}{1000}[/tex]
In a lottery game where the player must match a repeatable sequence of three numbers ranging from 0-9, the probability of a single ticket having the winning sequence is 1/1000, or 0.1%.
Explanation:The subject of this problem is probability in Mathematics, specifically in a lottery context. Each digit in the sequence can be any number from 0 to 9. Because these numbers are repeatable, this means there are 10 possible numbers for each of the three digits in the sequence. Therefore, to find the total number of possible sequences, you multiply the ten options for the first digit by the ten for the second and the ten for the third, which comes to 10 * 10 * 10 = 1000 total possible sequences.
Since you are only looking for one specific sequence being the winning number, that means there’s only 1 favorable outcome out of 1000. Therefore, the probability of your ticket having the winning number sequence is 1/1000, or 0.001 in decimal form or 0.1% in percentage form.
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Mike deposited $850 into the bank in July. From July to December, the amount of money he deposited into the bank increased by 15% per month. What's the total amount of money in his account after December? Round your answer to the nearest dollar. Show your work. 4.
Answer:
$1.710
Step-by-step explanation:
Mike deposited $850 into the bank in July.
In August his balance will be: $850×1.15 = $977.5
In September his balance will be: $977.5×1.15 = $1124.125
In October his balance will be: $1124.125×1.15 = $1292.74375
In November his balance will be: $1292.74375×1.15 = $1.486,6553125
In December his balance will be: $1.486,6553125×1.15 = $1.709,653609375
Therefore, the amount of money he will have after december will be $1.710
For the mathematics part of the SAT the mean is 514 with a standard deviation of 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the ACT. Use z-scores to determine on which test he performed better.
Answer:
Bob performed better in mathematics part of the SAT than the ACT
Step-by-step explanation:
We need to calculate the z-scores for both parts and compare them.
Z-score for the SAT is calculated using the formula:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where [tex]\mu=514[/tex] is the mean and [tex]\sigma=113[/tex] is the standard deviation, and [tex]X=660[/tex] is the SAT test score.
We plug in these values to obtain:
[tex]Z=\frac{660-514}{113}[/tex]
[tex]Z=\frac{146}{113}=1.29[/tex] to the nearest hundredth.
We use the same formula to calculate the z-score for the ACT too.
Where [tex]\mu=20.6[/tex] is the mean and [tex]\sigma=5.1[/tex] is the standard deviation, and [tex]X=27[/tex] is the ACT test score.
We substitute the values to get:
[tex]Z=\frac{27-20.6}{5.1}=1.25[/tex] to the nearest hundredth.
Since 1.29 > 1.25, Bob performed better in mathematics part of the SAT
Using z-scores to determine where Bob's performance stands compared to others, we find that he performed slightly better on the SAT with a z-score of 1.29, than on the ACT with a z-score of 1.25.
Explanation:To determine on which test Bob performed better, we have to calculate his z-scores on both the SAT and ACT. Z-score is a statistical measurement that describes a score's relationship to the mean of a group of scores. It indicates how many standard deviations an element is from the mean.
Here is how you calculate the z-score: z = (X - μ) / σ, where X is the individual score, μ is the mean, and σ is the standard deviation.
We can apply this formula to both of Bob's scores. For the SAT: z = (660 - 514) / 113 ≈ 1.29 For the ACT: z = (27 - 20.6) / 5.1 ≈ 1.25
Comparing the z-scores, Bob's score is above the mean by 1.29 standard deviations on the SAT and by 1.25 standard deviations on the ACT. Therefore, Bob performed slightly better on the SAT than on the ACT when comparing his scores to other test takers.
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A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 15 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.
Answer:
The probability that the racket is wood or defective is 0.57.
Step-by-step explanation:
Let W represents wood racket, G represents the graphite racket and D represents the defective racket,
Given,
n(W) = 100,
n(G) = 100,
⇒ Total rackets = 100 + 100 = 200
n(W∩D) = 15,
n(G∩D) = 14,
⇒ n(D) = n(W∩D) + n(G∩D) = 15 + 14 = 29,
We know that,
n(W∪D) = n(W) + n(D) - n(W∩D)
= 100 + 29 - 15
= 100 + 14
= 114,
Hence, the probability that the racket is wood or defective,
[tex]P(W\cup D) = \frac{114}{200}[/tex]
[tex]=0.57[/tex]
The principal randomly selected six students to take an aptitude test. Their scores were: 81.6 72.0 81.1 86.4 70.2 83.1 Determine a 90% confidence interval for the mean score for all students
Answer:
84.38, 73.74
Step-by-step explanation:
score given 81.6, 72.0, 81.1, 86.4, 70.2, 83.1
sample size (n) = 6
[tex]mean = \dfrac{81.6+ 72.0+ 81.1+ 86.4+ 70.2+ 83.1}{6}[/tex]
mean = 79.06
standard deviation
[tex]\sigma =\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}[/tex]
[tex]\sigma =\sqrt{\frac{ (81.6-79.06)^2+(72-79.06)^2+(86.4-79.06)^2+(70.2-79.06)^2+(81.1-79.06)^2+(83.1-79.06)^2}{6-1}}[/tex]
σ = 6.47
level of significance (α) = 1 - 90% = 10%
confidence interval
[tex]\bar{x} \pm t_{\alpha}(\frac{S}{\sqrt{n}})\\79.06 \pm 2.015(\frac{6.47}{\sqrt{6} })[/tex]
=79.06 ± 5.32
= 84.38, 73.74
The 90% confidence interval for the mean score is calculated using the sample mean, standard deviation, and the Z-value from a Z-distribution table. The resulting range gives us a 90% confidence that the real population mean lies within this interval.
Explanation:To compute a 90% confidence interval for the mean score, we use the sample data we have, our sample mean, and our standard deviation. The confidence interval gives us a range of values that likely includes the true population mean. We use the standard statistical formula for the 90% confidence interval: X ± (Z(α/2) * (σ/√n))
First, calculate the sample mean (X) and the standard deviation (σ). The scores are: 81.6, 72.0, 81.1, 86.4, 70.2, 83.1. The X will be the total of all the scores divided by 6, and σ will be a measure of how much they deviate from the mean.
Next, insert these values into the determining a confidence interval formula. You will need the Z(α/2) value for a 90% confidence interval, which is 1.645 in a Z-distribution table. Finally, take your X ± the calculated result to achieve the 90% confidence interval.
Remember: a 90% confidence interval means that you can be 90% confident that the true mean for all students lies within this interval.
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Rewrite the system of linear equations as a matrix equation AX = B.
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2x1 + 5x2 − 2x3 + x4 + 2x5 = 1
x1 + x2 − 2x3 + x4 + 4x5 = 5
Answer:
Given: [tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]
[tex]2x_{1}+5 x_{2} - 2_{3} + x_{4} + 2x_{5}\\[tex]
[tex]x_{1}+ x_{2} - 2_{3} + x_{4} + 4x_{5}\\[/tex]
The system of linear equations in matrix form may be written as:
AX=B,
where,
A is coefficient matrix of order [tex]2\times 4[/tex] and is given by:
A = [tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]
X is variable matrix of order [tex]5\times 1[/tex] and is given by:
X= [tex]\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}[/tex]
and B is the contant matrix of order [tex]2\times 1[/tex] and is given by:
B = [tex]\begin{bmatrix}1\\5\end{bmatrix}[/tex]
Now, AX=B
[tex]\begin{bmatrix}2&5&-2&1&2\\1&1&-2&1&4\end{bmatrix}[/tex]. [tex]\begin{bmatrix}x_{_{1}}\\x_{_{2}}\\x_{3}\\x_{4}\\x_{5}\end{bmatrix}[/tex] = [tex]\begin{bmatrix}1\\5\end{bmatrix}[/tex]
6. Use the element method and proof by contradiction to prove that for any sets A,B and C, if B nCCA, then (C - A) n (B - A)=0.
Answer:
Suppose,
(C - A) ∩ (B - A) ≠ ∅
Let x is an element of (C - A) ∩ (B - A),
That is, x ∈ (C - A) ∩ (B - A),
⇒ x ∈ C - A and x ∈ B - A
⇒ x ∈ C, x ∉ A and x ∈ B, x ∉ A
⇒ x ∈ B ∩ C and x ∉ A
⇒ B ∩ C ⊄ A
But we have given,
B ∩ C ⊂ A
Therefore, our assumption is wrong,
And, there is no common elements in (C - A) and (B-A),
That is, (C - A) ∩ (B - A) = ∅
Hence proved...