Answer:
(1.218 ; 1.322)
the confidence interval is appropriate
Step-by-step explanation:
The confidence interval :
Mean ± margin of error
Sample mean = 1.27
Sample standard deviation, s = 0.80
Sample size, n = 914
Since we are using tbe sample standard deviation, we use the T table ;
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 914 - 1 = 913
Tcritical(0.05, 913) = 1.96
Margin of Error = 1.96 * 0.80/√914 = 0.05186
Mean ± margin of error
1.27 ± 0.05186
Lower boundary = 1.27 - 0.05186 = 1.218
Upper boundary = 1.27 + 0.05186 = 1.322
(1.218 ; 1.322)
According to the central limit theorem, sample means will approach a normal distribution as the sample size increases. Hence, the confidence interval is valid, the sample size of 914 gave a critical value at 0.05 which is only marginally different from that will obtained using a normal distribution table. Hence, the confidence interval is appropriate
express the ratio as a fraction in the lowest terms 100cm:5m
Step-by-step explanation:
we know that 1m=100cm
so 1m:5m(final)
1:5
Answer:
1/5
Step-by-step explanation:
Since 100cm = 1m
then
100cm:5m becomes 1m:5m
which in fraction is 1/5
SCC U of 1 pt 3 of 1 1.2.11 Assigned Media A rectangle has a width of 49 centimeters and a perimeter of 216 centimeters. V The length is cm.
Answer:
The length is of 59 cm.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with width w and length l is given by:
[tex]P = 2(w + l)[/tex]
Width of 49 centimeters and a perimeter of 216 centimeters:
This means that [tex]w = 49, P = 216[/tex]
The length is cm.
We have to solve the equation for l. So
[tex]P = 2(w + l)[/tex]
[tex]216 = 2(49 + l)[/tex]
[tex]216 = 98 + 2l[/tex]
[tex]2l = 118[/tex]
[tex]l = \frac{118}{2}[/tex]
[tex]l = 59[/tex]
The length is of 59 cm.
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated samplingg distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.5 years and a standard deviation of 2.1 years. Random samples of size 17 are drawn from the population and the mean of each sample is determined.
a. 1.33 years, 2.1 years
b. 5.5 years, 0.12 years
c. 5.5 years, 0.51 years
d. 1.33 years, 0.51 years
Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
a garden has more roses than daisies, and it has 9 daisies.furthermore, each flower in the garden has more then 3 petals.Let r represent the number of roses and let P represent the total number of petals in the garden. let’s compare the expressions P and 3(r+9). which statement is correct
Answer:
There is not enough info to tell
Step-by-step explanation:
Khan acadamey
how much water consumed by Aguilar family as shown in the meter reading
Answer:
?????????????????
Step-by-step explanation:
????????
Evaluate for x=2 and y=3: x^2y^-3/x^-1y
Answer:
8/81
Step-by-step explanation:
It's most efficient to simplify the quotient algebraically before inserting the values of the variables x and y.
The given expression reduces to x³ / y^4.
Substituting 2 for x and 3 for y, we get:
(2)³ 8
--------- = ---------- (Agrees with first given possible answer)
(3)^4 81
ok i think you guys can do it
[tex] {64}^{ \frac{2}{3} } \div {27}^{ \frac{5}{3} } \times 54 \\ = > \: {({2}^{3} )}^{ \frac{2}{3} } \div ({{3}^{3}})^{ \frac{5}{3} } \times 54 \\ = > \: {2}^{2} \div {3}^{5} \times 54 \\ = > \: 4 \div 243 \times 54 \\ = > \: 4 \div 13122 \\ = > \: \frac{4}{13122} \\ = > \: \frac{2}{6561} [/tex]
Hope it helps!!!!!!!!!!
PLEASE HELP MATH⚠️⚠️⚠️⚠️⚠️
Convert this into algerbraic expression:
The difference of a number cubed and the same number
Step-by-step explanation
n^3-n.
Hope this will help you :) <3
Find an expression for the general term of each of the series below. Use n as your index, and pick your general term so that the sum giving the series starts with n=0.
A. x^3cosx^2=x^3-(x^7)/2!+(x^11)/4!-(x^15)/6!+...
general term =
B. x^3sinx^2=x^5-(x^9)/3!+(x^13)/5!-(x^17)/7!+...
general term =
Answer:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
Step-by-step explanation:
A
Let's start with the first function:
[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 3, 7, 11, 15...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.
so let's put the two things together:
[tex](-1)^{n}x^{4n+3}[/tex]
Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
So now we can build the whole series:
[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]
B
Now, let's continue with the next function:
[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]
In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a
[tex](-1)^{n}[/tex].
This will guarantee us that the terms will always change their signs so that will be the first part of our expression.
next, the power of the x. Notice the given sequence: 5, 9, 13, 17...
we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.
so let's put the two things together:
[tex](-1)^{n}x^{4n+5}[/tex]
Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!
This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!
So let's put it all together so we get:
[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
So now we can build the whole series:
[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]
List all factors of the number 52. SHOW ALL WORK!!!
Answer:
Factors of number 52
Factors of 52: 1, 2, 4, 13, 26 and 52.
Negative Factors of 52: -1, -2, -4, -13, -26 and -52.
Prime Factors of 52: 2, 13.
Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.
Sum of Factors of 52: 98.
20. In the image, ABC has measure 58°. What is the measure of ABD?
A. 116°
OB. 29°
O C. 58
OD. There is not enough information to determine LABD.
Answer:
Option B, 29°
Step-by-step explanation:
The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.
Answered by GAUTHMATH
If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)
A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2
Hey there!
We are given two functions - one is Exponential while the another one is Linear.
[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]
1. Operation of Function
(f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]
2. Substitution
Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]
3. Evaluate/Simplify
Cancel out the brackets and combine like terms.[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]
4. Final Answer
(f+g)(x) = 4^x+5x-2We know that the remainder Rn will satisfy |Rn| ⤠bn + 1 = 1 (n + 1)9n + 1. We must make n large enough so that this is less than 0.0001. Rounding to five decimal places, we have b2 = _________ , b3 =_________and b4 =__________
This question is incomplete, the complete question is;
We know that the remainder R[tex]_n[/tex] will satisfy | R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex].
We must make n large enough so that this is less than 0.0001.
Rounding to five decimal places,
we have b₂ = _________ , b₃ =_________and b₄ =__________
Answer:
b₂ = 0.00617, b = 0.00046 and b₄ = 0.00004
Step-by-step explanation:
Given the data in the question;
| R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]
Now,
b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]
b₂ = b[tex]_{ 1 + 1[/tex] = 1 / ( 1 + 1 )9[tex]^{ 1 + 1[/tex] = 1 / (2)9² = 1 / 162 = 0.00617 { 5 decimal places }
b₃ = b[tex]_{ 2 + 1[/tex] = 1 / ( 2 + 1 )9[tex]^{ 2 + 1[/tex] = 1 / (3)9³ = 1 / 2187 = 0.00046 { 5 decimal places }
b₄ = b[tex]_{ 3 + 1[/tex] = 1 / ( 3 + 1 )9[tex]^{ 3 + 1[/tex] = 1 / (4)9⁴ = 1 / 19683 = 0.00004 { 5 decimal places }
Therefore, b₂ = 0.00062, b = 0.00046 and b₄ = 0.00004
Find the value for the side marked below.
Round your answer to the nearest tenth.
у
100
49°
y = [?]
Answer:
y = 75.5
Step-by-step explanation:
Reference angle (θ) = 49°
Hypotenuse = 100
Opposite = y
Apply trigonometric function, SOH. Which is:
Sin θ = Opp/Hyp
Plug in the values
Sin 49 = y/100
100*Sin 49 = y
y = 75.5 (nearest tenth)
every student from different schools planted as many plants of their number if they planted 4225 plants how many students were there
Answer:
65 students.
Step-by-step explanation:
Given that :
Every student planted as many plant as their number ;
Then let the number of student = x
Then the number of plant planted by each student will also = x
The total number of plants planted by all the students = 4225
The Number of students can be obtained thus ;
Total number of plants = Number of plants * number of plants per student
4225 = x * x
4225 = x²
√4225 = x
65 = x
Hence, there are 65 students
f(x) = 1
g(x) = x - 4
Can you evaluate (g•f)(0)? Explain why or why not?
Answer:
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Step-by-step explanation:
We are given the following functions:
[tex]f(x) = 1[/tex]
[tex]g(x) = x - 4[/tex]
Can you evaluate (g•f)(0)?
This is a multiplication of functions g and f, and these functions have no restrictions(such as a even root or a fraction), and thus [tex](g \mult f)(0) = g(0)f(0) = -4(1) = -4[/tex]
Answer:
To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.
You must evaluate the function f first.
Division by 0 is undefined.
The composition cannot be evaluated.
How long will it take the same crew to clear the entire plot of 2 1/2 acres?
Answer:
It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Step-by-step explanation:
Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:
1/3 = 0.333
1/2 = 0.5
0.333 = 2
2.5 = X
2.5 x 2 / 0.333 = X
15 = X
Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.
Translate the sentence into an inequality.
The sum of 5 and c is greater than – 22.
what da hell the answer ?
Answer:
5 + c > -22
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
InequalitiesStep-by-step explanation:
Step 1: Define
Sum of 5 and c is greater than -22
↓ Identify
Sum = addition
5 + cIs greater than = inequality
>Add them all together:
5 + c > -22
There are twelve shirts in my closet. Five are red, four are blue, and three are green. What is
the probability that I choose a red or blue shirt to wear tomorrow?
O 65%
0 75%
0 80%
60%
58%
Answer:
the probability that I chose red or blue is 75%
75%
What was the original price of the car? Show all work
Answer:
I got u, it is litearly 16540/83.8 = $19737.5
Step-by-step explanation:
its very simple sincen 100-16.2=83.8
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
Can someone help me?
Answer:
x = 80
Step-by-step explanation:
3x/2=120°
3x=240°
x=80°
Answered by GAUTHMATH
SOMEONE HELP PLEASE! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Using the following distribution, calculate the following measures of central tendency:
State Proportion of Residents Without Health Insurance Louisiana 0.19 New Jersey 0.13 New York 0.16 Pennsylvania 0.11 Rhode Island 0.09 South Carolina 0.13 Texas 0.25 Washington 0.14 Wisconsin 0.10
N = 9
Identify the variable:
Identify the median:
Identify the mean:
How would you describe the shape of the distribution:
Answer:
(a) Residents
(b) [tex]Median = 0.13[/tex]
(c) [tex]\bar x = 0.14[/tex]
(d) Right skewed
Step-by-step explanation:
Given
The data of residents without health insurance
Solving (a): The variable
The variable is the residents
Solving (b): The median
First, we sort the data
[tex]Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25[/tex]
So, the median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{9 + 1}{2}[/tex]
[tex]Median = \frac{10}{2}[/tex]
[tex]Median = 5th[/tex]
The 5th element of the dataset is: 0.13
So:
[tex]Median = 0.13[/tex]
Solving (c): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}[/tex]
[tex]\bar x = \frac{1.3}{9}[/tex]
[tex]\bar x = 0.14[/tex]
Solving (d): The shape of the distribution
In (b) and (c), we have:
[tex]Median = 0.13[/tex]
[tex]\bar x = 0.14[/tex]
By comparison, the mean is greater than the median.
Hence, the shape is: right skewed.
Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.
Answer:
A. false B. true C. false D. true
Whope you all like this answer
Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did was correct and/or incorrect.
Part 2:
Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.
3x^2 + kx - 8
If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.
The first binomial can be further factored:
8x + 12 = 4(2x + 3)Part 2The quadratic expression needs to have two roots in order to be factored as two binomials.
The discriminant must be positive or zero:
D = b² - 4ac ≥ 0We have a = 3, b = k, c = -8
So we get following inequality:
k² - 4*3*(-8) ≥ 0k² + 96 ≥ 0Since k² is positive for any value of k, the solution is any value of k:
k ∈ RHope this attachment helps you.
PUWID, du then solve.
Timothy's father will build a shed for his tools. It will be a square with a
1 side that measures 8 m. What is the area of the shed?
1. What is asked?
testy
Answer:
The area of the shed=[tex]64m^2[/tex]
Step-by-step explanation:
We are given that
Side of square =8m
We have to find the area of the shed.
To find the area of shed we will find the area of square.
We know that
Area of square=[tex]side\times side[/tex]
Using the formula
Area of square=[tex]8\times 8[/tex]
Area of square=[tex]64m^2[/tex]
Area of shed=Area of square
Area of shed=64 square m
Hence, the area of the shed=[tex]64m^2[/tex]
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 140 in. and the height is 186 in.
Answer:
The volume is increasing at a rate of 27093 cubic inches per second.
Step-by-step explanation:
Volume of a cone:
THe volume of a cone, with radius r and height h, is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
In this question:
We have to differentiate implictly is function of t, so the three variables, V, r and h, are differenciated. So
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s.
This means that [tex]\frac{dr}{dt} = 1.4, \frac{dh}{dt} = -2.4[/tex]
Radius is 140 in. and the height is 186 in.
This means that [tex]r = 140, h = 186[/tex]
At what rate is the volume of the cone changing?
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{\pi (140)^2}{3}(-2.4) + \frac{2\pi 140*186}{3}1.4[/tex]
[tex]\frac{dV}{dt} = -0.8\pi(140)^2 + 62*2\pi*1.4*140[/tex]
[tex]\frac{dV}{dt} = 27093[/tex]
Positive, so increasing.
The volume is increasing at a rate of 27093 cubic inches per second.
What fraction of the total number of students are boys?
Step-by-step explanation:
total number of students are :4x 3 = 12
Fraction that's boys are : 3÷12
Solve the inequality. |X+19|<7
Answer:
x<-12
Step-by-step explanation: hope this helps!
