A small lawnmower company produced 1,500 lawnmowers in 2008. In an effort to determine how maintenance-free these units were, the company decided to conduct a multiyear study of the 2008 lawnmowers. A sample of 200 owners of these lawnmowers was drawn randomly from company records and contacted. The owners were given an 800 number and asked to call the company when the first major repair was required for the lawnmowers. Owners who no longer used the lawnmower to cut their grass were disqualified. After many years, 183 of the owners had reported. The other 17 disqualified themselves. The average number of years until the first major repair was 3.3 for the 183 owners reporting. It is believed that the population standard deviation was 1.47 years. If the company wants to advertise an average number of years of repair-free lawn mowing for this lawnmower, what is the point estimate? Construct a 95% confidence interval for the average number of years until the first major repair.
Answer:
The 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).
Step-by-step explanation:
The (1 - α)% confidence interval for the average using the finite correction factor is:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}[/tex]
The information provided is:
[tex]N=1500\\n=183\\\sigma=1.47\\\bar x=3.3[/tex]
The critical value of z for 95% confidence level is,
z = 1.96
Compute the 95% confidence interval for the average number of years until the first major repair as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\cdot\sqrt{\frac{N-n}{N-1}}[/tex]
[tex]=3.3\pm 1.96\times\frac{1.47}{\sqrt{183}}\times\sqrt{\frac{1500-183}{1500-1}}\\\\=3.3\pm 0.19964\\\\=(3.10036, 3.49964)\\\\\approx (3.1, 3.5)[/tex]
Thus, the 95% confidence interval for the average number of years until the first major repair is (3.1, 3.5).
Find the volume between the cone
X= sqrt(y^2 + z^2) and the sphere
x^2 + y^2 + z^2 = 16.
The volume between the cone and the sphere is approximately 23.55 cubic units.
We are given that;
[tex]X= sqrt(y^2 + z^2)[/tex]
[tex]x^2 + y^2 + z^2 = 16.[/tex]
Now,
To find the volume between the cone and the sphere, we can use a triple integral in spherical coordinates.
The cone corresponds to the equation [tex]$\rho = 2\cos(\phi)$[/tex], where [tex]$\rho$[/tex] is the radial distance, [tex]$\phi$[/tex]is the polar angle, and [tex]$\theta$[/tex] is the azimuthal angle. The sphere corresponds to the equation [tex]$\rho = 4$[/tex]. The limits of integration are:
[tex]$0 \leq \theta \leq 2\pi$$0 \leq \phi \leq \frac{\pi}{4}$$2\cos(\phi) \leq \rho \leq 4$[/tex]
The volume element in spherical coordinates is [tex]$\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Therefore, the volume is:
[tex]$V = \int_{0}^{2\pi}\int_{0}^{\frac{\pi}{4}}\int_{2\cos(\phi)}^{4}\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Evaluating this integral, we get:
[tex]$V = \frac{32}{3}\pi - 8\sqrt{2}\pi + 16\pi$[/tex]
Therefore, by volume of cone the answer will be 23.55 cubic units.
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Help me please!!!
Which of the following is a like term of -5.92?
Answer:
C. -7.78
Step-by-step explanation:
If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator . To do this, you need to find the least common multiple (LCM) of the two denominators. To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.
Step 1: Keep the denominator the same. Step 2: Add or subtract the numerators. ...
Step 1: Find the Lowest Common Multiple (LCM) between the denominators. ...
Step 1: Convert all mixed numbers into improper fractions. ...
In this second method, we will break the mixed number into wholes and parts. ...
Thus, is equivalent to.
Fractions
Fractions can be thought of as another way of seeing division. If you have one whole pizza and two people want to share it equally, they will divide it into two halves:
The bottom number of a fraction is the denominator. It tells how many parts a whole has been divided into. In this case our pizza is divided into two parts.
Proper Fractions, Improper Fractions, and Mixed Numbers
A proper fraction is one in which the numerator is smaller than the denominator.
An improper fraction is one in which the numerator is larger than the denominator. If the numerator is larger than the denominator, the fraction equals a number that is greater than one.
Lowest Terms
Want to learn more? Take an online course in Basic Math.
Finding the GCF (Greatest Common Factor)
The greatest common factor is the largest factor that divides two numbers. We find this by figuring out what prime numbers are multiplied together to make up each number. A prime number is a number that can only be divided by itself or by one. Examples of prime numbers are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. We want to focus on those that are less than ten in most cases.
Finding the LCD (Lowest Common Denominator)
Adding and Subtracting Fractions
To add or subtract two fractions, the two fractions must have the same denominator. Therefore, you will have to find the lowest common denominator and change each fraction to an equivalent fraction. Then you add or subtract the numerators as indicated and put the resultant number over the denominator and reduce the fraction to lowest terms.
Answer:
B
Step-by-step explanation:
N/A
Please answer all 6!!! Will give brainliest!!!
David owns a food truck that sells tacos and burritos. He sells each taco for $4.50 and each burrito for $7.75. Yesterday David made a total of $519.25 in revenue from all taco and burrito sales and there were twice as many tacos sold as there were burritos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
The completely factored form of z^5 + 4z^4 - 12z^3
Answer:
−108z 5−64z 3+3z 2−24z−384/6
Step-by-step explanation:i just looked it up.
Find the product of the binomial (4x+3) with the trionomial (2x square -5x -3)
Answer:
The product of given binomial and trinomial is:
[tex]8x^3-34x^2-27x-9[/tex]
Step-by-step explanation:
A binomial is a polynomial with 2 terms and trinomial is a term with 3 terms.
Given
[tex](4x+3)\\and\\(2x^2-5x-3)[/tex]
Distributive property can be used to find the result.
Writing mathematically
[tex](4x+3)(2x^2-5x-3)\\= 4x(2x^2-5x-3)+3(2x^2-5x-3)\\= 8x^3-40x^2-12x+6x^2-15x-9[/tex]
Combining alike terms
[tex]= 8x^3-40x^2+6x^2-12x-15x-9\\= 8x^2-34x^2-27x-9[/tex]
Hence,
The product of given binomial and trinomial is:
[tex]8x^3-34x^2-27x-9[/tex]
Help plz and thank you
Answer:
A- Mother Nature
Step-by-step explanation:
Mother Nature= $.40 per pound
That is better than all others
Amy types at an average speed of 38 words per minute. She has already typed 1,450 words of her final paper, which will be more than 4,000 words. Which inequality can be used to solve for x, the number of minutes it will take Amy to finish typing her paper?
A. 38x- 1,450>76
B. 38(x + 1,450)>4,000
C. 38x> 4,000
D. 38x + 1,450> 4,000
The perimeter of a rectangle is 304 cm. The length is 40 cm longer than the
width. Find the length and width. show steps pls
Answer:
p=2(L+W)
p=304
L=40+w
p=2(40+w+w) ,40+w is the value of L
304=2(40+2w)
304/2=2(40+2w)/2 divided both side by 2
152=40+2w
152-40=2w
112=2w
112/2=2w/2
w=56
and L =40+w
40+56=96.
so L=96 and W=56.
A simple random sample of 64 observations was taken from a large population. The sample mean and the standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is:________
a. 1.875
b. 40
c. 5
d. 15
e. None of the above
Answer:
The correct option is d
Step-by-step explanation:
From the question we are told that
The sample size is n = 64
The mean is [tex]\= x = 320[/tex]
The standard deviation is [tex]\sigma = 120[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_x = \frac{\sigma}{ \sqrt{n} }[/tex]
=> [tex]\sigma_x = \frac{120}{ \sqrt{64} }[/tex]
=> [tex]\sigma_x =15[/tex]
can u pls help me with this question
Answer:
45 cookies
Step-by-step explanation:
Use a unit rate.
With a unit rate, we find the number of cookies that are baked using 1 scoop.
(30 cookies)/(6 scoops) = 5 cookies/scoop
The rate of 30 cookies to 6 scoops is the same as the unit rate of 5 cookies/scoop.
Now we multiply the unit rate by 9 scoops.
9 scoops * 5 cookies/scoop = 45 cookies
Answer: 45 cookies
Caitlin has a $10 gift certificate to the music
store. She has chosen a number of CDs from the $7
bargain bin. If the cost of the CDs is $32 after the gift
certificate is credited, how many CDs did Caitlin buy
9514 1404 393
Answer:
6
Step-by-step explanation:
Before application of the $10 credit, Caitlin's purchase was $32 +10 = $42. Your knowledge of multiplication facts tells you that 42 = 6×7. If each CD was $7, Caitlin bought 6 of them.
_____
If you need an equation, you could use ...
7x -10 = 32 . . . . the final value of Caitlin's purchase
7x = 42 . . . . . . . .add 10
x = 42/7 = 6 . . . . Caitlin bought 6 CDs.
HELP!!! 98 POINTS!!!Evaluate the expression for x = 1.7. Enter your answer in the box.
x2 + 3x
Answer:
7.99
Step-by-step explanation:
x2 = x^2 I am assuming.
So,
x^2 + 3x = (1.7)^2 + 3(1.7) = 2.89 + 5.1 = 7.99
Answer:
x^2+3x=(1.7)^2+3(1.7)=2.89+5.1=7.99
make x the subject of the formula
Step-by-step explanation:
first cirscross it come 2nˆ4X=3L4mˆ2and divide each by 2nˆ4 to make X alone and it come, X=3L4mˆ2/2nˆ4. try my best ,if i am wrong tell me.
The perimeter of a rectangle is 40 feet. The ratio of the width to the length is 2:3 find the length and the width
Width : Length
2 : 3
Perimeter = 2* width + 2*length
Ratio becomes:
Width : Length
4 : 6
Total units = 4 + 6 = 10
Perimeter = 40
Answer: Width is 8 ft and Length is 12 ft.
7. Emma is varnishing the floor of a circular room with diameter 8m. One tin of varnish will cover an area of 3m?.
How many tins of varnish will she need to buy to varnish the floor of the room
Answer:
a = 16*3.1415/3 = 16.76
Step-by-step explanation:
a =pi*r^2
r =D/2
r = 8/2
r = 4
a = pi*4^2
a=pi16
pi = 3.1416
If YX=3x-4 and MO=9x-20, then MO=? {Diagram not necessarily drawn to scale.} *
Answer:
Step-by-step explanation:
I assume that XY is midsegment of a triangle, then MO = 2 XY
9x - 20 = 2( 3x - 4 )
9x - 20 = 6x - 8
3x = 12
x = 4
MO = 9(4) - 20 = 16 units
Postal Packages shipped a total of 120 packages last week, and 24 of them were shipped internationally. What percent of the packages were shipped internationally?
Answer:20% OF THEM WERE SHIPPED INTERNATIONALLY IT IS THE BLUE MODEL NOT THE PINK ONE
Step-by-step explanation:
2
if x + 7 x = 9 then x =
Answer:
x = 1.12
Step-by-step explanation:
1.2 + 7 x 1.12 = 9.04
May I have brainliest please? :)
Answer:
x=9/8
Step-by-step explanation:
1. Combine like terms.
x+7x=9 ----> 8x=9
2. Divide both sides of the equation by the same term
8x=9 -----> 8x/8 = 9/8
3. Simplify
x = 9/8 or 1.125
Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 150 pounds of blended coffee beans selling for $5.54 per pound. She plans to do this by blending tighter a high-quality bean costing $6.25 per pound and a cheaper bean $3.25 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend.
let p= pounds of expensive $6.50 coffe
Then 140-p = pounds of $2.00 coffee
6.5p + 2(140-p) = 4.89(140)
Multiply through the parenthesis,
combine like terms... solve for p.
Then you know how many pounds of
$6.50 coffee to use.
Subtract that from 140 to get how many
pounds of $2.00 coffee the use.
Consider functions f and g. [tex]f(x) = 3\sqrt{x} + 1[/tex] What is the value of f(g(1))?
A. 1
B. 9
C. 0
D. 3\sqrt{2} + 1
Answer:
A. 1
Step-by-step explanation:
First, plug 1 into g(x). This is equal to 0.
The picture is like a table, so if the input is 1, the output is 0.
Then, plug 0 into f(x). This is equal to 1.
Answer:
1
Step-by-step explanation:
Solving Problems Involving Inverse Functions
With solutions please.
Answer:
10 non- permanent employeesStep-by-step explanation:
Let number of employees be x
Required equation:
12000 + 512x = 17120Solution:
512x = 17120 - 12000512x = 5120x = 5120/512x = 10Answer: 10 non- permanent employees
In a two-digit number, the first digit is less than the second digit. The number itself is three times the sum of its digits. What is the number?
Answer:
27
Step-by-step explanation:
2<7
(2+7)*3 = 27
OMEONE HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEE 36/9= 72/ BLANK FRACTIONS
Answer:
36/9 = 72/18
Step-by-step explanation:
36 times 2 is 72
Since the number on top was multiplied by two so is the number on the bottom
9 times 2 is 18
Therefore, 36/9 = 72/18
if a1=6 and an=2an-1 then find the value of a4
The value of A4 for the given condition if a1=6 and an=2an-1 is 48.
A1 = 6 means a(1) == 6
This is the first term of the sequence. Then you have the “rule” or the “closed form” of the sequence,
which is: an = 2an - 1 for n>1,
Should be written like this: a(n) == 2 × (an - 1) for n>1.
Now, It says that for any n>1, you should do this:
a(2) - that is the 2nd term is:
a(2) == 2 * (an - 1).
But (an -1) means “the term before this one”, which is the first term.
So, a(2) ==2 × 6 == 12, which is the 2nd term.
The 3rd term will be: a(3) == 2 × 12 = 24.
And the 4th term will be:
a(4) == 2 × 24 = 48.
So,the sequence will be:
6 , 12, 24, 48.
Thus, If a1=6 and an=2an-1, then the value of A4 under the indicated circumstance is 48.
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Name numbers that’s round to 140,000 or 240,000 when rounded to the nearest ten thousand
Answer:
150,000, 130,000
Step-by-step explanation:
well, 4 or below go down 5 and above go up so go from there
Help pleaseeeeeeeeeeeeeeeeeee
667 × 1.25 ≈ nbufw kfiwjbwufjfrfbfrbhf
Answer:
833.75
Step-by-step explanation:
Answer:833.75
Step-by-step explanation:
A line segment has endpoints at (1,6) and (9,-10).
The midpoint of the segment is located at what point?
Answer:
Use the midpoint formula M = (x1+x2/2 , y1+y2/2)
M = (1+9/2 , 6+ -10/2 ) = 5,-2
The midpoint is located at 5,-2.
Answer:(5,-2)
Step-by-step explanation:
(1+9)/2 , (6-10)/2 = (5,-2)