Answer:se
Step-by-step explanation:
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
The half-life of a radioactive isotope is the time it takes for a quantity of the Isotope to be reduced to half its initial mass. Starting with 210 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Round your answer to the nearest gram
Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
A restaurant gat an average of 14 calls in a 2 hr time period. What is the probability that at most 2 calls in 45 min period
Answer:
0.10512
Step-by-step explanation:
Given the following :
Mean number of calls(μ) in 2 hours = 14
2 hours = 60 * 2 = 120 minutes
Average number of calls in 45 minutes :
= (45 / 120) * 14
= 0.375 * 14
= 5.25
Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)
Using the poisson probability formula:
P(x, μ) = [(e^-μ) * (μ^x)] / x!
Where :
e = euler's constant
μ = 5.25
x = 0, 1, 2
Using the online poisson probability calculator :
P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)
P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
(x*129)-3=126 what is x
Answer:
x should equal 1
Step-by-step explanation:
(1*129)-3=126
129-3=126
126=126
Answer:
x=1
Step-by-step explanation:
We can start by adding 3 to both sides to get rid of the -3
That leaves us with 129x=129
It ends up working out really evenly because by dividing both sides by 129, we are left with x=1
The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year
Answer: The machine depreciates during the fifth year by $4000.
Step-by-step explanation:
Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.
When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.
Then, the machine depreciates A(x) during the fifth year as
[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]
Hence, the machine depreciates during the fifth year by $4000.
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
solve the rational equation 5/x = 4x+1/x^2
Answer:
x = 1
Step-by-step explanation:
Set up the rational expression with the same denominator over the entire equation.
Since the expression on each side of the equation has the same denominator, the numerators must be equal
5x =4x+1
Move all terms containing x to the left side of the equation.
Hope this can help you
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
A bag contains a collection of distinguishable marbles. The bag has two red marbles, three green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include exactly two green marbles
Answer:
63
Step-by-step explanation:
Given that;
The bag has two red marbles, n(red) =2
three green ones marbles, n(green) = 3
one lavender one marbles, n(lavender) = 1
two yellows marbles, n(yellow ) = 2
two orange marbles. n(orange) = 2
number of non green marbles = 2+1+2+2 = 7
The objective is to find out how many sets of four marbles include exactly two green marbles
Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)
= [tex]^3C_2 \times ^{7}C _2[/tex]
= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]
= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]
= [tex]3 \times 7\times 3[/tex]
= 63
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Section 8
Find the mean of these numbers:
24 18
37
82 17
26
Answer:
[tex]\boxed{Mean = 34.33}[/tex]
Step-by-step explanation:
Mean = Sum of Observations / No. Of Observations
Mean = (24+18+37+82+17+26)/6
Mean = 206 / 6
Mean = 34.33
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
At noon a passenger train leaves the Dupont Railway station and travels due east for 2 hours. At 12:45 pm the same day a second passenger train leaves the same railway station and travels due west for 1 hour and 15 minutes at a speed 10 kilometers per hour slower than the first passenger train. At 2pm the two trains were 215 kilometers apart. How fast had each train been traveling
Answer:
The speed of the first train is 70 km/hr
The speed of the second train is 60 km/hr
Step-by-step explanation:
For the first train:
Travel time = 2 hours
The speed = ?
we designate the speed as V
For the second train:
The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)
speed = 10 km/hr slower than that of the first train, we can then say
the speed = V - 10
The total distance traveled by both trains in the opposite direction of one another is 215 km
we can put this problem into an equation involving the distance covered by the trains.
we know that distance = speed x time
the distance traveled by the first train will be
==> 2 hrs x V = 2V
the distance traveled by the second train will be
==> 1.25 hrs x (V - 10) = 1.25(V - 10)
Equating the above distances to the total distance between the trains, we'll have
2V + 1.25(V - 10) = 215
2V + 1.25V - 12.5 = 215
3.25V = 215 + 12.5
3.25V = 227.5
V = 227.5/3.25 = 70 km/hr this is the speed of the first train
Recall that the speed of the second train is 10 km/hr slower, therefore
speed of the second train = 70 - 10 = 60 km/hr
The speed of the trains are 70km/hr and 60km/hr respectively.
The distance of the first train will be represented by: = 2 × D = 2D
The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).
Based on the information given in the question, the equation to solve the question will be:
2D + 1.25(D - 10) = 215
Collect like terms
2D + 1.25D - 12.5 = 215
3.25D = 215 + 12.5
3.25D = 227.5
D = 227.5/3.25
D = 70km/hour
The speed of the second train will be:
= 70 - 10 = 60km per hour.
Read related link on:
https://brainly.com/question/24720712
explain square roots
Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
What is 0.09% written as a decimal?
A. 0.9
B. 0.009
C. 0.0009
D. 0.09
Answer:
C. 0.0009
Step-by-step explanation:
0.09/100
= 0.0009
Answer:A
Step-by-step explanation:0.09=0.9
when using the rational root theorem, which of the following is a possible root of the polynomial function below f(x)=x^3-5x^2-12x+14
A.9
B.3
C.7
D.5
Answer:
[tex]\Large \boxed{\sf \ \ 7 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The polynomial function is
[tex]x^3-5x^2-12x+14[/tex]
The rational root theorem states that each rational solution
[tex]x=\dfrac{p}{q}[/tex]
, written in irreducible fraction, satisfies the two following:
p is a factor of the constant term
q is a factor of the leading coefficient
In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.
Let's proceed with the prime factorisation of 14:
14 = 2 * 7
Finally, the possible rational roots of this expression are :
1
2
7
14
and we need to test for negative ones too
-1
-2
-7
-14
From your list, the correct answer is 7.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
the answer is C.) 7
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C