Answer:
It is 10√2
Step-by-step explanation:
[tex] = \sqrt{200} \\ = \sqrt{2 \times 100} \\ = ( \sqrt{2} ) \times ( \sqrt{100} ) \\ = \sqrt{2} \times 10 \\ = 10 \sqrt{2} [/tex]
1. In 2020, the populations of City A and City B were equal. From 2015 to 2020, the population of City A increased by 20% and the population of City B decreased by 10%. If the population of City A was 120,000 in 2015, what is the population of City B in 2015?
2. A chef is preparing a sauce for a steak she offers as a key dish in her menu. To prepare the sauce she needs to prepare a mix with 40% butter, with the rest being egg yolk. In the kitchen right now, she only has a sauce that has 20% butter (rest is egg yolk) and a sauce that has 50% butter (rest is egg yolk) in stock. In what ratio should she mix the 20% sauce with the 50% sauce in order to obtain the 40% sauce that she needs to prepare her famous recipe?
3. A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)
4. At a retail store, they needed to do surveys of 32 stores which equals 40% of all their stores. How many stores does the retailer have in total?*
Answer:
180000 people
1 : 2
$40
80 stores
Step-by-step explanation:
1.)
Population in 2020 are equal : Let population =
City A increased by 20% From 120,000 in 2015
(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000
Hence, city A = 144,000.
Since, city A and B have equal population ; city B also has a population of 144000 in 2020.
Let population in 2015 = x
(1 - 0.2) * x = 144000
0.8x = 144000
x = 144000/0.8
x = 180,000
2.)
Let proportion of 20% butter = x and proportion of 50% butter = 1 - x
0.2x + 0.5(1 - x) = 0.4
0.2x + 0.5 - 0.5x = 0.4
-0.3x + 0.5 = 0.4
-0.3x = 0.4 - 0.5
-0.3x = - 0.1
x = 0.1/0.3
x = 0.3333
(1-x) = 1 - 0.33333 = 0.6666%
0.3333% of 20% butter
0.6666% of 50% butter
Hence ;
0.3333 : 0.6666
1 : 2
3.)
Let original price of book = x
Discount on sale = 30%
Sale price = $28
Sale price = original price * (1 - discount)
$28 = (1 - 0.3) * x
$28 = 0.7x
x = $28/0.7
x = $40
4.)
Let total number of stores = x
Store surveys needed = 32
40% of total stores = 32 stores
0.4x = 32
x = 32 / 0.4
x = 80
A student is chosen at random from a large statistics class and asked how much time (in whole hours) she spent studying during the past 24 hours. Describe the sample space S of possible outcomes:
Answer:
24
Step-by-step explanation:
The sample space is the total possible values of an experiment or research. Since the total number of hours is 24, then the total possible number (or the limit she can use have) is 24. This she cannot exceed this 24 hour limit. Then we call this the total possible outcome and thus the sample space.
A drink bottler needs to fill 16 one-pint bottles and he has two tanks: one that contains 2 gallons of soda and a second that contains 3 gallons which will he need to fill the bottles?
Answer:
2 Gallons of Soda
Step-by-step explanation:
that is the answer above
n
The graph of which function has a minimum located at (4, -3)?
O f(x) = - 5x2 + 4x - 11
f(x) = -2x? + 16x -35
O f(x) = 4x2 - 4x + 5
O f(x) = 2x2 - 16x + 35
9514 1404 393
Answer:
(d) f(x) = 2x^2 - 16x + 35
Step-by-step explanation:
The x-coordinate of the extreme will be found at ...
x = -b/(2a)
where the function is f(x) = ax²+bx+c.
The extreme will be a minimum when a > 0. (eliminates choices A and B)
The x-coordinates of the extremes are ...
C: -(-4)/(2(4)) = 1/2
D: -(-16)/(2(2)) = 4 . . . . . matches the requirement
The appropriate choice is ...
f(x) = 2x^2 - 16x + 35
2^x + 3^y = 9
2^x+1 - 3^y+1=8
find x and y
Suppose :
2^x = t ..**&**.. 3^y = u
_____________________________
t + u = 9 × 3 3t + 3u = 27
=====》
2t - 3u = 8 2t - 3u = 8
+ __________
5t = 35
5 × t = 5 × 7
t = 7
&
u = 2
________________________________
Thus :
2^x = 7 ===》 x = Log _ 2 { 7 }
3^y = 2 ===》 y = Log _ 3 { 2 }
A mountain path is 12.1 miles long. If a hiker walks along the path at a rate of 1.96 miles per hour, in approximate how many hours will the hiker walks the entire trail ?
Answer:
6.2 hours
Step-by-step explanation:
d=rt where d is distance, r = rate and t - time
12.1 = 1.96t
Divide each side by 1.96
12.1/1.96 = 1.96t/1.96
6.17346 = t
Answer: 6.2 hours
Step-by-step explanation: I divided 12.1 by 1.96
Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 90â% confidence that your error is no more than 0.02.
The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - α can be found by using the following expression:
E = zα/2âp1q1/n1 + p2q2/n2
Replace n1 and n2 by n in the preceding formula (assuming that both samples have the same size) and replace each of p1, q1, p2, and q2 by 0.5 (because their values are not known). Solving for n results in this expression:
n = Z2α/2/2E^2
Answer:
n= p1+q1×p2 4pq
n= q2÷ 0.5= q4.5
Please help me thank you
9514 1404 393
Answer:
y = 32.1x +779.91165 cases in 2010Step-by-step explanation:
A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...
y = 32.1x +779.9
The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.
y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1
The number of cases is projected to be 1165 in 2010.
_____
We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.
a. A simple random sample of size 80 has a mean of 7.31. The population standard deviation is 6.26. Construct a 99% confidence interval for the population mean
Answer:
5.503484≤x≤9.116516
Step-by-step explanation:
The formula for calculating the CI is expressed as;
CI = x±z*s/√n
x is the mean= 7.31
z is the 99% z-score = 2.58
s is the standard deviation = 6.26
n is the sample size = 80
Substitute into the formula
CI = 7.31± 2.58*6.26/√80
CI = 7.31± 2.58*6.26/8.94
CI = 7.31± (2.58*0.7002)
CI = 7.31±1.806516
CI = (7.31-1.806516, 7.31+1.806516)
CI = (5.503484, 9.116516)
Hence the 99% confidence interval for the population mean is
5.503484≤x≤9.116516
Solve the system of equations below using the inverse of matrix
Answer:
(x, y) = (4,-3)
Step-by-step explanation:
...............
.
.
.
.
The angles in a triangle are 100, 40, and 40 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer:
F. Obtuse isosceles
Step-by-step explanation:
Since we have an angle that is 100 degrees, we have an obtuse angle
We have two angles that are 40, which means we have two sides that are equal length, because two angles have the same measure. That means it is isosceles
The triangle is an obtuse isosceles
A biologist is researching a newly discovered species of bacteria. At time t = 0 hours, she puts 100 bacteria into what she has determined to be a favourable growth medium. The population of bacteria doubles every 3 hours. How many bacteria are there in 6 hours? a)200 b)100 c)400 d)600
Answer:
I'm sorry but I don't know this one
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
find the lcm of 2.5, 1.0 and 70
Answer:
Step-by-step explanation:
2.5 = 5 * .5
1 = 1
70 = 2 * 5 * 7
LCM = 2 * 5 * 7
If you include the 1/2, you will reduce the LCM to 35, but 70 will be left out of the LCM.
Given the flag ABCDE, determine the single rule (x,y) that creates the
transformed figure A'B'C'D'E'. Fill in your answer below in the format (x,y)--
>
WILL GIVE BRAINLIEST
Answer:
(y, -x)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ---> (y, -x)
Rotation of 90°
(CounterClockwise)
(x, y) --> (-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ---> (-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ---> (-y, x)
Rotation of 270°
(CounterClockwise)
(x, y) ---> (y, -x)
Need Help this is due in 30 minutes!
Answer:
E
Step-by-step explanation:
Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by
[tex]10 {}^{2} [/tex]
So our new equation is
[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]
Solve by AC method
[tex]ac = - 462[/tex]
[tex]b = 71[/tex]
We must think of two numbers that
Multiply to -462 and Add to 71. Set up equation
The numbers are 77 and -6.
So our new equation is
[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]
Solve by factoring by grouping
[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]
Factor out 11 for the first equation
[tex]11x(3x + 7) - 2(3x + 7)[/tex]
So our factors are
[tex](11x - 2)(3x + 7)[/tex]
Set each equal to zero
[tex]11x - 2 = 0[/tex]
[tex]11x = 2[/tex]
[tex]x = \frac{2}{11} [/tex]
[tex]3x + 7 = [/tex]
[tex]3x = - 7[/tex]
[tex]x = \frac{ - 7}{3} [/tex]
Consider the series ∑n=1∞an where
an=(n+9)n(2n+8)n
In this problem you must attempt to use the Root Test to decide whether the series converges.
Compute
L=limn→∞|an|−−−√n
Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.
L=
Which of the following statements is true?
A. The Root Test says that the series converges absolutely.
B. The Root Test says that the series diverges.
C. The Root Test says that the series converges conditionally.
D. The Root Test is inconclusive, but the series converges absolutely by another test or tests.
E. The Root Test is inconclusive, but the series diverges by another test or tests.
F. The Root Test is inconclusive, but the series converges conditionally by another test or tests.
Conducting the root test yields the limit
[tex]\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\frac{(n+9)^n}{(2n+8)^n}\right|} = \lim_{n\to\infty}\frac{n+9}{2n+8} = \frac12 < 1[/tex]
so the series converges (absolutely).
HELP. Need help on this
Answer:
what are the answers
Step-by-step explanation:
A DVD is available at a store for $17.68. The list price of this DVD was 5 18.99. What was the percent discount?
Answer:
6.9%
Step-by-step explanation:
The amount of the discount was ...
18.99 -17.68 = 1.31
As a percentage of the original price, that is ...
1.31/18.99 × 100% ≈ 0.06898 × 100% ≈ 6.9%
The discount was about 6.9%.
Which expression is equivalent to 27 + 45?
Answer:
8 x 9
Have a nice day!
A pair of fair dice are rolled. Find the probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Answer:
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
Sum being multiplies of 3 or multiples of 4, so:
(1,2), (1,3), (1,5)
(2,1), (2,2), (2,4), (2,6)
(3,1), (3,3), (3,5), (3,6)
(4,2), (4,4), (4,5)
(5,1), (5,3), (5,4)
(6,2), (6,3), (6,6)
3 + 4 + 4 + 3 + 3 + 3 = 20
Probability:
[tex]p = \frac{20}{36} = 0.5555[/tex]
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
help me please!! please help!
Answer:
1. 7:20hrs round to 7 hours (1 hour =60 minuite, and 20 is less than half of 60)
2. All numbers when divide by 1 is equal to itself (you can try with any number)
3. 9365<9635
the the second digit of 9635 is 6
the the second digit of 9365 is 3
Thus 9635 is greater
Brainliest please~
Question 1
The perfect square among the following options is
8
Say
27
216
256
Answer:
217 is the perfect swuare i think
The diagonal of rectangle ABCD measures 2 inches in
length.
What is the length of line segment AB?
3
1 inch
B
60°
03 inches
04 inches
43 inches
2
30
D
Answer:
B. √3 inches
Step-by-step explanation:
Apply trigonometry ratio to solve for AB
AB = DC (opposite sides of a rectangle are equal)
Given,
reference angle (θ) = 30°
Hypotenuse = BD = 2
Adjacent = DC = ?
Apply CAH, which is:
Cos θ = Adj/Hyp
Substitute
Cos 30° = DC/2
2*Cos 30° = DC
2*√3/2 = DC (Cos 30° = √3/2)
DC = √3 in.
AB = DC. Therefore,
AB = √3 inches
The table below represents average food costs broken down by meal. If you
were planning a trip, how much should you budget for food costs per day?
Breakfast
Lunch
Dinner
$12.98
$18.95
$26.58
A. $20.00
B. $60.00
C. $80.00
D. $45.00
By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00
How much should you budget for food costs per day?Here we have the following table of average costs:
Breakfast $12.98Lunch $18.95Dinner $26.58Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.
It gives:
Total cost: $12.98 + $18.95 + $26.58 = $48.51
Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.
Learn more about additions:
https://brainly.com/question/25421984
#SPJ1
Answer:
45
Step-by-step explanation:
write √3 x √6 in the form b√2 where b is an integer
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{(9 \times 2)} [/tex]
Take the square root of 9 out of the square root and leave the 2 in.
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{3(6)}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
The average monthly salary of a worker is ₹8200. If there are 45 workers in a factory, then total expenditureincurred on expenditure is:
Answer: [tex]Rs.3,69,000[/tex]
Step-by-step explanation:
Given
average monthly salary of a worker is [tex]Rs.8200[/tex]
If there are 45 workers in a factory
Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory
[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]
!!!HELP PLEASE ASAP!!! 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.
Answer:
population standard deviation = 7.68sample standard deviation = 8.87Pick only one of these values. So if the first one doesn't work, then try the other one. Unfortunately, your teacher isn't clear on which value to go with.
===========================================================
Explanation:
Nice work on getting the mean so far.
To get the standard deviation, we'll use the value 236 in the table. This value is the sum of everything above it. So it's the sum of the [tex](x-\overline{x})^2[/tex] values. We call this the sum of the squared errors. The errors themselves being [tex]x-\overline{x}[/tex]
So we'll divide 236 over n = 4 to get 236/4 = 59
This will get us the population variance. Apply the square root to get [tex]\sqrt{59} \approx 7.68[/tex] which is the population standard deviation.
So if your teacher wants the population standard deviation, then the answer is 7.68
------------
If that answer doesn't work, then try this section.
Unfortunately, there are two flavors of standard deviation. The good news is that we don't have to do much work to find the sample standard deviation.
Instead of dividing by n = 4, we'll divide by n-1 = 4-1 = 3.
So 236/3 = 78.667
Since the value is approximate, I'll leave it as a fraction.
This represents the sample variance.
Apply the square root to get the sample standard deviation
[tex]\sqrt{\frac{236}{3}} \approx 8.87[/tex]
and that value is the sample standard deviation.
If the answer in the previous section doesn't work, then the answer must be 8.87
CAN SOMEONE PLEASE HELP??????
Maintaining your balance may get harder as you grow older. A study was conducted to see how steady the elderly is on their feet. They had the subjects stand on a force platform and have them react to a noise. The force platform then measured how much they swayed forward and backward, and the data is in table #7.3.10 ("Maintaining balance while," 2013). Do the data show that the elderly sway more than the mean forward sway of younger people, which is 18.125 mm? Test at the 5% level.
Table #7.3.10: Forward/backward Sway (in mm) of Elderly Subjects
19
30
20
19
29
25
21
24
50
Answer:
Reject H0 and conclude that adults sway more than the mean forward sway for younger people.
Step-by-step explanation:
H0 : μ = 18.125
H0 : μ > 18.125
Sample data: 19 30 20 19 29 25 21 24 50
Sample size, n = 9
Sample mean, xbar = Σx / n = 237 / 9 = 26.333
Sample standard deviation, s = 9.772 (calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (26.333 - 18.125) ÷ (9.772/√(9))
T = 8.208 / 3.2573333
T = 2.519 = 2.520
Decison :
Reject H0 ; If Pvalue < α
The Pvalue :
Degree of freedom, df = n - 1 ; df = 9 - 1 = 8
Pvalue(2.520; 8) = 0.0179
Since 0.0179 < 0.05 ; WE reject H0 and conclude that adults sway more than the mean forward sway for younger people.
35. Graph the following system of equations and find the x-coordinate of the solution.
3x+ 3y=3
Y=-1/2x+2
x=2
x= -2
X = 3
x=0
9514 1404 393
Answer:
(b) x = -2
Step-by-step explanation:
The graph shows the lines intersect at (x, y) = (-2, 3).
The x-coordinate of the solution is x = -2.
