a) Relation of recurrence for the number of bacteria remaining after n hours is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex]
b) the solution to this recurrence relationship is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]
c) There will be more than a million microorganisms after 7 hours.
A recurrence relation is an equation that states that some combination of the previous terms and the nth term in a series of numbers equals 1.
a) a₀ = 100, a₁ = 300 Every hour the bacteria - bacteria before two hours, and every hour the bacteria + 2(existing bacteria). Consequently, the corresponding recurrence relationship is [tex]a_{n} = a_{n-1} + 2a_{n-1} - a_{n-2} = 3a_{n-1}-a_{n-2}[/tex] where n is an hour reference.
(b) The associated difference equation is
r² - 3r + 1 = 0
⇒ r = [3 ± (√9 - 4)] / 2 = (3 ± √5) / 2
hence, the answer is [tex]a_{n} = a[(3 + \sqrt{5}) / 2] ^{n} + b [(3 - \sqrt{5}) / 2] ^{n}[/tex]
Using n = 0 as the initial condition, we have a₀ = 100 = a + b → (1)
putting n = 1,
⇒ √5 (a - b) = 300 → (2)
(1) ⇒ √5 (a + b) = 100√5
By combining these relationships, we have
a = [(300 + 100√5) / 2√5] = 50 + 30√5
therefore, b = 50 - 30√5
Consequently, the answer to the equation is [tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n}[/tex]
c) if there are more than one million bacteria, i.e.
[tex]a_{n} = (50 + 30\sqrt{5}) [(3 + \sqrt{5}) / 2]^{n} - (30\sqrt{5} - 50) [(3 - \sqrt{5}) / 2]^{n} > 1,000,000[/tex]
⇒ log (50 + 30√5) + n {log (3 + √5)} - log2} - log {30√5 - 50} - n {log (3 - √5) - log2} > log 1,000,000
⇒ 2.06849 + n {0.719 - 0.3010} - 1.2325 - n {-0.41797} > 6
⇒ 0.835975n > 5.16401
⇒ n > (5.16401 / 0.83975)
Therefore, n > 6.177, or after 7 hours, there will be more than 1 million bacteria.
To know more about the Recurrence Relation, refer to this link:
https://brainly.com/question/27618667
#SPJ4
the decimal representation of 30 kilogram and 43 gram is equal to_____kilogram
Answer:
3043kg
Step-by-step explanation:
30kg
43g
is this right
Please help me, as this is due tomorrow
The value of a and b based on the given table when the number of pairs of tiles is 2 is given by 30 cm and 40 cm respectively.
What is the value of the unknown from the table?Width of each tile = 10 cm wideWhen,
number of pairs of tiles is 1
Width of each tile = 20 cm
Length of each tile = 30 cm
number of pairs of tiles is 3
Width of each tile = 40 cm
Length of each tile = 50 cm
number of pairs of tiles is 2
Width of each tile, a = 20 cm + width of each tile
= 20 cm + 10 cm
= 30 cm
a = 30 cm
Length of each tile, b = 30 cm + width of each tile
= 30 cm.+ 10 cm
= 40 cm
b = 40 cm
In conclusion, the value of a and b from the above diagram is 30 cm and 40 cm respectively.
Read more on rectangle:
https://brainly.com/question/25292087
#SPJ1
Shaquana and her children went into a movie theater and she bought $53 worth of
candies and pretzels. Each candy costs $5 and each pretzel costs $3. She bought a
total of 13 candies and pretzels altogether. Determine the number of candies and the
number of pretzels that Shaquana bought.
Shaquana bought
candies and
Complete: 67%
pretzels.
Answer:
∴ Shaquana bought 7 candies and 6 pretzels.
Step-by-step explanation:
Suppose all the snacks she bought were candies.
13 × $5 = $65
$65 - $53 = $12
$5 - $3 = $2
$12 ÷ $2 = 6 pretzels
∴ Number of candies Shaquana bought
= 13 snacks - 6 pretzels
= 7 candies
Answer:
6 pretzels and 5 candies
Step-by-step explanation:
Let c be the number of candies and p the number of pretzels.
We can determine the total cost by multiplying the candy price by it's price, $5/candy. That would be $5*c. We can do the same for the pretzels: $3*p.
Thje total spent is: ($5)c + ($3)p = $53. Since the $ sign cancels out, let's rewrite this to simplify: 5c + 3p = 53.
We know that c + p = 13
Rearrange this to c = 13-p and then substitute this definition of c in the first equation:
5c + 3p = 53
5(13-p) +3p = 53
65 - 5p + 3p = 53
-2p = - 12
p = 6 Shaquana brought 6 pretzels.
Since c + p = 13, this means she bought 7 candies.
Check to see if this works:
Do 6 pretzels and 7 candies cost $53?
(6 prezels)*($3/pretzel) = $18
(7 candies)*($5/candy) = $35
Total = $53 YES
(4n+3)+(3x+9) simplified
Given W(2, -3) X(-4, 9) Y(5, y) and Z(-1, 1) find the value of y so that WX ¯¯¯¯¯¯¯¯¯¯¯⊥ YZ¯¯¯¯¯¯¯
The value of y so that WX ⊥ YZ is y = 4 .
In the question ,
it is given that
the line WX is perpendicular to line YZ
and the end points of WX is W(2,-3) and X(-4,9)
and the end points of YZ is Y(5,y) and Z(-1,1) .
let the slope of line WX = m₁
and slope of line YZ = m₂ .
we know that when two lines are perpendicular , then
m₁ * m₂ = -1
m₁ = (9-(-3))/(-4-2)
and m₂ = (1-y)/(-1-5)
Substituting the values of m₁ and m₂ in the equation m₁ * m₂ = -1 ,
we get
(9-(-3))/(-4-2) * (1-y)/(-1-5) = -1
(9+3)/(-6) * (1-y)/(-6) = -1
12/(-6) * (1-y)/(-6) = -1
-2* (1-y) = 6
-2 + 2y = 6
2y = 6+2
2y = 8
y = 4
Therefore , the value of y is = 4 .
The given question is incomplete , the compete question is
Given W(2, -3) X(-4, 9) Y(5, y) and Z(-1, 1) . find the value of y so that WX ⊥ YZ ?
Learn more about Lines here
https://brainly.com/question/20740355
#SPJ1
Please help me! I appreciate itt
Answer: The correct answer is on Day 39 they both have the same amount (38) of naxvips
Step-by-step explanation:
First, determine the rate of change for each using the formula (end-start/days):
Min-jun:
start=36
end=41
days (constant)=15
Rate=41-36/15=5/15 = 1/3 (increment/day)
Tran:
start=56
end=11
days (constant)=15
Rate=11-56/15=-45/15 = -3 (decrement/day)
Build the table using the rate of change for every 3 days:
DAY MJ ROC TRAN ROC
33 36 0 56 0 <---Start date
36 37 +1 47 -9
39 38 +1 38 -9 <-----SAME!
42 39 +1 29 -9
45 40 +1 20 -9
48 41 +1 11 -9
Please remember to vote this answer as Brainliest if I earned it!
Given the relation (9,2)(4,5)(7,3)(10,-5)Which ordered pair (a,b)Would result in a relation? That is not a function.
(10,2)
( 4,5)
( 6,7)
(7,1)
None of the above.
Given the relation (9,2)(4,5)(7,3)(10,-5), an ordered pair which would result in a relation that is not a function is: (10, 2).
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.
Based on the ordered pairs shown above, we can reasonably infer and logically deduce that (10, 2) is an ordered pair which does not represent a function because the value of "a" has already been mapped to -5.
Read more on function here: brainly.com/question/3632175
#SPJ1
What is the equation of the line that passes through (1, 4) and (2, 1)
y = -3x + 1
y = -3x + 4
y=-3x - 7
y=-3x + 7
|2x + 4| ≥ 5 i need help please!!! (Please put in your work need that as well)
The value of the given inequality mode function |2x + 4| ≥ 5 will be x ≥ 1/2 and x ≤ -4.5.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given mode function,
|2x + 4| ≥ 5
For 2x + 4 > 0 or x > -2
2x + 4 ≥ 5
2x ≥ 1
x ≥ 1/2
For 2x + 4 < 0 or x < -2
-(2x + 4) ≥ 5
2x + 4 ≤ -5
2x ≤ -9
x ≤ -9/2
x ≤ -4.5
Hence "The value of the given inequality mode function |2x + 4| ≥ 5 will be x ≥ 1/2 and x ≤ -4.5".
For more about inequality,
brainly.com/question/20383699
#SPJ1
12 times what will equal to minus 4 to equal zero
The answer that 12 times 1/3 will equal to -4 to 0, solving an equation.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
So the equation 12(x)-4 = 0
⇒12*x =4
⇒x=4/12
⇒x = 1/3
Hence, the equation will be solved and the number will be 1/3.
Learn more about equations, by the following link
https://brainly.com/question/2972832
#SPJ1
3x - 5y = 15
x-intercept =
y-intercept =
Answer:
x-intercept is 5
y-intercept is -3
Step-by-step explanation:
For the x-intercept:
[tex]3x - 5(0) = 15[/tex]
[tex]3x = 15[/tex]
[tex]x = 5[/tex]
For the y-intercept:
[tex]3(0) - 5y = 15[/tex]
[tex] - 5y = 15[/tex]
[tex]y = - 3[/tex]
Answer:
Y intercept= -3
x-intercept = 5
Step-by-step explanation:
So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:
1. Subtract 3x from both sides to get -5y= -3x+15
2. then you would divide each side by -5 to get y= [tex]\frac{3}{5}[/tex] x -3
And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.
sorry if this was long
Write one-hundred-two-and-eighty-one-hundredths in standard form.
Is it 102,8100? If not, tell me. I'll fix it!
Please Help!
Look at points C and D on the graph:
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.
4.54 units
5.00 units
5.83 units
34.00 units
Answer: 23456789ol.09876
Step-by-step explanation:
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
according to a survey, high school girls average 100 text messages daily. assume the population standard deviation is 20 text messages. suppose a random sample of 50 high school girls is taken.
The probability that the sample mean is greater than 105 is 0.0384.
What is meant by random sample?A simple random sample is a subset of persons chosen at random from a bigger collection. It is the process of randomly selecting a sample.
A simple random sample is a population subset chosen at random. Each member of the population has a precisely equal probability of being selected in this sampling approach, reducing the likelihood of selection bias.
Random sampling ensures that the results received from your sample are close to what would have been achieved if the full population had been measured.
The population mean is μ =100.
The population standard deviation is σ= 20.
n=50 is the sample size
Let [tex]\bar{x}[/tex] be the mean of the sample
The chance that the sample mean is greater than 105 is then given by :
P( [tex]\bar{x}[/tex]>105)=1-P( [tex]\bar{x}[/tex]≤105)
=1-P(( [tex]\bar{x}[/tex]-μ)/(σ/√n) ≤ (105-100)/(20/√50))
=1-P(z≤1.77)
=1-0.96164
=0.03836≈0.0384
To know more about random sample, visit:
https://brainly.com/question/12719645
#SPJ4
The complete question is:
"According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than 105? (Round answer to 4 decimal places.)"
if its 8:00 am on november 22 what time was it 22 hours ago
Answer:
10AM on November 21.
Step-by-step explanation:
START FROM THE END OF THE LIST BELOW, STARTING FROM 8AM (ANNE MERIDIAN), NOVEMBER 2[tex]2^{nd}[/tex].12am: - 32: November 21.
1am: - 31: November 21.
2am: - 30: November 21.
3am: - 29: November 21.
4am: - 28: November 21.
5am: - 27: November 21
6am: - 26: November 21.
7am: -25: November 21.
8am: -24: November 21.
9am: -23: November 21.
10am: -22 hours (22 hours ago): November 21 - ANSWER IS 10 AM.
11am: - 21: November 21.
12pm: - 20: November 21.
1pm: - 19: November 21.
2pm: - 18: November 21.
3pm: - 17: November 21.
4pm: - 16: November 21.
5pm: - 15: November 21.
6pm: -14: November 21.
7pm: -13: November 21.
8pm: -12: November 21.
9pm:-11: November 21.
10pm: -10: November 21.
11pm: - 9: November 21.
12am: - 8: November 22.
1am: -7: November 22.
2am: -6: November 22.
3am: -5: November 22.
4am: -4: November 22.
5am: -3: November 22.
6am: -2: November 22.
7am: -1: November 22.
8am: CURRENT TIME (RIGHT NOW): November 22 - START FROM HERE.
Six whole numbers have a median of 10 a mode of 11 a range of 4 work out a possible set of six numbers. Write the numbers in order.
The numbers in order are 7, 8, 9, 11, 11, and 11.
Mode:
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all
Here we have to arrange the number in order.
Range:
The difference between the lowest and highest values.
Pu the six numbers in order from small to large.
7,8,9,11,11,11
So the median of the number is = (9 + 11) /2
= 10
The mode of these numbers is = 11
As 11 is three times in the series.
The range of the numbers is = 11-7 =4
Therefore the order is 7, 8, 9, 11, 11, 11.
To know more about the mean, median and mode refer to the link given below:
https://brainly.com/question/14532771
#SPJ4
Leaping deer company purchased a tractor at a cost of $440,000. The tractor has an estimated residual value of $40,000 and an estimated life of 8 years, or 12,000 hours of operation. The tractor was purchased on january 1, 2015 and was used 2,400 hours in 2015 and 2,200 hours in 2016. What amount will leaping deer company report as total depreciation expense over the 8-year life of the equipment using straight-line depreciation?.
Leaping deer company purchased a tractor at a cost of $440,000. The tractor has an estimated residual value of $40,000 and an estimated life of 8 years, or 12,000 hours of operation. The tractor was purchased on January 1, 2015 and was used 2,400 hours in 2015 and 2,200 hours in 2016.
To find out which method of depreciation will produce maximum depreciation, Depreciation expense for 2018 shall be calculated using all methods.
1) Double-declining balance method: Under this method, depreciation is charged to an accelerated rate to the asset by applying double depreciation instead of a regular depreciation rate. This rate is applied to the value of the depreciable assets.
Depreciable Value of Tractor = Gross Value - Salvage Value = $240,000 - $40,000 = $200,000
The regular rate of depreciation = 100% / Life of Tractor = 100% / 8 Years = 12.5%
Double-declining rate of depreciation = Regular rate X 2 = 12.5 % X 2 = 25%
Depreciation expense for 2018 = Depreciable value of tractor X Dobule-decling rate
= $200,000 X 25%
= $50,000
Depreciation expense as per double-declining method = $50,000
2) Straight-line method: Under this method, the value of the depreciable asset is spread over the useful life of the asset evenly.
Depreciation for 2018 = Useful life of Tractor / Useful life
= $200,000 / 8 Years
= $25,000
Depreciation expense as per straight line method = $25,000
3) Units of production method: Under this method, the depreciable value of assets is depreciated with the level of usage with respect to the overall capacity of assets with respect to usage. Hence, more usage shall lead to higher depreciation.
Total hours available during the life of asset = 12,000
Depreciation to be charged for each hour of usage = Depreciable value / Total hours
= $200,000 / 12,000 Hours
= $16.67 per hour
Depreciation for 2018 = Total hours of usage in 2018 X Depreciation per hour
= 3,800 Hours X $16.67
= $63,346
Depreciation under units of production method = $63,346.
Hence, Highest amount of depreciation is produced under units of production method as tractor has been used for more than one-third of its usage hour capacity. As the other two methods do not take into account the level of usage, their depreciation is just based on time. Hence, Depreciation under the unit production method is highest.
To learn more about depreciation click here https://brainly.com/question/1203926
#SPJ4
The record high temperature for a certain us state is 104 f. the record low temperature for same state is -14 f. what is the difference between the record high and low temperatures for this state
The difference between the record high and low temperatures for this state is 118 degrees Fahrenheit or 118°F
Given that,
104 f is the highest temperature ever recorded in a particular US state. The state's all-time low temperature is -14 f.
To find : The difference between the record high and low temperatures for this state.
Difference can be calculated as
Difference equals to highest temperature minus lowest temperature in the state
Difference = 104 -(-14)
= 104+14=118°F
Therefore, The difference in temperature between the state's record high and low readings is 118 degrees Fahrenheit, or 118°F.
Learn more about Fahrenheit :
brainly.com/question/516840
#SPJ4
Which of these statements best describes the relationship between 7×(18-5) and 18-5
Answer:
I need your statements please
Step-by-step explanation:
a ferris wheel has a radius of 24 feet and travels 5.6 feet every second. at what constant angular speed does the ferris wheel rotate at (in radians per second)?
The angular speed is 0.233 radian per second.
What is angular speed?
Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ t where θ is the angular displacement, t is the time and ω is the angular speed.
given radius = 24 feet
distance covered = 5.6
First we will find the circumference
= 2πr
=48π
Time = 48π/5.6 = 26.91
Angular speed = 2π/TIME
=2π/26.91
= 0.233
To know more about angular speed, visit:
https://brainly.com/question/16407861
#SPJ4
a²+b²=c² to find the
base of the right triangle.
1600 ft
500 ft
Answer:
b=1519.87? (If not correct please clarify what sides the 1600 and 500 ft are on. In my answer the 1600 ft was the hypotenuse since it was the longest of the two and it said to find the base of the triangle. This means the 500 ft is the side adjacent to 90 degrees and 1600 ft is the hypotenuse. Sorry if it's not clear!)
Step-by-step explanation:
[tex]500^{2} +b^2=1600^2\\250000+b^2=2560000\\b^2=2560000-250000\\b^2=2310000\\\sqrt{b^2}=\sqrt{2310000}\\ b=1519.87[/tex]
Answer:
side 2 ([tex]b^{2}[/tex]) = 1519.87
OR
hypotenuse ([tex]c^{2}[/tex])= 1676.31
Explanation:
If 1600 ft = hypotenuse and 500 ft = side
[tex]1600^{2}[/tex] = [tex]500^{2}[/tex] + [tex]b^{2}[/tex]
2560000 = 250000 + [tex]b^{2}[/tex]
2560000 - 250000 = [tex]b^{2}[/tex]
2310000 = [tex]b^{2}[/tex]
[tex]\sqrt{2310000}[/tex] = [tex]\sqrt{b^{2} }[/tex]
[tex]b[/tex] = 1519.87
side 2 = 1519.87
OR
If 1600 ft = side 1 and 500 ft = side 2
[tex]1600^{2}[/tex] + [tex]500^{2}[/tex] = [tex]c^{2}[/tex]
2560000 + 250000 = [tex]c^{2}[/tex]
2810000 = [tex]c^{2}[/tex]
[tex]\sqrt{2810000}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]c[/tex] = 1676.31
hypotenuse = 1676.31
Bill plans to fund his individual retirement account (ira) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?.
$144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.
Given that,
For the next 20 years, Bill intends to contribute the maximum $2,000 each year to his individual retirement account (ira).
We have to find how much will Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.
We know that,
What is the Annuity's Future Value?The worth of repeated payments at a specific future date, less a specified refund rate or a discount rate, is known as the future annuity value. The annuity amount increases with the discount rate.
According to the information provided, Future Value of Annuity equals:
FV= A×[(1+r)ⁿ-1]/r
Here,
A is periodic payment
r is rate per period
FV is future value
n is number of period
FV=2000×[(1+0.12]²⁰-1]/0.12
FV=2000×72.05244
FV=$144104.88
Therefore, $144104.88 Bill have at the end of the twentieth year if he can earn 12 percent on his contributions.
To learn more about percent visit: https://brainly.com/question/28840349
#SPJ4
50 divided by 6 with a remandier
Answer: 8.3
Step-by-step explanation:
50/6= 8.3
help PLEASEEEEEE WILL GIVE BRAINLYEST FOR CORRECT ANSWER AND IF YOU REMIND ME
Answer:
Step-by-step explanation:
v = 1/3 (area of base) (height)
v = 1/3 (1/2*6*8) (7)
v = 1/3 (24) (7)
v = 8 (7)
v = 56 square inches
(-4,-7); slope = 3
What is the linear equation?
Pls Help Asap! Tysm if u do!
Step-by-step explanation:
I assume you need the slope-intercept form
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
since we have the slope and a point, we can start with the point-slope form
y - y1 = a(x - x1)
"a" is again the slope, (x1, y1) is a point on the line
so, we have
y - -7 = 3(x - -4)
y + 7 = 3(x + 4) = 3x + 12
and from there now the final equation :
y = 3x + 5
PLEASE HELP THIS IS DUE IN 20 MINUTES IM STUCK
Answer:
x=5
Step-by-step explanation:
Because we know the sum of the interior angles should be 180, we can use this to create an equation to solve for x.
60+(7x+3)+(180-20x)=180
Simplify to find that x = 5
If you're confused about where the 180-20x comes from:
The line it lays on is straight, meaning the angle it creates is 180 degrees.
Thus, 180 - known angle = unknown angle.
Answer:
the answer is c, x=5
Step-by-step explanation:
now, if we look at the pic, there is already one angle given.
and we know that sum interior angles of a triangle must be 180;
so the sum of the other two angles is: angle 2 +angle 3=180-60.
now, let's pick any number and put it into x.
first, if we put 15 into x: 7(15)+5=120,
so 180-(120+60)=0. and for there is another angle, it is invalid.
if we put 6: 7(6)+5=47,
180-(60+47)=73.
let's look at the third angle.
for x=6, the angle UBI is 120°. and we also know that the sum of angles on a horizontal line is always 180°, so 180-120=60, and for the third angle is NOT 73°, this one is also invalid.
if x=5: 7(5)+5=40, 180-(60+40)=80.
the angle UBI= 100°, 180-100=80°;
for 80°+60°+40° equals 180°, the answer c is correct.
Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches mattie’s house. What is the shortest distance between caroline’s and mattie’s houses?.
Caroline leaves her house and walks north 6 blocks. She turns and heads east 8 blocks until she reaches Mattie’s house.
The shortest distance between Caroline's and Mattie's house is 10 blocks.
If we assume this as a right angle triangle then height (BA) is 6 blocks long and base (BC) is 8 blocks
long.
Then, the shortest distance between Caroline's and Mattie's house will be the hypotenuse (AC) of this
triangle.
So, by applying Pythagoras theorem:
[tex](AC)^{2} = (BA)^{2} = (BC)^{2} = (6)^{2}+(8)^{2}[/tex] = 36+64 = 100
Thus, AC = [tex]\sqrt{100}[/tex] = 10 blocks.
Hence, the shortest distance we can take from Caroline's house to reach Mattie's house is 10 blocks.
Learn more about the Pythagoras theorem here
brainly.com/question/343682
#SPJ4
2. Which of the following statements is true? (1 point) OPositive numbers are always rational numbers. ONegative numbers are always irrational numbers. ONegative numbers are sometimes rational numbers. ONegative numbers are always integers.
Negative numbers are sometimes rational numbers. As, this statement is only true in all the following statements.
What is numbers ?A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them. the system of numbers
Following statements are given,
1. Positive numbers are always rational numbers.
2. Negative numbers are always irrational numbers.
3. Negative numbers are sometimes rational numbers.
4. Negative numbers are always integers.
According to statement Positive numbers are always rational numbers
As this statement is not always true because though √2 is positive, it is not a rational number.
According to statement Negative numbers are always irrational numbers.
This is also not true as always as -4 is negative and it can be expressed in the form of [tex]\frac{-4}{1}[/tex] , hence it is rational.
According to statement Negative numbers are sometimes rational numbers. As it can be both -2 is a negative rational number and -√2 is negative irrational number.
According to statement Negative numbers are always integers.This is not always true because [tex]\frac{-2}{3}[/tex] is a negative number with a fractional part, hence it is not an integer.
Hence, only 3rd statement is true ,
To know more about rational numbers, visit:
https://brainly.com/question/24398433
#SPJ1
A state politician is interested in knowing how voters in rural areas and cities differ in their opinions about gun control. For his study, 92 rural voters were surveyed, and 57 were found to support gun control. Also included in the study were 92 voters from cities, and 36 of these voters were found to support gun control. Let Population 1 be the voters in rural areas and Population 2 be the voters from cities.
Step 1 of 2 : Construct a 90% confidence interval for the true difference between the proportions of rural and city voters who favor gun control. Round the endpoints of the interval to three decimal places, if necessary.
The 90% confidence interval for the true difference between the proportions of rural and city voters who favor gun control is of:
(0.11, 0.346).
What are the mean and the standard error for the distribution of differences?For each sample, the proportion and the standard error are given as follows:
Rural voters: [tex]p_1 = \frac{57}{92} = 0.6196, s_1 = \sqrt{\frac{0.6196(0.3804)}{92}} = 0.0506[/tex]Urban voters: [tex]p_2 = \frac{36}{92} = 0.3913, s_1 = \sqrt{\frac{0.6196(0.3804)}{92}} = 0.0509[/tex]Hence the mean and the standard error for the distribution of differences is given by:
[tex]p = p_1 - p_2 = 0.6196 - 0.3913 = 0.2283[/tex][tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0506^2 + 0.0509^2} = 0.0718[/tex]What is the confidence interval?The bounds of the confidence interval are given by the rule defined as follows:
p ± zs
The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Then the bounds of the interval are obtained as follows:
Lower bound: 0.2283 - 1.645 x 0.0718 = 0.11.Upper bound: 0.2283 + 1.645 x 0.0718 = 0.346.More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
