The first truck did 62% of all the job.
When the two crews start working together?First, from the problem we know that the first truck does its job at a rate per hour:
And, the second truck has a rate per hour of:
So, the rate per hour with both trucks working together will be the sum:
Now, we have to find the time it will take to do the whole job with both trucks, the whole job done will be represented by 100% or 1:
Where t is the unknown time that it takes to do all the job. Solving this we have:
This means that the whole job will be done after 3.08 hours using both trucks. However, the problem is asking just about the first truck. To find that answer we just have to multiply its rate with the time:
This decimal number represents the portion that the first truck finished to have the job done. 0.62 means that it did 62% of all the job.
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correct question:
The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.
Answer:
Step-by-step explanation:
When the two crews start working together, the part of all the garbage bins that the first garbage truck will empty is; A: 0.6
We are told that the first truck empties all bins in 5 hours. Thus;
Rate of first truck per hour = ¹/₅
Second truck empties all bins in 8 hours. Thus;
Rate of second truck per hour = ¹/₈
If both trucks work together, their rate per hour is;
Combined rate per hour = ¹/₅ + ¹/₈
Combined rate per hour = ¹³/₄₀
Thus, number of hours it will take for both of them to do the whole job, we will solve as;
¹³/₄₀t = 1
where t is the time it will take both of them combined to finish the whole job.
Thus;
t = ⁴⁰/₁₃
The part that the first garbage truck will empty when they both work together = ¹/₅t = ¹/₅ * ⁴⁰/₁₃
⇒ Approximately 0.6
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Derrick has been saving his earnings from his lemonade stand. Derrick has 90 dollars to spend. If he buys a new hat for 35 dollars, how many scarves can he buy with the remaining money if they cost 8 dollars each?
Answer:
6 scarves
Step-by-step explanation:
So he has $90 and spends $35 so: [tex]90-35=55[/tex]
The scarves cost 8 dollars each so we need to divide: [tex]55[/tex]÷[tex]8=6.875[/tex]
You can't buy have .875 of the scarves so he can only buy 6 scarves
Answer: 6
Step-by-step explanation: 90-35=55 55-8-8-8-8-8-8=7
8. A man started his journey at 11:57am and was scheduled to arrive at 12:49pm. If he arrived 15 minutes late, how long did his journey take?
Answer:
Below
Step-by-step explanation:
From 11:57 to 12:00 is 3 min then add 49 min to get to 12:49 then add the 15 min late = 3 + 49 + 15 = 67 MIN or 1hr 7 min
Explain why this graph does not represent a function.
simplify a square minus b square + a upon a square + b square + b / a² + b square minus b Upon A minus A square minus b square
It is possible for two line segments to not intersect and also not be considered parallel.
true or false?
Oh yeah definitely, two lines don't have to be parallel or intersect. There are many examples. I'll give you one. Imagine two lines right now, one is flat horizontal, 180 degrees. Another line is above the horizontal line, at like 30 degrees. But they do not touch. So therefore, these lines are neither parallel or intersecting. The answer is true.
Sarah wants to install carpet to cover her rectangular dining room floor, which has a length of 12 feet and a width of 9 feet. The cost to install the carpet is $5 per square foot. Sarah predicts that the total cost to install the carpet will be $500. Which statement BEST explains why Sarah’s prediction is incorrect? PLS HELP TY
A. Sarah rounded the area of the floor to 110 square feet.
B. Sarah rounded the area of the floor to 100 square feet.
C. Sarah rounded the area of the floor to 98 square feet.
D. Sarah rounded the area of the floor to 108 square feet.
Answer:
B
Step-by-step explanation:
12 long 9 wide = 12*9 =108 sqft
$5/sqft
so she'll need 108*5 =540
but she rounded to 100 sqft
Please help solve this equation "m+1P4 =mP5
Answer:
m+1p4 =mp5
1p4= mp5-m
m=p5
Tracie works for a salary of $2,666 per month. She has federal income tax withheld at the rate of 15percent, Social Security tax at the rate of 6.2 percent, Medicare tax at the rate of 1.45 percent, and health insurance premiums of $95 per month. Tracie’s net pay is $____________.
Tracie net pay is,
⇒ $1,967.1
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Tracie works for a salary of $2,666 per month.
Here, She has federal income tax withheld at the rate of 15%
Hence, The amount for federal income tax is,
⇒ 15% of $2666
⇒ 15/100 × 2,666
⇒ $399.9
And, Social Security tax at the rate of 6.2%
Hence, The amount for Social Security tax is,
⇒ 6.2% of 2,666
⇒6.2/100 × 2666
⇒ $165.3
And, Medicare tax at the rate of 1.45%.
Hence, The amount of Medicare is,
⇒ 1.45% of $2,666
⇒ 1.45/100 × 2,666
⇒ $38.7
And, She have health insurance premiums of $95 per month.
Thus, The net pay is,
⇒ $2,666 - ($95 + $38.7 + $165.3 + $399.9)
⇒ $1,967.1
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Please solve this for me
The solutions to the equations are
a) The percentage of quokkas that weigh over 15.5 pounds is 2.1 %
b) The percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %
c) Percentage of quokkas that weigh between 15.5 and 11.9 pounds 22.0 %
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
The weights of the quokkas are described by the normal model as
N ( 10 , 2.7 )
So , the mean μ = 10
And , the standard deviation σ = 2.7
a)
The percentage of quokkas that weigh over 15.5 pounds is given by the equation P ( x > 15.5 )
On simplifying the equation , we get
From the z-score formula ,
P ( z > ( 15.5 - 10 ) / 2.7 )
P ( z > 2.037 ) = 0.020825
0.020825 = 2.0825 %
Hence , the percentage of quokkas that weigh over 15.5 pounds is 2.1 %
b)
The percentage of quokkas that weigh uncer 11.9 pounds is given by the equation P ( x < 11.9 )
On simplifying the equation , we get
From the z-score formula ,
P ( z < ( 11.9 - 10 ) / 2.7 )
P ( z < 0.7037 ) = 0.020825
0.75919 = 75.919 %
Hence , the percentage of quokkas that weigh uncer 11.9 pounds is 75.9 %
c)
Percentage of quokkas that weigh between 15.5 and 11.9 pounds is
P ( 11.9 < x < 15.5 )
On simplifying the equation , we get
From the z-score formula ,
P ( 11.9 < x < 15.5 ) = 1 - P ( x < 11.9 ) - P ( x > 15.5 )
P ( 11.9 < x < 15.5 ) = 1 - 0.020825 - 0.75919
P ( 11.9 < x < 15.5 ) = 0.219985
P ( 11.9 < x < 15.5 ) = 22.0 %
Hence , the equations are solved using z-score
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14. G is the incenter of AABC,
AC; GR = 7, and m< BAC = 60
GT:______
m>BAG:______
In the triangle where G is the incenter of AABC, GT = 7, m>BAG = 120.
What is an incenter in a triangle?An incenter is a position within a triangle where the triangle's three angle bisectors connect. The lines that divide the angles in a triangle into two equal pieces are known as angle bisectors. The incenter is equidistant from the triangle's three sides, which means that the distance from the incenter to each side is the same. The incenter is also the core of the inscribed circle of the triangle, which is the greatest circle that can fit within the triangle. The incenter is a crucial point in trigonometry and geometry because it may be used to compute angles, sides, and other triangle features.
Given:
AABC, AC; GR = 7, and m<BAC = 60
Step 1: Since the angle bisector of any angle in a triangle divides that angle into two equal parts, m<BAC = 60 implies m<BAG = 120.
Step 2: Since the incenter of a triangle is equidistant from the three sides, GR = 7 implies GT = 7.
Therefore, GT = 7 and m>BAG = 120.
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What is the common difference of the A.P. 11, - 1, - 13, - 25, . . . ?
Answer:
The common difference is -12
Step-by-step explanation:
Finding the common difference:
11, - 1, - 13, - 25, . . .
The difference between the first and second terms
-1 -11 = -12
The difference between the second and third terms
-13 - -1 = -13 + 1 = -12
The common difference is -12
1. Y is 200m North of X and Z is 200m East of Y. Find the bearing of Z from X
2. A man walks 800m on a bearing of 120°. calculate how far from east he is from his starting point
Answer:
see below
Step-by-step explanation:
1. XZ = √(200²+200²) =√2*200 = 282.8m
2. if the man started from 0,0 point & walks 120° meaning he's walking towards the northwest, so he'll be 400m west and 400√3 = 693m north from his starting point, because 120° -90° = 30° you are basically solving a problem of 3 sides length of a special straight triangle with an angle of 30. this type of triangle has a property of shorter side = 1/2 of the long side. 2nd shorter side = √3/2 of the long side. this, you should memorize. which will make lots of problems a piece of cake. good luck
Answer:
1. XZ = √(200²+200²) =√2*200 = 282.8m
2. Not sure
Step-by-step explanation:
If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and a estimated useful life of 20 years determine the following a. the depreciable cost b. The straight- line rate c.the annual straight-line depreciation
The depreciable cost,
$1,800,000
The straight-line rate,
5%
The annual straight-line depreciation,
90,000
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
If a building acquired the beginning of the year at a cost of 2,200,000 has an estimated residual value of 400,000 and an estimated useful life of 20 years.
The depreciable cost,
= cost - residual value
= 2,200,000 - 400,000
= $1,800,000
The straight-line rate,
=100/20
= 5%
The annual straight-line depreciation,
= 1,800,000 x 5/100
= 90,000
Therefore, all the required values are given above.
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If an ant can walk 7 inches per minute and the road is 28 feet wide, how many seconds will it take him to cross ?
Answer:
48 minutes
Step-by-step explanation:
Why did the ant cross the road?
Speed of ant = 7 inches per minute
Width of road = 28 feet
28 feet = 28 x 12 inches = 336 inches
At 7 inches per minute, to cross 336 inches , it would take 336/7 or 48 minutes
i need help please!!
Need help!!!!!
Isiwjsiwkkw
Answer:
63, 69, 75, 81
Step-by-step explanation:
to find the first 4 terms substitute n = 1, 2, 3, 4 into the explicit rule.
a₁ = 63 + (1 - 1) × 6 = 63 + 0 × 6 = 63 + 0 = 63
a₂ = 63 + (2 - 1) × 6 = 63 + 1 × 6 = 63 + 6 = 69
a₃ = 63 + (3 - 1) × 6 = 63 + 2 × 6 = 63 + 12 = 75
a₄ = 63 + (4 - 1) × 6 = 63 + 3 × 6 = 63 + 18 = 81
the first four terms are 63, 69, 75, 81
The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site of the Seattle P-I on April 25, 2005.
year make model mileage price
2004 Honda Odyssey EXL 20 26900
2004 Honda Odyssey EX 21 23000
2002 Honda Odyssey 33 17500
2002 Honda Odyssey 41 18999
2001 Honda Odyssey EX 43 17200
2001 Honda Odyssey EX 67 18995
2000 Honda Odyssey LX 46 13900
2000 Honda Odyssey EX 72 15250
2000 Honda Odyssey EX 82 13200
2000 Honda Odyssey 99 11000
1999 Honda Odyssey 71 13900
1998 Honda Odyssey 85 8350
1995 Honda Odyssey EX 100 5800
Compute the correlation between age (in years) and price for these minivans. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)
The correlation between age and price is -0.94. It indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.
What is correlation?A procedure for determining the connections between two variables is referred to as correlation. You discovered that plotting two variables on a "scatter plot" can help you determine whether or not they are generally connected. Correlation is the most widely applied strategy even though there are other measures of association for variables measured at the ordinal or higher level of measurement.
The data was collected in 2005. So, to obtain the age we subtract the data collection year from the make year:
Age (x): 1,1, 3,3,4,4,5,5,5,5,6,7,10
Now, the array of price given is:
Price (y): 26900,23000,17500,18999,17200,18995,13900,15250,13200,11000,13900,8350,5800.
Using the correlation equation in excel sheet we see that the correlation coefficient between the age and the price is: - 0.94.
-0.94 indicates a strong negative correlation. Hence, as the age increases the price of the car decreases.
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The U.S. per capita income for 2013 was $53143. If the average person operated like the federal government, how much money would the average person have spent in 2013?
Express your answer round to the nearest dollar.
Answer: divide $39857
Step-by-step explanation:
Please do it and show the work 10 points for brainliest answer
The rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.
What do you mean by rate?The idea of rate is used in mathematics to describe how one quantity changes in relation to another. It is frequently expressed as a fraction or ratio and is a measurement of how quickly one thing is changing in relation to another.
For instance, velocity is the measure of how quickly a position changes in relation to time. Acceleration is the measure of how quickly a velocity changes with relation to time. The derivative of a function, which denotes the instantaneous rate of change at a specific location, is the rate of change of any function with regard to its independent variable.
The rate of inflation for each item can be calculated using the formula:
r = (P2/P1)¹/ⁿ - 1
where P1 is the price per pound in 2009 and P2 is the price per pound in the given year, and n is the number of years between the two prices (in this case, n = 1 year).
For Potatoes:
P1 = $0.620
P2 = $0.749
n = 1
r = (0.749/0.620)¹/¹ - 1 = 0.21 or 21%
For Oranges:
P1 = $0.910
P2 = $1.280
n = 1
r = (1.280/0.910)¹/¹ - 1 = 0.40 or 40%
For Ground beef:
P1 = $2.251
P2 = $3.775
n = 1
r = (3.775/2.251)¹/¹ - 1 = 0.67 or 67%
So, the rate of inflation for potatoes was 21%, for oranges it was 40%, and for ground beef it was 67%.
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If 6 is an element in the domain of f(x) = (8x-16)/2, what is the corresponding element in the range?
If 6 is an element in the domain of f(x) = (8x - 16)/2, the corresponding element in the range include the following: [16].
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
What is a range?In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Based on the information provided, we have the following function rule:
Function, f(x) = y = (8x - 16)/2
When the domain x = 6, the range (y) of this function is given by;
Range, y = (8(6) - 16)/2
Range, y = (48 - 16)/2
Range, y = 32/2
Range, y = 16.
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5.
If "x" and "y" are integers and 8^2x-y = 5^x-y+8, which of the
following is the value of x + y ?
A) 24
B) 22
C) 18
D) 12
For the equation [tex]8^{2x-y} = 5^{x-y+8}[/tex], the value for sum of integers x and y is option A: 24.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
The given equation is [tex]8^{2x-y} = 5^{x-y+8}[/tex].
The first step is to make the base same-
Multiply the left-hand side with 5 and right-hand side with 8.
[tex]5(8)^{2x-y} = 8(5)^{x-y+8}\\40^{2x-y} = 40^{x-y+8}[/tex]
Since, the bases are same, the power values can be taken into consideration -
2x - y = x - y + 8
Collect the like terms -
2x - x = - y + y + 8
x = 8
Substitute the value of x in any one side of the equation -
2x - y = 0
2(8) - y = 0
16 - y = 0
-y = -16
y = 16
So, now the value of expression x + y is -
8 + 16 = 24
Therefore, the final value is obtained as 24.
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The population of a town increased from 3200 in 2008 to 5700 in 2009. Find the absolute and relative (percent) increase.
Absolute increase:
Relative increase:
%
Give answers accurate to at least 1 decimal place.
If the population of a town increased from 3200 in 2008 to 5700 in 2009, the absolute and relative (percent) increases are:
Absolute Increase = 2,500Relative Increase = 78.125%.What is the difference between absolute and relative increases?
Absolute increase refers to a numerical addition to the quantity of an item.
The absolute increase is the difference between the current value and the initial value.
On the other hand, the relative increase is expressed in percentage terms.
To compute the relative increase, divide the absolute increase by the initial value.
The population of the town in 2008 = 3,200
The population in 2009 = 5,700
The absolute increase in population = 2,500 (5,700 - 3,200)
The relative increase in population = 78.125% (2,500/3,200 x 100)
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Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 50% syrup? 5% syrup? 75% syrup? 1.5% syrup?
DONT LEAVE OUT HOW MUCH LB OF SYRUP SHE WOULD HAVE IN EACH CASE
Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup
Calculatng lbs of syrupTo determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:
Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)
50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:
0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar
Mass of Water = 0.5 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs
5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:
0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar
Mass of Water = 9 lbs
The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs
75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:
0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar
Mass of Water = 0.33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs
1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:
0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar
Mass of Water = 33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs
So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.
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Answer:
Step-by-step explanation:
Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup
Calculatng lbs of syrup
To determine how much water Ella should add to make a specific concentration of syrup, you need to use the formula:
Syrup Concentration = (Mass of Sugar) / (Mass of Sugar + Mass of Water)
50% syrup: In this case, the syrup concentration is 0.50, so you can use the formula as follows:
0.50 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.5 - 0.5 lbs of sugar
Mass of Water = 0.5 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.5 lbs of water = 1.0 lbs
5% syrup: In this case, the syrup concentration is 0.05, so you can use the formula as follows:
0.05 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.05 - 0.5 lbs of sugar
Mass of Water = 9 lbs
The total amount of syrup will be 0.5 lbs of sugar + 9 lbs of water = 9.5 lbs
75% syrup: In this case, the syrup concentration is 0.75, so you can use the formula as follows:
0.75 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.75 - 0.5 lbs of sugar
Mass of Water = 0.33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 0.33 lbs of water = 0.83 lbs
1.5% syrup: In this case, the syrup concentration is 0.015, so you can use the formula as follows:
0.015 = (0.5 lbs of sugar) / (0.5 lbs of sugar + Mass of Water)
Rearranging the formula, we get:
Mass of Water = (0.5 lbs of sugar) / 0.015 - 0.5 lbs of sugar
Mass of Water = 33 lbs
The total amount of syrup will be 0.5 lbs of sugar + 33 lbs of water = 33.5 lbs
So, to summarize, Ella will have 1.0 lbs of 50% syrup, 9.5 lbs of 5% syrup, 0.83 lbs of 75% syrup, and 33.5 lbs of 1.5% syrup.
A) Which statement is not true?
A) When you add same signs, find the sum, keep the sign.
B) When you multiply or divide different signs the answer is always positive.
C) Subtraction means to add the reciprocal.
D) The product of a number and its reciprocal is 1
Answer:
B
Step-by-step explanation:
The statement isn't true because when you multiply or divide different signs the answer is always negative.
Both B and C are false.
Your teacher tells you that the mean score for a test was a 70 and that the standard deviation was 7 for your class. You are given that the z-score for your test was 2.5. What did you score on your test?
Answer:
Check the image for the answer!
Step-by-step explanation:
Please mark me Brainliest!
is x+y=8
and x^2+y^2=80
then what is xy?
a. 16
b. -8
c. 8
d.-16
e.-32
Answer: Given the two equations x + y = 8 and x^2 + y^2 = 80, we can use the first equation to solve for x or y and substitute that expression into the second equation.
Let's solve for y:
y = 8 - x
Now we can substitute this expression for y into the second equation:
x^2 + (8 - x)^2 = 80
Expanding the square and collecting terms gives:
x^2 + 64 - 16x + x^2 = 80
Combining like terms:
2x^2 - 16x + 16 = 80
Moving all terms to the left side:
2x^2 - 16x - 64 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a = 2, b = -16, and c = -64
x = (-(-16) ± √((-16)^2 - 4 * 2 * -64)) / (2 * 2)
x = (16 ± √(256 + 512)) / 4
x = (16 ± √768) / 4
x = (16 ± 8√6) / 4
Since x and y must be real numbers, we reject the negative square root. Therefore, x = (16 + 8√6) / 4.
Finally, substituting x into the first equation to find y:
y = 8 - x = 8 - (16 + 8√6) / 4 = (8 - 16) / 4 - 8√6 / 4 = -8 / 4 - 8√6 / 4 = -2 - 2√6.
Therefore, xy = x * y = (16 + 8√6) / 4 * (-2 - 2√6) = -16 - 16√6.
The answer is d. -16.
Step-by-step explanation:
HELP ASAP QUESTION 1!
Answer:
The answer is 313° degrees.
A monkey types on a 26-letter keyboard that has lowercase letters only. Each letter is chosen independently and uniformly at random from the alphabet. If the monkey types n = 1,000,004 letters. what is the expected number of times the sequence "proof" appears?
The expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.
How to solve for the number of times that proof would appearThe expected number of times the sequence "proof" appears in a randomly generated string of n = 1,000,004 letters can be calculated using the formula:
expected_occurrences = (n - 4) / 26^4
where 26^4 is the number of possible 4-letter sequences that can be formed using a 26-letter keyboard. Plugging in n = 1,000,004, we get:
expected_occurrences = (1,000,004 - 4) / 26^4
≈ 36.08
So, the expected number of times the sequence "proof" appears in a randomly generated string of 1,000,004 letters is approximately 36.
Read more on sequences here:https://brainly.com/question/6561461
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The hypotenuse of a right triangle is on the line y = 3x + 2. The shorter leg of
the triangle is parallel to the x-axis and is 3 units long. Find the perimeter of the
triangle.
Answer:
The perimeter of the triangle is 30.5.
Step-by-step explanation:
To find the perimeter of the triangle, we need to find the length of the other leg.
We can use the equation of the line that defines the hypotenuse, y = 3x + 2, to find the coordinate of the endpoint of the shorter leg. The endpoint has x-coordinate equal to 3 (since the length of the leg is 3), and the y-coordinate can be found by substituting x = 3 into the equation:
y = 3x + 2
y = 3 * 3 + 2
y = 11
So the endpoint of the shorter leg is (3, 11).
Next, we can use the Pythagorean theorem to find the length of the other leg:
a^2 + b^2 = c^2
where a is the length of the shorter leg (which we know is 3), b is the length of the other leg, and c is the length of the hypotenuse (which is also on the line y = 3x + 2).
We can use the coordinates of the endpoint of the shorter leg to find the length of the hypotenuse:
c = √((3 - 0)^2 + (11 - 2)^2)
c = √(3^2 + 9^2)
c = √(9 + 81)
c = √90
So the length of the hypotenuse is √90.
Using the Pythagorean theorem, we can now find the length of the other leg:
3^2 + b^2 = (√90)^2
9 + b^2 = 90
b^2 = 81
b = 9
So the length of the other leg is 9.
Finally, the perimeter of the triangle is 3 + 9 + √90, which is approximately 12 + 9 + 9.5 = 30.5.
If y = -5x + 3, determine the value of y when x = -4
Answer: Y = 23
Step-by-step explanation: -5 x -4 = positive 20 then add 3 which equals 23. 23 is the value of y