The answer, t would have to be less than2, t< 2 hours in inequality.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Given, If "t" represents the time it takes to mow the lawn,
So the t< 2 hours in inequality.
Hence, the inequality will be t< 2.
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Jean deposits $730 in an account that pays 2.8% simple interest. He neither adds more money nor withdraws any moneyfrom his account. What amount will be in Jeans account after 5 years?
Answer:
832.2
Step-by-step explanation:
730 x 0.028 = (assuming per year) 20.44
20.44 x 5 = 102.2
102.2 + 730 = 832.2
Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2
The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.
We will first calculate the numerator:
As (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :
\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))
= 100(\(87^2\) - 87 * 13 + \(13^2\))
Now, calculate the denominator:
\(87^2 - 87 * 13 + 13^2\)
As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):
\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)
\(= 74^2\)
So by solving the equation further:
\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)
As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:
\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)
So, the value of the given expression is 100.
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mathstatistics and probabilitystatistics and probability questions and answerschristmas lights are often designed with a series circuit. this means that when one light burns out, the entire string of lights goes black. suppose the lights are designed so that the probability a bulb will last 2 years is 0.995. the success or failure of a bulb is independent of the success or failure of the other bulbs. a) what is the probability that
Question: Christmas Lights Are Often Designed With A Series Circuit. This Means That When One Light Burns Out, The Entire String Of Lights Goes Black. Suppose The Lights Are Designed So That The Probability A Bulb Will Last 2 Years Is 0.995. The Success Or Failure Of A Bulb Is Independent Of The Success Or Failure Of The Other Bulbs. A) What Is The Probability That
Christmas lights are often designed with a series circuit. This means that when one light burns out, the entire string of lights goes black. Suppose the lights are designed so that the probability a bulb will last 2 years is 0.995. The success or failure of a bulb is independent of the success or failure of the other bulbs.
A) What is the probability that in a string of 100 lights all 100 will last 2 years?
B) What is the probability at least one bulb will burn out in 2 years?
A) The probability that all 100 lights will last 2 years is 0.9048.
B) The probability that at least one bulb will burn out in 2 years is 0.0952.
What is the probability?A) To find the probability that all 100 lights will last 2 years, we assume that the success or failure of each bulb is independent.
The probability of a single bulb lasting 2 years is 0.995, so the probability of all 100 bulbs lasting 2 years is:
P(all 100 bulbs last 2 years) is (0.995)¹⁰⁰ ≈ 0.9048
B) The probability that at least one bulb will burn out in 2 years is determined using the complement rule.
P(at least one bulb burns out) = 1 - P(no bulbs burn out)
Since the probability of a single bulb lasting 2 years is 0.995, the probability of a single bulb burning out in 2 years is 1 - 0.995 = 0.005.
The probability of at least one bulb burning out in 2 years is:
P(at least one bulb burns out) = 1 - P(no bulbs burn out)
P(at least one bulb burns out) = 1 - 0.9048
P(at least one bulb burns out) ≈ 0.0952
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Harvey is 3 times as old as Jane. The sum of their ages is 52 years. Find the age of each.
Jane is 13 and Harvey is 39
Jane is 12 and Harvey is 48
Jane is 13 and Harvey is 48
Answer:
13, 39
Step-by-step explanation:
H +J =52
H =3J
3J +J =52
4J =52
J =52 :4 =13 (Jane is 13
H =3 ×13 =39 (Harvey is 39
Answer:
Jane is 13 and Harvey is 39
Step-by-step explanation:
Prove that
secθ+1 / tanθ = tanθ / secθ−1
To prove that secθ + 1 / tanθ = tanθ / secθ−1, we can use trigonometric identities.
First, we will define secθ as 1/cosθ and tanθ as sinθ/cosθ.
Now, we can substitute these definitions into the equation to get:
secθ + 1 / tanθ = (1/cosθ) + 1 / (sinθ/cosθ)
And, tanθ / secθ−1 = (sinθ/cosθ) / (1/cosθ) - 1
Expanding both sides using basic algebraic manipulations, we get:
(1/cosθ) + 1 / (sinθ/cosθ) = (1/cosθ) * ((sinθ/cosθ) + cosθ/cosθ)
= (sinθ/cosθ) / (1/cosθ) - 1
= (sinθ/cosθ) * (cosθ/1) - 1
= (sinθ) / 1 - 1
= sinθ.
Therefore, secθ + 1 / tanθ = tanθ / secθ−1 has been proven.
Which equation can be used to find the area of the figure below?
F.A = (10⋅82
)+
(16⋅8
)
G.A = (6⋅82
)+
(10⋅8
)
H.A = (6⋅82
)+
(6⋅8
)
J.A = (6⋅8
)+
(10⋅8
)
The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
What is area of composite figure?The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.
A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.
The area of the rectangle is given as:
A = (l)(w)
A = 10(8)
A = 80 sq. units
The area of the triangle is:
A = 1/2(b)(h)
In the figure:
b = 16 - 10 = 6 and h = 8.
A = 1/2(6)(8)
A = 24 sq. units
The total area of the figure is:
Area = area of rectangle + area of triangle
Area = 80 + 24
Area = 104 sq. units
Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).
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Assinala o numero de molas necessarias para pendurar 18 guardanapos uns a seguir aos outros de modo que 2 guardanapos partilhem a mesma mola
To hang 18 napkins one after another in a way that two napkins share the same clip, we need to determine the number of clips required.
If each napkin is hung separately, we would need 18 clips. However, we want to find the number of clips needed when two napkins share the same clip. To accomplish this, we can think of each clip as a separator between two napkins. So, if we have 18 napkins, we will have 17 separators (clips) between them.
Therefore, the number of clips needed to hang 18 napkins such that two napkins share the same clip is 17. By using 17 clips, we can create 18 sections, with each section consisting of two adjacent napkins sharing the same clip.
It's important to note that if we had fewer clips, we wouldn't be able to ensure that two napkins share the same clip. Similarly, if we had more clips, some clips would remain unused. Hence, 17 clips are necessary and sufficient to achieve the desired arrangement.
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Jamil found that he reads 1/5 of his 115 - page book in 1/4 of an hour. At this rate how many pages does he read in an hour.
Answer:
Step-by-step explanation:
1/5 of 115= 23
so in 15mins he reads 23 pages.
15mins x 4=60mins
23x4=92
Have a nice day sunshine
write an explicit formula for an,the nth term of the sequence 72,12,2
Answer:
\(a_n = 432 \cdot \left(\frac{1}{6}\right)^n\) OR \(a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}\)
Step-by-step explanation:
The first term is 72, and each term is equal to the previous term multiplied by 1/6. This yields the expression \(a_n = 72 \cdot \left(\frac{1}{6}\right)^{n-1}\), which is equivalent to \(a_n = 432 \cdot \left(\frac{1}{6}\right)^n\).
Answer:
\(n _{th} = n _{1} {r}^{n - 1} \\ n _{th} = 72 \times 12 {}^{(n - 1)} \\ n _{th} = 72 \times ( {12}^{n} .12^(-1)) \\ n _{th} = 6 × {12}^{n} \)
Andrea and Ashley are middle-distance runners for their school’s track team. Andrea’s times in the 400-meter race are approximately Normally distributed with a mean of 62 seconds and a standard deviation of 0. 8 seconds. Ashley’s times are approximately Normally distributed with a mean of 62. 8 seconds and a standard deviation of 1 second.
a) The school record for the 400-meter is 60. 0 seconds. What is the probability that Andrea breaks the record in her next race?
b) Assuming that Andrea and Ashley’s times in any race are independent, what is the probability that Ashley beats Andrea in their next race?
the probability of Andrea breaking the record in the next race is 0.002555
The probability that Ashley beats Andrea in their next race is 0.2661
Andrea has mean 62 and sd, so P(x <= 60) = P(z <= (60-62)/.8) = P(z <= 2.5) = norm.s.dist(-2.5,1) = .00621
Ashley has mean 62.8 and sd 1, so P(x <= 60) = P(z <= (60-62.8)/1) = P(z <= -2.8) = norm.s.dist(-2.8,1) = 0.002555
The mean difference for Ashley - Andrea = 62.8 - 62 = 0.8
The variance of the difference, given independence, is .8^2 + 1^2 = 1.64
Ashley is faster if the difference is less than 0.
Then, P(x <= 0) = P(z <= (0 - 0.8)/sqrt(1.64) ) = norm.s.dist(-.8/sqrt(1.64),1) = 0.2661
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1. The scatter plot shows July temperature data for some Ontario communities.
a) One data point is for Fort Frances, at latitude 48°N. Average Daily Maximum Temperature in July
What is the average daily maximum temperature in
Fort Frances in July?
b) How many of the communities represented on this
graph have average daily maximum temperatures
greater than 22°C? What are their latitudes?
c) Is there a relationship between the two variables?
Identify the two variables and explain your answer.
Temperature (°C)
24
23-
22
21
20-
19-
18-
17
16-
15
14
.
40 42 44 46 48 50 52 54
Latitude (N)
a.) Based on the scatter plot, the estimated average daily maximum temperature in Fort Frances in July is around 25°C.
b) There are four communities with average daily maximum temperatures greater than 22°C. Their latitudes are approximately:
Toronto: 44°N
Windsor: 42°N
London: 43°N
Ottawa: 45°N
c.)
. Based on the scatter plot, there seems to be a relationship between latitude and temperature .
As latitude increases, temperature generally decreases because places closer to the equator receive more direct sunlight and therefore tend to be warmer, while places farther away receive less direct sunlight and tend to be cooler.
What is latitude?Latitude is described as a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body.
there are some exceptions to this general trend that states that as latitude increases, temperature decreases because places closer to the equator receive more direct sunlight and therefore tend to be warmer, while places farther away receive less direct sunlight and tend to be cooler. which could be due to other factors such as elevation, proximity to water, or local weather patterns.
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A house was purchased in 2005 for $150,000. It is now valued at $ 235,000. What is the rate (percent) of appreciation for t he house?
Emmy just got her hair cut, colored, and styled for $70. She wants to leave the stylist
a tip of 20%. How much is the tip?
Answer:
20% of 70 is 14
Step-by-step explanation:
l
you make 100$ doing 10 hours of yard work. find the unit rate in dollars per one hour
Which is the more reasonable measurement of the distance between the tracks on a railroad:
1.435 ⋅ 10−3 mm or 1.435 ⋅ 103 mm?
If you're comparing 1.435 * 10^(-3) mm to 1.435 * 10^3 mm, then the more reasonable measurement is 1.435 * 10^3 mm since,
1.435 * 10^3 mm = 1435 mm = 1.435 meters
1 meter is about 3.28 feet approximately
So 1.435 meters is slightly larger (about 4.708 feet) which is a fairly reasonable distance between the tracks on a railroad.
-------------------
Something like 1.435 * 10^(-3) mm is equal to 0.001435 mm, which is far less than 1 mm.
an irs representative claims that the average deduction for medical care is $ 1250. a taxpayer who believes that the real figure is lower samples 32 random families and comes up with a sample mean of $934 and a sample standard deviation of $619. what null and alternative hypothesis would you use to test this claim?
These tests would allow us to determine if the observed sample mean of $934 is significantly different from the claimed average of $1250, providing evidence to support or reject the alternative hypothesis.
To test the claim made by the IRS representative that the average deduction for medical care is $1250, we can formulate the null and alternative hypotheses as follows:
Null Hypothesis (H0): The average deduction for medical care is $1250.
Alternative Hypothesis (H1): The average deduction for medical care is lower than $1250.
In this case, the taxpayer who believes that the real figure is lower has collected a sample of 32 random families. The sample mean is $934, and the sample standard deviation is $619. The null hypothesis assumes that the average deduction is $1250, while the alternative hypothesis suggests that it is lower than $1250.
To statistically test these hypotheses, we can use a one-sample t-test or a z-test, depending on the sample size and whether the population standard deviation is known.
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does tan^2x = sin^2x/cos^2x
Answer:
Yes they both are equal
Why does nobody care about may the 4th be with you (star wars day)
One of the video editors in your company is worried that he may lose a lot of data if his hard drive fails. He has asked you to come up with a solution. To do this, you have decided to implement a RAID 10 solution on his desktop workstation.Which of the following is the MINIMUM number of hard disks that can be used?a. 6b. 5c. 4d. 3e. 2
The minimum number of hard disks that can be used for implementing a RAID 10 solution is four (option c).
The minimum number of hard disks that can be used for implementing a RAID 10 solution on the video editor's desktop workstation is four (option c). RAID 10, also known as RAID 1+0, combines elements of RAID 1 (mirroring) and RAID 0 (striping) to provide both data redundancy and improved performance.
In RAID 10, data is mirrored across multiple drives to ensure redundancy. To implement RAID 10, we need at least two sets of mirrored drives, where each set contains a minimum of two hard disks.
The data is striped across these mirrored sets to enhance performance.
With four hard disks, you can create two mirrored sets, each consisting of two drives.
The data is then striped across these mirrored sets, providing both redundancy and improved read/write speeds.
If one drive fails in each mirrored set, the system can still function without data loss due to the mirroring.
This setup provides a balance between data protection and performance.
While more hard disks can be used in RAID 10 for larger capacities and better performance, the minimum requirement is four hard disks.
Using fewer drives would not allow for the necessary mirrored sets and striping required for RAID 10.
By implementing a RAID 10 solution with four hard disks on the video editor's workstation, you can help safeguard against data loss in case of drive failure, ensuring the integrity and availability of important video editing data.
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X = 9 y = 4 is a solution of the linear equation (a) 2x+y=17 (b) x+y=17 (c) x+2y=17 (d) 3x-2y=17
Answer:
(c) is correct.
Step-by-step explanation:
(c) 9 + 2(4) = 9 + 8 = 17
A survey was done that asked people to indicate whether they preferred to ride a
street bike or a mountain bike. The results of the survey are shown in the two-way
table.
Amjed is making a relative frequency table from this data.
What operation should Amjed perform to determine the relative frequency of a
person over 30 years old who prefers to ride a mountain bike? 1) Subtract 25 from 462, then divide by 462. 2) Divide 25 by 462. 3) Add 180 to 462, then divide by 463. 4) Divide 180 by 462
The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:
2) Divide 25 by 462.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of people is given as follows:
58 + 164 + 215 + 25 = 462.
Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:
25/462.
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30% of a sum of money is rupees 300. what is the total amount?
step by step explanation please
subject: linear equations in math
the total amount is 9000
Erica and Dana are collecting canned food to donate to a local charity. This morning, Dana had twice as many cans as Erica. Then Dana collected 8 more cans. If Dana has 42 cans of food. How many cans of food does Erica have? (Let e represent the number of cans of food Erica has).
Answer:
its 42÷2= 21 i think
Step-by-step explanation:
because dana has twice the nb of cans erica has so it dana has 48 then erica has the half number
A commercial jet and a private airplane fly from Denver to Phoenix. It takes the commercial jet 2. 7 hours for the flight, and it takes the private airplane 4 hours. The speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. Round your answer to one decimal place if necessary
the speed of the private airplane is approximately 214.3 miles per hour. Rounding to one decimal place is not necessary but if you round it the answer will be 214 miles.
Let's call the speed of the private airplane "s". According to the problem, the speed of the commercial jet is 103 miles per hour faster than the speed of the private airplane. So, the speed of the commercial jet is:
s + 103
We know that the distance from Denver to Phoenix is the same for both planes. Let's call this distance "d".
Using the formula distance = rate x time, we can set up two equations:
For the private airplane:
d = s × 4
For the commercial jet:
d = (s + 103) × 2.7
Since both equations represent the same distance, we can set them equal to each other and solve for s:
s × 4 = (s + 103) × 2.7
4s = 2.7s + 278.1
1.3s = 278.1
s = 278.1 / 1.3
s = 214.3
Therefore, the speed of the private airplane is approximately 214.3 miles per hour.
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9. find a particular solution for y 00 4y 0 3y = 1 1 e t using transfer functions, impulse response, and convolutions. (other methods are not accepted)
the point P_0(2,1,2) lies on the tangent plane, we can use it to find the equation of the normal line:
x - 2 = 2
We start by finding the characteristic equation:
r^2 + 4r + 3 = 0
Solving for r, we get:
r = -1 or r = -3
So the complementary solution is:
y_c(t) = c_1 e^{-t} + c_2 e^{-3t}
Next, we need to find the transfer function H(s):
s^2 Y(s) - s y(0) - y'(0) + 4s Y(s) - 4y(0) + 3Y(s) = 1/s + 1/(s-1)
Applying the initial conditions y(0) = 0 and y'(0) = 1, we get:
(s^2 + 4s + 3) Y(s) = 1/s + 1/(s-1) + 4
Y(s) = [1/(s+1) + 1/(s+3) + 4/(s^2 + 4s + 3)] / (s^2 + 4s + 3)
We can factor the denominator of the second term in the numerator:
Y(s) = [1/(s+1) + 1/(s+3) + 4/((s+1)(s+3))] / [(s+1)(s+3)]
Using partial fraction decomposition, we get:
Y(s) = [2/(s+1) - 1/(s+3) + 1/((s+1)(s+3))] / (s+1) + [-1/(s+1) + 2/(s+3) - 1/((s+1)(s+3))] / (s+3)
Taking the inverse Laplace transform, we get:
y(t) = 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})
So the general solution is:
y(t) = y_c(t) + y_p(t) = c_1 e^{-t} + c_2 e^{-3t} + 2e^{-t} - e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})
To find a particular solution, we need to solve for the unknown coefficients. Using the initial conditions y(0) = 1 and y'(0) = 0, we get:
c_1 + c_2 + 3/2 = 1
-c_1 - 3c_2 - 1/2 = 0
Solving this system of equations, we get:
c_1 = -2/5
c_2 = 9/10
So the particular solution is:
y_p(t) = (-2/5) e^{-t} + (9/10) e^{-3t} + (1/2)(1 - e^{-t}) - (1/2)(1 - e^{-3t})
Finally, the tangent plane at P_0(2,1,2) is given by the equation:
2x + 4y + 3z = 24
which corresponds to option (B) in the given choices.
To find the normal line, we first need to find the normal vector to the tangent plane, which is simply:
n = <2, 4, 3>
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|5x|=3
this is absolute value of five x equals three
The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.
What is a modulus function ?In mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.
According to the given question |5x| = 3.
We know |x| = a implies x = a or x = -a.
∴ |5x| = 3 is
5x = 3
x = 3/5
Or
5x = -3.
x = -3/5.
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HELPPPPPPPPPPPPPPPPPP 7th Grade
Answer:
Step-by-step explanation:
a line is 180° so we subtract 109 from 180 to find mLUE
180-109=
71
a triangle is also 180° so we add up the angles we have so far and subtract that from 180°
180-(71+49)
180-(120)
mULE = 60°
1. 3 6 12 24 2. 2 9 16 23 3. 53 46 39 32 4. 5 12 26 54 5. 5 20 50 110
FIND 3 NEXT TERMS
Answer:
Step-by-step explanation:
1. 48 96 192 (multiplying by 2)
2. 30 37 44 ( adding 7)
3. 25 18 11 ( subtracting 7)
4. 110 232 456 ( adding 7, 14, 28, 56 and so on)
5. 230 470 950 (adding 15, 30, 60 120 and so on)
Nine times a number, diminished by 4, is 95
Answer:
the number is 11
Step-by-step explanation:
"Diminished" is another word for subtraction, so our equation is : 9x - 4 = 95
Add 4 on each side: 9x = 99
Divide each side by 9: x = 11
I hope this helped, please mark Brainliest, thank you!
Answer:
Step-by-step explanation:
Let a number be X
So
Nine times a number, diminished by 4, is 95
9x-4=95
9x=95+4
9x=99
X=99/9
X=11
So the number is 11
x to the power of 2 = 121 what is x
Answer: x = -11, x = 11
Step-by-step explanation:
x² = 121
\(\sqrt{x^2}=\sqrt{121}\)
x = ±11
x = -11, x = 11