Is this sum rational or irrational? Explain.
1.12 + 18/7 (1 point)
The sum is rational because both 1.12 and 18 are rational, and the sum of rational numbers is rational.
The sum is irrational because 1.12 is irrational, and the sum of a rational number and an irrational number is irrational..
The sum is rational because both 1.12 and 18 are positive, and the sum of positive numbers is rational.
The sum is irrational because 18 is irrational, and the sum of a rational number and an irrational number is irrational.
Answer: The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational
Step-by-step explanation:
Given the two numbers :
1.12 and 18/7
1.12 is a rational number as it is a not a non-terminating decimal and can accurately be expressed in the form a/b, where a and b are integers, thus 1.12 is equivalent to 112 / 100
18/7 on the other hand is an irrational number as it is a non-terminating decimal.
Hence, takingbthe sum of both numbers (rational and irrational) results in an irrational output.
18 / 7 = 2.57142857....
Taking the sum of both,
1.12 + 2.57142857... = 3.69142857... ; which is irrational
Answer:
The sum is irrational because 18/7 is irrational, and the sum of a rational number and an irrational number is irrational.
Step-by-step explanation:
NEED THE ANSWER ASAP! THANK YOU!
Select the correct answer.
These instructions for inscribing a regular hexagon in circle C contain an error.
Step 1: Set the compass width to the diameter of the circle.
Step 2: Place the fixed part of the compass on point B, and draw an arc that intersects the circle.
Step 3: Move the fixed part of the compass to the point of intersection, and draw another arc that intersects the circle.
Step 4: Repeat step 3 three more times.
Step 5: Connect the points of intersection to complete the hexagon.
Which step requires revision, and how should it be corrected?
A. In step 1, the compass width should be set to the length of BC.
B. In step 2, the fixed part of the compass should be placed at point C.
C. In step 3, the fixed part of the compass should be placed at point C.
D. In step 4, it should say to complete step 3 six more times.
A step that requires revision, and how should it be corrected include the following: A. In step 1, the compass width should be set to the length of BC.
What is a regular polygon?In Euclidean geometry, a regular polygon can be defined as a form of polygon which has all of its sides and interior angles being equal.
By critically observing the polygon shown in the image attached below, we can reasonably infer and logically deduce that it represents a regular hexagon because it has a total of six (6) sides with equal angles.
Additionally, the radius of this regular polygon (hexagon) is line segment BC and as such, you should set the compass width should be set to the length of BC in order to inscribe a regular hexagon in circle C.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
You are a district sales manager at the sales target for your team135,000 per month ?
You are a district sales manager at the sales target for your team 135,000 per month. Your team's annual sales target is $1,620,000.
To calculate the annual sales target for your team, you need to multiply the monthly target by 12 (the number of months in a year):
Annual sales target = Monthly sales target x 12
Given that the monthly sales target for your team is $135,000, the annual sales target would be:
Annual sales target = $135,000 x 12
= $1,620,000
A Sales Manager is a professional responsible for managing a team of sales representatives within a specific geographic area or district. The role typically involves setting and achieving sales targets, developing and implementing sales strategies, and managing relationships with key customers.
Sales Managers are responsible for recruiting, training, and supervising sales staff, as well as monitoring their performance and providing coaching and guidance as needed. They also work closely with other departments within the organization, such as marketing and finance, to ensure that sales goals are aligned with overall business objectives. They must possess strong leadership and communication skills, as well as a deep understanding of their company's products or services and the competitive landscape in which they operate.
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Complete Question:-
You are a district sales manager at the sales target for your team 135,000 per month ? What is your annual sales?
Enter the value of n for the equation
It’s shown in the picture that i put
Explain how you got it please need help asap!
The value of n in the given equation, 5⁸ = 5ⁿ · 5⁴, is 4
Indicial equations: Determining the value of nFrom the question, we are to determine the value of n in the given equation.
From the given information,
The given equation is
5⁸ = 5ⁿ · 5⁴
This can be written as
5⁸ = 5ⁿ × 5⁴
By applying the multiplication law of indices, we get
5⁸ = 5ⁿ ⁺ ⁴
Since the bases are equal, we can equate the powers
8 = n + 4
Now,
Solve the linear equation for n
8 = n + 4
Subtract 4 from both sides of the equation
8 - 4 = n + 4 - 4
4 = n
Therefore,
n = 4
Hence, the value of n is 4
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can you answer this?
Answer:
25
Step-by-step explanation:
Add all of the sides together
Need help please and thank you :)
Answer:
C. Yes, Because Each Side Length Is Less Than 15.
Step-by-step explanation:
Answer:
the person above me is right mark me brainiest for being right :D
Step-by-step explanation:
Which of the following is not one of the Counting Rules. O a. The Range Rule O b. The Combination Rule O c. The Permutation Rule O d. Fundamental Counting Rule
The Range Rule is not one of the Counting Rules.
The following are the Counting Rules: Permutation Rule: Used to calculate the number of arrangements of a set in a particular order. Combination Rule: Used to calculate the number of ways to pick objects from a larger set, without regards to order. Fundamental Counting Rule: Used to calculate the number of possible outcomes in an event by multiplying the number of outcomes in each category together .Range Rule: The range rule is used to calculate the variation of a data set by subtracting the minimum value from the maximum value. It is not a counting rule, but a statistical tool.
The Fundamental Counting Principle is a technique used in mathematics, more specifically in probability theory and combinatorics, to determine how many combinations of options, items, or outcomes are possible. The Rule of Multiplication, the Product Rule, the Multiplication Rule, and the Fundamental Counting Rule are some of its alternate names.
It has a connection to the Sum method, often known as the Rule of Sum, which is a fundamental counting method used to calculate probabilities.
According to the Fundamental Counting Principle, if a decision or event has a possible outcome or set of options, and a different decision or event has b possible outcomes or choices, then the sum of all the unique combinations of outcomes for the two is ab.
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write 3 over 11 as a ratio using a colon
Answer:
3/11
3:11
Step-by-step explanation:
Answer:
3:11 or/and 3/11
Step-by-step explanation:
Find the LENGTH OF THE MISSING SIDE in the following right triangle in inches.
Round to the nearest tenth, if necessary.
20 inches
21 inches
Answer:
If the missing side is long then it's 29 or if its short, then it's 6.4
Step-by-step explanation:
just do a^2 + b^2 = c^2 method
Please help??!?!??? Bplease
Answer:
radical 7<14÷5
bcoz radical 7 is 2.645
and 14÷5 is 2.8
On the coordinate grid draw the graph of y=2x-3
Use the value of x from -2 to +2
Answer:2x
Step-by-step explanation:
9.8. installation of a certain hardware takes random time with a standard deviation of 5 minutes. (a) a computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. compute a 95% confidence interval for the population mean installation time. (b) suppose that the population mean installation time is 40 minutes. a technician installs the hardware on your pc. what is the probability that the installation time will be within the interval computed in (a)?
There is an 80.8% chance that the installation time for a single computer falls within the confidence interval computed in part (a).
a) To compute the 95% confidence interval for the population mean installation time, we can use the formula:
CI = x ± z* (σ/√n)
where x is the sample mean installation time, σ is the population standard deviation, n is the sample size, and z* is the z-score associated with the desired confidence level (in this case, 95%).
Substituting the given values, we have:
CI = 42 ± 1.96 * (5/√64)
CI = 42 ± 1.225
CI = (40.775, 43.225)
Therefore, we can say with 95% confidence that the population mean installation time is between 40.775 minutes and 43.225 minutes.
(b) If the population mean installation time is 40 minutes, the probability that a randomly selected installation time falls within the confidence interval computed in part (a) can be calculated using the standard normal distribution. We first convert the interval to z-scores:
Lower bound z-score: (40.775 - 40) / (5/√64) = 1.39
Upper bound z-score: (43.225 - 40) / (5/√64) = 4.29
Using a standard normal table or a calculator, we can find the probability that a z-score falls between 1.39 and 4.29. This probability is approximately 0.808.
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1. How many more monthly payments are made for a five-year loan than for a three-year loan?
Answer: There are 24 more payments made.
Step-by-step explanation:
In a 5 year loan there is 60 months
In a 3 year loan there is 36 months.
Find the missing side lengths. leave your answers as radicals in simplest form 45 20v2
1) The missing side lengths are: Hypotenuse a = 4 Side b = 2√2
2) The missing side lengths are: Leg x = 2√2 Leg y = 2√2
1) In a right triangle with a 90° angle and an opposite angle of 45°, we can use the trigonometric ratios to find the missing side lengths.
Let's denote the hypotenuse as a, the side opposite the 45° angle as c, and the remaining side as b.
Using the sine function, we have:
sin(45°) = c / a
Since sin(45°) = √2 / 2, we can substitute the values:
√2 / 2 = 2√2 / a
To solve for a, we can cross-multiply and simplify:
√2 * a = 2√2 * 2
a√2 = 4√2
a= 4
Therefore, the hypotenuse (a) has a length of 4.
To find side b, we can use the Pythagorean theorem:
a² + b² = c²
Plugging in the known values:
(2√2)²+ b² = 4²
8 + b² = 16
b²= 16 - 8
b² = 8
b = √8 = 2√2
So, the missing side lengths are:
Hypotenuse (c) = 4
Side b = 2√2
2) In a right triangle with a 45° angle and a hypotenuse of 4, we can find the lengths of the other two sides. Let's denote the length of one leg as x and the length of the other leg as y.
Using the Pythagorean theorem, we have:
\(x^2 + x^2 = 4^2\\2x^2 = 16\\x^2 = 16 / 2\\x^2 = 8\)
x = √8 = 2√2
Therefore, one leg (x) has a length of 2√2.
To find the other leg, we can use the fact that the triangle is isosceles (since both acute angles are 45°). Therefore, the other leg (y) has the same length as x:
y = x = 2√2
So, the missing side lengths are:
Leg x = 2√2
Leg y = 2√2
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The complete question is:
Find the missing side lengths. leave your answers as radicals in simplest form
Let (N(t))t a Poisson process with rate 3 per min. Let Sn denote
the time of the n-th event.
Find a. E[S10]
b. E[S4|N(1) = 3]
c.Var(S10).
d. E[N(4) − N(2)|N(1) = 3].
e. P[T20 > 3].
For a Poisson process with rate λ, the interarrival times between events are exponentially distributed with parameter μ = 1/λ. So, the time between the (n-1)-th and n-th event, denoted as Tn, follows an exponential distribution with parameter μ = 1/3 minutes.
Since Sn is the sum of the first n interarrival times, we have:
Sn = T1 + T2 + ... + Tn
The sum of n exponential random variables with parameter μ is a gamma random variable with shape parameter n and scale parameter μ. Therefore, Sn follows a gamma distribution with shape parameter n and scale parameter μ.
In this case, n = 10 and μ = 1/3. So, E[S10] can be calculated as:
E[S10] = n * μ = 10 * (1/3)
= 10/3 minutes.
Therefore, E[S10] = 10/3 minutes.
b. E[S4|N(1) = 3]:
Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, the time of the 4th event, S4, will be the sum of the first 3 interarrival times plus the time between the 3rd and 4th event.
Using the same reasoning as in part a, we know that the sum of the first 3 interarrival times follows a gamma distribution with shape parameter 3 and scale parameter 1/3. The time between the 3rd and 4th event, denoted as T4, follows an exponential distribution with parameter 1/3.
So, S4 = T1 + T2 + T3 + T4.
Since T1, T2, T3 are independent of T4, we can calculate E[S4|N(1) = 3] as:
E[S4|N(1) = 3] = E[T1 + T2 + T3 + T4]
= E[T1 + T2 + T3] + E[T4]
= (3/3) + (1/3)
= 4/3 minutes.
Therefore, E[S4|N(1) = 3] = 4/3 minutes.
c. Var(S10):
The variance of Sn, Var(Sn), for a Poisson process with rate λ, is given by:
Var(Sn) = n * σ^2,
where σ^2 is the variance of the interarrival times.
In this case, n = 10 and the interarrival times are exponentially distributed with parameter μ = 1/3. The variance of an exponential distribution is \(\mu^2\)So, \(\sigma^2 = \left(\frac{1}{3}\right)^2\)
= 1/9.
Substituting the values into the formula, we have:
Var(S10) = 10 * (1/9)
= 10/9.
Therefore, Var(S10) = 10/9.
d. E[N(4) − N(2)|N(1) = 3]:
Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, at time t = 2 minutes, there will be 3 - 1 = 2 events that have already occurred.
Now, we need to find the expected value of the difference in the number of events between time t = 4 minutes and t = 2 minutes, given that there were 3 events at t = 1 minute.
Since the number of events in a Poisson process follows a Poisson distribution with rate λt, where t is
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I need help with geometry solve for x
The value of the y in the given right triangle is 3√3.
What is a right triangle?A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.
Given is a right triangle, here there are two more right triangles in it, all are similar by AA rule,
So, by the definition of similar triangle,
x / 9 = 12 / x
x² = 108
x = 6√3
Also, Using Pythagoras theorem, we will have, [c² = a²+b², where a, b and c are the sides of a right triangle]
x² = 9²+y²
108 = 81 + y²
y² = 27
y = 3√3
Hence, the value of the y in the given right triangle is 3√3.
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For the sequence below, explain the pattern in words.
14. 11. 8. 5....
Answer:
you subtract the number by 3
Step-by-step explanation:
the pattern is x-3 so the pattern is subtracting the number by 3 every time
What is the ratio of protonated/deprotonated acetic acid at ph 1.8, 5.8, and 10.8?
The ratio of protonated/deprotonated acetic acid at the given pH is:
pH 1.8: 1000:1, pH 5.8: 1:10, pH 10.8: 1:1000000What is acetic acid?Acetic acid, also known as ethanoic acid, is a colorless liquid with a strong, vinegar-like odor. It is referred to as glacial acetic acid when it is pure (100% acetic acid). Acetic acid is a byproduct of fermentation that gives vinegar its distinctive aroma. Vinegar contains approximately 4-6% acetic acid in water. More concentrated solutions are available in laboratories, and glacial acetic acid is pure acetic acid containing only traces of water. Human Reactions: Acetic acid, in vapor form, is a severe irritant to the eyes, mucous membranes, upper respiratory tract, and skin. When acetic acid solutions of 80% or higher come into contact with the skin or eyes, they can be corrosive, causing severe burns to any exposed tissue.The protonated/deprotonated acetic acid pH 1.8, 5.8, and 10.8 ratios are 1000:1, 1:10, and 1:1000000, respectively.Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:
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he average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27 Quantity A uantity HB The average of the 150 measurements 25 Quantity A is greater Quantity B is greater
The average of the 150 measurements is 24.33, and Quantity B with a value of 25 is greater.
To compare the averages of the 150 measurements, let's calculate the total sum of all the measurements.
For the first set of 100 measurements with an average of 23, the total sum is 100 * 23 = 2300. For the second set of 50 measurements with an average of 27, the total sum is 50 * 27 = 1350.
To find the average of all 150 measurements, we need to find the total sum of all 150 measurements. Adding the two total sums calculated above, we have 2300 + 1350 = 3650.
To find the average, we divide the total sum by the total number of measurements: 3650 / 150 = 24.33.
Comparing the average of the 150 measurements to the individual averages A and B:
Quantity A: 24.33
Quantity B: 25
Since 25 is greater than 24.33, the answer is that Quantity B is greater.
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0.7/0.21 PLEASE HRURY 1 MIn
Answer: If you are asking what 0.7/0.21 is, that is 3.3 repeating.
Answer:
3.33333333
or 3.33
Parallelogram FIRE
Given:
\(fi = (3x - 5) \: cm\)
\(ir = (2y - 7) \: cm\)
\(re = (x + 7) \: cm\)
\(ef = (y + 3) \: cm\)
a. What is the value of x?
b. How long is FI?
c. What is the value of y?
d. How long is EF?
e. From your answers in b and d, what is the perimeter of parallelogram FIRE?
Answer:
See the solutions below
Step-by-step explanation:
First note that the opposite side of a parallelogram are equal, hence;
For Parallelogram FIRE
fi = re
ef = ir
Given
fi = (3x-5)cm
ir = (2y -7)cm
re = (x+7)cm
ef = (y+3)cm\
a) If fi = re, then;
3x - 5 = x+7
3x - x = 7+5
2x = 12
x = 12/2
x = 6
b) Since FI = 3x - 5
FI = 3(6) - 5
FI = 18 - 5
FI = 13cm
c) Also ef = ir
y+3 = 2y - 7
y - 2y = -7-3
-y = -10
y = 10
d) EF = y+3
EF = 10 +3
EF =13cm
e) Perimeter of the parallelogram = FI + IR + RE + EF
Perimeter of the parallelogram = 13cm + 13 + 13cm + 13cm
Perimeter of the parallelogram = 52cm
What is the missing measurement of this right triangle?
5 m (Opposite Side)
9 m (Hypotenuse)
x (Adjacent Side)
The missing measurement of this right triangle is x=2√14
5a + 2b = 40 solve for b
Answer:
5a-40=-2b
5a-40/-2=-2b/-2
-5a/2+20=b
Construction projects often use the Pythagorean Theorem. If you are building a sloped roof and you
know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find
the diagonal length of the roof's slope.
You can use this information to calculate the area of the roof that you would need to shingle.
BREATHE
DEFEND
SEAL
The roof has a vertical height of 8 feet. The house has a width of 20 feet.
What is the diagonal length of the roof top? Round your answer to the nearest whole number.
feet
8 feet
Diagonal Length
20 feet
30 feet
The horizontal length of the roof is 30 feet.
What is the total area of the roof that will need shingles?
square feet
The total area of the roof that will need shingles is 660 square feet.
Construction projects often use the Pythagorean Theorem.
If you are building a sloped roof and you know the height of the roof and the length for it to cover, you can use the Pythagorean Theorem to find the diagonal length of the roof's slope.
In order to find the diagonal length of the roof's slope, we must use the
Pythagorean Theorem which is: a² + b² = c²,
where a and b are the sides of a right triangle, and c is the hypotenuse.
Given that the roof has a vertical height of 8 feet and the house has a width of 20 feet, we need to calculate the diagonal length of the roof top.
We can use the Pythagorean Theorem to find the length of the roof's diagonal, which is represented by the hypotenuse of the right triangle.
Therefore,
a = 8 feet and b = 20 feet
c² = a² + b²
c² = 8² + 20²
c² = 64 + 400
c² = 464
c ≈ 21.54
The diagonal length of the roof top is ≈ 22 feet.
The horizontal length of the roof is 30 feet.
The total area of the roof that will need shingles can be calculated by multiplying the horizontal length of the roof by the diagonal length of the roof.
Therefore,
Total area of the roof that will need shingles = Horizontal length × Diagonal length
Total area of the roof that will need shingles = 30 feet × 22 feet
Total area of the roof that will need shingles = 660 square feet
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What is the image of the point (-7,5) after a rotation of 180° counterclockwise about
the origin
Answer:
(7,-5)
Step-by-step explanation:
If a point is rotated 180 degrees (the direction doesn't matter) you change the sign. So if the preimage is positive then the image will be negative and vice-versa.
Answer:
(7,-5)
Step-by-step explanation:
Find an equation of the line containing the point (2,-5) and parallel to y = – 4x – 2.
Write your answer in slope-intercept form.
Answer:
the desired equation is y = – 4x + 3
Step-by-step explanation:
Parallel lines have the same slope and thus similar equations. Thus, the equation of a line parallel to the given line has the form y = – 4x + C. We need only find C.
The new line goes through (2, -5), and so we substitute 2 for x and -5 for y to obtain
-5 = – 4(2) + C. Then -5 + 8 = C, or C = 3.
Then the desired equation is y = – 4x + 3
construct the indicated confidence interval for the population mean μ using the t-distribution. assume the population is normally distributed. c=0.99, x=12.6, s=2.0, n=8
the confidence interval for the population mean μ is approximately (10.125, 15.075) at a confidence level of 0.99.
To construct the confidence interval, we use the formula:
Confidence Interval = x ± t × (s / √n)
Where x is the sample mean, t is the critical value from the t-distribution corresponding to the desired confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.
Given c = 0.99, the confidence level is 0.99, which corresponds to an alpha level of 0.01. Since the sample size is small (n = 8) and the population standard deviation is unknown, we use the t-distribution.
To find the critical value, we look up the t-value for a two-tailed test with a 0.01 significance level and 7 degrees of freedom (n-1). From the t-table or a statistical calculator, the critical value is approximately 3.499.
Plugging the values into the formula, we have:
Confidence Interval = 12.6 ± 3.499 × (2.0 / √8)
Simplifying, we get:
Confidence Interval ≈ 12.6 ± 2.47
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Their centers are A and F.
What is the same about the two circles? What is different?
What is the length of segment AD? How do you know?
On the first circle, what segment is a diameter? How long is it?
Answer:
ihave the same one help me with it pls
Step-by-step explanation:
A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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a plane flies north at an airspeed of 210 km/h. a wind is blowing at 80 km/h toward the east. what is the speed of the plane relative to the ground? enter your answer in km/h.
The speed of the plane relative to the ground can be determined by considering the vector addition of the airspeed and the wind speed.
The plane's airspeed is 210 km/h in the north direction, while the wind is blowing at 80 km/h toward the east. To find the speed of the plane relative to the ground, we can use the Pythagorean theorem to calculate the magnitude of the resulting vector. The magnitude is given by √(airspeed^2 + wind speed^2). Plugging in the values, we have √(210^2 + 80^2) = √(44100 + 6400) = √50500 ≈ 224.86 km/h.
Therefore, the speed of the plane relative to the ground is approximately 224.86 km/h.
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