The sum of any number and zero is the original number: Identity property
When two numbers are added, the sum is the same regardless of the order of addends: Commutative property
When three or more numbers are added, the sum is the same regardless of how the addends are grouped: Associative property
What is the Commutative Property of Addition?A + B = B + A if A and B are any two whole numbers.
In other words, the sum of two whole numbers is true regardless of how the addends—or real numbers—are arranged.
Any order will work for adding the numbers. Even if the numbers are rearranged, the sum of the two numbers remains the same.
What is the Additive Identity of Addition?When an is a whole number, A + 0 equals 0 + A.
In other words, the number itself is equal to the sum of any whole number and zero. In other words, zero is the only whole number that when added to, does not alter the value (identity) of the original number.
The additive identity or identity element for the addition of whole numbers is the integer 0 (zero).
When zero is added to a number, the result is unchanged.
What is the Associative Property of Addition?If any three whole numbers are A, B, and C, then (A + B) + C = A + (B + C)
In other words, whole number addition is associative.
Any group or placement of the numbers has no effect on the sum when three or more are added.
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the expected value of an unbiased estimator is equal to the parameter whose value is being estimated. true/false
The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.
An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.
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what are the steps to solve 3x+1=4x-8
Answer:
x = 9
Step-by-step explanation:
3x+1=4x-8
-1 -1
3x=4x-9
-4x -4x
-x=-9
x=9
Which equation best represents the line graphed above?
A) y=2
B) y= x + 2
C) y=2x
D) x= 2
Answer:
x = 2
Step-by-step explanation:
The line goes straight through the x axis
Answer: x=2
Step-by-step explanation:
The line goes up and down, which is, Horizontal and Vertical Lines
Vertical lines go up and down and have a slope that is undefined. Graphs of horizontal lines are parallel to the x-axis. Graphs of vertical lines are parallel to the y-axis.
Describe and correct the error a student made in finding the midpoint cd with c(-4,5) and d(-1,-4).
Answer:
Step-by-step explanation:
The formula for finding the midpoint of two coordinates is expressed as;
M(X,Y) = \((\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\)
Given the coordinates c(-4,5) and d(-1,-4), x1 = -4, y1 = 5, x2 = -1 and y2 = -4.
For the X coordinate of the midpoint
X = x1+x2/2
X = -4+(-1)/2
X = -4-1/2
X = -5/2
X = -2.5
Similarly for Y:
Y = y1+y2/2
Y = 5+(-4)/2
Y = 5-4/2
Y = 1/2
Y = 0.5
Hence the midpoint coordinate of C(-4,5) and D (-1,-4) is (-2.5, 0.5)
The length of a rectangle is 3 inches less than 7 times its width. If the perimeter is 58 inches, find the width of the rectangle.
→ Let the width of the rectangle = x inches
∵ The length of the rectangle is 3 less than 7 times the width
∴ The length of the rectangle = 7(x) - 3
→ The perimeter of the rectangle P = 2(length + width)
\(\begin{gathered} \because P=2(7x-3+x) \\ \therefore P=2(8x-3) \\ \therefore P=2(8x)-2(3) \\ \therefore P=16x-6 \end{gathered}\)∵ The perimeter is 58 inches
\(\therefore16x-6=58\)→ Add 6 to both sides
\(\begin{gathered} \because16x-6+6=58+6 \\ \therefore16x=64 \end{gathered}\)→ Divide both sides by 16 to find x
\(undefined\)4(8x−1) = 19+32x
I need help with a question I am kinda stuck on please someone help and please give me some steps for it at least some.
Answer: 0 = 23
Almost positiveee :))
Step-by-step explanation:
What to do when stuck in the friend zone by your crush and your friend already asked him out for you?
Tara has softball practice Tuesday,Wednesday Thursday and Sunday Each practice Is 1 /1 3 hours. Tara says she will have practice for 3 hours this week.
Answer and Step-by-step explanation:
For the first part
Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour
So we can conclude that she practices minimum hours in a week
For the second part
Also in 4 days, she does practice \(1 \frac{1}{3}\) hours per day i.e \(5 \frac{1}{3}\)
Now convert \(1 \frac{1}{3}\) this into a fraction which comes \(\frac{4}{3}\)
For four days, it is
= \(4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}\)
Step-by-step explanation:
Without multiplying, explain how you know Tara is incorrect.
How long will Tara have softball practice this week? Write your answer as a mixed number.
Each practice is \(1\frac{1}{3}\) hours
Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.
So Tara is incorrect
Practice for 4 days
\(1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}\)
More than 5 hours .
Tara will have \(5\frac{1}{3}\) softball practice this week
Answer:
Tara will have \(5\frac{1}{3}\) hours softball practice this week
a trail is 5 miles long. carlos walks 2/3 of the trail and runs the rest. how many miles does carlos walk?
Answer:
as 1 mile = 1.609 km
so 5miles = 8.045 km
so 2/3 of the trail = 2/3 × 8.045 = 5.3633333 (ans)
Hope it helps
A trail is 5 miles long. Carlos walks 2/3 of the trail and runs the rest. Carlos walks 5.36 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A trail is 5 miles long. Carlos walks 2/3 of the trail and runs the rest.
we know that 1 mile = 1.609 km
then, 5 miles = 5 × 1.609
= 8.045 km
so, 2/3 of the trail = 2/3 × 8.045
= 5.3633
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lan earns 2/3
as much as Jill. His yearly income is $38,000. How much does Jill earn?
Pls answer asap! Worth 15 points!!
Answer:
Jill earns $57,000
Step-by-step explanation:
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Développer et réduire l'expression suivante
A=x(2x-3)+5x-2x²
Answer:
\(a = x(2x - 3) + 5 x - 2x ^{2} = \\ a = x - 1x + 5x + 4x ^{2} = \\ a = 1x - 1x + 5x + 4x ^{2} = \\ a = 5x + 4x ^{2} \)
Je pense que c'est la réponse
Help me please with my math questions
Answer:
ok
Step-by-step explanation:
Answer:
what math questions
..................
Step-by-step explanation:
.
Simplify : i) (〖6x〗^2+x-7)/(12x^2+14x)
An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of the given expression can be done as,
\(\dfrac{(6x)^2+x-7}{12x^2+14x}\\\\\\=\dfrac{36x^2+x-7}{12x^2+14x}\\\\\\=\dfrac{(6x)^2+x-7}{2(6x^2+7x)}\)
Hence, the simplification of the expression [(6x)²+x-7)/(12x²+14x) is (36x²+x-7)/[2(6x²+7x)].
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is m parallel to n. if so what theorem can you use.
You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.
can someone help me with this?!
Answer:
y=x+2.4
Step-by-step explanation:
If you take a number, times by 5 then add 7. You get the same as if you took the number, times by 9 then add 3. What is the number?
Answer: The number is 1
Step-by-step explanation:
5x + 7 = 9x + 3
5x + 7 - 5x = 9x - 5x + 3
7 = 4x + 3
7 - 3 = 4x + 3 - 3
4 = 4x
x = 1
Check work:
5(1) + 7 = 12
9(1) + 3 = 12
It works
customers send emails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the inter-arrival time is also 2 minutes. the online retailer has three employees answering emails. it takes 4 minutes to write a response email, on average. the standard deviation of the service times is 2 minutes. this is a g/g/k queue. what is the arrival rate? what is the service rate?
The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.
It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.
It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.
Therefore the arrival rate per hour is given by the following relation:
Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes
Given here,
No. of minutes in an hour = 60 minutes
Inter arrival time of the email taken in minutes = 2 minutes
∴ Arrival rate in 1 hr = 60 / 2
= 30 emails / hr
Hence the arrival rate is 30 emails per hour.
Now for finding out the service rate we have the following formula:
Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email
Given here,
No. of minutes in an hr = 60 minutes
No. of employes answering = 3
Average time that for writing response email = 2 minutes
∴ Service rate = 60 * 3 / 4
= 45 emails / hr
Hence the service rate is 45 emails per hour.
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Someone help please quickly
3(x-2)/4 + 3(x-3)/8 = 1/2
● 1/9
● 9
● 1/3
The / are the fraction lines not divide
9514 1404 393
Answer:
x = 25/9
Step-by-step explanation:
3(x-2)/4 + 3(x-3)/8 = 1/2 . . . . given
6(x -2) +3(x -3) = 4 . . . . . . . . multiply by 8
6x -12 +3x -9 = 4 . . . . . . . . . eliminate parentheses
9x -21 = 4 . . . . . . . . . . . . . . . collect terms
9x = 25 . . . . . . . . . . . . . . . . add 21
x = 25/9 . . . . . . . . . . . . . . divide by 9
Answer:
I got =
\(2 \ \frac{7}{9} \)
Step-by-step explanation:
\( \frac{3(x - 2)}{4} + \frac{3(x - 3)}{8} = \frac{1}{2} \)
\(6x - 12 + 3x - 9 = 4 \\ 9x - 21 = 4 \\ 9x = 25 \\ x = \frac{25}{9} = 2 \ \frac{7}{9} \)
In a neighborhood of 72 families. 18 families on one or more cats. Write the number of families who own one or more cat as a fraction. Then write the fraction as a decimal.
Answer:
0.25
Step-by-step explanation:
The fraction is 18/72. The decimal is different. If you divide 72 by 18, you get 4. That tells you how it is in a quarter, aka four pieces. Divide 100 by 4, you get 25. That’s why the answer is 0.25
Find the volume of the cone
to the nearest tenth with a
diameter of 2 ft and a height
of 8 ft
Answer:
I won't;))
Step-by-step explanation:
I will not Find the volume of the cone
to the nearest tenth with a
diameter of 2 ft and a height
of 8 ft:)
Answer:
33.493
Step-by-step explanation:
to find the volume of a cone the equation that you are going to use is:
\(V=\pi r^2 \frac{h}{3}\)
Step 1: Plugin
\(V=\pi 2^2 \frac{8}{3}\)
r/Diameter=2
h=8
step 2: solve
\(\pi =3.14\)
\(2^2=4\)
\(3.14 x 4x \frac{8}{3} = 33.49\)
suppose the data on natural birth weights (collected by the world health organization (who)) is normally distributed with the mean equal to 7.25 pound for a full-term birth and standard deviation of 1.0 pounds. what is the probability that a randomly selected baby will weigh more than 9.75 pounds at birth? 0.0062
The probability that a randomly selected baby will weigh more than 9.75 pounds at birth is 0.0062, or about 0.62%. This means that the vast majority of babies will weigh less than 9.75 pounds at birth, as this value is more than two standard deviations above the mean.
We can use the standard normal distribution to solve this problem by first standardizing the value of 9.75 pounds using the formula:
z = (x - mu) / sigma
where x is the value of 9.75 pounds, mu is the mean of 7.25 pounds, and sigma is the standard deviation of 1.0 pound.
Substituting the values, we get:
z = (9.75 - 7.25) / 1.0 = 2.5
We can then use a standard normal distribution table or calculator to find the probability of a z-score greater than 2.5. From the table or calculator, we find that this probability is approximately 0.0062.
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need help pleeassseeee !!
Answer: 5
Step-by-step explanation: f(3) = 2x - 1
substitute the x with 3. 2(3)-1
6-1
5
Answer:
The answer is 5, hope you like!
Write the quadratic function in the form f (x) = a (x - h)2 + k.
Then, give the vertex of its graph.
f (x) = – 2x² + 16x – 30
Writing in the form specified: f(x)=???
Vertex: (?,?)
Answer:
The vertex form is:
\(f(x)=-2(x-4)^2+2\)
Where the vertex of the function is (4, 2).
Step-by-step explanation:
We want to find the vertex and the vertex form of the quadratic function:
\(f(x)=-2x^2+16x-30\)
We have two methods of converting from standard form to vertex form: (1) by using the vertex formulas or (2) by completing the square.
Method 1) Using Formulas:
First, note that the leading coefficient of our function is -2.
The vertex of a quadratic equation is given by the formulas:
\(\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)\)
In this case, a = -2, b = 16, and c = -30. Find the x-coordinate of the vertex:
\(\displaystyle x=-\frac{(16)}{2(-2)}=\frac{-16}{-4}=4\)
In order to find the y-coordinate of the vertex, we substitute this value back in. Hence:
\(f(4)=-2(4)^2+16(4)-30=2\)
Therefore, our vertex is (4, 2).
Vertex form is:
\(\displaystyle f(x)=a(x-h)^2+k\)
Where a is the leading coefficient and (h, k) is the vertex.
Substitute. Our leading coefficient is -2 and our vertex is (4, 2). Therefore:
\(\displaystyle f(x)=-2(x-4)^2+2\)
Method 2) Completing the Square:
To complete the square, we first factor out the leading coefficient from the first two terms:
\(f(x)=-2(x^2-8x)-30\)
Then, we divide the coefficient of the b term by half and square it. This yields:
\(\displaystyle \left(\frac{-8}{2}\right)^2=16\)
We will add this value inside of the parentheses. Since we added 16 inside the parentheses, we will subtract 16 outside of the parenthese to remain the equality of the function. However, since the parentheses is multiplied by -2, we technically added -2(16) = -32 inside. So, we will subtract -32 outside. Thus:
\(f(x)=-2(x^2-8x+16)-30-(-32)\)
Simplify:
\(f(x)=-2(x^2-8x+16)+2\)
Factor using the perfect square trinomial:
\(f(x)=-2(x-4)^2+2\)
We acquire the same result.
I need this answered
The area of a circle is 9π m². What is the circumference, in meters? Express your answer in terms of π.
Assume that the duration of human pregnancies can be described by a normal model with mean 262 days and standard deviation 18 days Complete parts a) through d) below or Page a) What percentage of pregnancies should last between 26 and 275 days? % (Round to one decimal place as needed.) b) Al least how many days should the longest 30% of all pregnancies last? Pxz)-0,30 (Round to one decimal place as needed) c) Suppose a certain obstetrician is currently providing prenatal care to 80 pregnant women. Let y represent the mean length of their pregnancies According to the central limit theorem what is the mean and standard deviation SDL) of the nomal model of the distribution of the sample mean y The meanis 306) (Round to two decimal places as needed) d) What is the probability at the mean duration of the patients' pregnancies wil below than 200 days
a) To find the percentage of pregnancies that should last between 26 and 275 days, we can calculate the area under the normal curve between these two values.
Using the standard normal distribution, we need to standardize the values by subtracting the mean and dividing by the standard deviation.
For 26 days:
Z = (26 - 262) / 18 = -12.222
For 275 days:
Z = (275 - 262) / 18 = 0.722
Now, we can find the corresponding probabilities using a standard normal table or a calculator.
The probability of a pregnancy lasting less than 26 days is P(Z < -12.222) which is essentially 0.
The probability of a pregnancy lasting less than 275 days is P(Z < 0.722) = 0.766.
To find the percentage between 26 and 275 days, we subtract the probability of less than 26 days from the probability of less than 275 days:
Percentage = 0.766 - 0 = 0.766 = 76.6%
Therefore, approximately 76.6% of pregnancies should last between 26 and 275 days.
b) To find the number of days for the longest 30% of all pregnancies, we need to find the corresponding Z-score for the upper 30% of the standard normal distribution.
Z(0.30) = 0.524 (approximately)
Now, we can reverse the standardization process to find the corresponding number of days:
X = Z * σ + μ
X = 0.524 * 18 + 262
X ≈ 271.43
Therefore, the longest 30% of all pregnancies should last at least approximately 271.43 days.
c) According to the Central Limit Theorem, the distribution of the sample mean will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean (μ) of the sample mean (y) = Mean of the population = 262 days
Standard deviation (σ) of the sample mean (y) = Standard deviation of the population / √n
σ(y) = 18 / √80 ≈ 2.015
Therefore, the mean of the distribution of the sample mean is 262 days and the standard deviation is approximately 2.015 days.
d) To find the probability that the mean duration of the patients' pregnancies will be less than 200 days, we can standardize the value using the sample mean and standard deviation:
Z = (200 - 262) / (18 / √80) ≈ -7.150
Using a standard normal table or a calculator, we find that P(Z < -7.150) is essentially 0.
Therefore, the probability of the mean duration of the patients' pregnancies being less than 200 days is very close to 0.
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What is in the third quadrant of the unit circle
The third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees
The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane.
In the coordinate plane, the third quadrant is the quadrant that lies below the x-axis and to the left of the y-axis.
To find what is in the third quadrant of the unit circle, we need to look for the points on the circle that have negative x-coordinates and negative y-coordinates.
Since the radius of the unit circle is 1, we know that any point on the circle can be represented in terms of sine and cosine. Specifically, for any point (x, y) on the circle, we have:
x = cos(θ)
y = sin(θ)
where θ is the angle between the positive x-axis and the line connecting the origin and the point (x, y).
In the third quadrant, both the x-coordinate and the y-coordinate are negative. Therefore, we need to find the angle θ such that cos(θ) is negative and sin(θ) is negative.
We know that cos(θ) is negative in the second and third quadrants, and sin(θ) is negative in the third and fourth quadrants. Therefore, the third quadrant of the unit circle contains the points where:
cos(θ) is negative (i.e., θ is between 90 and 270 degrees or π/2 and 3π/2 radians), and
sin(θ) is negative (i.e., θ is between 180 and 360 degrees or π and 2π radians).
So the third quadrant of the unit circle contains all the points where:
-1 ≤ x ≤ 0 (cosine is negative in this quadrant), and
-1 ≤ y ≤ 0 (sine is also negative in this quadrant).
In other words, the third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees (or π and 3π/2 radians) and has both x and y values that are negative.
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write a summary of the concepts in your own words. Your summary should contain a description of the Commutative, Associative, and Distributive properties.
The summary of the description of the Commutative, Associative, and Distributive properties is given below
What is commutative, associative and distributive properties?The commutative property is one whose law is known to states that with the use of addition and multiplication of numbers, a person can be able to alter the order of the numbers in a given problem and it will not have an affect on the answer.
The associative property is known to be one that that if in the process of adding or multiplying, the grouping symbols is one that a person can rearranged and it will not alter the result. This therefore is stated as (a+b)+c=a+(b+c).
The distributive property is known to be one that is seen as a multiplication method that entails the multiplication of a number by the use of all the separate add ends of another given number.
Hence, The distributive Property implies that when a factor is said to be multiplied by the sum/addition of two terms, it is said to multiply each of the two numbers by its factor, and finally carry out the addition operation.
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Marcus borrowed 9000 from his bank to buy a car. The bank charged him a simple interest rate of 1.25%. By the time he paid back the money he had pad a total of 9281.25. How long did it take Marcus to pay back the money?
Answer:
2.5 years
Step-by-step explanation:
Given data
P=9000
r= 1.25%
A= 9281.25
The simple interest expression is given as
A=P(1+rt)
substitute
9281.25= 9000(1+0.0125*t)
9281.25=9000+112.5t
collect like terms
9281.25-9000=112.5t
281.25= 112.5t
t= 281.25/112.5
t= 2.5
Hence the time is 2.5 years
3 On their first dive, researchers explore a part of the ocean floor that is 60 feetbelow sea level. This depth can be represented by the integer - 60. On theirsecond dive, researchers explore a deeper depth.Part AWrite an inequality that represents the possible depth, d, of the researchers'second dive.Answer:Part 8On the number line below, graph the inequality that represents the possibledepth of the researchers' second dive.A++ + ++++-150-120-90 -50 -30 0306090120150
we have that
The inequality that represents the possible depth, d, of the researcher's second dive is
d < -60All real numbers less than -60
Part B
see the figure below
In a number line, the solution is the shaded area at the left of x=-60 (open circle)
the solution is the interval (-infinite, -60)