When it comes to the variable terms, a^2 and b^2, we cannot directly determine their common factors based on the given information. The GCD of 3a^2 and 3b^2 will depend on the prime factors of a^2 and b^2, which are not provided in the question.
The greatest common divisor (GCD) of two numbers represents the largest positive integer that divides both of them without leaving a remainder. In this case, we are given that the GCD of a and b is 100.
To determine the GCD of 3a^2 and 3b^2, we need to analyze the factors present in each expression. Let's break down both expressions:
3a^2 can be written as 3 * a * a, where a is a variable and can have its own prime factors.
3b^2 can be written as 3 * b * b, where b is a variable and can have its own prime factors.
Since the GCD of a and b is 100, it means that both a and b have a common factor of 100. Now let's examine the expressions 3a^2 and 3b^2.
3a^2 = 3 * a * a
3b^2 = 3 * b * b
From these expressions, we can see that both 3a^2 and 3b^2 have a common factor of 3. This is because both expressions contain the factor 3.
However, when it comes to the variable terms, a^2 and b^2, we cannot directly determine their common factors based on the given information. The GCD of 3a^2 and 3b^2 will depend on the prime factors of a^2 and b^2, which are not provided in the question.
Therefore, without additional information about the prime factors of a^2 and b^2, we cannot determine the GCD of 3a^2 and 3b^2. The only common factor we can determine with the given information is 3, as both expressions have a factor of 3.
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Write in expanded form. Use to indicate multiplication. 5 2
The value of the exponent 5^2 is equivalent to 25
Indices expressionsAccording to the equation, we are to write the expression 5^2 as a product
Since the exponent is 2, hence the value the base will be repeated twice.
Given
5^2 = 5^1 * 5^1
5^2 = 5 * 5
5^2. = 25
Hence the value of the exponent 5^2 is equivalent to 25
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Proportions - 5/10
earn 5 coins
A recipe needs 2 tablespoons of vegetable oil for every cup of flour. If you plan to use 3 cup
Flour, how much vegetable oil will you need?
Answer:
2 t / 1 c
2/1=x/3
6=x
6 tablespoons
Answer:
8 Tablespoons trust me.
Step-by-step explanation:
find the sampling distribution of the sample mean for a random sample of measurements from this distribution. put the answers in ascending order for .
To put the answers in ascending order, you will need to obtain the sample means from multiple random samples. Then, calculate the mean of each sample and arrange them in ascending order.
To find the sampling distribution of the sample mean for a random sample of measurements from a given distribution, you need to consider the properties of the population distribution. Specifically, if the population distribution is approximately normal, then the sampling distribution of the sample mean will also be approximately normal.
The mean of the sampling distribution of the sample mean will be equal to the mean of the population distribution. Additionally, the standard deviation of the sampling distribution, also known as the standard error, will be equal to the standard deviation of the population divided by the square root of the sample size.
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The histogram shows the ages of the players in an adult volleyball league. Which of the
following statements is true?
Volleyball Players' Ages
More than half of the players are under age
40.
25
There must be 5 players between 50 and 55.
Number of Players
The older the age group, the greater the
number of players
There are 30 players between ages 20 and 25.
20's 30's 40's 50's 60's 70's
Age Group
The histogram provided shows the ages of the players in an adult volleyball league. From the histogram, it is clear to see that the number of players in the league decreases with each increasing age group.
This can be seen with the highest number of players being in the 20-25 age group, followed by the 30-35 age group, and so on. Therefore, the statement that the older the age group, the greater the number of players, is false. Additionally, the histogram shows that there are only 5 players between the ages of 50 and 55, so the statement that there must be 5 players between those ages is true. Finally, the histogram shows that there are 30 players between the ages of 20 and 25, making the statement that there are 30 players between those ages also true.
The histogram provided shows the ages of the players in an adult volleyball league. It is evident that the number of players in the league decreases with each increasing age group. Therefore, the statement that the older the age group, the greater the number of players, is false. Additionally, the histogram shows that there are only 5 players between .the ages of 50 and 55, and 30 players between the ages of 20 and 25, making those statements true.
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a random sample of size n is selected from a population with standard deviation of 10. what is the standard error of the mean if
The standard error is 0.447.
Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ. The Standard deviation of the sample distribution is known as standard error.
The Standard error is the measure in which it measures the accuracy of sample distribution by using standard deviation. The Standard error is denoted as SE.
According to the given problem, n = 100 and σ = 10
Standard error(SE) = σ /√\(\sqrt{n}\)
= 10 / \(\sqrt{500}\)
= 10 / 22.36
SE = 0.447
Therefore, the standard error of the sample mean is 0.447 if n = 500.
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The complete question is
A random sample of size n is selected from a population with a standard deviation of 10. what is the standard error of the sample mean if n = 500?
a. 0.235
b. 0.447
c. 0.548
d. 0.612
the mass of a plastic triangle is 3g and rhe mass of a plastic square is 7 g Samson has a collection of plastic triangles and squares if there are 14 triangles and squares altogether and their combined mass is 58 g calculate how many triangles and how many squares Samson has.
Answer:
4 squares
10 triangles
Step-by-step explanation:
t=3g
s=7g
t+s=14 t=14-s
3t+7s=58
substitute
3(14-s)+7s=58
42-3s+7s=58
reduce
4s+42=58
4s=16
s=4
t=14-4=10
if a super set Y involves a proper subset x......is that, the proper subset x, integral, to Y as a superset? or can Y as superset Y be without a proper subset in the set superset Y?
Whenever a set X is a subset of set Y, we say the Y is a superset of X and we write, Y ⊇ AX.
Symbol ⊇ is used to denote ‘is a super set of’
What is this ?? Pls help
WILL MARK BRAINLIEST!
If cos u = 4/5 and tan v = - 12/5 while (3pi)/2 < u < 2pi and pi/2 < v < pi find:
cos2u
Answer:
Cos 2u = 7/25
Step-by-step explanation:
Here, we want to find the value of cos2u
Using formula, we can rewrite cos 2
Mathematically;
cos 2u = 2cos^2 U - 1
Thus, we have that
cos 2u = 2(4/5)^2 - 1
cos 2u = 2(16/25) - 1
cos 2u = 32/25 - 1
cos 2u = (32-25)/25 = 7/25
Help please Quick Fix Inc. repairs bikes. The company's revenue is modeled by the function R(h)-220h-160 for every h hours spent
repairing bikes. The company's overhead cost is modeled by the function C(h)-20h²-400
After how many hours does the company break even?
Enter your answer in the box
The number of hours that it takes for the company to break even is given as follows:
0 hours.
How to obtain the break even point?The profit function is obtained subtracting the revenue function by the cost function, hence:
P(h) = R(h) - C(h).
P(h) = 220h - 160 - 20h² + 400.
P(h) = -20h² + 220h + 240.
The break even point is the value of h for which P(h) = 0, hence:
-20h² + 220h + 240 = 0.
The coefficients of the quadratic function is given as follows:
a = -20, b = 220, c = 240.
Using a quadratic equation calculator, the smallest root is given as follows:
h = -1.
As the number of hours cannot be negative, we consider that the company breaks even initially, hence the number of hours is of zero.
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Determine whether the given value is a statistic or a parameter. After taking the firstexam, 15 of the students dropped the class:1-Parameter?2-Statistic?
Given: After taking the first exam, 15 of the students dropped the class.
Required: To determine whether the given value is a statistic or a parameter.
Explanation: Parameter and statistic are very similar. The parameter is when the complete data of the population is presented. The statistic is when a particular data is used for fraction of the population.
Since it is given that among all the students in the class 15 students dropped out. Hence the given data is Parameter.
Final Answer: Parameter.
What is the y-intercept of function gif g(x) = 2/(x) + 1;
The y-intercept of the function g(x) = 2/x + 1 is (0, 3).
The y-intercept is the point where the graph of the function intersects the y-axis. To find the y-intercept, we set x=0 and evaluate the function at that value.
So, when x=0, g(x) becomes 2/0 + 1, which is undefined since division by zero is not allowed. However, we can take the limit of the function as x approaches zero from the positive side (i.e., x → 0+) or the negative side (i.e., x → 0-) to determine the y-intercept.
Taking the limit as x approaches 0+ (i.e., x → 0 from the positive side), we get:
lim(x → 0+) g(x) = lim(x → 0+) 2/x + 1 = ∞
This means that the function approaches positive infinity as x approaches zero from the positive side. Similarly, taking the limit as x approaches 0- (i.e., x → 0 from the negative side), we get:
lim(x → 0-) g(x) = lim(x → 0-) 2/x + 1 = -∞
This means that the function approaches negative infinity as x approaches zero from the negative side.
Since the function approaches positive and negative infinity as x approaches zero from opposite sides, the graph of the function has a vertical asymptote at x=0, meaning it approaches the y-axis but never touches it. Therefore, the function does not have a y-intercept in the traditional sense.
However, we can define a "removable" y-intercept as the point where the function would intersect the y-axis if the vertical asymptote were removed. In this case, if we "remove" the vertical asymptote by restricting the domain of the function to all real numbers except 0, we get a new function:
g'(x) = { 2/x + 1, x ≠ 0 }
This new function is continuous everywhere except at x=0, and its graph intersects the y-axis at the point (0, 3). Therefore, we can say that the "removable" y-intercept of the original function g(x) is (0, 3).
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A supermarket gives a special
offer to cus-
tomers who purchase at least a pack of
vests and a pack of T-shirts. The offer is
restricted to a total of 7 of these items.
a) Write down three inequalities which
must be satisfied.
(b) Draw the graphs of the above condi-
tions and shade the region that satis-
fies them.
(c) If the supermarket makes a gain of N5
on each vest and N8 on each T-shirt,
find the maximum gain made by the
supermarket.
A) the three inequalities that must be satisfied are:
The number of vests, represented by x, must be a non-negative integer: x ≥ 0.The number of T-shirts, represented by y, must also be a non-negative integer: y ≥ 0.The total number of vests and T-shirts must not exceed 7: x + y ≤ 7.B) Graph shaded and satisfying all conditions is attached.
What is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.
It is most commonly used to compare the sizes of two numbers on a number line.
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Mark, Paul and Brian share some sweets in the ratio 1:3:5. Mark gets 14 sweets. How many
did Brian get?
Answer:
7
Step-by-step explanation:
hope it helps
Prove, using the definition of the derivative, that if f(x) = cos (x), then f'(x) = -sinx.
The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.
\(f(x) = cos(x) then f'(x) = -sin(x)\).
Let's proceed with the proof. Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:
\(f(x) = cos(x) f(x + h) = cos(x + h)\)
Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)
We can then simplify the expression by using the trigonometric identity for the difference of two angles:
\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)
Applying this identity to the numerator of the difference quotient, we obtain:
\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)
We can then factor out a cos(x) term from the numerator:
\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)
We can then apply the limit laws to separate the limit into two limits:
\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)
The first limit can be evaluated using L'Hopital's rule:
\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)
Therefore, the first limit becomes zero:
\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)
Applying L'Hopital's rule to the second limit, we obtain:
\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)
Therefore, the second limit becomes 1:
\(f'(x) = -sin(x)\)
Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).
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- 1/2 + ( 3/4 x 4/9)
Answer:- 1/6
Step-by-step explanation:
I already found the answer but it wasn't on brainly, so i want to help by putting it here The athlete’s salary, in thousands, for year n can be represented by: an = 400(1.05)n-1. Find the first four terms, in thousands, of the geometric series. Round to the nearest thousand. a1 = ⇒ 400 a2 = ⇒ 420 a3 = ⇒ 441 a4 = ⇒ 463
Answer:
the next one is s4=(4En=1)400(1.05)n-1
Step-by-step explanation:
The distance of a golf ball from the hole can be represented by the right side of a parabola with vertex (-1,8). The ball reaches the hole 1 second
after it is hit, at time 0.
What is the equation of the parabola, in vertex form, that represents the ball's distance from the hole, y, at time x?
y =
(x +
Answer:
Let's suppose that the hole is at y = 0m, where x is the time variable.
we know that:
The vertex is (-1s, 8m).
(i suppose x in seconds and y in meters)
At x = 1s, the ball reaches the hole, so we also have the point:
(1s, 0m).
Remember that the vertex of a quadratic equation y = a*x^2 + b*x + c is at:
x = -b/2a,
then we have:
-1 = -b/2a.
Then we have tree equations:
8m = a*(-1s)^2 + b*-1s + c
0m = a*(1s)^2 + b*1s + c
-1s = -b/2a.
First we should isolate one variable in the third equation, and then replace it in one of the other two:
1s*2a = b.
So we can replace b in the first two equations bi 1s*2a.
8m = a*1s^2 - 1s*2a*1s + c
0m = a*1s^2 + 1s*2a*1s + c
We can simplify both equations and get:
8m = a*( 1s^2 - 2s^2) + c = -a*1s^2 + c.
0m = a*(1s^2 + 2s^2) + c = a*3s^2 + c.
Easily we can isolate c in the second equation and then replace it into the first equation:
c = -a*3s^2
The first equation becomes:
8m = -a*1s^2 - a*3s^2 = -a*4s^2
a = 8m/-4s^2 = -2m/s^2.
Now with a, we can find the values of c and b.
c = -a*3s^2 = -(-2m/s^2)*3s^2 = 6m.
b = 1s*2a = 1s*(-2m/s^2) = -2m/s.
Then the equation is:
y = (-2m/s^2)*t^2 + (-2m/s)*t + 6m
What is 2+2+5+4753%-474\3674
Answer:
54.4009853
Step-by-step explanation:
Simplify each term.
2 + 5 +47.53 − 237 /1837
Find the common denominator.
2 ⋅ 1837 /1837 + 5 ⋅ 1837 /1837 + 47.53 ⋅ 1837/1837 − 237 /1837
Combine fractions.
3674 + 9185 + 87312.61 − 237 /1837
Simplify the numerator.
99934.61 /1837
Divide 99934.61 by 1837 .
=54.4009853
Nesly has 6 pink masks, 2 blue masks, and 4 purple masks in a box. She will randomly choose 1 mask from the box. What is the probability Nesly will choose a purple mask
Answer:
4/12 = 1/3
Step-by-step explanation:
hope this helps
Use the polygon below to find the value of x.
Alissa would like to make a deposit into her savings account. she filled out a deposit ticket and handed it to the teller at her bank. the teller apologizes to alissa and explains that she cannot accept the deposit ticket in its current form. determine what, if anything, alissa will have to change in order for her deposit ticket to be accepted. a deposit ticket. the amount deposited is 899 dollars and 86 cents and she is taking 260 dollars out as cash. the total on the slip is 629 dollars and 86 cents. a. the sub total is calculated incorrectly b. alissa forgot to sign the deposit ticket for less cash back c. the total is calculated incorrectly d. alissa forgot to date the deposit ticket please select the best answer from the choices provided a b c d
Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
What is a deposit ticket?A deposit ticket is a little paper where you are required to fill in the details of the deposit that you seek to make into your savings account. All information in the ticket ought to be filled accurately.
The teller may have declined to receive the ticket due to incorrect total amount filled on the ticket. Alisa should either fill out a new ticket or write the correct amount and append her signature beside it.
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Answer:
a. the subtotal is calculated incorrectly
Step-by-step explanation:
I'm good at math ;)
what does the rational form of the ratio a:b look like
Answer:
a/b
Step-by-step explanation:
The rational form of a:b or simply a/b is in the simplest form.
Answer:
Step-by-step explanation:
the answer is option 2 from the above sheet
Find the solution of the system of equations.
Answer:
the answer for your problem should be (1,2)
2/5 divided by 1 7/8 in the as a fraction in it simplest form
7/20
hope this helps dude
The fraction to represent the 2/5 divided by \(1\frac{7}{8}\) is 16/75.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, 2/5 divided by \(1\frac{7}{8}\) =15/8.
Here, 2/5 ÷ 15/8
When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction reversing its numerator and denominator is the first step in dividing fractions. Multiply the two numerators after that. Multiply the two denominators after that.
2/5 × 8/15
= 16/75
Therefore, the fraction is 16/75.
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If Z is a standard normal random variable, then P(-1.75 ZS -1.25) is: O a. 0.106 O b. 0.040 OC. 0.854 O d. 0.066
The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.
Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.
Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25
Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211
Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709
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Please help!!!!!!!!! today right now pleaseeeeeeeee Which is multiple 3,2 and 5
Answer:
30
Step by step explanation:
You can multiply 3 with 10 to get 30
You can mulitply 2 with 15 to get 30
And lastly you can multiply 5 with 6 to get 30
El precio de un pantalon es de $1,245= si se le aplica un descuento de el cliente paga $1,171.50 por elQue porcentaje de descuento tiene el pantalon?
Answer:
5.9%
Step-by-step explanation:
1245 - 1171.50 = 73.5
73.5/1245 × 100% = 5.9%
NEED HELP! PLS NO LINKS OR FILES! Need it ASAP thank u.
Answer:
157.079633 cm^3
Step-by-step explanation:
Answer:
157.079633 cm^3
Step-by-step explanation:
katie would like to start a small business. as she writes out her business plan, she is interested in the average number of years until a business turns a profit. based on previous research, it takes 5 years, on average for a small business to turn a profit. katie believes this average is different.
Based on previous research, it takes an average of 5 years for a small business to turn a profit. However, Katie believes this average is different. To determine if Katie's belief is accurate, she can conduct her own research and gather data on small businesses in her industry. Here's how she can do it:
1. Identify the industry: Katie should determine the industry she plans to enter with her small business, as different industries have varying profit timelines.
2. Research similar businesses: Katie can research other small businesses in her industry to find out how long it took them to turn a profit. She can gather data from reliable sources such as industry reports, case studies, or interviews with business owners.
3. Analyze the data: Katie should analyze the data she collected and calculate the average number of years it took for these businesses to become profitable. This will give her a clearer understanding of the industry average.
4. Compare to previous research: Katie should compare her findings to the previous research that suggested a 5-year timeline. If her data differs significantly, she can conclude that the average number of years until a business turns a profit in her industry may be different.
In conclusion, Katie can determine the average number of years until a business turns a profit in her industry by conducting her own research and comparing it to previous studies. This will help her assess whether the previous average of 5 years applies to her specific business venture.
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