The correct answer is A) smaller than.
The statement refers to the concept of the Central Limit Theorem (CLT). According to the CLT, when random samples are drawn from a population, the distribution of sample means will tend to follow a normal distribution, regardless of the shape of the population distribution, given that the sample size is sufficiently large. This means that as the number of samples increases, the variability of the distribution of sample means will decrease.
In this case, drawing 1,000 samples of size 100 from a population and computing the mean of each sample implies that we have a large number of sample means. Due to the CLT, the distribution of these sample means will have less variability (smaller standard deviation) compared to the variability of the raw scores in any one sample. Thus, the variability of the distribution of sample means will tend to be smaller than the variability of the raw scores in any one sample.
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if the displacment (x) of a body at a certain time (t) is given from the relation
x= At +B \(\sqrt{2t\\}\)
so the dimensions of A and B are = ...............
The dimensions of A and B are
\(A= LT^{-1}\)
\(B = LT^{-1/2}\)
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be x
x = At + B√2t
where x is the displacement
t is the time taken
So , the dimension of x will be L
And , the dimension of t will be T
Now ,
The equation is x = At + B√2t
So , the first term At should have dimension of L
And , the second term B√2t should have dimension of L
Therefore , the equation will be
So , The dimension of A will be
\(A= LT^{-1}\)
And the dimension of B will be
\(B = LT^{-1/2}\)
Hence , The dimensions of A and B are
\(A= LT^{-1}\)
\(B = LT^{-1/2}\)
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two equal sides of a triangle are each 8 m less than six times the third side. if its perimeter is 23 m, what are its side-lengths?
The side lengths of the given triangle are 3 m, 10 m, and 10 m.
Let's assume the length of the third side of the triangle is x.
According to the given information, the two equal sides of the triangle are each 8 m less than six times the third side. Therefore, the lengths of the two equal sides can be expressed as:
6x - 8
6x - 8
The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 23 m:
x + (6x - 8) + (6x - 8) = 23
Simplifying the equation:
x + 6x - 8 + 6x - 8 = 23
13x - 16 = 23
13x = 23 + 16
13x = 39
x = 39 / 13
x = 3
Now that we have the value of x, we can find the lengths of the two equal sides:
Equal side 1 = 6x - 8 = 6 * 3 - 8 = 10 m
Equal side 2 = 6x - 8 = 6 * 3 - 8 = 10 m
Therefore, the side lengths of the triangle are 3 m, 10 m, and 10 m.
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consider two events, a and b. the probability of a is 0.5, the probability of b is 0.3, and the probability of a union b is 0.3. what is the probability of a intersect b is 0.2. What is the probability of A union B?
A has a probability of 0.3, B has a probability of 0.5, and A intersects B has a probability of 0.3. The probability of A ∪ B is 0.5.
We have been given that
P (A) = 0.3
P (B) = 0.5
P ( A∩B) = 0.3
Now, we have the formula of
P (A∪B) = P (A) + P (B) - P ( A∩B)
= 0.3 + 0.5 - 0.3
= 0.5
Probability denotes the possibility of commodity passing. It's a fine branch that deals with the circumstance of a arbitrary event. The value ranges from zero to one. Probability has been introduced in mathematics to prognosticate the liability of circumstances being.
Probability is defined as the degree to which commodity is likely to do. This is the abecedarian probability proposition, which is also used in probability distribution, in which you'll learn about the possible results of a arbitrary trial. To determine the liability of a particular event being, we must first determine the total number of indispensable possibilities.
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Correct question:
Consider two events A and B. The probability of A is 0.3, the probability of B is 0.5, and the probability of A intersect B is 0.3. What is the probability of A union B?
expand the expression 4(x-5)
Answer:
4x-20
Step-by-step explanation:
Chi-square distributions that are positively skewed have a research hypothesis that is?
Answer:
A one tailed test
Step-by-step explanation:
Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.
Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.
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One-Tailed Test
In probability theory and statistics, the chi-square distribution with k degrees of freedom is the distribution of the sum of squares of k independent standard normal random variables. The chi-square distribution is a continuous probability distribution. The shape of the chi-square distribution depends on its degrees of freedom k. It is used to describe the distribution of the sum of squares of random variables. The chi-square distribution is positively skewed, with decreasing skewness as the degrees of freedom increase. The chi-squre distribution approaches the normal distribution on increase of degree of freedom.Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.
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would the sample size be large enough if the population is school-aged children and young adults in the united states? explain in 2-3 sentences.
Yes, the sample size would be large enough if the population is school-aged children and young adults in the United States as this is a simple random sampling.
Simple random sampling is used for randomly selecting the sample size for research. No member in the population has a higher chance in comparison to others for selection in sampling. Every individual has an equal chance to be a part of the sample for the study. This is a type of probability sampling method.
The probability sampling method states that every individual has a fair and equal chance to be selected as a research sample. It includes simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Here the researchers have picked around 150 students and young adults which is an appropriate amount of simple random sample for the study.
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You deposit $2500 in a bank account. Find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly. Round to the nearest dollar.
pls help test today!!
After 3 years, the balance in the account would be approximately $2,708.
To find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final balance
P is the principal amount (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case:
P = $2500
r = 2.5% = 0.025 (as a decimal)
n = 12 (monthly compounding)
t = 3 years
Plugging in these values into the formula, we get:
A = $2500(1 + 0.025/12)^(12*3)
A = $2500(1.00208333333)^(36)
Using a calculator, we can evaluate the expression inside the parentheses and calculate the final balance:
A ≈ $2500(1.083282498) ≈ $2708.21
Therefore, after 3 years, the balance in the account would be approximately $2,708.
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1. what is the smallest number that you know? Do you think it is really the smallest number?
2. what does zero stands for?
3. when you subtract 8 from 10, what is the difference?
4. How about if you subtract 10 from 8? Is there an answer?
5. Are fractions considered as integers?
6. Do you know fractions? Give some examples.
Answer:
There are numbers that are smaller than zero also ie. - 1,-2,-3,-4,-5 etc.
When u subtract 8 from 10 the answer is 2
And,when u subtract 10 from 8,the answer is -2,so there is a lot of difference.
Which of the following sets of numbers could represent the three sides of a right triangle? a. {13, 48, 50} b. {49, 55, 73} c. {16, 63, 65} d. {20, 72, 75}
Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Correct answer is option (c).
To determine which set of numbers could represent the three sides of a right triangle, we can use the Pythagorean theorem:
a. {13, 48, 50}:
Using the Pythagorean theorem: 13² + 48² = 169 + 2304 = 2473 ≠ 50²
Therefore, this set of numbers does not represent the sides of a right triangle.
b. {49, 55, 73}:
Using the Pythagorean theorem: 49² + 55² = 2401 + 3025 = 5426 ≠ 73²
Therefore, this set of numbers does not represent the sides of a right triangle.
c. {16, 63, 65}:
Using the Pythagorean theorem: 16² + 63² = 256 + 3969 = 4225 = 65^²
Therefore, this set of numbers represents the sides of a right triangle.
d. {20, 72, 75}:
Using the Pythagorean theorem: 20² + 72² = 400 + 5184 = 5584 ≠ 75²
Therefore, this set of numbers does not represent the sides of a right triangle.
Based on the Pythagorean theorem, the set of numbers {16, 63, 65} represents the sides of a right triangle.
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Find the coordinates of the centroid of the triangle with the given vertices.
F(1, 5), G(-2, 7), H( – 6, 3)
The coordinate of the centroid of the given triangle will be at (-2.33,5).
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The given triangle with vertices has been drawn.
The midpoint of H( – 6, 3) and F(1, 5) will be as,
x = (-6 + 1)/2 = -2.5
y = (3 + 5)/2 = 4 so D(-2.5,4)
The coordinate of the centroid will intersect 2:1 of the median from the vertex side.
Thus by intercept formula,
x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)
x = -2.33 and y = 5
So the coordinate of vertices will be (-2.33,5).
Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".
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Which equation has the solution x=-4? a 2(x-4)=16 b 3x+6-2x=-2 c 1/4x+4=3 d(x+6)3=-6 need help plz
Answer:
C: 1/4x + 4 = 3
Step-by-step explanation:
1/4x + 4 = 3
1/4x = 3 - 4
x = - 4
Thus, option c gives out the solution x = - 4.
Ocala software systems operates a technical support center for its software customers. if customers have installation or use problems with ocala software products, they may telephone the technical support center and obtain free consultation. currently, ocala operates its support center with one consultant. if the consultant is busy when a new customer call arrives, the customer hears a recorded message stating that all consultants are currently busy with other customers. the customer is then asked to hold and is told that a consultant will provide assistance as soon as possible. the customer calls follow a poisson probability distribution, with an arrival rate of seven calls per hour. on average, it takes 8.5 minutes for a consultant to answer a customer's questions. the service time follows an exponential probability distribution. to improve customer service, ocala software systems wants to investigate the effect of using a second consultant at its technical support center. what is the probability that a customer will have to wait for one of the consultants
The probability that a customer has to wait for one of the consultants (Pw) is 0.9516.
To find the probability that a customer will have to wait for one of the consultants, we need to analyze the current system and compare it to the proposed system with two consultants. Here's a step-by-step explanation:
1. Identify the given parameters:
- Arrival rate (λ) = 7 calls per hour
- Service rate (µ) = 1 call per 8.5 minutes = 60 minutes / 8.5 minutes = 7.06 calls per hour (approximately)
2. Calculate the traffic intensity (ρ):
- ρ = λ / µ = 7 / 7.06 = 0.9915 (approximately)
3. Find the probability of 0 customers in the system (P0) for a 2-consultant system:
- P0 = 1 / (1 + (2 * ρ) + (ρ^2 / (1 - ρ))) = 1 / (1 + (2 * 0.9915) + (0.9915^2 / (1 - 0.9915))) ≈ 0.0086
4. Calculate the probability that a customer has to wait for one of the consultants (Pw):
- Pw = (ρ^2 / (2 * (1 - ρ))) * P0 = (0.9915^2 / (2 * (1 - 0.9915))) * 0.0086 ≈ 0.9516
So, there is approximately a 95.16% chance that a customer will have to wait for one of the consultants at Ocala Software Systems' technical support center when two consultants are employed.
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Valerie has a rectangular window with an area of 15.75 ft2 . One side of the window
measures 3.5 feet. What is the measure of the other side in feet?
Answer:
4.5ft
Step-by-step explanation:
to find the area of a rectangle its area = length * width. u know the area 15.75 and one side that u could represent as length or width its up to u and then what ever is left solve be getting the variable by itself.
heyy! i’ll give brainliest please help.
Answer:
Weather values are ranges, while climate values are averages.
Step-by-step explanation:
If one of the movies is chosen at random, what is the probability that the movie was given at least 3 stars?
The probability that the movie chosen at random was given at least 3 stars is \(7/20\) or \(0.35\) (in decimal form).
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, and is used to make predictions and estimate the likelihood of future events.
If we suppose that, there are a total of \(20\) movies. Let X be the random variable that represents the number of movies that were given at least 3 stars.
Let's assume that there are 7 movies that were given at least 3 stars.
Therefore, the probability that the movie chosen at random was given at least 3 stars is \(7/20\) or \(0.35\) (in decimal form).
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The complete question is: What is the probability that a randomly chosen movie has been given at least 3 stars?
the use of numeric data to demonstrate a point are known as? group of answer choices inform persuade statistics entertain
Numeric data can be used to present facts, show relationships between variables, and support an argument.
Numeric data is a powerful tool that can be used to present facts, demonstrate relationships between variables, and support an argument. It is often used to provide evidence for a particular point of view, and it can be used to persuade an audience or inform them about a particular topic. Numeric data can be presented in various forms such as graphs, tables, and charts, and when used effectively, it can be a very effective tool for conveying information. It is important to understand how to interpret numeric data correctly, as it can be used to draw false conclusions if the data is misinterpreted.
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help whats
\( - 4 \ \frac{1}{3} \ \times 1\frac{3}{5} \)
I'll give brainliest <3
\(\displaystyle -4\frac{1}{3}\cdot 1\frac{3}{5}=-\frac{13}{3}\cdot \frac{8}{5} =-\frac{104}{15}=-6 \frac{14}{15}\)
\(\implies- 4 \ \frac{1}{3} \ \times 1\frac{3}{5}\)
\(\implies- \ \frac{13}{3} \ \times \frac{8}{5}\)
\(\implies- \ \frac{104}{15} \)
\(\implies- 6 \ \frac{14}{15} \)
The area A of a circle is the product of π and the radius r squared
i need written in a algebraic equation
Answer:
A=πr^2
Step-by-step explanation:
A=π*r^2
Where, A is area of circle
r is radius of circle
π is constant
.
Hope it's help and I think I have give brainleist answer
Answer:
πr^2
Step-by-step explanation:
it's just πr^2.
easy
I need help with these two please
Answer:
\(21(2-x)+12x=44\)
\(42-21x+12x=44\)
\(42-9x=44\)
\(42-9x-42=44-42\)
\(-9x=2\)
\(-9x=2\\-9 ~~-9\)
\(x=-2/9\)
-----------------------
hope it helps..
have a great day!!
tiffany answered 90% of questions on her math test correctly there were 50 questions on the test how many questions did tiffany answer correctly
I'll give you brainlist if u help :)A certain culture of yeast increases by 50% every three hours. A scientist places 9 grams of the yeast on a culture dish. write the explicit and recursive formulas for the geometric sequences formed by the growth of the yeast.
Answer:
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Answer:
plz mark me as a brainelist
hope it helps you
points $a$, $b$, $c$ and $d$ are midpoints of the sides of the larger square. if the larger square has area 60, what is the area of the smaller square?
Points $a$, $b$, $c$, and $d$ are the midpoints of the sides of the larger square. If the larger square has an area of 60, the smaller square's area is 15 square units.
A square's midpoints connect, making it possible to divide the square into four equal squares. Each of these four squares has a side length of half that of the larger square.
Consider the fact that the area of the larger square is 60, with sides of $s$ units. \($s^2=60$\\\). Now, the smaller square is created by connecting the midpoints of the larger square. Each side of the smaller square has a length of \($s/2$\) units.
Since the area of a square is \($s^2$\), the area of the smaller square is \($\left(\frac{s}{2}\right)^2$\). Simplifying gives \($\left(\frac{s}{2}\right)^2=\frac{s^2}{4}$\). So, the area of the smaller square is \($\frac{1}{4}$\) of the larger square's area.
We know that the area of the larger square is 60. Therefore, the area of the smaller square is \($\frac{1}{4}$\) (60) = 15 square units.
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Help help help help !
Answer:Its D
Step-by-step explanation:
What is a truth table in logic gate?
The Truth Table in logic gate is used to specify the output of the logic gate for all possible combinations of the input signals. , it is the breakdown of all the possible truth values returned by the logical expression.
What is Truth Table ?
The truth table is a tabular representation of all combinations of values for inputs and their respective outputs.
It can be called as a mathematical table which shows all possible outcomes that would occur from all the possible scenarios that are considered as factual.
Truth tables are generally used for the logic problems as in Boolean algebra and electronic circuits.
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Answer:
Step-by-step explanation:
A truth table for a logic gate is the table that specifies the logic value/state of the output of the gate for all possible combinations of the logic states of all inputs.
Let's take the example of the AND gate with two logic inputs A and B and one output Y.
A B Y
0 0 0
0 1 0
1 1 1
1 0 0
This is the truth table for the AND gate.
If Geo had 3/8 of a pizza and his sister had 7/9 of another pizza, how much pizza do they have in all?
Answer:
[see below]
Step-by-step explanation:
Geo has 3/8 of a pizza. His sister has 7/9 of another pizza.
Add the values:
\(\frac{3}{8}+\frac{7}{9}\\\\ \text{The LCM of the denominators is 72.}\\\\\frac{3*9}{8*9}=\frac{27}{72}\\\\\frac{7*8}{8*9}=\frac{56}{72}\\\\\frac{27+56}{72}=\frac{83}{72}\\\\\frac{83}{72}=1\frac{11}{72}\\\\\boxed{\frac{3}{8}+\frac{7}{9} = 1\frac{11}{72}}\)
a landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. if the area of the garden is 8 square feet, find the dimensions of the garden that minimize the cost.
the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.Let the length of the rectangular garden be L and the width be W. Then, the area of the garden is given as L x W = 8.
The cost C of enclosing the garden is given by:
C = 20L + 10(2L + W)
Substituting the value of W from the area equation, we get:
C = 20L + 10(2L + 8/L)
Differentiating C with respect to L and equating it to zero to find the minimum cost:
dC/dL = 20 + 20 - 80/L^2 = 0
Solving for L, we get L = 2 ft
Substituting L = 2 in the area equation, we get:
W = 4 ft
Therefore, the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.
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19. What is the length of side JN? (Round your answer to the nearest tenth.) 65 39 53
We οbtain JN 44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly 44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.
What is the measurement οf a triangle's side?
The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.
The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.
Law of sines
sin(∠A)/a = sin(∠B)/b = sin(∠C)/c
Therefore,
39/sin(53°) = JN/sin(65°)
JN = (39×sin(65°))/sin(53°)
JN = 44.3
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If the length of a rectangle in terms of x is 5x2 + 4x - 4 centimeters and its
width is 3x² + 2x + 6 centimeters, what is the perimeter of the rectangle?
Answer:
Step-by-step explanation:
1222235567899.99978..88694..6.4.4.6.4.4.5
20% of a is 11. what is a
Answer:
20% of 11 is 2.2
Step-by-step explanation:
11 x .20 = 2.2
Please can someone explain place value to me. I failed in my test dunno how tho cause I studied place value in year 3 lol
Answer:
Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that whilst a digit can be the same, its value depends on where it is in the number.
Step-by-step explanation:
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