The phenomenon that the sampling distribution of the sample mean can be approximated by a normal distribution as the sample size become large is called: Central Limit Theorem.
What is Central Limit Theorem?The central limit theorem (CLT) of probability theory states that, under the assumption that all samples are of equal size and regardless of the population's actual distribution shape, the distribution of a sample variable approaches a normal distribution (i.e., a "bell curve") as the sample size increases.
Now,
As stated in the definition of the Central Limit Theorem, sampling distribution of the sample mean can be approximated by a normal distribution as the sample size become large with the help of the stated theorem.
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a pie-shaped (triangular) lake-front lot has a perimeter of 1300 feet. one side is 100 feet longer than the shortest side, while the third side is 300 feet longer than the shortest side. find the lengths of all three sides.
The lengths of the three sides of the triangular lot are: 100 feet, 200 feet and 400 feet.
What is a triangle and its perimeter?
A triangle is a polygon with three edges and three vertices.
Given:
Perimeter of triangular lot = 1300 feetOne side is 100 longer than the shortestOther is 300 feet longer than the shortest.To find: All the sides of the triangular lot.
FInding:
Let the shortest side of the triangular lot be 'x'.
Then, according to the question, one side of the triangular lot = 100 + x and other = 300 + x
As perimeter of a triangle = sum of all the sides,
=> 1300 = x + 100 + x + 300 + x
=> 1300 - 400 = 3x
=> 900 = 3x
=> 300 = x
Hence, the shortest side = 100 feet, a longer side = 200 feet, the longest side = 400 feet for the given triangular lot.
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Margaret drove to a business appointment at 70 mph. Her average speed on the return trip was 60 mph. The return trip took 1/3 hr longer because of heavy traffic. How far did she travel to the appointment?
Answer:
70t = 60t + 10
10t = 10
t = 1 hour
----------
1 hour 70 mi/hr = 70 miles
Step-by-step explanation:
a scientist measured the weights (in grams) of 11 female guinea pigs (cavia porcellus) and got the following: 582 904 311 410 688 541 470 709 525 478 402 calculate the iqr
278 is the value of IQR.
What do we mean by IQR?The interquartile range (IQR) is a way of measuring statistical dispersion, or the spread of data, in descriptive statistics. The IQR is also known as the midspread, the middle 50%, the fourth spread, or the Spread. It is defined as the difference between the data's 75th and 25th percentiles. To calculate the interquartile range (IQR), first, compute the median (middle value) of the data's lower and upper halves. These are quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The IQR is the distinction between quarters three and one.To find the IQR:
Arrange in ascending order as follows:
311, 402, 410, 470, 478, 525, 541, 582, 688, 709, 904The middle value or the median is 525.
IOR = Q₃ - Q₁Q₁ from the lower half is 410 and Q₃ from the upper half is 688.
So, IOR = 688 - 410 = 278Therefore, the value of IQR is 278.
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An opaque bag contains 22 yellow marbles and 11 teal marbles. if two marbles are randomly chosen from the bag at the same time, find the probability that both marbles are teal. round your answer to four decimal places.
If two marbles are randomly chosen from the bag contains 22 yellow marbles and 11 teal marbles, then the probability that the both marbles are teal is [tex]\frac{10}{99}[/tex]
Given,
The number of yellow marbles = 22
Number of teal marbles = 11
Total number of marbles = 22+11= 33 marbles
Then two marbles are chosen randomly
We know,
The probability = Number of favorable outcomes/ Total outcomes
Probability that first marble is teal =[tex]\frac{11}{33}[/tex]=[tex]\frac{1}{3}[/tex]
Probability that second marble is teal =[tex]\frac{10}{33}[/tex]
Here we are considering without replacement
Then the probability that both marbles are teal = [tex](\frac{1}{3})(\frac{10}{33})=\frac{10}{99}[/tex]
Hence, if two marbles are randomly chosen from the bag contains 22 yellow marbles and 11 teal marbles, then the probability that the both marbles are teal is [tex]\frac{10}{99}[/tex]
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Which table shows a function that is decreasing only over the interval (–1, ∞)?
Answer:
The 4th option.
Step-by-step explanation:
f(x) is increasing from x = -3 to x = -1 then it starts to decrease as x increases.
suppose that mean retail price per gallon of regular grade gasoline is with a standard deviation of and that the retail price per gallon has a bell-shaped distribution. note: please use empirical rule approximations for this problem.
68.26 % of regular gasoline sold between $ 3.25 & $ 3.65.
What do you mean by the term standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. the curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.
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The larger bag of ferret food is on sale at the SuperPetMart
for $89. Ferroza made the following table. Explain to
Ferroza why the cost of food at SuperPetMart is not a
proportional relationship.
Ferret Food
Weight
(pounds)
0
5
30
Cost
($)
$0
17.50
89
Relationships that have a uniform or constant rate are said to be proportional relationships. Because it does not employ a uniform rate, the price of food does not follow a proportional connection.
The missing table looks like this:
Bag cost
0 0
5 17.5
30 89
First, we calculate the slope (m) of the table using:
(x₁ y₁) = (0,0)
(x₂ y₂) = (5,17.5)
m₁=(y₂-y₁)/(x₂ -x₁)
m₁=(17.5-0)/(5-0)
m₁=3.5
The slope for the following points
(x₁ y₁) = (0,0)
(x₂ y₂) = (30,89)
m₂=(y₂-y₁)/(x₂ -x₁)
m₂=(89-0)/(30-0)
m₂=2.97
3.5 ≠2.97
Hence, the cost of food is not a proportional relationship because it does not use a uniform rate.
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30 points for anyone who solves this
Answer: The answer is 2 1/12
Step-by-step explanation:
Please can you answer this for me, I will mark you as the brainliest
Answer:
Area of the shaded region is 53.47 square yd
|60| ___ |-60|
=
<
>
Answer:
|60| = |-60|
Step-by-step explanation:
Now the value of,
→ |60| = 60
→ |-60| = 60
Then the sign will be,
→ |60| = |-60|
→ 60 = 60
Hence, the sign is (=).
In the language of functions, all of the following are true except one. Identify the false statement.
The dependent variable (output) is a function of the independent variable (input).
The phrase DEPENDENT VARIABLE means output.
The phrase INDEPENDENT VARIABLE means input
The input is determined by the output
1........answe is 1............
Write the equation of the given circle.
center at origin, d=12
must first specify a coordinate system in order to find the components of each arrow.) this problem gives you some practice with the components. let vectors a⃗
The calculated vectors are:
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4)
[tex]\vec{B}-\vec{C}[/tex]=(-5,4,0)
[tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3)
[tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)
Calculate the following, and express your answers as ordered triplets of values separated by commas.?Generally, the equation for is mathematically given a
[tex]\vec{V}+\vec{W}=\left(V_1, V_2, V_3\right)+\left(W_1, W_2, W_3\right)\\\\\vec{V}+\vec{W}=\left(V_1+W_1, V_2+W_2, V_3+W_3\right) \text { }[/tex]
[tex]\vec{V}-\vec{W}=\left(V_1, V_2, V_3\right)-\left(W_1, W_2, W_3\right)\\\\\vec{V}-\vec{W}=\left(V_1-W_1, V_2-W_2, V_3-W_3\right)[/tex]
[tex]\alpha \cdot \vec{V}=\alpha \cdot\left(V_1, V_2, V_3\right)\\\\\alpha \cdot \vec{V}=\left(\alpha \cdot V_1, \alpha \cdot V_2, \alpha \cdot V_3\right)[/tex]
[tex]\vec{A}-\vec{B}=(1,0,-3)-(-2,5,1)\\\vec{A}-\vec{B}=(3,-5,-4) \\\\&\vec{B}-\vec{C}=(-2,5,1)-(3,1,1)\\&\vec{B}-\vec{C}=(-5,4,0) \\\\&-\vec{A}+\vec{B}-\vec{C}=-(1,0,-3)+(-2,5,1)-(3,1,1)\\-\vec{A}+\vec{B}-\vec{C}=(-6,4,3) \\\\&3 \vec{A}-2 \vec{C}=3(1,0,-3)-2(3,1,1)\\3 \vec{A}-2 \vec{C}=(3,0,-9)-(6,2,2)\\3 \vec{A}-2 \vec{C}=(-3,-2,-11)[/tex]
In conclusion,
[tex]\vec{A}-\vec{B}[/tex]=(3,-5,-4) [tex]\vec{B}-\vec{C}[/tex]=(-5,4,0) [tex]-\vec{A}+\vec{B}-\vec{C}[/tex]=(-6,4,3) [tex]3 \vec{A}-2 \vec{C}[/tex]=(-3,-2,-11)Read more about Vectors
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CQ
In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors A rightarrow = (1,0, -3), rightarrow = (-2,5,1), and C rightarrow = (3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.
13. Measuring bone density Individuals with low bone
density have a high risk of broken bones (fractures).
Physicians who are concerned about low bone density
(osteoporosis) in patients can refer them for special-
ized testing. Currently, the most common method for
testing bone density is dual-energy X-ray absorptiom-
etry (DEXA). A patient who undergoes a DEXA test
usually gets bone density results in grams per square
centimeter (g/cm²) and in standardized units.
7.
Judy, who is 25 years old, has her bone density
measured using DEXA. Her results indicate a bone
density in the hip of 948 g/cm² and a standardized
score of z = -1.45. In the reference population of
25-year-olet women like Judy, the mean bone density
in the hip is 956 g/cm².6
(b) Use the information provided to calculate the standard
deviation of bone density in the reference population.
Using the normal distribution, the standard deviation of bone density in the reference population is of 5.52 g/cm².
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the parameters are given as follows:
[tex]X = 948, z = -1.45, \mu = 956[/tex]
Hence we solve for [tex]\sigma[/tex] to find the z-score as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.45 = \frac{948 - 956}{\sigma}[/tex]
[tex]-1.45\sigma = -8[/tex]
[tex]\sigma = \frac{8}{1.45}[/tex]
[tex]\sigma = 5.52[/tex]
The standard deviation of bone density in the reference population is of 5.52 g/cm².
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v = u + at
u = 2 a = -7 t = 0.5
whats v
Answer:
A= 3. 5 u=7 t=0.5
Step-by-step explanation:
It will be 8.75
erik went to the store and bought 4.8 pounds of chocolate covered almonds and 3.7 pounds of yogurt covered almonds how much did he spend
Answer: svsdvcvsdvsdvsdv
vdsvds
Step-by-step explanation:
ght 4.8 pounds of chocolate covered almonds and 3.7 pounds of yogurt covered almonds how much did he spend
Answer:
43.6
Step-by-step explanation:
Find these common multiple for five and nine
Answer: 45
Step-by-step explanation:
The LCM of 5 and 9 is 45. To find the least common multiple of 5 and 9, we need to find the multiples of 5 and 9 (multiples of 5 = 5, 10, 15, 20 . . . . 45; multiples of 9 = 9, 18, 27, 36 . . . . 45) and choose the smallest multiple that is exactly divisible by 5 and 9, i.e., 45.
What is the equation of the line that passes through the point (3,-4) and has a
slope of -5/3?
Answer:
y = -5/3x + 1
Step-by-step explanation:
as the photo saying
Suppose the cost in dollars of producing x model kits is
given by the polynomial 500,000 + 2x and the revenue generated from sales is
given by the polynomial 30x - 0.00005 x^2 . Find a polynomial expression for the
profit from making and selling x model kits. Then evaluate the expression for
x = 300,000.
Answer:
1100000
Step-by-step explanation: If x = 300,000, that means 2x is 2 x 300,000, and that makes the equation 500,000 + ( 2 x 300,00). Please don't judge me, I am only in 7th grade. Thank you.
The polynomial expression for the profit from making and selling x model kits is 28x - 500,000 - 0.00005 x² and the profit is 3400000.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that:
Suppose the cost in dollars of producing x model kits is given by the polynomial 500,000 + 2x and the revenue generated from sales is given by the polynomial 30x - 0.00005 x².
The profit = revenue - cost
The profit = (30x - 0.00005 x²) - (500,000 + 2x)
The profit = 30x - 0.00005 x² - 500,000 - 2x
The profit = 28x - 500,000 - 0.00005 x²
Plug x = 300,000 in the profit expression.
The profit = 3400000
Thus, the polynomial expression for the profit from making and selling x model kits is 28x - 500,000 - 0.00005 x² and the profit is 3400000.
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The formula d = 16t to the second power describes the number of feet d a skydiver falls in t seconds of free fall assuming there is not air resistance. How far does a skydiver fall between the third and fourth seconds?
Answer:
D=16(3)
=48 feet
D=16(4)
=64 feet
The distance between third and fourth second=64 feet-48 feet
=16 feet
question 4(multiple choice worth 1 points) (01.02 mc) bruno solved the following equation: 4x (10x − 4)
The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.The equation is referred to as a linear equation in one variable if just one variable is contained in the equation.Now,
We are given the linear equation: [tex]4x + \frac{1}{2}(10x-4)=6[/tex]
4x + 5x -2 = 6 (Distributive property)9x - 2 = 6 (combining the like terms)9x = 8 (additive property of equality)x = 8/9 (division property of equality)Hence, The third and fourth solutions are correct when using the division property of equality, i.e., The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).
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An automobile purchased for $37000 is worth $2600 after eight
years. Assuming that the value decreased steadily each year,
what was the car worth at the end of the fifth year?
The car has a value of $ 15 500 at the end of the fifth year.
What is the value of a car in time?
In accordance with the statement, the value of an automobile decreases in time and decreases steadily. A stead decrease means that the value decreases linearly in time, whose formula is shown below:
C' = C + r · t (1)
Where:
C - Initial value of the car, in dollars.C' - Final value of the car, in dollars.r - Decrease rate, in dollars per time.t - Time.If we know that C = $ 2 600, C' = $ 37 000 and t = 8, then the value of the car at the end of the fifth is:
r = (C' - C) / t
r = (2 600 - 37 000) / 8
r = - 4 300
t = 5
y = 37 000 - 4 300 · 5
y = 15 500
The car has a value of $ 15 500 at the end of the fifth year.
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In a 5000 m race on a 400 m track, each athlete must run 12 ½ laps. kara runs the race at a constant pace and finishes in 17.5 min, while hannah runs at a faster pace and finishes 15.3 min. in fact, hannah ran fast enough that she passed kara during the race. how many laps had hannah run when she caught and passed kara?
Hannah had run 6 complete laps and is running the 7th lap when she surpasses the athlete Kara.
Who is an athlete?An athlete (sometimes known as a sportsman or sportswoman) is a person who participates in one or more sports that require physical stamina, speed, or strength.
Professional and amateur athletes both exist. The majority of elite athletes have extremely well-developed bodies because to rigorous physical training, stringent exercise, and a tight food regimen.
Isotonic exercisers had a greater mean left ventricular end-diastolic capacity and are less prone to experience depression. Athletes are far more prone than the general public to go to massage parlors and pay for the services of massotherapists and masseurs due to their demanding physical activity. Athletes whose sport favors endurance over strength typically consume less calories than other athletes.
Calculations:
Total length of the race (L) = 5000 m
Time taken by Kara (tk) = 17.9 min = 1074 s
Kara's speed (vk) = L/tk = 5000/1074 m/s
Time taken by Hannah (th) = 15.3 min = 918 s
Hannah's speed (vh) = L/th = 5000/918 m/s
Let the number of laps Hannah had run when she passes Kara be n
Distance travelled by Hannah in this time = n*400 = 400n meters
Time taken by Hannah to run n laps = 400n/(5000/918)=367200n/5000=73.44n
Distance travelled by Kara in this time = (n-1)*400 = 400n - 400 meters
Time taken by Kara to run (n-1) laps = (400n-400)/(5000*1074)=(429600n-429600)/5000=85.92n-85.92
= 85.92n - 85.92 = 73.44n
= 12.48n = 85.92
= n = 6.88
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George is making a peperoni pizza using a circular pan with a 14-inch diameter. What is the area
of the pizza that George will cover with sauce?
The area of the pizza that George is 153.938040026 [tex]inch^{2}[/tex].
What is area?The area of the pizza that George is [tex]\pi r^{2}[/tex]
area = [tex]\pi[/tex]×[tex]7^{2}[/tex] = 153.938040026 [tex]inch^{2}[/tex]
The number of unit squares that are equivalent in size to the surface, which is included inside a set of lines; see Metric System Table, Weights and Measures Table.
The extent of a notion, action, or activity: the entire realm of international policy.
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
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You are solving a measurement problem where the numbers 2.058 × 10^9 and 3.0571 × 10^−4 are divided. How many significant digits should the quotient have?
Based on the numbers being divided, the number of significant digits that the quotient should have is 4 significant digits.
How many significant digits should be seen?The number of significant digits from a quotient where numbers divided each other should be the significant digits in the number with the smaller number of significant digits.
The number with the lower significant digits here is 2.058 × 10^9.
In this number, there are 4 significant digits because 0 is between non zero numbers.
The quotient would therefore have 4 significant digits.
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A study was performed with a random sample of 513 bolts produced at one factory. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?.
Given that the study was conducted using a sample of 513 bolts produced at a single facility when there is no bias resulting from data gathering procedures, broad inferences may then be drawn.
All bolts manufactured by that factory would be covered by the conclusion?
Due to the fact that bolts made in the same factory will follow the results of an analysis of a sample made up of bolts from the same factory. The finding or conclusion would therefore be applicable to all bolts produced in the same factory because the environment for experimentation and production is the same there while it may differ in other factories. Conclusions from the study may not apply to the bolts made by other companies as a result of this bias.
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how to solve this with steps?
Answer:
its at simplest form
Step-by-step explanation:
Answer:
6x + 9 = 75
explantion : in the photo just writing this so brainly could let me post the picture but here you go
A recipe requires 11 pints of water. How many fluid ounces of water are in 11 pints of water?
how are the cards and the proportional relationships useful for determining the diameter of the sun?
This investigation's goal is to demonstrate how quickly and easily we can determine the diameter of the sun using basic geometry.
How to determine the diameter of the sun?The cards must remain parallel and separated by a predetermined amount. Then, a tiny hole must be cut on one card so that sunlight can pass through and create the sun's picture on the other card. We base the formula described above on the diameter of this photograph of the sun. The diameter of the sun's picture on the card is now measured because we can choose the distance between the cards, and we already know that the sun is nearly 150 million kilometers away from the earth. i.. e. Since three of the values are known, we can use the technique above to determine the fourth unknown quantity and measure the diameter.
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Solve the absolute value equation - 5 | x + 1 | + 2 = 12 if there is no solution, state no solution
Answer:
Let's solve your equation step-by-step.
−5(|x+1|)+2=12
Step 1: Add -2 to both sides.
−5(|x+1|)+2+−2=12+−2
−5(|x+1|)=10
Step 2: Divide both sides by -5.
−5(|x+1|)
−5
=
10
−5
|x+1|=−2
Step 3: Solve Absolute Value.
|x+1|=−2
No solutions. (Absolute value cannot be less than 0.)
Step-by-step explanation: