Using ratios, Carl will receive 24 oranges, while Dina will get 40 oranges, and Eva will receive 36 oranges.
What is a ratio?A ratio shows the relative size of one quantity compared to another quantity or value.
Ratios are expressed in standard ratio forms using the colon (:), in decimals, fractions, or percentages.
The total number of oranges shared between Carl, Dina, and Eva = 100
The ratio Carl's oranges to Dina's oranges = 3:5
The ratio Carl's oranges to Eva's oranges = 2:3
Based on the above ratios, for every 2 oranges that Carl receives, Eva receives 3.
For Carl to receive 3 oranges, Eva will receive 4.5 oranges (3 x 3/2)
The ratios among the three friends are 3: 5: 4.5
The sum of ratios = 12.5 (3 + 5 + 4.5)
Carl's share = 24 (3/12.5 x 100)
Dina's share = 40 (5/12.5 x 100)
Eva's share = 36 (4.5/12.5 x 100)
Thus, based on the ratios, the number of oranges Carl receives is 24.
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Three numbers of the repeating decimal produced by the fraction 3/9
The repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
What is fraction?A fraction is a way of expressing a part of a whole or a ratio between two quantities. It is represented as one quantity divided by another quantity, with a horizontal line called a fraction bar between them.
According to question:The fraction 3/9 can be simplified to 1/3 by dividing both the numerator and denominator by their greatest common factor, which is 3.
When we divide 1 by 3, we get a quotient of 0.3, and a remainder of 1. To continue the long division, we add a decimal point and a zero, and bring down the next digit, which is also a zero. We then divide 10 by 3, which gives us a quotient of 3, and a remainder of 1. We repeat the process, adding a decimal point and another zero, and bringing down another zero. We continue this process infinitely, getting a sequence of 3s that repeat without end.
Therefore, the repeating decimal produced by the fraction 3/9 is 0.33333..., with the digit 3 repeating infinitely.
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2,188,180 rounded to nearest tenth
Answer:
2,188,180
Step-by-step explanation:
since 0 can't give anything to 8 the number would stay the same
Does anyone know how to answer this?
The probability that Esteban wins the game is 29/49.
What does probability mean?Probability is a concept that refers to the likelihood of a particular event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's consider an example: Esteban is playing a matching card game where he wins if the cards are identical. To calculate the probability of winning, we can use the following formula:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
If we assume that the deck of cards contains seven crosses and seven stars, the probability of getting a cross on both cards is:
2/7 x 2/7 = 4/49
The probability of getting a star on both cards is:
5/7 x 5/7 = 25/49
To calculate the overall probability of winning the game, we add the probabilities of getting a cross on both cards and getting a star on both cards:
4/49 + 25/49 = 29/49
Therefore, the probability that Esteban will win the game is 29/49.
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The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α
= 0.01 is:
A) 2.33
B) 2.96
C) 2.05
D) 2.575
The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α = 0.01 is 2.575. The right option is (D).
What is a hypothesis test?In statistics, a hypothesis test is an examination of a particular hypothesis regarding a population parameter with the help of data from a sample. Hypothesis testing is a statistical method used to make decisions about a population based on a sample's data.
The following are the four stages of hypothesis testing:
1. Formulation of Hypothesis
2. Selection of a Significance Level
3. Calculation of Test Statistics
4. Acceptance or Rejection of the Null Hypothesis
The critical value for a two-tail hypothesis test is 2.575 when the sample size is greater than or equal to 30, the population standard deviation is known, and the significance level is α=0.01.
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Find the exact side length of a square with an area of 9/49 square meters.
Answer:
3/7 meters
Step-by-step explanation:
[tex] \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]
a sample of 179 students using method 1 produces a testing average of 55.9 . a sample of 176 students using method 2 produces a testing average of 89.8 . assume the standard deviation is known to be 8.92 for method 1 and 16 for method 2. determine the 95% confidence
The 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is -36.54 to -31.26.
To calculate the 95% confidence interval for the true difference between the testing averages of the two instructional methods, we can use the following formula
Confidence interval = (X1 - X2) ± Z*(σ1^2/n1 + σ2^2/n2)^0.5
Where
X1 is the testing average for Method 1
X2 is the testing average for Method 2
Z is the critical value for a 95% confidence interval, which is 1.96
σ1 is the known standard deviation for Method 1
σ2 is the known standard deviation for Method 2
n1 is the sample size for Method 1
n2 is the sample size for Method 2
Substituting the values given in the problem, we get
Confidence interval = (55.9 - 89.8) ± 1.96*(8.92^2/179 + 16^2/176)^0.5
= -33.9 ± 2.64
Therefore, the 95% confidence interval using Method 1 and students using Method 2 is -36.54 to -31.26.
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The given question is incomplete, the complete question is:
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 179 students using Method 1 produces a testing average of 55.9. A sample of 176 students using Method 2 produces a testing average of 89.8. Assume the standard deviation is known to be 8.92 for Method 1 and 16 for Method 2. Determine the 95% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2
The temperature at 8 P.M. was - 6.8 degrees Celsius. • Between 8 P.M. and 10 P.M., the temperature change was -3.9 degrees Celsius. • The temperature change was -4.4 degrees Celsius between 10 P.m. and midnight. What was the temperature at midnight?
Using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we can solve for the temperature as follows:
8 pm = -6.8
8 - 10 pm = -6.8 -3.9 = -10.7
10 - 12 midnight = -10.7 -4.4 = -15.1°C
Therefore, using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
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Reasoning: If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two quadratic equations share a solution? Explain why or why not. If so, give two quadratic equations that meet this criterion. HELP ASAP PLS (55 points)
Two quadratic equations can share a solution if one quadratic equation has a positive discriminant and another quadratic equation has a discriminant equal to 0
What is meant by quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means it involves an unknown variable (usually denoted as x) that is raised to the power of 2.
If one quadratic equation has a positive discriminant, it means that the quadratic equation has two distinct real roots. On the other hand, if another quadratic equation has a discriminant equal to 0, it means that the quadratic equation has only one real root that is repeated.
Therefore, it is possible for two quadratic equations to share a solution if one quadratic equation has a positive discriminant and another quadratic equation has a discriminant equal to 0, but only if the repeated root of the second quadratic equation is one of the two roots of the first quadratic equation.
To illustrate this, let's consider the following two quadratic equations:
Quadratic equation 1: [tex]$x^2 - 4x + 3 = 0$[/tex]
Quadratic equation 2: [tex]$x^2 - 2x + 1 = 0$[/tex]
The discriminant of quadratic equation 1 is [tex]$b^2-4ac = 4 - 4(1)(3) = -8$[/tex], which is negative. Therefore, quadratic equation 1 has two distinct real roots, which can be found using the quadratic formula:
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Substituting the values of a, b, and c from quadratic equation 1, we get:
[tex]$x=\frac{4\pm\sqrt{(-4)^2-4(1)(3)}}{2(1)}$[/tex]
[tex]$x=2\pm\sqrt{1}$[/tex]
[tex]x=3$ or $x=1$[/tex]
Therefore, the roots of quadratic equation 1 are [tex]x=3$ and $x=1$[/tex].
The discriminant of quadratic equation 2 is [tex]$b^2-4ac = 2^2 - 4(1)(1) = 0$[/tex]. Therefore, quadratic equation 2 has one repeated real root, which is:
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
Substituting the values of a, b, and c from quadratic equation 2, we get:
[tex]$x=\frac{2\pm\sqrt{2^2-4(1)(1)}}{2(1)}$[/tex]
[tex]$x=1$[/tex] (repeated root)
As we can see, the repeated root of quadratic equation 2 is equal to one of the roots of quadratic equation 1, which is [tex]$x=1$[/tex]. Therefore, these two quadratic equations share a solution.
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The volume of a right cone is 33\piπ units^3
3
. If its circumference measures 6\piπ units, find its height.
Let's denote the radius of the cone as 'r' and the height as 'h'.
The formula for the volume of a cone is:
V = (1/3) * π * r^2 * h
And the formula for the circumference of the base of a cone is:
C = 2 * π * r
We know that the volume of the cone is 33π/3, so:
(1/3) * π * r^2 * h = 33π/3
Simplifying this equation, we get:
π * r^2 * h = 99π
r^2 * h = 99
We also know that the circumference of the base of the cone is 6π, so:
2 * π * r = 6π
Simplifying this equation, we get:
r = 3
Now we can substitute this value of 'r' into the equation we obtained earlier:
r^2 * h = 99
3^2 * h = 99
h = 11
Therefore, the height of the cone is 11 units.
what is the probability of being delt 4 hearts from a standard 52 card deck if only 4 cards are to be delt
The probability of being dealt 4 hearts from a standard 52 card deck if only 4 cards are to be dealt is 0.0026.
There are 52 cards in a standard deck, 13 of which are hearts.
We want to find the probability of getting dealt four hearts out of a four-card hand.
Since order doesn't matter, we will use combinations to calculate this probability.
P(A) = number of favorable outcomes / total number of possible outcomes.
There are 13 choose 4 ways to choose four hearts from the deck, and there are 52 choose 4 ways to choose any four cards from the deck.
So the probability of being dealt four hearts from a standard 52 card deck if only 4 cards are to be dealt is:
P(A) = (13 choose 4) / (52 choose 4)P(A)
= (715) / (270725)P(A)
= 0.002641056.
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On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of his family were on their way. His wife sue had baked a cake. They'd all eat it by the lake. After the party the grandkids would play with all of the dogs then roll in the hay. He'd look out the window and what would he see? EIGHTY-FOUR legs and heads THIRTY-THREE!! grandpa Bill's question for you is not very hard. How many dogs and grandchildren will be in the yard?
Answer:
187
Step-by-step explanation:
If 70th after he see 84 and legs 33 so the answer is 70+84+33=187
Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. How much interest will he have earned after 3 years?
Answer:
$45
Step-by-step explanation:
Interest earned in a year
5/100x300= $15
Interest earned in 3 years
=$15x3
=$45
What is one barrier that can affect the assessment phase of financial planning?
Clients may project their anxiety onto the financial counselor, causing them to make accusations and instigate conflicts
O Clients may have too much to assess at one given time, which can make developing a financial plan difficult and tedious.
O Clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information
Clients may ask if the financial counselor could help another family member or friend free of charge while they are in the process of helping
the initial client
This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves methods for summarizing and describing data, making inferences and predictions about a population based on a sample, testing hypotheses, and identifying patterns and relationships within data. Statistics can be applied in a wide range of fields, including business, finance, social sciences, engineering, medicine, and more. It provides a framework for making informed decisions based on empirical evidence, and plays a crucial role in scientific research and data-driven decision making.
The barrier that can affect the assessment phase of financial planning is when clients may be anxious or embarrassed which can make them reluctant to share complete and accurate information. This can lead to incomplete or inaccurate financial plans, which can ultimately harm the client's financial well-being. It is important for financial counselors to establish trust and create a comfortable environment for clients to feel safe sharing their financial information. This can be done by actively listening to clients' concerns, being non-judgmental, and explaining the importance of accurate information in developing a comprehensive financial plan.
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in how many ways can we list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions?
There are 144 ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions.
We have to list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions. We can use the knowledge of permutations and combinations to solve this problem. We can start by selecting the positions for the distinct digits, i.e., (3, 4, 5). There are 3 distinct digits, so there are 3! = 6 ways to arrange them.
Once we have placed the distinct digits, we can place the two 1's and two 2's in the remaining positions such that no two identical digits are in consecutive positions. To do this, we can use the following approach:
We can start by placing one of the 1's. There are 4 positions available for the first 1.
We can then place one of the 2's. There are 3 positions available for the first 2.
We can then place the second 1. There are 2 positions available for the second 1.
We can then place the second 2. There are 1 positions available for the second 2.
Therefore, the total number of ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions is:
6 (arrangements of distinct digits) x 4 x 3 x 2 x 1 = 144.
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f(x) = x + 6 g(x) = 5x Work out the value of gf(3)
Answer:
45
Step-by-step explanation:
[tex]g(f(x))=5(x+6)[/tex]
[tex]g(f(3))=5(3+6)\\[/tex]
[tex]g(f(3))=5(9)\\[/tex]
[tex]g(f(3))=45[/tex]
Answer:
f(x) =x + 6g(x) =5x =
Calculate the formula weights:
mass of mole of
F(x) = x + 6g (x) = 5x = 19g
Find the distance between 9.4− 6.2
Answer: 3.2
Step-by-step explanation: put the 9.4 over the 6.2 (not as a fraction) subtract and then you get 0.2 when you take the .4 - .2 and 9 - 6 is 3 then you would put the 0.2 with the 3 to get 3.2
What is the answer in the photo
The sale price of the reusable water bottle is $18.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating these symbols. It is a broad area that includes various subfields such as elementary algebra, abstract algebra, and linear algebra, among others.
In elementary algebra, the focus is on the basic rules and operations involving variables, numbers, and equations. These concepts are used to solve problems in a wide range of fields, such as science, engineering, and finance. Abstract algebra, on the other hand, deals with the study of algebraic structures such as groups, rings, and fields. Linear algebra is the study of vector spaces and linear transformations, and is used extensively in fields such as computer science, physics, and engineering.
The discount on the reusable water bottles is 10%, which means that the customer pays only 90% of the regular price. To find the sale price, we can multiply the regular price by 90% or 0.9.
Sale price = Regular price x (1 - Discount rate)
Sale price = $20 x (1 - 0.1)
Sale price = $20 x 0.9
Sale price = $18
Therefore, the sale price of the reusable water bottle is $18.
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a company plans to manufacture a rectangular box with a square base, an open top, and a volume of 246 in.3. the cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch. determine the dimensions of the box that will minimize the cost of manufacturing it. what is the minimum cost?
The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in
And the minimum cost is 32.65 cents
Let us assume that x represents the base side of the box, and y represents the height of the box.
The volume of the box would be:
V = x²y
246 = x²y ........(1)
The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.
Since this box has 4 sides and 1 base, the total cost would be,
C = (0.2 × x² × 1) + (0.3 × 4 × xy)
C = 0.2x² + 1.2x(246x⁻²) (from (1) y = 246x⁻²)
C = 0.2x² + 295.2 x⁻¹
Consider derivative with respect to x,
dC/dx = 0.4x - 295.2 x⁻²
Consider dC/dx = 0
So, 0.4x - 295.2 x⁻² = 0
0.4x³ = 295.2
x³ = 738
So, x = 9.04
So, the value of y would be:
y = 246 x⁻²
y = 246 × (9.04)⁻²
y = 3.01
So, the minimum cost would be:
C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)
C = 32.65
Therefore, the minimum cost is: 32.65 cents
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What fraction of 1/2 square centimeter 1/2 centimeter square?
1/4 square centimeter is therefore equal to 1/2 square centimeter.
In math, what is a fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears inside the numerator and denominator of a complex fraction. The numerator of a proper fraction has a smaller denominator.
While "1/2-centimeter square" refers to a square having the side length of half a centimeter, the marking "1/2 square centimeter" typically refers to an area equal half a square centimeter. Even though these aren't the same object, we can still calculate the ratio of one to the other.
The area of such a square of side length 1/2 centimeter is:
(1/2 cm) x (1/2 cm) = 1/4 square centimeter
We may divide 1/4 by 1/2 to determine the percentage of 1/2 square centimeter that corresponds to 1/4 square centimeter:
(1/4 square cm) ÷ (1/2 square cm) = (1/4) x (2/1) = 1/2
Hence, 1/4 square centimeter is equal to 1/2 square centimeter in size.
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119. What is the linear equation for the pricing formula for Logan's Paint? One gallon cost $11 (1,11) and 5 gallons cost $35 (5, 35).
The linear equation is y = 6x + 5
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
To find the equation for the pricing formula, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the cost, x is the number of gallons, m is the slope (i.e., the rate of change of the cost per gallon), and b is the y-intercept (i.e., the cost when x = 0).
Using the given information, we can calculate the slope:
m = (35 - 11) / (5 - 1) = 24 / 4 = 6
The y-intercept can be found by plugging in one of the points:
11 = 6(1) + b
b = 5
Therefore, the linear equation for the pricing formula for Logan's Paint is:
y = 6x + 5
where y is the cost in dollars and x is the number of gallons.
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Jackie purchases a monthly pass to see movies at the theater in order to buy each movie ticket at a discounted rate. The graph shows the costs for different numbers of movie tickets. Find the slope and y-intercept and their meaning.
Fill the blanks.
(A) The slope is $____________ and means that________________
(B) The y-intercept is $________ and means that________________
(A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
What is slope?
Slope is a measure of the steepness of a line. It describes the rate at which the line rises or falls as it moves horizontally, and it is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Mathematically, slope can be represented as:
Slope = (change in y-coordinates) / (change in x-coordinates)
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1,30) and (3,40) to find the slope:
m = (40 - 30) / (3 - 1) = 10 / 2 = 5
Now we can use any of the given points and the slope to find the y-intercept. Let's use the point (1,30):
y = mx + b
30 = 5(1) + b
30 = 5 + b
b = 30 - 5
b = 25
So the equation of the line passing through the points (1,30), (3,40), (5,50), and (7,60) is:
y = 5x + 25
Therefore, (A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
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bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
if f(x)=1-2x then what is 2f(x)
functions
The given function is f(x) = 1 - 2x.
To find 2f(x), we simply multiply the function f(x) by 2:
2f(x) = 2(1 - 2x)
Distributing the 2 across the expression, we get:
2f(x) = 2 - 4x
Therefore, 2f(x) = 2 - 4x.
Complete the statements. Keith's strategy for finding the product is select and the product of 21. 5 and 5. 3 is select
When multiplying 31. 5 by 5. 3, Keith found the product using the following steps. (31 + 6. 5)(5 + 6. 3) = (35 * 5) + (5. 5 * 5. 3) = 155 + 5. 15
Keith found that the product of 31.5 and 5.3 is 160.15
Keith's strategy for finding the product is breaking the numbers into parts and then adding the results.
The product of 21.5 and 5.3 is
(20 + 1 + 0.5) × (5 + 0.3) = (20 × 5) + (20 × 0.3) + (1 × 5) + (1 × 0.3) + (0.5 × 5) + (0.5 × 0.3) = 100 + 6 + 5 + 0.3 + 2.5 + 0.15 = 114.95
When multiplying 31.5 by 5.3, Keith used a similar approach, breaking the numbers into parts and then adding the results. Specifically, he expanded the terms as (31 + 0.5)(5 + 0.3), added the partial products, and then rounded the result to two decimal places.
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Find the nth term of 23,17,11,5
Answer:
Find the nth term of 23,17,11,5:
23,17,11,5,-1,-7,-13...
HELP PLEASE MATH IS HARD
The box plot displays the number of flowers planted in a town last summer. A box plot uses a number line from 6 to 21 with tick marks every one-half unit. The box extends from 10 to 15 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 20. The graph is titled Flowers Planted In Town, and the line is labeled Number of Flowers. Which of the following is the best measure of center for the data shown, and what is that value? The mean is the best measure of center and equals 11. The mean is the best measure of center and equals 12. The median is the best measure of center and equals 11. The median is the best measure of center and equals 12.
After answering the presented question, we can conclude that thus, the equation correct answer is: The median, which equals 11, is the best measure of center.
What box plot represent?The box plot depicts the distribution of the quantity of flowers planted in a town last summer based on the information provided. The box spans the number line from 10 to 15, with a line at 11 inside the box and lines outside the box ending at 7 and 20.
The median is depicted by the line in the box, which is positioned at 11 in the box plot. As a result, the median is the best measure of center for the data provided, and its value is 11.
Thus, the correct answer is: The median, which equals 11, is the best measure of center.
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paint samples are often sold by the pint; a pint of paint will cover 50 square feet. if the dimensions of a room are 138 inches by 117 inches, how many pints of paint would you need to purchase to paint the ceiling of this room?
To paint the ceiling of a room that is 138 inches by 117 inches, you would need to purchase 3 pints of paint.
To find out how many pints of paint are needed to paint the room's ceiling, we must first convert its dimensions from inches to feet:138 inches is equivalent to 11.5 feet (138 ÷ 12 = 11.5)117 inches is equivalent to 9.75 feet (117 ÷ 12 = 9.75)To determine the total square footage of the room, multiply the room's length and width:11.5 feet × 9.75 feet = 112.125 square feet
To calculate the amount of paint needed, divide the total square footage by the number of square feet that one pint of paint will cover:112.125 square feet ÷ 50 square feet per pint = 2.24 pints
Therefore, you would need to purchase approximately 2.24 pints of paint to paint the ceiling of a room that is 138 inches by 117 inches. However, since paint is often sold in whole pints, you would need to purchase 3 pints of paint.
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find the median of 14,19,16,13,16,14
Answer:
15
Step-by-step explanation:
Place the number in order from least to greatest. 13,14,14,16,16,19
then take one away from each side till there is one left. 14,14,16,16 14,16.
in this case there is two from this point on you find the average of the two number you have left so in this case, 14+16=30 30/2=15 The median is 15
2.8 is what percent of 2.24
Bob's dog, Buster, is a finicky eater. Bob is trying to determine which of two brands of
canned cat food Buster prefers, Busted Nuggets or Busted Tenders. For two months, he
flips a coin each day to decide which of the two foods to feed Buster, and weighs how
much Buster eats (in grams). Here are the data:
Dog Food
n X
S
Busted Nuggets 31 152.6 4.45
Busted Tenders 31 163.7 5.75
Construct and interpret a 98% confidence interval for the difference in mean amount of
food Buster eats when he is offered Busted Nuggets and when he is offered Busted
Tenders.
We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams
Hοw tο cοnstruct cοnfidence interval?Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.
The sample mean difference is:
X1 - X2 = 152.6 - 163.7 = -11.1 grams.
The standard errοr οf the difference can be calculated as fοllοws:
SE = √(S1²/n1 + S2²/n2)
where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.
Substituting the values, we get:
SE = √(4.45²/31 + 5.75²/31) = 1.463
ME = t x (SE) = 2.365 x 1.463 = 3.466
Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:
-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466
-14.566 < µ1 - µ2 < -7.634
Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.
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What is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?
a) 0.17583334
b) 0.00000026
c) 0.00000214
d) 0.00000029
e) 0.00000016
The probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards is option (c) 0.00000214.
The probability of selecting exactly 3 hearts if 7 cards are chosen from a well-shuffled deck of 52 playing cards can be calculated using the hypergeometric distribution.
The total number of ways to choose 7 cards from 52 is given by the combination C(52,7), which is the total number of possible outcomes.
The number of ways to choose 3 hearts and 4 non-hearts is given by the product of the number of ways to choose 3 hearts from 13 and the number of ways to choose 4 non-hearts from 39. That is:
C(13,3) [tex]\times[/tex] C(39,4)
Therefore, the probability of selecting exactly 3 hearts is:
P(3 hearts) = [C(13,3) [tex]\times[/tex] C(39,4)] / C(52,7)
Calculating this probability gives:
P(3 hearts) ≈ 0.00000214
Therefore, the correct answer is option (c).
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