By using the concept of maxima, it can be calculated that
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
What is maxima of a function?
Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.
Let the length of the rectangle be l m and width of the rectangle be w m
Perimeter (P) = 2(l + w)
By the problem,
2(l + w) = 72
l + w = [tex]\frac{72}{2}[/tex]
l + w = 36
w = 36 - l
Area (A) = l [tex]\times[/tex] w
A = l [tex]\times[/tex] (36 - l) = [tex]36l - l^2[/tex]
Differentiation with A with respect to l
[tex]\frac{dA}{dl} = 36 - 2l[/tex]
For maximum area,
[tex]\frac{dA}{dl} = 0[/tex]
36 - 2l = 0
2l = 36
l = [tex]\frac{36}{2}[/tex]
l = 18 m
[tex]\frac{d^2A}{dl^2} = -2 < 0[/tex]
Hence area is maximum
w = 36 - 18 = 18 m
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
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:
Ethan needs to add together two whole numbers
and wants to estimate the answer first.
He rounds both numbers to 1 significant figure,
which gives him 300 and 600, and adds them
together to get an estimate of 900.
What is the greatest possible difference
between his estimate and the true answer to the
addition?
The required greatest difference between the estimate and the true value is 45.
Given that,
Ethan needs to add together two whole numbers and wants to estimate the answer first. He rounds both numbers to 1 significant figure, which gives him 300 and 600 and adds them together to get an estimate of 900.
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
For the estimated number 900, the least number that can be rounded to the number 900 is 855,
Now,
Difference = 900 - 855 = 45
Thus, the required greatest difference between the estimate and the true value is 45.
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question 17 options: $3,000 to have the vehicle restored $9,000 to have the vehicle restored $6,000 to have the vehicle restored $11,000 to have the vehicle restored
Cybil would be financially better off by $ 3000 to have the vehicle restored.
Cybill is either going to sell the car for $ 10000
Or he can have it restored and then sell it for 22000
The restoration will cost him $9000
Incremental revenue = selling price after restoration - selling price without restoration
Incremental revenue = $ 22000 - 10000 = $ 12000
Incremental costs = 9000
Incremental income = 12000 - 9000 = 3000
Therefore, Cybil would be financially better off by $ 3000 to have the vehicle restored.
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In experiments in which participants manually tracked a complex pattern that consisted of two segments that were random patterns on every trial and one segment that was the same every trial, the results showed that the participants improved
more on the repeated segment than the two random segments, and reported they were not aware that one segment was the same on every trial.
For the given experiments , participants concluded that complexity is more on the random patterns on every trials compare to one segment that was same for every trial.
As given in the question,
Steps for the experiment where participants manually tracked a complex pattern which consists of two segments are as follow:
In first case : One segment consists of random patterns on every trial that is on every new trial there is new random pattern which participant has to follow.
In second case : Another segment consists of same pattern on every new trial.
After conducting experiment reports conclude that repeated segment with the same pattern present more improved result compare to random patterns. As participants were aware of the same segment on each new trial.
Therefore, given experiments of participants proves the complexity is more on the random patterns on every trials compare to one segment same for every trial.
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What is the remainder when x 2 2x 1 is divided by x 1?.
The remainder when x² + 2x + 1 is divided by x + 1 is 0.
Given,
The polynomial functions; x² + 2x + 1 and x + 1
We have to find the remainder when x² + 2x + 1 is divided by x + 1
Remainder theorem;-
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.
Here,
p(x) = x² + 2x + 1
g(x) = x + 1
Now,
x + 1 = 0
x = -1
Then,
p(-1) = -1² + 2 x -1 + 1 = 1 - 2 + 1 = - 1 + 1 = 0
That is,
The remainder when x² + 2x + 1 is divided by x + 1 is 0.
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Two cards are selected from a standard deck of 52 playing cards. The first card is not replaced before the second card is selected. Find the probability of selecting a three and then selecting a fiveThere are 4 threes in the deck so the probability of selecting a three is 4/52. Then, for the second draw, there are 4 fives as well but, since you already selected a card and didn't replace it, there are now only 51 cards in the deck so the probability of selecting a five is 4/51The probability of both events happening is the product of the two individual probabilities so 4/52 * 4/51 = 16/2652 = 4/663 = 0.6%
The probability of selecting a three and then selecting a five is 0.6%
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.
Probability is computed by dividing the number of possible outcomes by the total number of possible outcomes. Probability and odds are two distinct ideas. Odds are calculated by dividing the probability that something will occur by the probability that it will not occur.
Because there are four threes in the deck, the probability of picking one is 4/52.
Then, for the second draw, there are four fives as well, but because you already chose a card and did not replace it, there are only 51 cards in the deck, therefore the likelihood of drawing a five is 4/51.
The product of the two individual probabilities is the likelihood of both events occurring.
So,
(4/52) × (4/51)= 16/2652
= 4/663
= 0.6%
Hence, the probability of selecting a three and then selecting a five is 0.6%
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x d and y d are two points in d-dimensional euclidean space. the euclidean distance between x and y is: be the region inside the d-dimensional hypersphere with radius r, centered at the origin. the volume of s is the gamma function that we saw earlier in class when talking about the beta distribution.
The calculation of the separation between two locations on a plane is done using the Euclidean distance formula. This equation estimates the separation between two places.
[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]
Our perception of space is frequently incorrect in high dimensions since it was created in two and three dimensions. Think about randomly distributing 100 points into a unit square. The range [0, 1] is used to produce each coordinate independently and evenly at random.
Choose a point, calculate the distances between it and every other point, and then chart the distribution of those distances. The points are then uniformly generated at random in a 100-dimensional unit cube when the dimension is increased. Around an average distance, the distribution of distances becomes concentrated.
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please helo me with both of them thank u
Answer:
13: 22 < x < 74
14: Side DF, Side DE, side EF
Step-by-step explanation:
So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.
For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.
Hope this helps!!! :)
This item has two parts: Part A and Part B. Use the information and table to complete Part A and Part B.
The table shows how the total number of views of two internet videos are changing over time.
Video Views
Date Video 1 Total Views Video 2 Total Views
July 10 5,000 20,000
July 11
15,000 50,000
July 12
45,000 100,000
July 13
135,000 150,000
July 14
405,000 190,000
Part A
Which of the following statements is TRUE?
The total number of views for Video 2 are linear because they increase by equal differences over equal intervals.
The total number of views for Video 1 are exponential because they grow by equal factors over equal intervals.
The total number of views for Video 2 are exponential because they grow by equal factors over equal intervals.
The total number of views for Video 1 are linear because they increase by equal differences over equal intervals.
Part B
What is the average rate of change of the total number of views for Video 2 between July 12 and July 14?
45,000
30,000
190,000
90,000
a. The correct statement regarding the classification of the functions as exponential and linear is given as follows:
The total number of views for Video 1 are exponential because they grow by equal factors over equal intervals.
b. The average rate of change of the total number of views for Video 2 between July 12 and July 14 is of: 45,000 views a day.
How to classify the functions?The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:
Equal factor: exponential.Equal difference: linear.Hence the functions are classified as follows:
Video 1: Exponential, as each term is the previous term multiplied by 3.Video 2: Neither, as there is no pattern between the views for each day.The average rate of change is given by the change in the output divided by the change in the input, hence it is of:
r = (190000 - 100000)/2 = 45,000 views a day.
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given that there are three conditions/levels of the independent variable, how many orders of the conditions are possible in dr. davis's study?
6 orders of the conditions are possible in dr. davis's study.
What is an independent variable?
What it means to be an independent variable is exactly what it is. It is a variable that is independent of the other factors you are attempting to assess. Age is just one example of an independent variable.
What distinguishes a variable from a dependent one?
The cause is the independent variable. The other factors in your study have no bearing on its value.
Effect is the dependent variable. The independent variable's changes determine its value.
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g at what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 18.4 cm/s? (use decimal notation. give your answer to three decimal places.) rate is cm/s
The diagonal of a cube increasing at a rate of 31.869 cm/s.
It is given that edges are increasing at a rate of 18.4 cm/s.
We know the formula of diagonal of cube which is
D = [tex]\sqrt{3}[/tex] a
where a is the edge.
Now we will differentiate the diagonal equation with respect to time er get,
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] [tex]\frac{da}{dt}[/tex]
Given that edges are increasing at a rate of 18.4 cm/s, this means
[tex]\frac{da}{dt}[/tex] = 18.4 cm/s
Therefore
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] (18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 1.732(18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 31.869 cm/s
Hence the diagonal of a cube increasing at a rate of 31.869 cm/s.
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The perimeter of a square is 64 cm.
Calculate the area of the square.
Answer:
256
Step-by-step explanation:
area of square= side × side
64÷4= one side
16= side
16 × 16
=256
Select the graph that correctly displays the solution of the system of inequalities.
y> 2x²+x-3
y<-x² + 5x
By plotting the obtained solutions on the graph we get graph as below.
The given system of inequalities are y >2x²+x-3 and y <-x² + 5x.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Put x=0, 1, 2 and 3 in the given inequalities, we get
Now, with y >2x²+x-3
When x=0
y >2(0)²+0-3
y >-3
When x=1
y >2(1)²+1-3
y >0
When x=2
y >2(2)²+2-3
y >7
When x=2
y >2(3)²+3-3
y >18
With the inequalities y<-x²+5x
When x=0
y<-0²+5(0)
y<0
When x=1
y<(-1)²+5(1)
y<6
When x=2
y<(-2)²+5(2)
y<14
When x=3
y<(-3)²+5(3)
y<24
By plotting the obtained solutions on the graph we get graph as below.
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In the following exercise eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. x=sqrt 3t, y=3t-8
The rectangular equation is y = x² - 8.
Given;
The rectangular equation to sketch the plane curve represented by the given parametric equations,
x = √3t
y = 3t - 8 -∞ < t < ∞
Now,
3t = x²
t = x²/3
Now,
y = x² - 8
Therefore, the rectangular equation is y = x² - 8
Where, x ≥ 0
And the graph is a curve as shown below,
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70 pupils in a sports centre are surveyed. The pupils can only use the swimming pool and the gym. 28 pupils use the swimming pool and the gym. 48 pupils use the swimming pool. 39 pupils use the gym. Find the probability to select a pupil that uses neither the swimming pool nor the gym.
The probability that a pupil uses neither pool nor gym is 11/70
What is Probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.
Number of pupil that can use pool and gym = 28
Number of people that can use pool = 48
Number of people that can use gym = 39
Number of people that can use pool only = 48 - 28 which is 20
Number of people that can use gym only = 39 - 28 = 11
Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59
Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.
Probability = required outcome / possible outcome
Required outcome = 11
possible outcome = 70
Probability = 11/70
In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70
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Ted used a balance scale to weigh a 2.233 g sample of copper sulfate. which of these measurements made by ted is the most accurate? 2.1 g 2.2 g 2.4 g 2.5 g
Ted used a balance scale to weigh a 2.233 g sample of copper sulfate, the most accurate measurements made by Ted is 2.2 g.
Accuracy is a measure of how close you are the true value.
In this case,Ted used a balance scale to weigh a 2.233 g sample of copper sulfate using only 2 significant figures, that would be the value of 2.2 g
Precision is how close a test result when repeated. In precision, the actual value is not examined. You only need to look at the result.The standard deviation should be small.
Accuracy is how close the test results to the standard known value. The standard deviation might be big.
Ted used a balance scale to weigh a 2.233 g sample of copper sulfate, the most accurate measurements made by Ted is 2.2 g.
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Single exponential smoothing (SES)
is a forecasting technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period.
The weightage is given to the most recent values in the time series.
What is Simple Exponential Smoothing (SES)?SES is a simple forecasting technique that is easy to implement and can be used with data that has a consistent trend. However, it is not well suited for data that is highly volatile or has a lot of noise.
One of the simplest forecasting techniques is single exponential smoothing (SES). It is a weighted average of past time-series values, where the weightage is given to the most recent values in the time series. This technique is easy to implement and can be used with data that has a consistent trend. However, it is not well suited for data that is highly volatile or has a lot of noise.
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Is 17 a median number?.
If 17 is the middlie number in a series when it is arranged either in ascending or decending order, then 17 is the median number
The median is the middle number in an ordered data set. The mean is the sum of all values divided by the total number of values.
Arrange the data points from smallest to largest or from largest to smallest. If the number of data points is odd, the median is exactly the middle data point in the list. If the number of data points is even, then the median is the average of the two middle data points in the list.
Therefore, if 17 is the middlie number in a series when it is arranged either in ascending or decending order, then 17 is the median number
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easy points for all u peoples
2+( 7x5)=?
A)45
B)98
C)37
D)70
Answer:
C. 37
Step-by-step explanation:
2 + (7x5)
= 2 + (35)
= 2 + 25
= 37
Answer: 37
Step-by-step explanation:
Following PEMDAS* we then get 2+35. Adding that we will get 37.
*(Parenthesis, exponents, multiplication, division, addition, subtraction )
the ratio of men to women working for a company is to . if there are men working for the company, what is the total number of employees?
A ratio displays the multiplicity of two numbers, the total number of employees is 187.
Describe ratio.The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared.
How is ratio calculated?Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare one data point (A) to another data point (B). This indicates that you are multiplying data A by data B.
So the ratios are-
men : women
4:7
x:119
Now, relationship between 7and 119 is -
men : women
4:7
7*17
x:119
Now,
men : women
4:7
4*17 :7*17
68:119
Total number
68+119= 187
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The average of 3 numbers is 19 two of the numbers are 17 and 24 what is the third number.
The required third number of the given triad is 16.
What is average?The average is characterized as the mean worth which is equivalent to the proportion of the amount of the quantity of a given arrangement of values to the complete number of values present in the set.
According to question:Given two number are 17 and 24.
Let the third number is x,
Average of three number is 19
17 + 24 + x/3 = 19
41 + x = 57
x = 16
Thus, the third number is 16.
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Which ordered pair makes both inequalities true y 3x 1 y x 4?.
The ordered pair (4, 0) makes both inequalities true.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
In inequality, we compare two values.
y < 3x -1 …. (1)
y > -x + 4 …. (2)
Take the point (4, 0)
Consider inequality (1)
y < 3x-1
0 < 3 (4) - 1
0 < 12 - 1
0 < 11 which is true
In inequality (2)
y ≥ - x + 4
0 ≥ -4 + 4
0 ≥ 0 …. Which is true
Therefore, the ordered pair (4, 0) makes both inequalities true.
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Question:
Which ordered pair makes both inequalities true? y < 3x – 1 y > –x + 4
(4,0) (1,2) (0,4) (2,1)
Answer:
A its A
Step-by-step explanation:
Find the values of x and y. Y= 3x+29
Answer:
x= 37 , y= 143
Step-by-step explanation:
okay so to start out we must write an equation in order to find the angles of a parallelogram.
2x+2y=360 (the angles of a parallelogram always equal 360 degrees)
next, since we know that the angle for y is "y+3" we can substitute this into the equation
2x+2(y+3)=360
next, since it is given that y=3x+29 we can now substitute that into the equation
2x+2[(3x+29)+3]=360
now, SOLVE!
[tex]2x+2[(3x+29)+3]=360 \\2x+2(3x+32)=360 \\2x+6x+64=360\\8x+64=360\\8x=296\\x=37[/tex]
okay, now we know that x=37 degrees so now we must find y. this can be done by substituting 37 into (3x+29)+3 or simply, 3x+32
[tex]y=3x+32\\y=3(37)+32\\y=111+32\\y=143[/tex]
don't forget to check your work!
2(37)+2(143)=360
there you go! so x= 37 degrees and y= 143 degrees
How would the function change if the base of the exponent were 1?.
If the base of the exponent is 1, the function remains constant. The graph becomes a horizontal line. The function fails if the base of the exponent is less than 1 and greater than 0.
The exponential function in base b is defined by
y = bˣ where b > 0 and b is a constant.
The independent variable is x and the range is real.
For example, f(x) = 3ˣ is exponential function.
Exponential Base
If f(x) = bˣ , we call "b" the exponential base. Base
must always be positive.
exponent base is 1
if f(x) is exponential with base 1 i.e. if f(x)=1ˣ
n,m∈N then f (n/m) = 1ⁿ/ᵐ= m√1ⁿ = 1
In fact, for any real number x , 1ˣ = 1, f(x)=1ˣ is a constant function f(x) = 1. For this reason, we usually don't talk much about exponential functions with base equal to 1.
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What are the 4 types of linear functions?.
Answer: direct variation, slope-intercept form, standard form and point-slope form.
Step-by-step explanation:
What are the types of linear functions?
There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
What are basic linear functions?
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
levels of calcium in the blood are tightly regulated. click to select the physiological responses that occur in response to low blood levels of calcium.
The physiological responses that occur in response to low blood levels of calcium are bones release calcium into the blood, the kidneys retain more calcium, intestines absorb more calcium
Calcium is a chemical element which plays an important role in building and maintaining strong bones. It also plays other significant roles in blood clotting, muscles contraction, and normal heart rhythms regulation, and nerve functions. Calcium ions are essential in several cellular processes and the body tightly regulates calcium levels within a narrow physiological range as relatively small changes can have dramatic effects, including heart failure, muscle and brain dysfunction, and even death. Blood calcium levels are regulated by parathyroid hormone (PTH), produced by the parathyroid glands. PTH is released in response to low blood calcium levels and improves calcium levels by targeting the skeleton, the kidneys, and the intestine. The physiological responses that occur in response to low blood levels of calcium are bones release calcium into the blood, the kidneys retain more calcium, intestines absorb more calcium
Note: The question is incomplete as it is missing options which are a) liver releases calcium into the blood. b) bones release calcium into the blood. c) kidneys retain more calcium. d) intestines absorb more calcium.
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If $2x-y=7,$ what is the value of $7-8x+4y$?
Answer:
[tex]7-8x+4y=-21[/tex]
Step-by-step explanation:
[tex]2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21[/tex]
se strong induction to show that every natural number can be expressed as the sum of distinct powers of 2. (for exam- ple, 21
It is proved that every natural number can be expressed as the sum of distinct powers of 2 using strong induction.
What is natural number?Natural numbers are those in mathematics that are utilized for counting and ordering. Cardinal numbers are those used for counting, while ordinal numbers are those used for ranking. The positive integers, also referred to as non-negative integers, are a subset of the natural numbers. A few examples are 1, 2, 3, 4, 5, 6,.... In other words, the set of all whole numbers other than 0 (i.e., 23, 56, 78, 999, 100202, etc.) is known as the natural numbers.
Here,
The statement is obviously true for n=0.
Assume that we are given an n≥1 and that it is true for all m with 0≤m<n.
When n=2^m then m<n and therefore m=∑k2^pk with finitely many pk, all of them different. It follows that n=∑2^(pk+1) with all pk+1 different.
When n=2^(m+1) with an m as before then n=2^0+∑k2^(pk+1) with all pk+1 different and different from 0.
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the sum of independent normally distributed random variables is normally distributed with mean equal to the sum of the individual means and variance equal to the sum of the individual variances. if x is the sum of three independent normally distributed random variables with respective means 100, 150, and 200 and respective standard deviations 15, 20, and 25, the probability that x is between 420 and 460 is closest to which of the following?
The probability that x is between 420 and 460 is 0.25778
The sum of independent normally distributed random variables is normally distributed with mean equal to the sum of the individual means and variance equal to the sum of the individual variances.
so, the mean would be,
μ = 100 + 150 + 200
μ = 450
and standard deviation would be,
σ = 15+ 20 + 25
σ = 60
We need to find the probability that x is between 420 and 460.
P(420 < x < 460)
= P( 420 - μ < x - μ < 460 - μ)
= P((420 - μ)/σ < (x - μ)/σ < (460 - μ)/σ)
= P((420 - 450)/60 < Z < (460 - 450)/60)
= P (-1/2 < Z < 1/6)
= P(-0.5<x<0.167)
= 0.25778
Therefore, the probability is P(420 < x < 460) = 0.25778
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Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below. 16,14,14, 21,15 Find the mean boxes sold. Provide your answer below
The mean boxes that were sold is 16 when Alice wants to know the average number of candy boxes she sells at the baseball game.
Given that,
Alice wants to know the average number of candy boxes she sells at the baseball game. Below is a list of the scores from the games so far. 16,14,14, 21,15.
We have to find the mean boxes that were sold.
We know that,
The mean of the number is
16,14,14, 21,15
Mean = 16+14+14+21+15/5
Mean = 80/15
Mean=16
Therefore, The mean boxes that were sold is 16 when Alice wants to know the average number of candy boxes she sells at the baseball game.
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I'm having trouble finding 2 quare root to etimate 10. Can omeone pleae help me? Thank you
As per the question, for finding the 2 square root to estimate 10 will come out to be as [tex]\sqrt{10} = 3.162[/tex]
In order to find [tex]\sqrt{10}[/tex], pick a perfect square less than 10 and another perfect square greater than 10. [tex]\sqrt{9}[/tex] = 3. [tex]\sqrt{16}[/tex] = 4, so. [tex]\sqrt{10}[/tex] is therefore far closer to [tex]\sqrt{9}[/tex] than the projected number. The outcome of multiplying an integer by itself is referred to as the number's square root. The square root of a number can be found by looking for a number that, when squared, yields the original value. The square value of a number is acquired by multiplying it by itself. The square root of a number x is a number y such that [tex]y^{2}[/tex] = x or a number y whose square is x.
To learn more about square root: https://brainly.com/question/3617398
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