The standard deviation is the positive square root of the sample variance.
Describe Standard Deviation?Standard deviation is a measure of the spread or dispersion of a set of data from its mean (average) value. It tells us how much the individual values in a dataset deviate from the average value. In other words, it indicates the extent to which the data points are spread out or clustered around the mean.
The formula for standard deviation is the square root of the variance, which is calculated by finding the average of the squared differences between each data point and the mean. The standard deviation is expressed in the same units as the original data and is denoted by the symbol "σ" for the population standard deviation or "s" for the sample standard deviation.
A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are spread out over a wider range. The standard deviation can be used to determine the range of values within which the majority of the data points lie. For example, if the standard deviation is 2, then about 68% of the data points will be within 2 standard deviations of the mean.
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HELP NEEDED!! need this solved
If A, B, and C are nxn invertible matrices, does the equation C^-1(A+X)B^-1=In have a solution, X? if so, find it
If A, B, and C are nxn invertible matrices, the equation C^-1(A+X)B^-1=I(n) has a solution which is X=CB-A. Since invertible matrices are those whose inverse matrix exists.
For A to be the matrix here A⁻¹ is the inverse of it, so AA⁻¹=I, here I is the identity matrix ,since the matrix equation given to us is: C⁻¹(A+X)B⁻¹=In, now multiplying B on the right side and C on the left side we get :CC⁻¹(A+X)B⁻¹B=CIₙB
=>Iₙ(A+X)Iₙ=CIₙB
=>A+X=CB, according to the property of the identity matrix.Now adding -A on both sides we get,
=>A+X+(-A)=CB+(-A)
=>X=CB-A, so here the solution for the given matrix equation is: X=CB-A
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The weight of an organ in adult males has aâ bell-shaped distribution with a mean of 330 grams and a standard deviation of 15 grams. Use the empirical rule to determine the following. â(a) About 68â% of organs will be between whatâ weights? â(b) What percentage of organs weighs between 285 grams and 375 âgrams? â(c) What percentage of organs weighs less than 285 grams or more than 375 âgrams? â(d) What percentage of organs weighs between 300 grams and 375 âgr
The empirical rule states that in a normal distribution, 68% of the observations lie within 1 standard deviation from the mean, 95% of the observations lie within 2 standard deviations from the mean, and , 99.7% of the observations lie within 3 standard deviations from the mean.
a) - Mean = U = 330 grams
standard deviation= [tex]\sigma=40 \: grams[/tex]
As per the empirical rule, 68% of the observations lie within 1 standard deviation from the mean.
Let [tex]X_1[/tex] and [tex]X_2[/tex] be the 2 random value, between which 68% of the observations lie.
Mathematically,
[tex]X1=U-\sigma[/tex]
[tex]X1[/tex] = 330 - 40
[tex]X1[/tex] = 290
Similarly,
[tex]X1=U-\sigma[/tex]
[tex]X1[/tex] = 330 + 40
[tex]X1[/tex] = 370
Thus, about 68 % of organs will be between 290 and 370 grams in weight.
b) - In this, we need to find the percentage of organs weighing between 250 grams and 410 grams.
We can rewrite 250 as follows:
250= 330− 80 ⇒ 30−2(40) ⇒ 330−2(σ)
The above value (250) lies within 2 standard deviations from the mean.
Similarly,
We can rewrite 410 as follows:
410 = 330+80 ⇒ 330+2(40) ⇒ 330+2(σ)
The above value (410) lies within 2 standard deviations from the mean.\
As per the empirical rule, 95% of the observations lie within 2 standard deviations from the mean.
Thus, 95% of organs weighs between 250 grams and 410 grams.
c)-As we have calculated in part(b) that 95% of the organs lie within 250 and 410 grams.
So, area outside these values = Total area under curve - 95%
= 100 - 95 ⇒ 5%
So, 5% of the area lies outside the 250 and 410 grams range.
From the property of normal curve, we know that the area under the curve is divided into 2 equal parts.So, we divide the area- 5% into 2 equal parts which gives 2.5%.
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25. The circle has a radius of 7. Angle C
intercepts the arc with a length of 28.
What is the measure of angle C in radians?
The measure of angle C in radians is 3.6 radians.
What is arc length of circle formula?The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.
Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.
We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr
28π= θ/360×2π×7
4= θ/360×7
θ=1440/7
θ=205.7
θ=3.6 radians
Therefore, the measure of angle C in radians is 3.6 radians.
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How do i get desmos to show both square roots?
To get Desmos to show both square roots, you can use the formula y = √x + √(-x). Desmos can then graph this equation, showing both the positive and negative square roots.
To get Desmos to show both square roots, you can use the formula y = √x + √(-x).This formula can be used to graph two square roots. The first square root is √x, which is the positive square root of x. The second square root is √(-x), which is the negative square root of x. To calculate the roots, you would take the square root of both x and -x. For example, if x is 4, the two roots would be √4 = 2 and √(-4) = 2i, where i is the imaginary unit. Desmos can then graph this equation, showing both the positive and negative square roots.
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Solve the following problem: "Justin's car insurance has a $750 deductible per incident. This means that Justin pays $750 toward a claim, and his insurance pays all costs beyond $750. If Justin files a claim for $2100, how much will he pay, and how much will his insurance company pay?"
Answer:
$1350.
Step-by-step explanation:
If Justin files a claim for $2100, he will pay the first $750 toward the claim, and his insurance company will pay the remaining costs.
So, Justin will pay $750.
And, the insurance company will pay $2100 - $750 = $1350.
One hundred people were asked about their favorite sport. Part A Complete the two-way frequency table. 19 29 40 60 Males Females Total Soccer 31 50 Basketball 21 50 Total 100 Part B Which of the following statements is true? Select all that apply. A. More males were surveyed than females. B. More females like soccer. C. An equal number of people like soccer and basketball. D. Twice as many females than males like basketball.
The statement which is true is more males were surveyed than females, the correct option is A.
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n
List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of X_i and Y_j (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
We are given that;
Males Females Total
Soccer | 31 | 50 | 81
Basketball | 21 | 50 | 71
Total | 52 | 100 | 152
Now,
A. More males were surveyed than females.
True. From the table, we can see that 52 males were surveyed, while only 100 females were surveyed.
B. More females like soccer.
False. From the table, we can see that 31 males and 50 females like soccer, so a total of 81 people like soccer. This is the same as the number of females surveyed, so we cannot say that more females like soccer.
C. An equal number of people like soccer and basketball.
False. From the table, we can see that 81 people like soccer, while 71 people like basketball.
D. Twice as many females than males like basketball.
False. From the table, we can see that 21 males and 50 females like basketball. Twice the number of females who like basketball is 100, which is the total number of females surveyed, but this is not twice the number of males who like basketball.
Therefore, by the two-way table the answer will be more males were surveyed than females.
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30% of 750 using a table
what is 2t + 5 = 2t +5?
Answer: 0 or No answer
Step-by-step explanation:
2t-2t is 0 so there is no t and 5-5 is 0 so theres no number.
8. Fill in the missing statements and reasons to complete the following proof
The completed two-column table used to prove that the quadrilateral WXYZ is a parallelogram is presented as follows;
Statement [tex]{}[/tex] Reason
1. m∠y = 49, m∠z = 131°, m∠w = 49 [tex]{}[/tex] Given
2. m∠y + m∠z + m∠w + m∠x = 360 [tex]{}[/tex] 1. ∠ sum property of a quadrilateral
3. 49 + 131 + 49 + m∠x = 360[tex]{}[/tex] Substitution Property of Equality
4. 229 + m∠x = 360 [tex]{}[/tex] 2. Summation of values
5. m∠x = 131 3. Subtraction Property of Equality
6. ∠x ≅ ∠z and ∠w ≅ ∠y [tex]{}[/tex] Angles with equal measures are ≅
7. WXYZ is a parallelogram 4. The opposite ∠s of a ║ are ≅
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel facing sides.
The details of the reasons used in the two-column table method to prove that the quadrilateral WXYZ is parallelogram are illustrated as follows;
∠ sum property of a quadrilateral
The angle (∠) sum property of a quadrilateral, indicates that the addition of the four interior angles of a quadrilateral has a result of 360°
Summation of a set of values
The sum of the values 49 + 131 + 49 is 229
Subtraction Property of Equality
The subtraction property of equality states that the subtraction of the same amount from both sides of an equation produces two new quantities or expressions on both sides of the equation that remain equivalent.
Angles with the same measures are ≅
Angles that are congruent, ≅, are angles that have the same measure
The opposite angles of a ║ are ≅
The angles located in the facing corners of a parallelogram, ║, are congruent.
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How do you find the Laplace inverse on a calculator?
Answer:
Step-by-step explanation:
The Laplace inverse is not a standard function on most calculators. However, if you have a graphing calculator that supports Laplace transforms, you can use it to find the Laplace inverse by performing the inverse Laplace transform on a function.
Here's the general procedure for finding the Laplace inverse on a graphing calculator:
Enter the Laplace transform of the function you want to find the inverse of.
Select the inverse Laplace transform function from the calculator's menu.
Enter the desired complex variable, usually represented by "s" in Laplace transform notation.
The calculator will return the inverse Laplace transform of the function, which represents the original function in the time domain.
Note: The exact steps for finding the Laplace inverse on a graphing calculator will vary depending on the model and brand of the calculator. It's best to consult the manual or a reference guide for your specific calculator to determine how to perform the inverse Laplace transform.
10 pnt sooo come help me please 2+(-2)
5x+1=2x+10 (Please include the steps)
Answer:
x = 3
Step-by-step explanation:
5x + 1 = 2x + 10
1.) Subtract 2x from both sides to get 2x on the other side
5x - 2x + 1 = 10
2.) Subtract 1 from both sides to get 1 to the other side
5x - 2x = 10 - 1
3.) Combine like terms
3x = 9
4.) Divide 3 on each side to get x by itself
x = 3
Kelly’s taxable income is $110,000. Approximately what percent of her taxable income is her tax?
Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.
What is taxable income?The term "taxable income" describes the basis on which an income tax system levies tax. In other words, the amount of income that was taxed by the government.
In most cases, it covers some or all sources of income and is then diminished by costs and other deductions. Every gross income received and utilized to determine your tax liability is referred to as taxable income.
It can be stated simply as your adjusted gross income less any deductions. This covers all pay, gratuities, salaries, and bonuses received from employers. Investments and ill-gotten gains are also mentioned.
The given taxable income is over $43,650. So use the information on line 3 to determine the tax.
Tax =$5,975+25% of the amount over 43,650
=5,975+0.25(110,000 - 43,650)
=5.975+16587.50
=22,562.50
Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.
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a man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship .he returns by the same means he has 6 airlines and 4 shipping lines to choose from .in how many ways can he make his journey without using the same airline or shipping line
There will be 360 different ways without using the same airline or shipping line.
What is a combination?A combination in mathematics is a selection of items from a set with distinct members, where the order of selection is irrelevant.
Let's first consider the number of ways the man can choose his outbound journey. He has 6 airlines to choose from, and once he has made his choice of airline, he has 4 shipping lines to choose from.
Therefore, there are 6 × 4 = 24 ways he can choose his outbound journey.
For his return journey, he cannot use the same airline or shipping line that he used for his outbound journey.
This means he now has 5 airlines and 3 shipping lines to choose from. Therefore, there are 5 × 3 = 15 ways he can choose his return journey.
The total number of ways he can make his journey is:
24 × 15 = 360
Therefore, he can make his journey in 360 different ways without using the same airline or shipping line.
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To catch up to Group B, Group Aw
4) Group A: y = 3x
Group B: y = 2x + 1
Graph the equation y = 3x.
The graph of the equation is added as an attachment
How to determine the graph of the equationFrom the question, we have the following parameters that can be used in our computation:
y = 3x
The above expression is a linear equation
A linear equation is represented as
y = mx + c
Where
Slope = m and y-intercept = c
This means that
y = 3x has a slope of 3 and a y-intercept of 0
Next, we plot the graph
See attachment for the graph of the equation
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Write a function that models y in terms of x. Round any coefficients to the nearest tenth. x 0 5 10 15 20
y 0 4.02 5.69 6.97 8.05
The function that models y in terms of x is y=0.804x
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
m=4.02-0/5-0
m=4.02/5 = 0.804
Now let us find y intercept
0=0.804(0)+b
b=0
Hence, the function that models y in terms of x is y=0.804x
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Ms. Liu has a cylinder container measuring 12 cm tall and 6 cm across. The height of Jeff's container is twice Ms. Liu's but the width is 1/3 of Miss Liu's container. Julie's cylinder container has the same width as Miss Liu but it has twice the height of Miss Lui's container. Who has the largest container and who has the smallest container?
The person with the largest container is Julie and the person with the smallest container is Jeff.
Who has the largest container and the smallest container?The volume of each container has to be determined.
Volume of a cylinder = πr²h
Where:
π = 3.14r = radius = diameter / 2 h = heightVolume of Ms. Liu's container:
r = 6/2 = 3h = 123.14 x 3² x 12 = 339.12 in³
Volume of Ms. Julie's container:
h = 12 x 2 = 24 r = 6/2 = 3Volume = 3.14 x 3² x 24 = 678.24 in³
Volume of Jeff's container:
h = 2 x 12 = 24 d = 1/3 x 6 = 2 r = 2/2 = 1Volume = 3.14 x 1² x 24 = 75.36 in³
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Solve Another Problem
7. You want to survey the people at the local pool about the food
served in the snack shack. You decide to walk around the kiddy
pool and survey parents. Is this a random sample? Why or why not?
In the research effort where a researcher want to survey the people at the local pool about the food served in the snack shack by deciding to walk around the kiddy pool and survey parents, this is an example of random sample because every parent in the pool have equal chance of being chosen for the study.
What does a random sample mean at first?A random sample is drawn at random from the entire population to represent the entire data set, with each member having an equal chance of being chosen. Researchers can generate a random sample by employing techniques such as lotteries or random draws.
Because the data set is chosen using random selection, every member of the population has an equal chance of being chosen.
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everyone please help me show ur solutions
Step-by-step explanation:
FCP fundamental counting principle :
in total there are
3×3×2 = 18
different combinations
listing method means listing all different triplets of such outfit combinations.
white shirt = ws
red blouse = rb
floral shirt = fs
short = sh
jeans = j
jogger pants = jp
shoes = s
sandals = sa
{
(ws, sh, s),
(ws, sh, sa),
(ws, j, s),
(ws, j, sa),
(ws, jp, s),
(ws, jp, sa),
(rb, sh, s),
(rb, sh, sa),
(rb, j, s),
(rb, j, sa),
(rb, jp, s),
(rb, jp, sa),
(fs, sh, s),
(fs, sh, sa),
(fs, j, s),
(fs, j, sa),
(fs, jp, s),
(fs, jp, sa)
}
tree diagram (I cannot draw here) :
OOTD
/ | \
ws rb fs
/ | \ / | \ / | \
sh j jp sh j jp sh j jp
/ | / | / | / | / \ / | / | / | / |
s sa s sa s sa s sa s sa s sa s sa s sa s sa
as you can see, we get a expected 18 different triplets in our listed set, and we get 18 different end leaves in and therefore 3-level paths through our tree.
What is the value of R for the following sequence
2, 10, 50, 250, 1250…
The next value R in the sequence is 6250.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
2, 10, 50, 250, 1250, R
Now,
We see that the next number in the sequence is a multiple of 5 of the previous number.
i.e
2 x 5 = 10
10 x 5 = 50
50 x 5 = 250
250 x 5 = 1250
So,
R = 1250 x 5
R = 6250
Thus,
The next value R in the sequence is 6250.
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Find the asymptotes, domain and range.
For the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given function is
[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]
The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.
The horizontal asymptote of the function is when x tends to ∞ .
[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]
The horizontal asymptote of function is at y = -5/4.
Since at x = -5/4, the function becomes undefined.
The domain is all real numbers except x = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Since the function is not defined at y = -5/4 as well, the range is also
(-∞,-5/4) ∪ (-5/4,∞) .
Therefore for the given function,
Vertical asymptote = -5/4
Horizontal asymptote = -5/4
Domain = (-∞,-5/4) ∪ (-5/4,∞)
Range = (-∞,-5/4) ∪ (-5/4,∞)
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10. Sixteen teams play in a one-game elimination
match. The winners of the first round go on to
play a second round until only one team remains
undefeated and is declared the champion.
4
a. Make a table of values for the number of
rounds and the number of teams participating.
b. What is the reasonable domain and the range
of this function? Explain.
c. Find the rate of decay.
d. Find the decay factor.
a. Here's a table of values for the number of rounds and the number of teams participating:
Round Number of Teams
1 16
2 8
3 4
4 2
5 1 (Champion)
.b. domain: [1 5]
Range: {1 16]
C. Rate of decay = 8
D. Decay factor = 0.5
How to solve for the rate of decayb. The reasonable domain of this function would be the number of rounds, and the range would be the number of teams participating in each round.
The domain would be all positive integers from 1 to the maximum number of rounds,
The range would be all positive integers from 1 to the starting number of teams (16 in this case).
c. To find the rate of decay, we can calculate the ratio of the change in the number of teams to the change in the number of rounds.
Using Round 1 to Round 2,
= (16 - 8) / (2 - 1)
= 8.
d. The decay factor is the ratio of the number of teams in a given round to the number of teams in the previous round.
Using Round 1 to Round 2, the decay factor is
= 8 / 16
= 0.5
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3/4 x ( z^3 x 4) equivalent expressions
The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
her, we have,
We have been given expression as:
3/4 x ( z^3 x 4)
To determine the equivalent expression to the given expression
3/4 x ( z^3 x 4)
⇒ 3* z^3
Here the variable z has an exponent is 3 which is positive,
Rearrange the terms of variables z in the above expression
⇒3 · z³
Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).
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Which of the following numbers is between 0.62 and 1.05?
Answer: D, 1.01
1.01 is in between 0.62 and 1.05
Answer: D-1.01
Step-by-step explanation:
Assume all intersecting sides meet at right angles.
Answer:
8 cm
Step-by-step explanation:
15 - 7 = 8
The length of the right side equals the length of the left side. The left side has a length of 15 and the part that we know for the right side is 7.
Helping in the name of Jesus.
PLEASE HELP ASAP
Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting.
Write an inequality that can be used to determine how many hours, x, Matilda will need to babysit to buy the dress.
The inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress is 40 + 9x >= 112 , here the x needs to be greater than or equal to 8 i.e. x >=8.
Given, Matilda needs at least $112 to buy a new dress.
Money she has =$40
Money she earns for each hour of babysitting = $9
Let, x be the number of hours she will work to earn the minimum amount.
Therefore, the inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress = 40 + 9x >= 112
x >=8 hour
So, The inequality that can be used to determine how many hours Matilda will need to babysit to buy the dress is 40 + 9x >= 112 . She needs to work for at least 8 hours to earn the minimum required amount.
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help help help help help help
A TYPE OF GREEN PAINT IS MADE BY MIXING 2 CUPS OF YELLOW WITH 3.5 CUPS OF BLUE FIND A MIXTURE THAT WILL MAKE THE SAME SHADE OF GREEN BUT A LARGER AMOUNT
The mixture of different shade of green that is bluer will be; ⇒ 2 cups of yellow and 4 cups of blue.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
now,
Since, A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.
Hence, The mixture of different shade of green that is bluer is find as;
Let Cups of yellow = 2
And, Cups of blue = x
So, we can formulate;
⇒ 2/x < 2/3.5
⇒ x > 3.5
So, Assume x = 4
Hence, The mixture of different shade of green that is bluer will be;
⇒ 2 cups of yellow and 4 cups of blue.
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John measured a line to be 1.7 inches long. If the actual length of the line is 1.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percent error of the measurement, to the nearest tenth of a percent, is 5.6.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
John measured a line to be 1.7 inches long.
The actual length of the line is 1.8 inches.
The amount of error = 1.8 - 1.7
The amount of error = 0.1
Let 1 - n be the required percentage of error.
Then applying the percentage formula,
1.8 x n /100 = 1.7
Applying cross multiplication,
we get,
1.8n = 170
n = 170/1.8
n = 94.4
So, 1 - n = 100 - 94.4 = 5.6
Therefore, the percentage is 5.6.
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