a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3) is 12/7.
b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1) is 3/2.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …
This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = (-12) / [1 - (4/(-3))]
Simplify the denominator by multiplying both numerator and denominator by (-3):
S = (-12) / [-3 - 4]
S = (-12) / (-7)
S = 12/7
Therefore, the exact value of the sum is 12/7.
B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)
This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:
S = a (1 - rⁿ) / (1 - r)
As n approaches infinity, rⁿ approaches zero and the sum converges to:
S = a / (1 - r)
Substituting the values of a and r, we get:
S = 1 / (1 - 1/3)
S = 3/2
Therefore, an expression that gives the exact value of the sum is 3/2.
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#1 Brainlist!
Answer and show steps and I will make you brainlist.
Answer:
Multiplying the second equation by 5, we get:
15x + 20y = 180
Now, we can add this equation to the first equation:
26x = 208
x = 8
Substituting x = 8 in the second equation:
3(8) + 4y = 36
4y = 12
y = 3
Therefore, the solution to the system is (8, 3).
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
180
Step-by-step explanation:
Form an equation
27x+17=180
Solve it for x
x = 6.0recurring
the perimeter is 180
Let me know if it helps
PLS HELP GEOMETRY 15 POINTS
polygon ABCD is similar to polygon ZYXW list the relationship between angles and sides
Answer:
Step-by-step explanation:
sorry I don't know
Help I need help fast.
The new points A', B', and C' after rotating triangle ABC 90 degrees counterclockwise about the origin and reflecting it over the x-axis are (-3,1), (0,3), and (2,4) respectively.
How rotate and reflect a point?
To rotate a point in a two-dimensional plane counterclockwise about the origin by a certain angle θ, we can use the rotation matrix. This matrix has the values of sine and cosine of the angle θ and can be used to multiply with the original point's coordinate vector to get the new coordinate vector after rotation. To reflect a point over the x-axis, we negate its y-coordinate.
Calculation the coordinates of the new points :
To rotate triangle ABC 90 degrees counterclockwise about the origin, we can use the rotation matrix:
[ cosθ -sinθ ]
[ sinθ cosθ ]
where θ is the angle of rotation, in this case 90 degrees, so we have:
[ 0 -1 ]
[ 1 0 ]
We can apply this matrix to each of the points of the triangle ABC to obtain their new coordinates after the rotation.
Then, to reflect the triangle over the x-axis, we simply negate the y-coordinate of each point.
So, to find the new points A', B', and C', we perform the following operations:
A' = (1, -3) * [ 0 -1 ] = [ (-3) (-1) ] -> reflect over x-axis -> [ (-3) 1 ]
[ 1 0 ]
B' = (3, 0) * [ 0 -1 ] = [ 0 (-3) ] -> reflect over x-axis -> [ 0 3 ]
[ 1 0 ]
C' = (4, -2) * [ 0 -1 ] = [ 2 (-4) ] -> reflect over x-axis -> [ 2 4 ]
[ 1 0 ]
Therefore, the new points are (-3,1), (0,3), (2,4).
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Determine the number of factors of the given whole number
The formula for the total number of factors for a given number is given by; Total Number of Factors for N = (a+1) (b+1) (c+1)
A veterinarian has an annual income of $128,610. The income tax the veterinarian has to pay is 8%. What is the amount of income tax in dollar and cents the veterinarian has to pay?
the veterinarian has to pay $10,288.80 in income tax. To calculate the amount of income tax that the veterinarian has to pay, we can multiply their annual income by the tax rate. In this case, the tax rate is 8%, so we can calculate the income tax as follows:
Income tax = Annual income x Tax rate
Income tax = $128,610 x 0.08
Income tax = $10,288.80
Therefore, the veterinarian has to pay $10,288.80 in income tax.
Income tax is a tax imposed on income earned by individuals or businesses. The tax rate may vary depending on the income level, the type of income, and the tax laws of the country. In this case, the tax rate is 8%, which means that the veterinarian has to pay 8% of their annual income as income tax.
It's important to note that income tax is usually paid on a regular basis, such as monthly or quarterly, throughout the year. The amount of income tax paid is based on the estimated income for the year, and at the end of the year, the actual income and tax liability are calculated, and any overpayments or underpayments are reconciled.
In conclusion, the veterinarian has to pay $10,288.80 in income tax based on their annual income of $128,610 and a tax rate of 8%.
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the length of the diagonal of a square is 12 cm what is the length of which side
The equation and graph show the distance traveled by a covertible and a limousine in miles, y, as a function of time in hours, x.
The rate of change of the distance for limousine is less than the rate of change of the convertible.
What is rate of change?How much a quantity changes over a specific time period or interval is the subject of the mathematical notion of rate of change. Several real-world occurrences are described using this basic calculus notion.
In mathematics, the ratio of a quantity change to a time change or other independent variable is used to indicate the rate of change. For instance, the rate at which a location changes in relation to time is called velocity, and the rate at which a velocity changes in relation to time is called acceleration.
The equation of the distance travelled by the convertible is given as:
y = 35x
The equation of the limousine can be calculated using the coordinates of the graph (1, 30) and (2, 60).
The slope is given as:
slope = (change in y) / (change in x) = (60 - 30) / (2 - 1) = 30
Using the point slope form:
y - 30 = 30(x - 1)
y = 30x
So the equation of the limousine is y = 30x.
Comparing the rates, that is the slope we observe that, the rate of change of the limousine is lower than the rate of change of the convertible.
Hence, the rate of change of the limousine is less than the rate of change of the convertible.
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Find three positive numbers whose sum is 270 and whose product is a maximum. (Enter your answers as a comma-separated list.)
The three positive numbers whose sum is 270 and whose product is a maximum is 67.5, 135, 67.5.
Let x, y, and z be the three positive numbers.
Write an equation relating x, y, and z based on the given constraint: x + y + z = 270.
Use algebra to solve for one of the variables in terms of the others.
Solving for z in terms of x and y: z = 270 - x - y.
Substitute the expression for z into the equation for the product of the three numbers:
P = x * y * z = x * y * (270 - x - y).
Expand the expression for P and simplify as P = 270xy - x²y - xy².
Using calculus to find the critical points of P, which occur when the derivative of P with respect to x is zero:
dP/dx = 270y - 2xy - y²= 0.
Solving for x in terms of y: x = (270y - y²)/(2y).
Simplify the expression for x as x = 135 - (y/2).
Since x and y must be positive, we know that 0 < y < 270/2 = 135.
Therefore, we can choose y = 135.
Using the equation for x in terms of y, we can find x as x = 135/2 = 67.5.
Using the constraint x + y + z = 270, we can find z as z = 67.5.
Check that x, y, and z are positive and that they add up to 270.
Therefore, the three positive numbers whose sum is 270 and whose product is a maximum are 67.5, 135, and 67.5.
The product of these three numbers is (67.5) * (135) * (67.5) = 614062.5.
So the maximum product is 614062.5.
Thus, the answer is: 67.5, 135, 67.5.
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After randomly selecting 1,009 adults and surveying each of them, 545 of them indicated that they were not comfortable with a drone delivering packages to them. The pollster concluded from the data that precisely 54 percent of all American adults are therefore not comfortable having drones make deliveries to them.
Determine whether the pollster’s conclusion makes sense. Address whether the pollster is correct in drawing this conclusion based upon the given information. In preparing your answer, include the following terms:
statistics and parameters,
estimation,
margin of error,
and any other concepts from the assigned readings and/or class sessions you deem helpful and appropriate.
Based on the information, the pollster's conclusion makes sense.
How do you know if the pollster is right with his conclusion?To know if the pollster is right with his conclusion we must perform the following operation.
1,009 / 100 = 10.0910.09 * 54 = 544.86In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.
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hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.
The steps for proof by mathematical induction that P(n) is true for all positive integers n, All options are true.
The steps for a proof by mathematical induction that P(n) is true for all positive integers n are as follows:
a. Verify that P(1) is true.
b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k.
c. Verify that P(1), P(2), P(3), ..., P(k) is all true, where k is a specific large, positive integer.
d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k.
e. Demonstrate that P(k+1) implies Plk) is true for all integers k.
Therefore, option (a), option (b), option (c), option (d), and option (e) are the steps for proof by mathematical induction that P(n) is true for all positive integers n.
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In a hostel, 50 students have food enough for 54 days. How many students should be added in the hostel so that the food is enough for only 45 days ?
We need to add 10 students to the hostel so that the food is enough for only 45 days.
How many students should be added in the hostel so that the food is enough for only 45 days? Let's assume that "x" students need to be added to the hostel so that the food is enough for only 45 days.
We know that the total amount of food available is fixed, so the product of the number of students and the number of days that the food will last must also be fixed.
We can use this fact to set up an equation:
50 × 54 = (50 + x) × 45
To solve for x, we can simplify and solve for x:
Expand using FOIL method
50 × 54 = (50 + x)45
50 × 54 = 45 × 50 + 45 × x
2700 = 2250 + 45x
450 = 45x
x = 10
Therefore, number of students to be added is 10.
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If staff salaries were $44,000/month last year and $53,000/month this year, what is the approximate labor cost Increase in percentage?
A: 3%
B: 7%
C: 10%
D: 21%
The approximate labor cost increase in percentage is approximately 21%, which is closest to option D.
To calculate the approximate labor cost increase in percentage, we can use the following formula:
Labor cost increase percentage = ((new labor cost - old labor cost) / old labor cost) x 100%
Plugging in the given values, we get:
Labor cost increase percentage = ((53,000 - 44,000) / 44,000) x 100%
Labor cost increase percentage = (9,000 / 44,000) x 100%
Labor cost increase percentage = 0.2045 x 100%
Labor cost increase percentage ≈ 20.45%
Therefore, the approximate labor cost increase in percentage is approximately 21%, which is closest to option D.
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A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 600 liters of 21% acid solution?
[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]
Each side of a sandbox is 4 feet long. It will cost $2.00 per square foot to replace the sand in the sandbox. What would be the total cost to replace the sand?
Answer:
It would cost $32.00
Step-by-step explanation:
Total square feet:
length * width
4 * 4 = 16 sq ft.
Cost per square foot: $2.00
And so...
16 sq ft. * $2.00 = $32.00
The mass of a car is 2006 kg rounded to the nearest kilogram. The mass of a person is 62.2 kg rounded to 1 decimal place.. Write the error interval for the combined mass, m, of the car and the person in the form a ≤m
The error interval for the combined mass, m, of the car and the person is: [tex]$$2067.65 kg \leq m \leq 2068.75 kg$$[/tex].
How to find error interval?The mass of the car is given as 2006 kg rounded to the nearest kilogram, which means its actual mass could be as low as 2005.5 kg or as high as 2006.5 kg.
The mass of the person is given as 62.2 kg rounded to one decimal place, which means their actual mass could be as low as 62.15 kg or as high as 62.25 kg.
To find the error interval for the combined mass of the car and the person, we need to add the upper and lower bounds of each mass:
Lower bound of combined mass: 2005.5 kg + 62.15 kg = 2067.65 kg
Upper bound of combined mass: 2006.5 kg + 62.25 kg = 2068.75 kg
Therefore, the error interval for the combined mass, m, of the car and the person is: [tex]$$2067.65 kg \leq m \leq 2068.75 kg$$[/tex].
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Answer: give proper question
Step-by-step explanation:
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
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10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ?
Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute. Let the random variable x represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet arrivals have a Poisson distribution. If we want to use the formula P(x)= μx•e−μ x! to find the probability of exactly 3 arrivals in one thousandth of a minute, what are the values of μ, x, and e that would be used in that formula?
The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a minute, are given as follows:
μ = 6000/13719.x = 3.e = 2.71828.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:
μ = 6000/13719.
The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:
x = 3.
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Help Me Find Y
Show Work
Answer:
y = 12
Step-by-step explanation:
if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is
y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )
y = [tex]\sqrt{144}[/tex] = 12
which of the following is true about the regression line? o it's an estimation of a linear relationship between dependent and independent variables by assuming the minimum error term it's just a straight line drawn through the data points between x and y axis.o it provides the actual value of a dependent variable for a given value of the independent variable(s)o it indicates a linear relationship between dependent variable and independent variable(s) o it provides the estimation of the value of a dependent variable for a given value of the independent variable(s)
The statement about regression line that is true is "it indicates a linear relationship between dependent variable and independent variable(s)."
In statistics, regression is a method of modeling the connection between a dependent variable (also known as a response variable) and one or more independent variables (also known as explanatory variables or predictors). It's also known as a linear regression model.
A regression model is established in order to identify the linear relationship between the dependent variable and one or more independent variables. The line of best fit is represented by the regression line in a simple linear regression model, which represents the relationship between the dependent variable and independent variable(s).
The line of best fit is determined by minimizing the sum of the squares of the residuals (errors). The objective of the regression model is to obtain a relationship between the dependent variable and the independent variable that explains the variance of the dependent variable based on the independent variable(s).
Hence, the correct option is: it indicates a linear relationship between dependent variable and independent variable(s).
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The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $60; if she loses, she must pay $3. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)
The expected value of X is -$1.11. This means that on average, Mary can expect to lose $1.11 per game.
The probability that Mary will not win is 0.97; hence, the probability that she will win is 0.03.
Probability:Probability is the likelihood of an event happening. It is a way of measuring the chance or the likelihood of an event occurring. Probability is measured on a scale from 0 to 1, where 0 is impossible and 1 is certain.
Probability = (number of favorable outcomes) / (total number of outcomes)
Expected value:The expected value is the sum of the products of each outcome and its probability. It represents the average value that one can expect to win from a game by placing a bet on that game.
In a game where the probability of winning is 0.03 and the probability of losing is 0.97,
Mary will win $60 if she wins and lose $3 if she loses.
Then, the expected value of X (the amount of money Mary wins or loses) can be calculated as:
E(X) = (0.03)($60) + (0.97)($-3)
E(X) = $1.80 - $2.91E(X) ⇒ $-1.11
The expected value of X is -$1.11 (a negative value).
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Mr Hall's salary increases from £25,000 to £28,000 a year. Find the percentage increase in his salary.
Answer:
Step-by-step explanation:
To find the percentage increase in Mr Hall's salary, we can use the following formula:
percentage increase = (new value - old value) / old value x 100%
Substituting the given values, we get:
percentage increase = (28000 - 25000) / 25000 x 100%
Simplifying the expression, we get:
percentage increase = 0.12 x 100%
percentage increase = 12%
Therefore, Mr Hall's salary increased by 12%.
Divide. 8 /52.08 baba boy
Answer:
To divide 8 by 52.08, we can use long division as follows:
0.15 (quotient)
__________
52.08 | 8.00
7.81 (subtract 7.81 from 8.00 to get 0.19)
----
1.19 (bring down the next digit 0, and add a decimal point)
1.04 (subtract 1.04 from 1.19 to get 0.15)
----
0.15 (no more digits to bring down, and the remainder is 0)
Therefore, 8 divided by 52.08 is approximately 0.15.
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
A sample of n = 9 basal areas, the two statistics, g1 and g2, such that the probability of the difference between the sample mean and population mean being between them is 90% are g1 = y - u - (1.64 * (s/sqrt(n))) and g2 = y - u + (1.64 * (s/sqrt(n))).
The goal of this exercise is to find two statistics, g1 and g2, such that the probability of the difference between the sample mean, y, and population mean, u, being between them is 90%. To do this, we will use the z-score equation to calculate the standard deviations, which we will then use to calculate the two statistics.
Given that we are using a sample of n = 9 basal areas, we can calculate the sample standard deviation s using the following equation: s = sqrt[ (1/8) * Σ (x - y)^2], where x is the individual sample value and y is the sample mean.
Once we have the sample standard deviation, we can calculate the two statistics using the following equations:
g1 = y - u - (1.64 * (s/sqrt(n)))
g2 = y - u + (1.64 * (s/sqrt(n)))
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the u.s. department of transportation recently reported that 81.5% of u.s. airline flights arrived on time. find the probability that among 12 randomly selected flights exactly 10 arrive on time.
The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667
How do we calculate the probability?The probability that, among 12 randomly selected flights, exactly 10 arrive on time is 0.1667. This is calculated by using the binomial probability formula:
[tex]P(x) = nCx (p^x) (1-p)^{(n-x)}[/tex]
Where:
n = 12 (number of flights)x = 10 (number of flights arriving on time)p = 0.815 (probability of one flight arriving on time)[tex]P(x) = 12C10 (0.815^{10}) (0.185)^2 = 0.1667[/tex]
The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667
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I need help please help me
Answer:
54 sq in.
Step-by-step explanation:
For a cube, try using the rectangular prism formula. (there's an easier way but I prefer this one)
2lw + 2hw + 2lh
(2 × 3 × 3) + (2 × 3 × 3) + (2 × 3 × 3)
18 + 18 + 18 + 18
SA = 54 sq in
hope i explained it (you can search up the formula for a cube but i like this one)
Tiana has a new beaded necklace. The necklace has 3 blue beads and 17 white beads. What percentage of the beads on Tiana's necklace are blue?
Therefore, 15% of the beads on Tiana's necklace are blue.
What is percentage?Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.
Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:
Percentage of girls = (number of girls / total number of students) x 100%
= (20 / 40) x 100%
= 50%
by the question.
Tiana's necklace has a total of 3 + 17 = 20 beads.
To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:
percentage of blue beads = (number of blue beads / total number of beads) x 100
percentage of blue beads = (3 / 20) x 100
percentage of blue beads = 15
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Identify three points that are solutions to
each system.
The solutions for the systems of inequalities are:
a) (0, -100), (0, -150), (0, -1000)
b) (0, 50), (0, 55) , (0, 1,204).
How to identify 3 solutions of each system?When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.
The first one is:
y ≤ x - 8
y < -3x - 9
Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:
-100 ≤ 0 - 8 = -8
-100 < - 3*0 - 9 = -9
Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.
For the second system:
y > 5x + 1
y > 3
Let's do the same thing, x = 0 and y gets really large values, like y = 50
50 > 5*0 + 1 = 1 this is true.
50 > 3 this is true.
so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).
Learn more about systems of inequalities:
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