16 percentage of seniors will score a 31 or higher on the ACT. This can be solved using the concept of standard deviation.
What is Z-score?The Z-score provides information on how much a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score. Essentially, standard deviation is a measure of the degree of variability within a given data collection.
Given that,
SAT score is normally distributed with a mean score of μ = 1500 and the standard deviation of σ = 250,
The ACT score is also normally distributed with a mean score of μ = 21 and the standard deviation of σ = 5,
To calculate the percentage of scores above x = 21 is calculated by finding the Z score which is calculated as:
Z = (x - μ) / σ
Z = 31 - 21 / 5 = 2
now since 68% of scores is between 1 standard deviation and the shape is symmetric hence (100-68)/2 = 16% of values will be above 1 standard deviation.
Thus 16% of scores will be have score higher than 31.
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Helppppppppppppppppppppp
Answer:The answer is letter E
Step-by-step explanation:
If you divide 4/15 you get 0.2666.
If you solve all of the choices letter E is equivalent to the expression.
Solve the right triangle
lmk is anything is unclear. This would also work with cosine but it would have to be set up a little differently.
One link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm. How much plastic coating would be needed to coat the surface of the chain link? Use 3.14 for π.
The plastic coating required to cover the surface of the coating is 527.52 cm²
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr². Substitute to get V = πr²h.
Given here: The radius is 3 cm and a height 25 cm
We know the total surface area of the cylinder is
TSA=2πrh + 2π r².
=2πr(r+h)
=2×3.14×3(3+25)
=527.52 cm²
The plastic coating required to cover the surface of the coating is 527.52 cm²
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Answer:
To find the surface area of the cylinder that makes up the chain link, we need to add the area of the top and bottom circles (which are congruent) to the lateral surface area of the cylinder.
Therefore, we need approximately 527.52 square centimeters of plastic coating to coat the surface of the chain link. The closest answer choice is 471, but that is not correct. The closest answer to the actual surface area is 345.4 cm².
Step-by-step explanation:
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is 3.14.
The formula for the area of a circle is:
Area of circle = πr²
Substituting the given values, we get:
Area of top and bottom circles = 2 x π x 3²
Area of top and bottom circles = 56.52 cm² (rounded to two decimal places)
Lateral surface area = 2 x 3.14 x 3 x 25
Lateral surface area = 471 cm²
Total surface area = Area of top and bottom circles + Lateral surface area
Total surface area = 56.52 + 471
Total surface area = 527.52 cm²
When you divide 33 from a natural number (n) you get the remainder 5. What are all possible values of n? PLEASE HELP I HAVE RSM IN TWO DAYS I NEED THIS ITS MY LAST QUESTION PLS
The possible values of n are 5 and 6.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, divide 33 from a natural number (n) you get the remainder 5.
Now, 33/n =5
n=33/5
n=5.5
So, the possible values are 5 and 6
Therefore, the possible values of n are 5 and 6.
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A certain instructor asked the girls in his class to estimate his weight. Their responses were
190, 230, 105, 180, 130, 160, and 170 pounds.
a. Compute the sample mean.
b. What is the sample median?
Answer: sample mean is 166,4285714285714
and sample median is 170
Step-by-step explanation: sorry if its wrong
Answer:
Step-by-step explanation:
a. To compute the sample, mean, we add up all the weights and divide by the number of responses (in this case, 7):
(190 + 230 + 105 + 180 + 130 + 160 + 170) / 7 = 1265 / 7 ≈ 180.71
Therefore, the sample mean weight estimate is approximately 180.71 pounds.
b. To find the sample median, we need to put the responses in order from smallest to largest and then find the middle value. In this case, the ordered list of weights is:
105, 130, 160, 170, 180, 190, 230
The middle value is the average of the two values in the middle of the list, which in this case is:
(170 + 180) / 2 = 175
Therefore, the sample median weight estimate is 175 pounds.
A random sample of 130 full-grown lobsters had a mean weight of 21 ounces and a standard
deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean μ.
20 oz<μ<22 oz
O21 oz <μ< 23 oz
0 19 oz <μ< 21 oz
20 oz <μ< 23 oz
The 98% confidence interval for the population mean μ is 20 < μ < 22
How to construct a 98% confidence interval for the population mean μ.From the question, we have the following parameters that can be used in our computation:
n = 130
μ = 21
σ = 3
To construct a 98% confidence interval for the population mean μ, we can use the following formula:
μ ± (z * σ / √n)
Where
z = 2.33 i.e. the Z-score for a 98% confidence level
So, we have
21 ± (2.33 * 3 / √130)
Evaluate
21 ± 0.61
This gives
20.39 < μ < 21.61
Approximate
20 < μ < 22
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Identify the horizontal and vertical asymptotes, if any, of the given function.
f(x) = (x^2 - 16) / (-x^2 - 16)
Separate multiple answers by commas. Enter DNE if an asymptote does not exist. a) Horizontal asymptote(s): y =___?
b) Vertical asymptote(s): x=____?
The vertical asymptote of the function are 4. -4 and the horizontal asymptote is -1.
What are asymptotes?An asymptote is a line that a curve approaches but never touches. i.e., an asymptote is a line to which the graph of a function converges. When graphing functions, asymptotes are typically not required. However, when we graph them using dotted lines (imaginary lines), we have to be careful that the curve doesn't hit the asymptote. The asymptotes are therefore essentially made-up lines.
Given that, the function:
f(x) = (x² - 16) / (-x² - 16)
The horizontal asymptote of the function when both the degrees of numerator and denominator are equal is:
HA = Leading coefficient of numerator / leading coefficient of denominator
HA = 1 / -1
HA = -1
To calculate the vertical asymptote simplify the function:
f(x) = (x² - 16) / (-x² - 16)
f(x) = (x - 4) (x + 4) / (-x - 4) (-x + 4)
Equate the denominator to 0:
-x - 4 = 0, x= -4
- x + 4 = 0, x = 4
Hence, the vertical asymptotes of the function are 4. -4 and the horizontal asymptote is -1.
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Isabel will only consume chocolate bars and glasses of milk in a ratio of 3-to-1, meaning whenever she has 3 chocolate bars, she also has 1 glass of milk. 2nd attempt Isabel currently has 6 chocolate bars and 2 glasses of milk. Determine whether the bundles shown below would be equally preferred, more preferred, or less preferred than what Isabel currently has. Items (5 items) (Drag and drop into the appropriate area below) More Preferred Less Preferred Equally Preferred (9 chocolate bars, 1 glass of milk) (6 chocolate bars, 3 glasses of milk) (9 chocolate bars, 3 glasses of milk) (3 chocolate bars, 2 glasses of milk) (9 chocolate bars, 2 glasses of milk)
The ratio of chocolate bars More Preferred: (9 chocolate bars, 3 glasses of milk); Equally Preferred: (6 chocolate bars, 3 glasses of milk); Less Preferred: (3 chocolate bars, 2 glasses of milk) and (9 chocolate bars, 2 glasses of milk).
The ratio of chocolate bars to glasses of milk that Isabel consumes is 3-to-1. This means that whenever she has 3 chocolate bars, she also has 1 glass of milk. Currently, Isabel has 6 chocolate bars and 2 glasses of milk. The bundles listed above are compared to Isabel's current consumption. Out of the five bundles, the one with 9 chocolate bars and 3 glasses of milk is more preferred than what Isabel currently has because it has more of the ratio than Isabel's current consumption. The bundle with 6 chocolate bars and 3 glasses of milk is equally preferred because it holds the same ratio as Isabel's current consumption. The bundles with 3 chocolate bars and 2 glasses of milk and 9 chocolate bars and 2 glasses of milk are less preferred because they both have less of the ratio than Isabel's current consumption.
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David has a smart phone data plan that costs $30 per month that includes 6 GB of data, but will charge an extra $10 per GB over the included amount. How much would David have to pay in a month where he used 4 GB over the limit? How much would David have to pay in a month where he used went over by x x GB?
If David uses 4 GB over the limit, then he has used a total of 6 + 4 = 10 GB of data in that month. Since his plan includes 6 GB of data, he has exceeded the limit by 4 GB.
For the extra 4 GB of data, he will be charged an additional $10 per GB, so his total extra charge will be $10 x 4 = $40.
Therefore, in a month where David used 4 GB over the limit, he would have to pay $30 (the base cost of the plan) plus $40 (the extra charge for the additional data), for a total of $70.
If David went over the limit by x GB, then his total data usage for the month would be 6 + x GB. He would then be charged $10 for each GB over the limit, so his extra charge would be $10 x x.
Therefore, in a month where David went over the limit by x GB, he would have to pay $30 (the base cost of the plan) plus $10x (the extra charge for the additional data), for a total of $30 + $10x.
In 1999, a sample of a radioactive substance had a mass of 750 milligrams. Since then, the sample has decayed by 7.1% each year.
Let t be the number of years since 1999. Let y be the mass of the substance in milligrams,
Write an exponential function showing the relationship between y and t.
Answer:
Below
Step-by-step explanation:
If it decays 7.1 % ( which is .071 in decimal ) then .929 remains at the end of each year and the equation becomes
y = 750 (.929^t) where t is years since 1999 and y is mg
A hardware store spent $13,290 on print and TV advertising last year.
2
If of that amount was spent on print advertising, how much was
spent on TV advertising?
Select one:
O a. $5,316
O b. $13,290
O c. $18,606
C.
O d. $7,974
So the correct answer is $6,645, or option D. If just a portion of that sum was spent on print advertising.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. A division in mathematics is the process of dividing a specified amount into equal pieces. For example, we can split a group of 20 people into four groups of five people each, or five groups of four people each, and so on.
Here,
If half of the $13,290 was spent on print advertising, then $13,290 / 2 = $6,645 was spent on print advertising.
Therefore, $13,290 - $6,645 = $6,645 was spent on TV advertising.
So, the answer is $6,645, or option D If of that amount was spent on print advertising.
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Matias preformed an operation with 7.6 and a number. He ended up moving the decimal point in 7.6 two places to the left. Matias divided 7.6 by 10 raised to the power of
Therefore , the solution of the given problem of equation comes out to be Matias operated with the number 760.
A linear equation is precisely what?A straightforward regression graph is created using the equation y=mx+b. B is the slope, and m is the y-intercept. Even though the portion before it consists of separate sections, it is frequently described as just a "simple algorithm combining many variables". Two factors make up bivariate linear equations. There are no solutions known for application issues involving linear equations.
Here,
When Matias moved the decimal point in 7.6 two places to the left, he essentially divided 7.6 by 100, which is equivalent to dividing by 10 raised to the power of 2.
So, if we let x be the number Matias operated with, we can set up the equation:
x ÷ 10² = 7.6
Simplifying:
x ÷ 100 = 7.6
Multiplying both sides by 100:
x = 760
Therefore, Matias operated with the number 760.
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Determine the value of h in the equation 1/7+h=9/7
Cereal for Breakfast. A cereal company announced 80% of Americans start the day with cereal for breakfast. You believe the percentage of Americans that start the day with cereal is less. To test your claim, you randomly sample 100 Americans and ask them what they eat for breakfast. 70 of them say cereal. Test your claim that percent of Americans that start the day with cereal for breakfast is less than 80% at a 5% level of significance.
(b) Find the p-value (round to four decimal places
The null hypothesis is that the percentage of Americans who start the day with cereal for breakfast is 80%. The alternative hypothesis is that the percentage is less than 80%.
Let p be the true proportion of Americans who start the day with cereal. The sample proportion is 70/100 = 0.7. The standard error is √(p(1-p)/n) = √(0.8(0.2)/100) = 0.04.
The test statistic is (0.7 - 0.8) / 0.04 = -2.5. From the standard normal distribution table, the p-value for a one-tailed test with a test statistic of -2.5 is 0.0062.
Since the p-value (0.0062) is less than the significance level (0.05), we reject the null hypothesis. There is evidence to support the claim that the percentage of Americans who start the day with cereal for breakfast is less than 80%.
the range of temperature, t on the surface of a planet is from -150°c to 18c. translate this statement into algebraic or compound inequality.
Answer:
-150 ≤ t ≤ 18
Step-by-step explanation:
A man and his spouse are expecting a baby. Their current health insurance costs $116 per month, but doesn't cover prenatal care or delivery. They can upgrade to a policy that will cover their prenatal care and delivery, but their new premium will be $291 per month. The cost of prenatal care and delivery is approximately $3000.
The best choice for the man and his spouse is that they should upgrade to the new policy because the current policy costs $1,044 for nine months, which is significantly less than the upgrade which costs $2,619 for nine months. That is option A.
What is a health insurance?A health insurance is defined as the amount of money deducted from a salary account which is used for health care services of the individual when accumulated over time.
The man and his spouse are expectant and they believe that the money for prenatal care and delivery would be from the health insurance.
Therefore, they should upgrade to the health insurance that pays $291 per month so as to accumulate an amount such as $2,619 which is approximately $3000.
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Complete question:
Analyze the following situation and determine which decision would be the best decision to make. Explain your answer. A man and his spouse are expecting a baby. Their current health insurance costs $116 per month, but doesn't cover prenatal care or delivery. They can upgrade to a policy that will cover their prenatal care and delivery, but their new premium will be $291 per month. The cost of prenatal care and delivery is approximately $3000. Select the correct choice below and fill in any answer boxes within your choice.
O A. They should upgrade to the new policy because the current policy costs $ for nine months, which is significantly less than the upgrade which costs $ for nine months.
OB. They should keep their current policy because it costs $ for nine months, which is significantly less than the upgrade which costs $ for nine months.
Select the correct answer from the drop-down menu.
Three segments AB, AC, and AE share a common endpoint A. Point D lies on segment AB. Arc BC and arc DE is drawn. The length of arc between segments AB and AC is 1.18 radians. The length of arc between segments AE and AC is 2.36 radians.
If AD=2/3 AB , the ratio of the length of BC to the length of DE is [1/6, 1/4, 3/2, 3/4].
The ratio of the length of BC to the length of DE is 1/2.
What is Arc Length?Arc length is defined as the distance between any two points on a section of a circle or curve.
The figure in the question is given below.
The formula to find the length of an arc is given as,
Arc length, l = rθ, where r is the radius and θ is the central angle in radians.
Given that,
Central angle for arc BC, θ = 1.18 radians.
Radius for arc BC, r = AC = AB
Arc length of BC = rθ
= 1.18 (AB)
Central angle for arc DE, θ = 1.18 + 2.36 = 3.54 radians
Radius for arc DE, r = AE = AD = 2/3 AB
Arc length of DE = rθ
= 3.54 × (2/3) AB
= 2.36 (AB)
Arc length of BC / Arc length of DE = 1.18 (AB) / 2.36 (AB) = 1/2
Hence the ratio of BC to DE is 1/2.
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Answer:
DE: 3/4
Step-by-step explanation:
PlatoGang
What is the measure of QR?
Answer:
Step-by-step explanation:
The answer to the question is 15
Grandma Anni insists that corresponding lines must be congruent for figures
to be similar. Is she wrong explain
Answer:
Grandma Anni is correct, so no. One of the criteria for comparing two figures is that their corresponding lines must be congruent. Similar figures can vary in size while maintaining the same shape. They are therefore proportionate and have identical matching angles. The shapes of the figures will match if the associated lines are congruent.
Hope it helps! : )Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answer:
see below
Step-by-step explanation:
memorize this formula for cone volume:
V = 1/3 * π r²*h
so r = 18/2 =9
h = 3
solve V = 81π = 254
Answer:
254.47
Step-by-step explanation:
in the figure below, trapezoid mnrs is made up of trapezoid mnpt, triangle tpq, and parallelogram pqrs. the area of triangle tpq is 84 square feet. the lengths of np, pq, and qr are in the ratio 2: 1.5:1. find the area of trapezoid mnrs
The area of the trapezoid MNRS is 378 square feet.
What is a trapezoid?An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.
In the figure below, trapezoid MNRS is made up of trapezoid MNPT,
triangle TPQ, and parallelogram TQRS.
The area of triangle TPQ is 84 square feet.
The lengths of NP, PQ, and QR are in the ratio 2 : 1.5 : 1.
The heights of the parallel base are,
a = 18 feet and b = 16 + 12 + 8 = 36 feet.
Let h be the perpendicular height.
So,
1/2 x h x 12 = 84
h = 14 feet.
The area of the trapezoid MNRS,
= 1/2 x (36 + 18) x 14
= 378 square feet.
Hence, the area is 378 square feet.
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5. If the figure below is rotated 180° counterclockwise. What will the new coordinates of B' be?
O (-1, -3)
O (3, 1)
O (-3,1)
O (1, -3)
-10
The new coordinates of B' is (-3, 1)
What will the new coordinates of B' be?From the question, we have the following parameters that can be used in our computation:
B = (3, -1)
The figure is rotated 180° counterclockwise.
This is represented as
(x, y) = (−x,−y)
Substitute the known values in the above equation, so, we have the following representation
B' = (-3, 1)
Hence, the image poont is (-3, 1)
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Write an equation in point-slope form line with slope m=6 that passes through the point (-1,9). Without doing any calculations, what are the values of m,x[tex]x_{0}[/tex] and y_{0}[/tex] in the point slope form.
M=
x0=
y0 =
y =
Without doing any calculations, the values of m, x_{0} and y_{0} in the point-slope form include the following:
M = 6
x_{0} = -1
y_{0} = 9.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₀ = m(x - x₀)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Initial point on the x-axis, x₀ = -1.
Initial point on the y-axis, y₀ = 9.
Slope, m = 6.
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find the mean and standard deviation for each binomial random value: of n = 26, pi = .90
The mean and standard deviation for each binomial random value: of n = 26, pi = .90
Mean = 23.4
Standard Deviation = 1.53
What is mean?In one of the branches of mathematics called statistics, We use one term known as mean; it generally tells us what is the central tendency of the data set.
Generally, we use three terms for measurement of central tendency like, mean, median, mode.
In simple words, mean is an average of all the dataset.
formula;
Mean = Sum of all the dataset/Total number of dataset
Given that,
A binomial distribution with parameters,
n = 26 and p = 0.9,
the mean (expected value) of the distribution is given by:
E(X) = n x p
= 26 x 0.9
= 23.4
The standard deviation of the distribution is given by:
σ = √(n x p x (1 - p))
= √(26 x 0.9 x (1 - 0.9))
= √(26 x 0.9 x 0.1)
= √(2.34)
= 1.53
So the mean of the distribution is 23.4 and the standard deviation is 1.53.
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is the process of selecting and prioritizing innovation projects to ensure that they are consistent with a firm's strategy and development capacity.
This statement describes the process of innovation portfolio management.
What is statement?A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is another name for a statement. The main point is that there should be no uncertainty. A sentence cannot be both true and untrue in order to be a statement. A mathematical statement is made up of two components. The hypothesis or assumptions come first, followed by the conclusion. When a mathematical sentence makes a mathematically accurate statement, it is true.
Here,
This statement describes the process of innovation portfolio management. Innovation portfolio management involves evaluating and selecting innovation projects in line with an organization's goals and resources, and ensuring that these projects are aligned with the overall strategy of the firm. The aim of innovation portfolio management is to optimize the allocation of resources and maximize the return on investment in innovation.
By selecting and prioritizing innovation projects, companies can ensure that they are working on initiatives that have the greatest potential to drive growth and success, while also balancing risk and resource constraints.
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can someone tell me how to find this problem?
Step-by-step explanation:
play the video that is in the activity
Please help solve this:
Answer:
f' = cg' = ah' = bStep-by-step explanation:
Given a sawtooth, a parabola, and a logistic function, you want to identify the graphs that represent their derivatives.
SawtoothThe "zigzag" sawtooth function has constant positive slope alternating with constant negative slope. This is shown in derivative graph (c).
ParabolaThe slope of the parabola changes smoothly from positive to negative, going through zero in the middle. This is shown in derivative graph (a).
Logistic functionThe slope of the logistic curve is positive everywhere, with a higher rate of change in the middle. This is shown in derivative graph (b).
100 POINTS HELP Where might unearned income appear on a general ledger?
A. as a debit
B. as a credit
C. as a normal entry
D. as a footnote
En la A:
Step-by-step explanation:
Answer:
B. as a credit
Step-by-step explanation:
Explain/describe in your own words what happens to the graph when
k
increases.
For the graph [tex]f(x)= a(x-h)^{2}+k[/tex] The graph goes upward if k > 0, but it shifts downward if k < 0.
A quadratic function is represented in its standard form as [tex]f(x)= a(x-h)^{2}+k[/tex], where (h, k) is the vertex. This form is also referred to as the vertex form of a quadratic function because the vertex occurs in the quadratic function's standard form.
To understand how the graph differs from the graph of y = x², the standard form is helpful. This fundamental function's graph is shown in the figure below.
A constant, k, can be added to or subtracted from the graph of f(x) = x² to represent a vertical (up, down) shift.
The graph goes upward if k > 0, but it shifts downward if k < 0.
Describe graphs.Mathematicians use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects.
A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
Piecewise functions are exactly what their name implies: groups of several functions (subfunctions) on a single graph.
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A container is 90% filled with chemical solution the container holds 1490 L of chemical solution how many liters of chemical solution are needed to fill the container to the top
The amount of chemical solution needed to fill the container to the top is 165.56 L.
If the container is already 90% filled with a chemical solution, then the remaining empty space is 10% of the total volume. We can calculate the total volume of the container using the formula:
total volume = volume of solution/fraction of container filled
Plugging in the given values, we get:
total volume = 1490 / 0.9
total volume = 1655.56 L
So, the total volume of the container is 1655.56 L. To fill the container to the top, we need to add the amount of solution that fills the remaining 10% of the container. This is equivalent to:
volume of remaining space = 0.1 * 1655.56
volume of remaining space = 165.56 L
Therefore, we need to add 165.56 L of a chemical solution to fill the container to the top.
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