A cylinder-shaped sediment tank at a wastewater treatment plant has a diameter of 80 ft. If the liquid inside the tank is 25 ft deep, how many ft of wastewater will the tank hold?

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.

The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.

To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.

Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)

So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.

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Answer:

Length = Width * 3

Width = 2 ft

Length = 2 ft * 3 = 6 ft

Perimeter = (L * 2) + (W * 2)

P = 16 ft

Area = L * W = 12 square feet

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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The upper control limit (UCL) at a 99% confidence interval with a z value of 3 is 0.165.(option c)

In statistical process control, the UCL is a key parameter used to determine the upper boundary for acceptable variation in a process. To calculate the UCL for a defect rate, we use the formula UCL = p' + z * sqrt(p'(1-p')/n), where p' is the proportion of defects in the sample, z is the z value corresponding to the desired confidence level, and n is the sample size.

In this case, we have collected 20 samples of 100 items each, and the total number of defective items is 75. Therefore, the proportion of defects in the sample is 75/2000 = 0.0375. Using the formula mentioned earlier, with a z value of 3 and n value of 100, we can calculate the UCL as follows: UCL = 0.0375 + 3 * sqrt(0.0375 * (1-0.0375)/100) ≈ 0.165.

Therefore, the correct answer is C. 0.165.

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Answer:

\(y = - 4x - 42\)

Step-by-step explanation:

The equation of the line that is parallel to the line we are trying to find is

\( - 3y + 4x = 9 \\ or \\ - 3y = - 4x + 9 \:(standard form) \\ \\therefore \: the \: slope \: of \: the \: line \\ \: is \: - 4\)

We can recall that when two lines are parallel it means that they have the same slope. Therefore the slope of the line we are trying to find is also -4. We now know that:

\(y = 6 \: \: \: x = - 12 \: \: \: slope = - 4\)

Therefore the equation of the line is:

\(y = mx + c \\ 6= ( - 4)( - 12) + c \\ 6 = 48 + c \\ 6 - 48 = c \\ - 42 = c\)

\(y = mx + c \\ y = - 4x - 42\)

Answer:

$74.34

Step-by-step explanation:

Because $63 + 18% = $74.34

Answer:

57°,123°,57°,123°

Step-by-step explanation:

as vertical angles are equal

so one angle=114/2=57°

other angle=180-57=123°

Answer:

pic pls

Step-by-step explanation:

The general solution of the given differential equation dy/dt = -ty + 3, where lower case c represents a constant, is y = (3 ± C\(e^{(-t)}\))/t

To find the general solution of the given differential equation dy/dt = -ty + 3, we can use the method of separation of variables.

Let's start by separating the variables:

dy/(-ty + 3) = dt

Now, let's integrate both sides with respect to their respective variables:

∫(1/(-ty + 3)) dy = ∫dt

To integrate the left side, we can use a substitution. Let u = -ty + 3, then du = -tdy, and the integral becomes:

-∫(1/u) du = ∫dt

-ln|u| = t + C1

-ln|(-ty + 3)| = t + C1

To remove the absolute value, we can rewrite the equation as:

-ty + 3 = ±\(e^{(-t - C1)}\)

Now, let's solve for y:

y = (3 ± \(e^{(-t - C1)}\))/t

We can simplify the expression further by combining the constants:

y = (3 ± C\(e^{(-t)}\))/t

Where C = ±\(e^{(-C1)}\) is the constant of integration. Therefore, the general solution of the given differential equation is:

y = (3 ± C\(e^{(-t)}\))/t

Here, the lower case c is represented by the constant C.

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The area around the given curve according to the green theorem is \(F. dr = 0\).

According to the statement

we have to find the area enclosed by the simple closed curve that encloses the origin.

So, We know that the

The given equation is

\(f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }\)

and

If function is in form of,

\(F = Pi + Qj\)

and C is any positively oriented simple closed curve that encloses the origin.

Then,by use of Green's theorem

Do the partial differentiation of the given function

Then

\(\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}\)

and

\(\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}\)

On substitution in Green's theorem,

We get the value

\(F. dr = 0\)

From this it is clear that the area around the given curve is zero.

So, The area around the given curve according to the green theorem is \(F. dr = 0\).

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The total weight of the barricade as a function of x.

W = 70 + 30x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Each box weighs 30 kilograms.

The table with 8 boxes on top weighs a total of 310 kilograms.

Weight of the table.

= 310 - 30 x 8

= 310 - 240

= 70 kg

Now,

The total weight of the barricade as a function of x.

W = 70 + 30x

Thus,

W = 70 + 30x

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Answer: table 2

Step-by-step explanation:

its because the rest of the tables do not have a pattern that ‘makes sense’ unlike table 2. for table 2, for every one 1 km there’s 10$

In the given problem, we need to determine the linear independence of the vectors (2 + x, e*) and the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)}. To show that (2 + x, e*) is linearly independent, we need to demonstrate that the only solution to the equation a(2 + x) + be* = 0 is a = b = 0. For the set S, we can determine linear dependence by checking if there exist scalars a, b, and c, not all zero, such that a(1,0,1,0) + b(0,2,0,2) + c(2,6,2,6) = 0.

To show that (2 + x, e*) is linearly independent, we assume that a(2 + x) + be* = 0 for some scalars a and b. Expanding this equation, we get 2a + ax + be* = 0. Since e* is a nonzero vector, the only way for this equation to hold is if a = b = 0. Thus, (2 + x, e*) is linearly independent.

For the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)}, we can determine linear dependence by checking if there exist scalars a, b, and c, not all zero, such that a(1,0,1,0) + b(0,2,0,2) + c(2,6,2,6) = 0. By performing the vector addition and scalar multiplication, we get (a + 2c, 2b + 6c, a + 2c, 2b + 6c) = (0, 0, 0, 0).

To determine if this equation has nontrivial solutions, we can set up a system of equations:

a + 2c = 0,

2b + 6c = 0,

a + 2c = 0,

2b + 6c = 0.

Simplifying these equations, we find that a = -2c and b = -3c. Since c can take any non-zero value, we have infinitely many solutions that satisfy the equation. Therefore, the set S is linearly dependent.

In conclusion, (2 + x, e*) is linearly independent, while the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)} is linearly dependent.

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Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer:

The correct option is;

LeftAngleBracket negative 16, 14 RightAngleBracket which is \(\left \langle -16, 14 \right \rangle\)

Step-by-step explanation:

The given coordinates of the points are;

The starting point, Q(23, 48) and the final point, R(7, 62)

Therefore, we have;

The x component = The x-value of R - The x-value of R = 7 - 23 = -16

The y component = The y-value of R - The y-value of R = 62 - 48 = 14

Therefore, the component form of the vector QR = \(\left \langle -16, 14 \right \rangle\)

Answer:

B on Edg.

Step-by-step explanation:

Yay

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

i got 45 but I'm not sure

Step-by-step explanation:

so if he is saving up fot the skate board,

you would need to multiply 40 × 3 that will give you 120, then after that I subtracted 85 from 120 and got 45 but like I said I'm not so sure

The required function be  y = 5000 - 250x.

Given that,

Amount of saving = $5000

Amount of withdraw and spend = $250

Number of months = x

If the total money in Ken's savings account after x number of months is represented by y,

Then, to calculate the entire amount in his savings account after x number of months, the program deducts 250x from the beginning amount of $5000.

Therefore, The function be,

y = 5000 - 250x

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Answer:

105.6 ft

Step-by-step explanation:

1 acre = 43,560 ft²

2/3(43,560) = 29,040

x = width of the lot

Area = (275 ft)(x) = 29,040 ft²

x = 29040/275 = 105.6 ft

9h is the correct answer I believe.

The formula for volume of a cube is Length × Width × Height

3 × 3 × h = 9h

Volume is cubed not squared, so I would choose 9h.

To find the Jacobian of the transformation, we need to calculate the partial derivatives of the new variables (x and y) with respect to the original variables (u and v). The Jacobian matrix is given by:

J = [ ∂x/∂u ∂x/∂v ]

[ ∂y/∂u ∂y/∂v ]

Let's calculate the partial derivatives:

∂x/∂u = 2 (since x = 2u)

∂x/∂v = 3v (since x = 3uv)

∂y/∂u = 0 (since y does not contain u)

∂y/∂v = 3u (since y = 3uv)

Therefore, the Jacobian matrix is:

J = [ 2 3v ]

[ 0 3u ]

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a. Annual interest on ABC 128; XYZ 17 = 12.8%, 1.7%

b. ABC 7.5; XYZ 8.4 = 7.5%, 8.4%

c. ABC 104 Three-fourths; XYZ 100 One-half = 10.475%, 10.05%

d. ABC 7 One-half; XYZ 7 Three-fourths = 7.5%, 7.75%

Given the bond listings for possible investments, we can calculate the annual interest earned on each bond. The bond listings indicate the percentage of interest paid per year for every $1,000 invested.

Let's find the annual interest for each bond:

a. ABC 128; XYZ 17

The annual interest for ABC = 128/1000 * 100% = 12.8%

The annual interest for XYZ = 17/1000 * 100% = 1.7%

b. ABC 7.5; XYZ 8.4

The annual interest for ABC = 7.5/100 * 100% = 7.5%

The annual interest for XYZ = 8.4/100 * 100% = 8.4%

c. ABC 104 Three-fourths; XYZ 100 One-half

The annual interest for ABC = 104.75/1000 * 100% = 10.475%

The annual interest for XYZ = 100.5/1000 * 100% = 10.05%

d. ABC 7 One-half; XYZ 7 Three-fourths

The annual interest for ABC = 7.5/100 * 100% = 7.5%

The annual interest for XYZ = 7.75/100 * 100% = 7.75%

Therefore, the annual interest on each bond is as follows:

a. ABC 128; XYZ 17 = 12.8%, 1.7%

b. ABC 7.5; XYZ 8.4 = 7.5%, 8.4%

c. ABC 104 Three-fourths; XYZ 100 One-half = 10.475%, 10.05%

d. ABC 7 One-half; XYZ 7 Three-fourths = 7.5%, 7.75%

So, the annual interest you would earn on each bond is:

a. ABC 128; XYZ 17 = 12.8%, 1.7%

b. ABC 7.5; XYZ 8.4 = 7.5%, 8.4%

c. ABC 104 Three-fourths; XYZ 100 One-half = 10.475%, 10.05%

d. ABC 7 One-half; XYZ 7 Three-fourths = 7.5%, 7.75%

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Answer:

Exam??

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Function A) Rate of change is 6 because it represents 'm' from mx (6x).

Function B) Rate of change is 5 because there is an increase of 5 as it moves to the right.

Answer:

Hey there!

The domain is the range of all the x values.

So for this graph, the domain would be \(-10<x\leq 8\).

Note that the open circle means < or > and the closed circle means ≤ or ≥.

Let me know if this helps :)

The completed table would look like this

Mass (kg)       12       24        36      48      60

Percentage   20%    40%   60%   80%   100%

The double number line represents Henrik's mass, which is 60 kg. The second tick mark on the Mass line corresponds to this value. The Percentage line ranges from 0% to 100%, representing the percentage of Henrik's mass. To complete the table, we need to calculate the different percentages.

To find a certain percentage of Henrik's mass, we locate the corresponding point on the Percentage line and draw a vertical line to intersect the Mass line. We can then read the mass value at that intersection point.

For example, to find 20% of Henrik's mass, we locate the point on the Percentage line labeled "20%." Drawing a vertical line from this point, it intersects the Mass line at a value of 12 kg. Therefore, 20% of Henrik's mass is 12 kg.

Similarly, for 40% of Henrik's mass, the vertical line intersects the Mass line at a value of 24 kg.

In summary, the completed table  would look like this

Mass (kg)       12       24        36      48      60

Percentage   20%    40%   60%   80%   100%

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Answer:

  4

Step-by-step explanation:

You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.

The leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.

The least significant digit of 0.014 is 4. The leaf unit is 4.

<95141404393>

Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Answer:

\(\frac{9}{16}\)

Step-by-step explanation:

\((\frac{1}{2} )^2+2*\frac{1}{2}*\frac{1}{4}+(\frac{1}{4})^2\)

\(\frac{1}{4}+1*\frac{1}{4}+\frac{1}{16}\)

\(\frac{1}{4}+\frac{1}{4}+\frac{1}{16}\)

\(\frac{2}{4}+\frac{1}{16}\)

\(\frac{8}{16}+\frac{1}{16}\)

\(\frac{9}{16}\)

Hope this helps!