HELP :/ At the local pet store, Bloodfin Tetra cost $1.50 each and Angelfish cost $4.75 each. If Sarah bought 8 fish for a total cost of $21.75, not including tax, how many of each type of fish did she buy?

To find the integral ∫ ∫ ∫ e z d v ∫∫∫ez dv, we first need to set up the triple integral in terms of the limits of integration. Since the solid is a tetrahedron with vertices (0,0,0), (1,0,0), (0,5,0), and (0,0,2), we can set up the limits of integration as follows:

0 ≤ x ≤ 1
0 ≤ y ≤ (5/4)x
0 ≤ z ≤ (1/2)x + (1/2)y

Note that the equation for the plane containing the three vertices (0,0,0), (1,0,0), and (0,5,0) is given by y = (5/4)x. The equation for the plane containing the three vertices (0,0,0), (1,0,0), and (0,0,2) is given by z = (1/2)x + (1/2)y.

Now we can evaluate the integral as follows:

∫∫∫ e^z dV = ∫₀¹ ∫₀^(5/4)x ∫₀^(1/2)x+(1/2)y e^z dz dy dx

Integrating with respect to z first, we get:

∫ ∫ ∫ e z d v = ∫₀¹ ∫₀^(5/4)x ∫₀^(1/2)x+(1/2)y e^z dz dy dx

= ∫₀¹ ∫₀^(5/4)x [ e^(1/2)x+(1/2)y - e^0 ] dy dx

= ∫₀¹ ∫₀^(5/4)x [ e^(1/2)x+(1/2)y - 1 ] dy dx

Integrating with respect to y next, we get:

∫∫∫ₑᶻ dv = ∫₀¹ ∫₀ˣ/₂ (e^(1/2)x+(1/2)y - 1) dy dx

= ∫₀¹ [(1/2)(e^x - 2) - x + 2] dx

Evaluating this integral, we get:

∫ ∫ ∫ e z d v ≈ 1.7971

Rounding to four decimal places, we get:

∫ ∫ ∫ e z d v ≈ 1.7971
To compute the triple integral ∫∫∫ez dv for the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,5,0), and (0,0,2), you should first set up the limits of integration. The tetrahedron can be defined as the region enclosed by the following planes:

x = 0, y = 0, z = 0, x + 5y + 2z = 10

Using these planes, you can express the limits of integration as follows:

0 ≤ x ≤ 1
0 ≤ y ≤ (1-x)/5
0 ≤ z ≤ (10-x-5y)/2

Now, you can set up and compute the triple integral:

∫(from 0 to 1) ∫(from 0 to (1-x)/5) ∫(from 0 to (10-x-5y)/2) ez dz dy dx

After evaluating the integral and rounding the result to four decimal places, you will get the volume of the tetrahedron.

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

Answer:

the answer is 200

Step-by-step explanation:

Answer:

So, the length (L) = 7 3/4 ft = 31/4 (as an improper fraction)

the width (W)  = (1/3)xL

So the width = 1/3 x (31/4) =

31/12 = 2  7/12 feet

Step-by-step explanation:

its up there

Answer:

19.90

Step-by-step explanation:

If wrong will post question and you can get points back

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The fate of the 22 checked bags can be considered the Bernoulli trials.

A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.

For a set of trials to be considered Bernoulli trials, the following conditions must be met:

In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:

Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.

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Answer:

Answer: There is 32in² more sand in the pyramid with greater volume.

step explanation:

In the situation, if you took another sample of 157 students and asked them for measurements of thumb and height, it is unlikely that you would get the exact same F ratio.

The F ratio is a statistical value that compares the variance between groups to the variance within groups. Here's why it might be different:

1. Sampling variability: Since you are taking another sample of 157 students, there is a chance that the measurements will be slightly different from the original sample. The new sample might have students with different thumb lengths and heights, which could lead to different variances and thus a different F ratio.

2. Measurement errors: Even if the actual relationship between thumb length and height remains constant, the process of measuring these variables can introduce errors. Errors in measurement can cause discrepancies in the data, leading to a different F ratio.

3. Population diversity: If the new sample is drawn from a different population, there could be differences in the relationship between thumb length and height in that population. This would also result in a different F ratio.

To summarize, while it is possible to get a similar F ratio in a new sample, it is unlikely that the F ratio would be exactly the same due to sampling variability, measurement errors, and potential population differences.

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Complete Question:

Aisha reduced the size of her square driveway. she made one side 10 feet shorter and the other side 15 feet shorter. the smaller rectangular driveway will have an area of no more than 800 square feet. write an inequality to represent the area of the smaller driveway.

Answer:

The inequality that represents the area of the smaller drive way is \(x(x-25) \leq 650\)

Step-by-step explanation:

Let the original length of the sides of Aisha's square driveway be = x

She made one side 10 ft short, i.e. (x - 10) ft

She made the other side 15 ft short, i.e. (x - 15) ft

Since the sides are no longer equal, the driveway is now a rectangle

The question states that the smaller rectangular driveway will have an area of no more than 800 square feet

Area of a rectangle = length * Breadth

Area = (x - 10)*(x - 15)

\(Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150\)

Area ≤ 800

\(x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650\)

Solving the above, x = 40.9 or -15.9

Since the length of a square cannot be negative, x = 40.9 ft

Answer:

(x-10)·(x-15)≤800

Step-by-step explanation:

imagine math

Check the picture below.

The area of the parallelogram will be 108 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The vertices of the parallelogram are (x₁, y₁), (x₂, y₂), (x₃, y₃), and ( x₄, y₄).

Then the area of the parallelogram will be calculated as below:-

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₄+x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄+y₄x₁)]|

We have

(x₁, y₁) ⇒ (-12, 2)

(x₂, y₂) ⇒ (6, 2)

(x₃, y₃) ⇒ (-2, -3)

(x₄, y₄) ⇒ (-20 , -3 )

Then the area will be

Area = 1/2[{(-12) x (2) + (6) x (-3) + (-2) x (-3) + (-20 x 2 )} – {(2) x (6) + (2) x (-2) + (-3) x (-20) + ( -3 ) ( -12 )}]

Area = 108 / 2  

Area = 54 square units.

Therefore, the area of the parallelogram will be 108 square units.

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Answer:

5

Step-by-step explanation:

Answer:

- 3 + 8 =5

Step-by-step explanation:

I hope this answer has helped you

Answer:

82

Step-by-step explanation:

The number can only round up if the number after is 5 or greater.

Remember that a whole number cannot have any decimal points.

1. Look at the tenths place to determine whether to round up or down

2. 2 is less than five so the whole number would stay the same.

So, 82. 265 rounded to the nearest whole number would be 82

Answer:

82

Step-by-step explanation:

Answer:

5 degrees in change

Step-by-step explanation:

Step-by-step explanation:

Initial Temperature = 5 degree

Final Temperature = 0 Degree

∆T = 0-5 degree

∆T = -5 degrees

.

Negative sign shows temperature drops

The steps that should be followed to create a copy of cab are listed below in the correct order. Mark a point X. Use a straightedge to draw a ray with endpoint X.

Place the compass point at X and draw an arc intersecting the ray. Mark the point Y at the intersection. Without changing the setting, place the compass point at Y and draw an arc. Label the point Z where the two arcs intersect.

Use a straightedge to draw XZ. Place the compass point at A. Draw an arc that intersects both rays of ZA. Label the points of intersection B and C. Place the compass point at C and open the compass to the distance between B and C. The above-mentioned steps should be followed in the given order to create a copy of cab.

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The process to create a replication of the cab includes marking a point x, drawing rays, drawing arcs with a compass, and repeating this process with several different points. The steps are done in a sequential, specific order.

To create a copy of the cab, the steps would be rearranged in this order:

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Answer:D

Step-by-step explanation:

you plug 4 in for x

f(4)=4^2+2(4)-3

=16+8-3

=24-3

=21

It must change systematically when the independent variable is changed for an extraneous variable to become a confounding variable that is option D.

This is because a confounding variable is a variable that is related to both the independent and dependent variables and affects the outcome of the study, making it difficult to determine the true effect of the independent variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.

A confounding variable is a variable that affects the outcome of a study but is not the variable of interest. This can create ambiguity in the results and make it difficult to determine if the observed effect is due to the independent variable or the confounding variable. In order for a variable to be considered a confounding variable, it must change systematically with changes in the independent variable.

This means that as the independent variable changes, the confounding variable also changes in a predictable way. Without controlling for this variable, the study may not accurately reflect the true effect of the independent variable. Therefore, it is important to identify and control for confounding variables in a study to ensure that the results are valid and reliable.

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There are 11 letters in the word mathematics. The probability of selecting the letter "e" first is 1/11, which is approximately 0.091 in decimal form when rounded to the nearest thousandth.

This is because there is only one "e" in the word mathematics, and we are selecting one letter out of the 11 total letters.

To find the probability that the first letter is "e" in the word "mathematics," follow these steps:

1. Count the total number of letters in the word: There are 11 letters in "mathematics."

2. Count the occurrences of the letter "e": There is 1 "e" in "mathematics."

3. Calculate the probability: Divide the occurrences of "e" by the total number of letters.

Probability = (Occurrences of "e") / (Total number of letters) = 1 / 11

In decimal form and rounded to the nearest thousandth, the probability that the first letter is "e" in the word "mathematics" when arranged randomly is approximately 0.091.

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120 cm^3

The equation for a triangle: 1/2bh.

1/2(a)(b)

1/2(10)(24)

1/2(240)

120 cm^3

Answer:

$3071

Step-by-step explanation:

Before Tax Price: $2,700.00

Sale Tax: 8.50% or $229.50

After Tax Price: $2,929.50

Now we add the other expenses to the after tax price.

Therefore Ann has to pay $3071 for all Charges.

Answer:

x=17

Step-by-step explanation:

Since these angles are supplementary, they will add up to 180 degrees, so you can set up the equation like this:

4x+8+104=180

First, combine like terms:

4x+(8+104)=180

4x+112=180

Next, subtract 112 from both sides:

4x+112(-112)=180(-112)

4x=68

Then, divide each side by 4:

4x(/4)=68(/4)

x=17

17 is your answer.

x = 3, y = 4

Let us find the equations represented by each of the tables

Calculate the slope for table 1 selecting the points (2, 5) and (3, 4)

The equation of the line is given as:

The equation represented by the first table is y = -x + 7

Calculate the slope for table 2 by selecting the points (0, 1) and (1, 2)

The equation represented by the second table is y = x + 1

The system of equations is:

y = -x + 7..........(1)

y = x + 1...........(2)

Equating equations (1) and (2)

-x + 7 = x + 1

x + x = 7 - 1

2x = 6

x = 6/2

x = 3

Substitute the value of x into equation (2)

y = 3 + 1

y = 4

The solution to the system of equations is x = 3, y = 4

Answer:

is 3, because ‘six’ has three letters

By using several transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

congruence: Two forms are congruent if they have comparable sides and corresponding angles. By using transformations, including reflection, translation, rotation, and stretching, geometry may be changed into congruent geometry.

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Answer:

See explanation below

Step-by-step explanation:

S has x-coordinate of 6 => the distance from origin to x-coordinate is 6 units, which is one leg of the right triangle

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

with c = 10, a = 6

10^2 = 6^2 + b^2

b^2 = 100 - 36 = 64

b = √64 = 8

Point S can have 2 y-coordinates, one (+) and one (-) depending on the location of point S, so S can be either (6,8) or (6,-8)

Answer:

n = 1

Step-by-step explanation:

6n(19_8)÷3=22

1114n_48n÷3=22

66n=66

n=1

For the statement to happen, the number should be 2.

An algebraic expression is is defined as the combination of numbers and variables in solving a particular mathematical question. Variable, usually letters, are used to denote the unknown quantity.

Let x = number

Based on the information given, add the number to the numerator of 11/35 and add twice the number to the denominator of 11/35, and the result should be equal to 1/3.

Hence, (11 + x) / (35 + 2x) = 1/3.

Simplify and solve for the value of x.

3(11 + x) = (35 + 2x)

33 + 3x = 35 + 2x

3x - 2x = 35 - 33

x = 2

number = 2

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