About 7.5 gallons of water full up 1 cubic foot of space.how many gallons of water will fill a goldfish pool shaped like the prism shown

Answer:

y = -21

Step-by-step explanation:

Hope this helps! :))

Therefore , the solution of the given problem of trigonometry comes out to be csc θ - csc(90° - θ) is equal to -√(13) / 6.

Mathematics and cubic splines relationships It is believed that astrophysics was created with in third century BC, when the various fields were merged. Many geometric equations can be solved or the results of computations involving them can be determined using precise mathematical methods. Trigonometry is the analysis of the six basic trigonometric formulas. They are known by a variety of titles and acronyms, including sine, dispersion, angle, angle, etc (csc).

Here,

=> h² = 2² + 3²

=> h² = 4 + 9

=> h² = 13

=> h = √(13)

Using the specification of csc, we can now determine the value of csc:

csc θ = hypotenuse / opposite

csc θ = sqrt(13) / 3

csc(θ) - csc(90° - θ) must be calculated using the identity:

csc(90° - θ) = sec θ

As a result, we have:

csc θ - csc(90° - θ) = csc θ - sec θ

= (hypotenuse / opposite) - (hypotenuse / adjacent)

= (√(13) / 3) - (√(13) / 2)

= √(13) / 6 * (2 - 3)

= -√(13) / 6

Therefore, in its simplest radical version, csc θ - csc(90° - θ) is equal to -√(13) / 6.

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Answer:

2:3 , 8:12

Step-by-step explanation:

Equivalent ratio means, multiply/divide the numerator and the denominator of the fraction with the same number. So, we need to multiply the numerator and the denominator with the same number. Hence, another ratio that is equivalent to 4 : 6 is 8 : 12

Hope this helped :D

(a) Vertical angles: [tex]$\angle 5$[/tex] and [tex]$\angle 2$[/tex]

(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)

A figure created by two lines meeting at the same place is called an angle. The lines that make up the angle are known as its sides, and the point is known as the vertex. Angles are expressed in degrees, ranging from 0 to 360. Angles that are perpendicular to one another when two straight lines connect are known as vertical angles. Angles 1 and 3 in the image below measure 90°, while angles 2 and 4 also measure 90°. Vertical angles have the same measure.

Supplementary angles make up the second set of angles in the figure. Supplementary angles are two angles that sum up to 180°. Angles 1 and 4 and 2 and 3 form extra angle pairs in the illustration below. Angles 1 and 4 are individually 90 degrees, while angles 2 and 3 are also 90 degrees. As a result, the two angle pairs displayed in the illustration are additional angles.

(a) Vertical angles: [tex]$\angle 1$[/tex] and [tex]$\angle 3$[/tex]

(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)

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Answer:

D or B

Step-by-step explanation:

from my perspective, that doesn't look like a or b, and it looks like it's 90 degrees. But it could also be "We need more information to solve this problem, due to it all being x. i hope I'm correct, sorry if I'm not, and Goodluck!!!!!

SEE ATTACHED SOLUTION

Answer:18

Step-by-step explanation:

Answer:

$1300

Step-by-step explanation:

To find the total account balance, use the simple interest account balance formula.

P(1+rt)

1000(1 + .06 · 5)

1000(1 + .3)

1000(1.3)

$1300

Answer: The length of one fairy fly is 1.39×10−4 meter. To find the total length of two fairy flies placed end to end, we need to add their lengths.

1 fairy fly = 1.39×10−4 meter

2 fairy flies = 2 × 1.39×10−4 meter (adding the lengths of two fairy flies)

= 2.78×10−4 meter

Therefore, the total length of two fairy flies placed end to end is 2.78×10−4 meter.

Step-by-step explanation:

The derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.

We can use the quotient rule to differentiate ƒ(x):

[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]

Therefore, the derivative of given ƒ(x) is:

[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]

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The values that make the inequality m + 4 > -6 true are -4, 0, and 5.

The values that make the inequality n - 3n ≤ 8 true are -4, 0, and 5.

The values that make the inequality -5 < 5f true are 0 and 5.

The values that make the inequality 7 ≤ -y + 7 true are -10, -4, 0, and 5.

An inequality for the statement "Hank's height (h) is less than or equal to 6 feet." is h ≤ 6.

An inequality for the statement "A magazine (m) cost more than $3.50" is m > $3.50.

An inequality for the statement "The temperature (t) is at least -5 degrees" is t ≥ -5.

In this exercise, we would evaluate the given inequalities as follows;

-4 + 4 > -6

0 > - 6 (True).

0 + 4 > -6

4 > - 6 (True).

5 + 4 > -6

9 > - 6 (True).

n - 3n ≤ 8

-4 - 3(-4) ≤ 8

8 ≤ 8 (True).

0 - 3(0) ≤ 8

0 ≤ 8 (True).

5 - 3(5) ≤ 8

-10 ≤ 8 (True).

Generally speaking, the phrase "at least" simply means or represents greater than or equal to and it can be denoted by this inequality symbol (≥).

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The response that would best help the customer recognize the fallacy behind the faulty inference is: D. "What if a child runs out into the street right in front of your car?"

This response uses an example of a potential emergency situation to show that having low tread on tires can be dangerous even if the customer "never drives very fast or far.

" It challenges the customer's assumption that low tread is only a concern for high-speed or long-distance driving and highlights the importance of having sufficient tread depth for unexpected situations.

Therefore the correct option is C.

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Since t = -2.41 < -2.145, reject [tex]H_o[/tex] and conclude Ha, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

(a) Are you willing to assume that the underlying variances are equal?

Absolutely not! The variances can NOT be assumed equal.

H_o: sigma1^2 = sigma2^2

H_a: sigma1^2 =/ sigma2^2

F = s1^2 / s2^2 = 2.78095 / 0.17143 = 16.222

alpha = .05, dfnum = 15-1 = 14 and dfdenom = 15-1 = 14

F-critical values

= .33573 = F.INV(.025,14,14) using Excel

= 2.978588 = F.INV(.025,14,14) using Excel

Since F = 16.222 > 2.978588, reject H_o and conclude H_a, i.e. that the population variances significantly differ.

Or, using the p-value from the TI-84... p-value = 5.59E-6 = .00000559 < alpha = .05, so we can reject H_o and conclude H_a, i.e. that the population variances significantly differ.

(b) Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?

Note: Since the population variances ARE significantly different, we can NOT use the pooled t-test as rapunzel shows.

H_o: mu1 = mu2

H_a: mu1 =/ mu2

t = (xbar1-xbar2) / sqrt(s1^2/n1 + s2^2/n2)

t = (3.73 - 4.80) / sqrt(2.78095/15 + .17143/15)

Note: We do NOT square the variances. They are already squared.

t = -2.41

t-critcal values

df = smaller of n1-1 and n2-1, i.e. the smaller of 15-1 = 14 and 15-1 = 14

--> df = 14

left tail critical value = -2.145 <-- alpha/2 = .025, df = 14

right tail critical value = +2.145 <-- alpha/2 = .025, df = 14

Since t = -2.41 < -2.145, reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

Or, using the p-value from the TI-84... p-value = .028486... < alpha = .05, so we can reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.

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An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25 centigrades for 4 weeks. The observation reported was the number of uncontaminated eggplant cuttings after the 4-week storage.

Disinfectant 95% Ethanols 20% Bleach

Mean 3.73 4.80

Variance 2.78095 0.17143

Pooled variance: 1.47619

Are you willing to assume that the underlying variances are equal?

Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?

Answer:

look in the comments and have a good day

The graph of straight line y = 2 - x with the given points are shown in graph.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The equation of straight line is,

⇒ y = 2 - x

Now, We have to given that;

Points on the graph are,

x  =  -3, 0, 5

y  =  5, 2, -3

Hence, We can plot the points and join all the points.

We get;

The graph of straight line with the given points as shown in figure.

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Answer:

3hours and 40 mins

Step-by-step explanation:

Answer:

Without coupon: 44 baseballs

With coupon: 56 baseballs

Step-by-step explanation:

Answer:

Step-by-step explanation:

pls finish question first

The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.

Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.

Step 1

Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.

However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.

Step 2

1 year

The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84

The cost of renting a house = 1 × 12× 900 = $10,800

So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.

Step 3

5 year

The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.

Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).

10 years

The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.

Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.

Step 4

15 years

The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.

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The permutation is a bijective function because it is both a one-one and an onto function.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. Here, the components of sets are arranged in a linear or sequential order.

The bijective function is both a one-one function and an onto function.

One-one function means that for every value of the domain, there is only one value of the range. This means that an output value never repeats.

An element x is mapped to each element y by the function f known as the onto function. In other words, there is an x for every y such that:        

                                    f(x) = y

Now we have to prove why permutation is defined as bijective.

The permutation is basically an arrangement of elements.

So for the new arrangement, at one position there is only one element.

So it is one-one.

Also, we are using the given number of elements. we are just changing its positions. So every element in the co-domain is mapped to at least one element in the domain. Also, the co-domain is the range.

So it is onto function.

Therefore the permutation is a bijective function because it is both one-one and onto function.

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The interpretation the transformation that creates the graph is 1 unit to the left and 4 units to the right.

The link between lines and points is described by a network's mathematical representation, a graph.

Given, that Figure X was transformed to produce Figure Y.

We must ascertain the transformation that is applied in this case.

The process of changing an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. A vertical reflection crosses the x-axis vertically and a horizontal reflection crosses the y-axis horizontally of a graph.

A graph can be horizontally translated by moving the base graph to the left or right in the y-axis direction.

Just a little bit of a tilt to the left and upward is made to the graph.

Figure X undergoes a translation of translation 1 unit left and 4 units up.

Hence translation 1 unit left, and 4 units up is the transformation which accomplish the graph.

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The complete question is:

Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?

Therefore , the solution of the given problem of unitary method comes out to be  fountain's diameter in the model is roughly 2.0556 inches.

The measurements taken from this nanosecond variable section must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit expression method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).

Here,

We can use proportionality to determine the breadth of the fountain in the model if the scale is 1 inch = 9 feet. The following percentage can be configured:

Model fountain width divided by one inch equals actual fountain width multiplied by nine feet.

The diameter of the fountain is stated to be 18 1/2 feet in real life, which is the same as 18.5 feet. Adding this number to the proportion results in:

1 inch of the model fountain's diameter divided by 18.5 feet by 9 feet

If we simplify, we get:

diameter of the model's fountain / 1 = 2.0556

By dividing the two edges by one inch, we obtain:

Modeled fountain width is 2.0556 inches.

As a result, the fountain's diameter in the model is roughly 2.0556 inches.

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The mean absolute variation for the group of integers 42, 45, 47, 50, 53, 56, 58, and 65 is therefore roughly 6.5.

What one standard deviation (SD) means. on a normal or bell-shaped distribution of the data. The region of a bell curve starting at position 13 on the y axis is approximately filled by 1 SD = one standard deviation = 68% of a ratings or data values.

Here's how to find the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65:

Find the mean:

mean = (42 + 45 + 47 + 50 + 53 + 56 + 58 + 65) / 8

mean = 50.375

Find the absolute difference between each number and the mean:

|42 - 50.375| = 8.375

|45 - 50.375| = 5.375

|47 - 50.375| = 3.375

|50 - 50.375| = 0.375

|53 - 50.375| = 2.625

|56 - 50.375| = 5.625

|58 - 50.375| = 7.625

|65 - 50.375| = 14.625

Find the average of these absolute differences:

mean absolute deviation = (8.375 + 5.375 + 3.375 + 0.375 + 2.625 + 5.625 + 7.625 + 14.625) / 8

mean absolute deviation ≈ 6.5

Therefore, the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65 is approximately 6.5.

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We proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

What are congruent traingles?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. It is necessary for both triangles to be superimposed on one another.

1) Consider triangles ΔPQR and ΔSTR

PQ ≅ ST     -   Given

QR ≅ TR     - Given

R is the midpoint of PS  - Given

PR ≅ SR  - Since R is the midpoint it cuts line PS equally

ΔPQR  ≅ ΔSTR - Since the corresponding sides of the triangles are equal, they are congruent triangles.

2) Consider triangles ΔJKL and ΔNKM

JL ≅ NM     -   Given

K is the midpoint of JN and LM  - Given

JK ≅ NK  - Since K is the midpoint it cuts line JN equally

LK ≅ MK  - Since K is the midpoint it cuts the line LM  equally

ΔJKL  ≅ ΔNKM - Since the corresponding sides of the triangles are equal, they are congruent triangles.

Therefore we proved that ΔPQR congruent to ΔSTR and  ΔJKL is congruent to ΔNKM using the given conditions.

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The solution to the variable x is 60/7

From the question, we have the following parameters that can be used in our computation:

The similar polygons

The scale factor from the big to the small polygon is represented as

Scale factor = 5/7

Using the above as a guide, we have the following:

x = 12 * 5/7

Evaluate

x = 60/7

Hence, the solution is 60/7

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The ordered pair is not the solution of the given equation. The solution has been obtained by using the substitution method.

One method for resolving equation systems is the substitution method. Use one equation to find an expression for one of the variables in terms of the other variable in order to apply the substitution procedure. Then, in the second equation, replace that variable with that expression.

We are given an equation as 7 = y - 5x.

The ordered pair is given as (4, 28).

On substituting this in the equation, we get

⇒7 = 28 - 5(4)

⇒7 = 28 - 20

⇒7 ≠ 8

Hence, the ordered pair is not the solution of the given equation.

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If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.

Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.

To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:

3 + 2 = 5

So there are 5 small triangles in the third row.

To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:

5 + 2 = 7

So there are 7 small triangles in the fourth row.

To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:

n = (last term - first term) / common difference + 1

n = (7 - 1) / 2 + 1

n = 4

So there are 4 rows in the triangle.

Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:

sum = (n / 2) * (first term + last term)

sum = (4 / 2) * (1 + 7)

sum = 4 * 4

sum = 16

So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:

area = 16 * (1/2)

area = 8

Therefore, the original triangle has an area of 8 square units.

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It would take approximately 11.6 years for the account balance to reach $20,000 if compounded annually.

The costs a borrower pays a lender for a loan are known as interest. For instance, banks charge interest on the loans that consumers take out.

Simple interest is the term used to describe interest that is based on the principle amount that a person borrows or invests. Contrarily, compound interest is computed on the principle borrowed or invested by the individual as well as the accrued interest from the prior period.

The formula for compound interest is:

A = P(1 + r/n)ⁿˣ

where, A is the amount

P is the principal amount = $10,000

r is the rate = 6% = 0.06

x is time.

n = 1

Substituting the values,

$20,000 = $10,000(1 + 0.06/1)¹ˣ

2 = (1.06)ˣ

Taking the natural logarithm of both sides:

ln(2) = t * ln(1.06)

t = ln(2) / ln(1.06) ≈ 11.6

Therefore, it would take approximately 11.6 years for the account balance to reach $20,000.

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The workers listed in order from least to greatest fraction of a shift worked are Lisa (1/4) < Jose (1/3) < Trent (2/3).

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. A fraction can be found in either the numerator or the denominator of a complex fraction.

Trent worked eight of the twelve hours, or roughly two-thirds of the shift.

By dividing the number of hours Jose worked by the total number of hours in the shift, we can turn the number of hours Jose worked into a fraction:

Jose worked (12 - 8)/12 = 4/12 = 1/3 of the shift.

Lisa worked of the shift:

Lisa worked (12 - 8 - 1)/12

= 3/12

= 1/4 of the shift.

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