A huge fish tank has a leak. 19.414 gallons of water has leaked out. Only 91,468 gallons of water remains in the tank. How many gallons of water was in the tank before the leak?​

by using log notation, the value of x =㏒₃500 or x = 5.657

Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.

we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.

in the above equation 3ˣ = 500

using log notation, we get ㏒₃500 = x

                                    x= 5.657

hence, the solution is x = 5.657

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The measure of the angles ∠1, ∠2, and ∠3 will be 38°, 65°, and 52°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

Angle ∠1 is given by the property of complementary. Then we have

∠1 + 38° = 90°

∠1 = 52°

Angle ∠1 and angle ∠3 are complementary angles. Then we have

∠1 + ∠3 = 90°

52° + ∠3 = 90°

∠3 = 52°

Angle ∠2 is given by the property of supplementary. Then we have

∠2 + 52° + 63° = 180°

∠2 = 65°

The measure of the angles ∠1, ∠2, and ∠3 will be 38°, 65°, and 52°, respectively.

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Dorothea needs 2.4 kilograms of filo pastry to make on pan of baklava.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

The quantity needed of filo pastry to make one pan of baklava = 400 grams

To find the quantity of pastry to make 6 pans of baklava

Use ratio property,

1 pan of baklava needed = 400 grams

6 pans of baklava needed = 400 x 6 = 2400 grams

Since, 1000 gram = 1 kilogram

2400 gram = 2.4 kilograms

Hence, Dorothea needs 2.4 kilograms of filo pastry.

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An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

In statistics, a truly random sample involves selecting people from a population with an equivalent probability; in other words, picking individuals from a group without bias.

Failing to accomplish this appropriately will result in a sampling bias, which can dramatically increase the sample error in a systematic fashion. For instance, using a sample from just one nation to estimate the average height of all people on Earth could lead to a significant over- or underestimation.

In practice, it might be challenging to select an impartial sample because various criteria (for instance, nation, age, gender, and so on) may substantially bias the estimator. It is important to make sure that none of these aspects are taken into consideration when choosing the sample.

Hence, An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

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In the Algebra prompt above, If f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.

We are given the following:

f(n)=1/2f(n-1) + 2; and

f(1) = 8

Thus,

f(2) = 1/2 x 8 + 2

= 4 + 2

f(2 )=  6

Hence,

f(3) = 1/2 x 6 + 2

= 3 + 2; thus,

f(3) = 5

Therefore,  it is correct to state that if f(1) = 8 and f(n)=1/2f(n-1) + 2 then  the value of f(3) is 5.

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The ratio between the number of edges and the number of vertice of a cube is 2:3. All Prisms have a ratio of edges and vertices will be the same as that of the cube.

Edge – The outlines where two cube sides touch one another.

Vertices – The indicates the point where a cube's three sides meet.

Number of edges of a cube = 12

Number of vertices in a cube = 8

The ratio of edges in vertices = 12 : 8

                                             = 3 : 2

Hence, the ratio between the number the edges and the number of vertices of a cube is 3 : 2

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average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends.

the difference between the y- and x-values is divided. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity.

Given that

the change in y value occurred in 9 minutes and the change in x value occurred in 4 minutes, the average rate of change was 9 minutes by 4 minutes, or2.25 minutes.

9 min / 4 min

= 2.25 min

average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

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Answer:

$7800

Step-by-step explanation:

1 year = 10%

3 years = 30%

30% = 0.3

6000 times 0.3 = $1800

6000 + 1800 = $7800

So, they will pay $7800

If we test the null hypothesis at the 5% level of significance, then the decision is (c)reject null hypothesis and conclude the means are different .

In the question ,

it is given that ,

the results of a mathematics placement exam for two different campuses of college ,

we have to test the hypothesis that the mean score on campus 1 is higher than on campus 2 .

sample size (n₁) is = 330

the sample size (n₂) is = 310

the sample mean (μ₁) = 33

the sample mean (μ₂) = 31

the standard deviation , σ₁ = 8

the standard deviation , σ₂ = 7

the test statistic test z can be calculated using the formula ,

z = (μ₁ - μ₂)/√(σ₁²/n₁ + σ₂²/n₂)

Substituting the values of the sample size , sample mean and standard deviation ,

we get ,

z = (33 - 31)/√(8²/330 + 7²/310)

Simplifying further ,

we get ,

Z = 3.37

the test is for the null hypothesis at the 5% level of significance .

that means ,

Z₀.₉₅ = 1.645 ;

So , the p value = P(Z > 3.37)

= 1 - P(Z < 3.37)

= 1 - 0.9996

= 0.0004

since the p-value is (0.0004) < the level of significance (0.05) .

we can reject the null hypothesis .

There is significant evidence to conclude that the mean score on campus 1 is higher than campus 2 .

Therefore , the correct option is (c) .

The given question is incomplete the complete question is

The results of a mathematics placement exam at two different campuses of mercy college follow: ( the table is given below)

The college wants to test the hypothesis that the mean score on campus 1 is higher than on campus 2. if we test the null hypothesis at the 5% level of significance, what is the decision ?

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Step-by-step explanation:

Area of rectangle is length x breadth.

Area = (x + 7)(x + 5)

= (x² + 5x + 7x + 35)

= (x² + 12x + 35)

By using the concept of algebraic expression, it can be concluded that

The expression will be equal for all real numbers except -6

First option is correct.

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

The given rational expression in simplified form is

[tex]\frac{(x-2)(x+6)}{7(x+6)} = \frac{x-2}{7}[/tex]

For x = -6, the denominator of the left hand side is zero

So the expression on the left hand side is undefined for x = -6

So the expression will be equal for all real numbers except -6

First option is correct.

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Answer:  D) 2.95 units

Step-by-step explanation:
I just took this

Answer:

The answer is : 9345.

Step-by-step explanation:

N/A

Answer:

w * (1 + 0.17) or w + (w * 0.17)

Step-by-step explanation:

Here are two expressions that represent the retail price of an item with an original cost of w dollars, assuming that the store marks up the price by 17%:

Retail price = w * (1 + 0.17)

This expression shows that the retail price is equal to the original cost multiplied by the markup percentage (0.17) plus 1. For example, if the original cost of the item is $100, the retail price would be $100 * (1 + 0.17) = $117.

Retail price = w + (w * 0.17)

This expression shows that the retail price is equal to the original cost plus the markup amount (which is equal to the original cost multiplied by the markup percentage). For example, if the original cost of the item is $100, the retail price would be $100 + ($100 * 0.17) = $117.

Answer:

Nelson's average speed was 8 miles per hour.

Step-by-step explanation:

To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.

Answer:

8 miles per hour

Step-by-step explanation:

In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.

[tex]\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}[/tex]

x= 8

Function h is the one with the lowest minimum value.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.

A function is more precisely defined as a set of ordered pairs (x,y) with the limitation that there may only be one ordered pair with the same value of x given a set of inputs (domain) X and a set of potential outputs (codomain).

A graph is considered to be a function if any vertical line formed can cross it at most one point. A vertical line cannot cross the graph at more than two points in any location.

Considering the query

f(x) = x² - 2x - 6

given the graph

at its lowest value (1,-7)

h(x) = 2(x-1)²

h(x) = 2 (x² + 1 -2x )

h(x) = 2x² - 4x + 2

Creating the graph

We may view the

Lowest value at (1,0)

The complete question is,

Consider continuous functions f, g, and k. Then complete the statements.

The function that has the least minimum value is function _____. The function that has the greatest minimum value is function _____.

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Answer:

Step-by-step explanation:

Q1. Since each of Bruce's tiles is one square foot in area, his equation is y=x, where y=area and x=#of tiles. The area increases by one square foot for every tile added.

Q2. If it takes 9 of Felicia's tiles to equal 1 square foot, her equation is y=(1/9)x. We can check the table to see if this equation is right. If you put 18 into this equation, you get 2, for 27 you get 3, and so forth

Q3. Bruce has the greater unit rate of 1 and has the tiles that cover the greatest area, as opposed to Felicia, whose unit rate is only 1/9, since each of her tiles covers 1/9 of a square foot

Q4. The slopes are the same as the unit rates. Bruce's is 1, Felicia's is 1/9. Both of their y intercepts are 0, because if they put down 0 tiles, there will be no area covered because the problem does not state that there were tiles placed already before Bruce and Felicia started. You can also see this by graphing their equations

Q5. Bruce's line is steeper, with a slope of 1, versus Felicia's slope, which is 1/9. This matches the comparison from part c where we discovered that Bruce had the greater unit rate

The slope and y-intercept of the linear function are -5 and 7 respectively.

Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.

A linear function has one independent variable and one dependent variable.

A linear function has the following form. y = mx + b.

where

Therefore, let's find the slope of the function.

slope = m = Δy / Δx

using (0, 7) and (4, -13)

slope = m = -13 - 7 / 4 - 0

slope = - 20 / 4

slope = -5

Let's find the y-intercept using (0, 7).

y = -5x + b

7 = -5(0) + b

b = y-intercept = 7

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Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:

a) Organizing the data into afrequency  distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.

b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.

c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.

Here are some of the benefits of using graphs of frequency distributions:

a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.

b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.

c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.

d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.

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Answer:

[tex]\dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Step-by-step explanation:

Given equation:

[tex]-4x^2 + 9y^2 + 32x + 36y - 64 = 0[/tex]

Collect like terms:

[tex]\implies 9y^2 + 36y -4x^2+ 32x - 64 = 0[/tex]

Move the constant to the right side of the equation:

[tex]\implies 9y^2 + 36y -4x^2+ 32x =64[/tex]

Factor out 9 from the terms in y, and 4 from the terms in x:

[tex]\implies 9(y^2 + 4y) -4(x^2-8x)=64[/tex]

Add the square of half the coefficient of the term in y and x inside the parentheses on the LHS, and the distributed values on the RHS:

[tex]\implies 9\left(y^2 + 4y+\left(\dfrac{4}{2}\right)^2 \right) -4\left(x^2-8x+\left(\dfrac{-8}{2}\right)^2 \right)=64+9\left(\dfrac{4}{2}\right)^2 \right+4\left(\dfrac{-8}{2}\right)^2 \right[/tex]

Simplify:

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=64+36-64[/tex]

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=36[/tex]

Factor the perfect trinomials:

[tex]\implies 9(y+2)^2 -4(x-4)^2=36[/tex]

Divide both sides by 36:

[tex]\implies \dfrac{9(y+2)^2}{36} -\dfrac{4(x-4)^2}{36}=\dfrac{36}{36}[/tex]

Simplify:

[tex]\implies \dfrac{\diagup\!\!\!\!9(y+2)^2}{\diagup\!\!\!\! 9\cdot 4} -\dfrac{\diagup\!\!\!\!4(x-4)^2}{9 \cdot \diagup\!\!\!\!4}=1[/tex]

[tex]\implies \dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Therefore, the function is a hyperbola with:

Answer:

Step-by-step explanation:To determine which store charges the least amount per bottle, you need to calculate the price per bottle for each store. You can do this by dividing the total price of the cases by the number of bottles in each case.

For Super Buy, the price per bottle is $3.96 / 12 bottles = $0.33 per bottle.

For Fresh Grocers, the price per bottle is $2.08 / 8 bottles = $0.26 per bottle.

For Saveway, the price per bottle is $5.52 / 24 bottles = $0.23 per bottle.

For Shop and Go, the price per bottle is $7.56 / 36 bottles = $0.21 per bottle.

Based on these calculations, it looks like Shop and Go charges the least amount per bottle at $0.21.

Answer: which triangle ;/

Step-by-step explanation:

the proportionality constant is 20 and in 8 ours it will cover 160 miles.

What is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

The slope of he given graph will be (30-10)/(2-1) = 20

So here the proportionality constant is 20.

we can write y = 20x

This means in 8 ours it will cover 8*20 = 160 miles.

Hence, the proportionality constant is 20 and in 8 ours it will cover 160 miles.

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The addition is 5x - 2. We can find out our answer using simple arithmetic calculations.

What are arithmetic calculations?

Arithmetic calculations are mathematical operations used to solve equations and perform numerical calculations. They include addition, subtraction, multiplication, and division. Arithmetic is a fundamental part of mathematics, and it is an important part of everyday life. Arithmetic is used to solve problems in a variety of fields, such as engineering, finance, and science. It is also used in everyday tasks such as grocery shopping and budgeting. Arithmetic calculations are essential for most people and can help them understand and solve a variety of problems. By mastering basic arithmetic calculations, people can make more informed decisions and better understand the world around them.

In algebraic expressions ,

same variables are added together and constants together.

In given equation,

2x and 3x are added i.e. 5x

and 5 and -7 are added  i.e. -2

So, the equation is 5x-2.

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Answer:

Below

Step-by-step explanation:

( Your question asks for m^2 discharge......I think you need m^3 discharge per minute)

Find the volume of a cylinder that is 8 meters long with radius of 8cm ( .08 m)

area = pi r^2 = pi (.08)^2 = .0201 m^2

    area * 8 m   = volume PER SECOND

        volume PER SECOND  *  60 = volume per minute

                 .0201   * 8 * 60 = 9.65 m^3 / min  discharge

There are 60 grams of protein in 9 ounces of sauteed fish.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that there are 20 grams of protein in 3 ounces of sauteed fish.

Let's assume that 9 ounces of sauteed fish contain x grams of protein.

As per the given information, we can write the ratio would be as:

20 grams of protein : 3 ounces = x grams of protein : 9 ounces

20/3 = x/9

x = (20 × 9)/3

x = 180/3

x = 60

Hence, there are 60 grams of protein in 9 ounces of sauteed fish.

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The question seems to be incomplete the correct question would be:

There are 20 grams of protein in 3 ounces of sauteed fish. If 3 ounces of sautéed then, what are the grams of protein fish has?

Answer:

72 = -4s

72 / (-4) = (-4s) / (-4)

-18 = s

Answer:

A. 147.5

B. 430.2

Step-by-step explanation:

A. 2001

2001 - 1998 = 3

y = 122.1(1.065)³

y = 147.49

y = 147.5

B. 2018

2018 - 1998 = 20

y = 122.1(1.065)²⁰

y = 430.23706225

y = 430.2

I hope this helps!