Define rational number in your own words.

It will take 80 gallons of water to fill the fish tank.

The amount of space occupied by a three-dimensional object or region of space.

Given that, Anna is going to clean the fish tank, which measures 48 inches long by 11 inches wide by 35 inches high

The fish tank is cuboidal,

Volume of cuboid = length*width*height

Therefore, volume of fish tank = 48*11*35 = 18,480 in³

1 gallon = 231 in³

So, 18,480  in³ = 18,480/231 gallons = 80 gallons

Hence, Volume of tank = 80 gallons

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48.4 % percent of all rodents on the ship preferred peanut butter.

acc to our question-

hence,48.4 % percent of all rodents on the ship preferred peanut butter.

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The total number of hours Donna used driving is 3 2/21 hours

A rate is a special ratio in which the two terms are in different units. For example, For 1 hour Donna is using 7/10 gallons of fuel while driving.

The two quantities there are time in hours and the quantity of fuel used in gallons.

If Donna used 7/10 gallon for 1 hour

then 1 gallon will last for 1÷7/10= 1× 10/7= 10/7

Therefore for 2 1/6 gallon = 10/7×2 1/6= 10/7×13/6

= 3 2/21 hours

Therefore the total number of hours used driving with 2 1/6 gallons is 3 2/21

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Answer:

6/7

Step-by-step explanation:

2÷3/7=2*3/7

6/7

Answer:

80

Step-by-step explanation:

x/ -4 = -20

I hope this helps!

By using the formula of acceleration, it can be calculated that

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

What is acceleration?

At first, it is important to know about velocity

Distance travelled by a body per unit interval of time in a particular direction is called Velocity

The rate of change of velocity is called acceleration.

Acceleration is a vector quantity as the direction is taken into account.

Initial velocity of earthworm (u)= 0.01 m/s

Final velocity of earthworm (v) = 0.02 m/s

Distance (s) = 0.9 m

We know,

[tex]v^2 = u^2 + 2as\\0.02^2 = 0.01^2 + 2 \times a \times 0.9\\0.02^2 - 0.01^2 = 1.8a\\(0.02 + 0.01)(0.02 - 0.01) = 1.8a\\a = \frac{0.03 \times 0.01}{1.8}\\a = 0.000167 \ ms^{-2}[/tex]

Again,

v = u + at

0.02 = 0.01 + 0.000167[tex]\times[/tex] t

t = [tex]\frac{0.02 - 0.01}{0.000167}[/tex]

t = 59.88 s

Time taken by an earthworm  to accelerate from a speed of 0.01 m/s to 0.02 m/s over a distance of 0.9 m is 59.88 s

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Answer:

27w+2=19w+6

27w+19w=6+2

w(27+19)=8

w(27+19)/27+19=8/27+19

w=8/(27+19)

The solution of the expressions are

(a) (30+10 ÷ 2)-5-10 = 20

(d) 30+ (10 ÷ 2·5)-10 = 24

What is meaning of expressions?

An expression is a combination of operations, variables, and numbers.

What is BODMAS rule?

According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.

Given expression is

(30+10 ÷ 2)-5-10

Applying BODMAS rule:

= (30 + 5) - 5 - 10

= 35 - 5 - 10

= 30 - 10

=40

Second expression is:

30+ (10 ÷ 2·5)-10

= 30 + (10 ÷ 10) - 10

= 30 + 1 - 10

= 31 -10

= 21

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The expression of the phrase " Nine increased by twice a number " is 2n + 9

The given phrase is

Nine increased by twice a number

We have to convert the the phrase to the expression

The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.

Consider the number as n

Twice the number = 2n

nine increased by twice a number = 2n + 9

Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9

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Answer:

Alessa's car would be able to drive 337.5 miles with 15 gallons of gas.

She drinks 1/12 gallons of milk each day

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

Size of milk = 1/2 gallons

Number of days = 6 days

These parameters can be represented as

(x, y) = (6, 1/2)

The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as

unit rate = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (6, 1/2)

Substitute the known values in the above equation

So, we have the following equation

Slope = (1/2 - 0)/(6 - 0)

Evaluate the quotient

Slope = 1/12

Hence, the number of gallons she drinks a day is 1/12

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The area of the shaded region is x=245 feet for both rectangle and circle.

The quantity area expresses the extent of a region on a plane or a curved surface. The area of a plane region or plane area refers to the area of a form or planar lamina, whereas surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be defined as the amount of material of a given thickness required to make a model of the shape, or the amount of paint required to cover the surface with a single coat. It is the two-dimensional equivalent of the length of a curve or the volume of a solid.

The area of a shape can be calculated.

Area of shaded region=Area of rectangle-1/2(Area of circle)

=L×B-1/2(πr²)

=23×14-1/2((22/7)×7×7)

=322-77

=245 feet

Therefore, the area of the shaded region=245 feet

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The value of k is 4.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Volume= 16

Width = 4

So, we can write the relation as

Volume= k (width)

k = Volume/ width

k= 16/4

k = 4

Hence, the value of k is 4.

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Answer:

y=x-7

Step-by-step explanation:

we know the y intercept is -7 since when x was 0 g(x) is -7

We write it in slope intercept form which is y=mx+b

m- slope

b- y- intercept

To find slope we do y2-y1/x2-x1

-5+7/2-0

2/2

1

1 is the slope so we just keep it X on the equation and the equation will be

y=x-7

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.

We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group. A fact involving multiplication is the result of two distinct integers. Additionally, the product is unaffected by the arrangement of the numbers. For instance, 32=6 and 23=6. The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.

Given,

Equations:

2x + 3y = 12

4x - 7y = -54

Multiplying the top equation by -2:

-2(2x + 3y) = -2(12)

-2(2x) -2(3y) = -24

Product:

-4x - 6y = -24

Taking - common,

-(4x + 6y) = -24

4x + 6y = 24

New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.

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The first term of the sequence is 12 and the common difference is -3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Given that a formula for the nth term. 5th term is 0​; 45th term is -120. The common difference is calculated as,

a₁ + d(5-1) = 0

a₁ + d(45 - 1) = -120

Solve the above equation,

a₁ + 4d = 0

-a₁ - 44d= +120

___________

     -40d = 120

          d = -3

The value of the first term is,

a₁ + 4d = 0

a₁ + 4 x -3 = 0

a₁ = 12

Therefore, the first term of the sequence is 12 and the common difference is -3.

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Answer:

Doesn't make a lot of sense. Can you be more specific.

Step-by-step explanation:

The Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit

Credit reporting companies, also known as credit bureaus or consumer reporting agencies, are companies that compile and sell credit reports.

Given are three credit reporting agencies.

Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit. Your creditworthiness is what creditors look at before they approve any new credit to you. The 3 C's of credit worthiness are Character, Capacity and Capital. Creditworthiness is determined by several factors including your repayment history and credit score.

Therefore, the Creditworthiness is how a lender determines that you will default on your debt obligations, or how worthy you are to receive new credit.

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The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms

Information from the question

each standard room can fill 2 guests

the maximum number of guests that all standard rooms can accommodate = ?

The problem is solved by multiplication

each standard room (1) = 2 guests

all standard rooms = ?

cross multiplying

? * 1 = 2 * all standard rooms

? = all standard rooms times two

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Answer:

bla blablablablabla

Step-by-step explanation:

blablablablablabla

Answer:

a. Given

b. thru any 2 points there exists a line (you can draw a line)

c. Definition of Regular Polygon

d. Definition of Regular Polygon

e. Given

f. Def of Midpoint

g. SAS: Side-Angle-Side congruence

h. CPCTC - Corresponding Parts of Congruent Triangles are Congruent

i. Definition of Regular Polygon

j. Reflexive

k. SSS: Side-Side-Side congruence

l. CPCTC

Step-by-step explanation:

I encourage you to look up all of the above reasons to get a better understanding of what they are!!

Answer:

h=3

Step-by-step explanation:

4h+8=9h-7

subtract 4h

8=5h-7

add 7

15=5h

divide 3

h=3

Answer:

[tex]f^{-1}(y) = \sqrt{x-5}[/tex]

Step-by-step explanation:

You have to switch the f(x) to x and the x's to y's

[tex]x = y^2 + 5[/tex]

[tex]\sqrt{x-5} = \sqrt{y^2}[/tex]

[tex]y = \sqrt{x - 5}[/tex]

Answer:

y=7

Step-by-step explanation:

-3(-3)-y=2

9-y=2

9-2=y

y=7

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The number of mainland countries is 20 and the number of island countries is 5 countries that Willy visited.

Let the number of mainland be represented by m

Let the number of island be represented by x.

This will be illustrated as:.

m + x = 25 .... i

2m + 5x = 65 .... ii

From equation i, m = 25 - x.

Put this into equation ii

2m + 5x = 65

2(25 - x) + 5x = 65

50 - 2x + 5x = 65

3x = 65 - 50

3x = 15

Divide

x = 15 / 3

x = 5

Island countries = 5

Since m + x = 25

m = 25 - 5 = 20

Mainland countries = 20

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Answer:

cubic root 10 power 1

Step-by-step explanation:

Apply the rule

x

m

n

=

n

√

x

m

to rewrite the exponentiation as a radical.

3

√

10

1

Anything raised to

1

is the base itself.

3

√

10

The result can be shown in multiple forms.

Exact Form:

3

√

10

Decimal Form:

2.15443469

…

A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.

In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.

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The value of x is 11° and measure of other two angles are 80° and 117°

A triangle can be defined as a polygon which has three angles and three sides. The interior angles of a triangle sum up to 180°, and the exterior angles sum up to 360°.

Given that, the interior angles of the triangle are 37° and (3x+47)° and an exterior angle measures (5x+ 62)°

We know that the sum of two interior angles equals to the measure of an exterior angle,

Therefore,  37° + (3x+47)° = (5x+ 62)°

x = 11°

Hence, The value of x is 11° and measure of other two angles are 80° and 117°

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Jan earns more than Rachel. The range of what Jan earns is  360 dollars to 480 dollars per week. The range of what Rachel earns is  220 dollars to 330 dollars per week.

Jan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour

the time that she has to work is given a 30 hours to 40 hours.

Hence the domain would be written as

domain : 30 ≤ t ≤ 40

we have to make use of the values of t

f(t) = 12 * 30 = 360

f(t) = 12 * 40 = 480

The range of Jan is going to be

range : 360 ≤ t ≤ 480

b. For Rachel, t is going to vary between 20 ≤ t ≤ 30

domain : 20 ≤ t ≤ 30

r*t = 11t

= 11 x 20 = 220

= 11 x 30 = 330

The range is given as

range: 220 ≤ t ≤ 330

Jan earns more per hour than Rachel

The amount earned is, Jan earns from 360 dollars to 480 dollars per week.

Rachel earns from 220 dollars to 330 dollars per week.

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