The empty gas tank of a motor boat is to be fllled. The tank is shaped like a rectangular prism with length 30cm, width 24cm, and height 18cm. Suppose gas Is pumped into the tank at a rate of 864cm^(3) per minute. How many minutes does it take to fill the empty tank?

Answer:

46 miles

Step-by-step explanation:

First, set up an equation:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

Add the miles in the parentheses:

(48 + 58 + 68 + 50 + x) ÷ 5 = 54

48 + 58 + 68 + 50 = 224

(224 + x) ÷ 5 = 54

Multiply by 5 on each side:

[(224 + x) ÷ 5] × 5 = (54) × 5

(224 + x) = 270

Subtract 224 on each side to isolate x:

(224 + x) - 224 = (270) - 224

x = 46 miles

Hope this helps! I'd appreciate brainliest but if not that's fine!

Answer:

The factored form of 27t^3 - 36t^2 - 12t + 16 is:

(3t - 4) (3t+2) (3t - 2)

The point is rotated 90° counterclockwise. The algebraic rule for rotation of 90° counterclockwise is (x, y)→(-y, x) .

Rotation of a graph is a transformation where the graph is rotated about a fixed point.

The given point is M(6,8) . The figure is rotated counterclockwise to get the image M'(-8,6).

Now we have to calculate the degree of rotation of the point.

M(6,8) lies in the first quadrant and M'(-8,6) lies in the second quadrant.

Therefore the rotation is less than 180° .

Now from the figure attached below we can say that the figure was rotated 90°

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The cost of a given number of handbags - Discrete

Amount of juice in a jug over time - Continuous

Area of a field based on length - Continuous

Tires in a number of cars -Discrete

A discrete function as its name suggests has distinct or separate values against one value. That is, one at a time values are in a discrete function. So its domain and image sets will have discrete values.

A continuous function has continuous values within intervals. Its domain will be intervals having a continuous range and images will also be in a  continuous range.

We need to check if the following will have a discrete or a continuous graph:

1. The cost of a given number of handbags.

This is a discrete function as the cost and number of handbags will have discrete values. So it will have a discrete graph.

2. Amount of juice in a jug over time

This is a continuous function. The variables here are the amount of juice and time in which time, clearly, is a continuous variable. So it will have continuous values in an interval. So the amount of juice can also be measured continuously. So the graph will be continuous.

3.  Area of a field based on length

Here the length can take continuous values in an interval. So the area can also be measured continuously giving a continuous graph here.

4. Tires in a number of cars.

Number of tires and number of cars both will take only discrete values. So it can only give a discrete graph.

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The mean time that a certain model of light bulb will last is ​hours is 900 hours and the required percentage of bulbs is 2.5%

Here,

x is the time that a certain bulb will last.

(in houses.

μ=900 hours;

σ=1200 hours.

The standardized value for a light bulbs lasts 1100 hours, is,

z=x-μ/σ

z=1100-900/100=2

We know, for a bell-shaped distance, Approximately,

68% of the data falls within M-uσ;

By rule (ii), here,

95% of the data falls within (μ-2σ,u+2σ)

(900-2x100,900+2x100)

(700,1100)

So (100-95=5%) falls outside of (700,1100)

Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is

5/2% =2.5%

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The probability that the 3 outcome of numbers obtained are three consecutive numbers is 1/9.

The probability of an event occurring is calculated by dividing the amount of favourable outcomes by total number of possible outcomes.

Now, as per the given question;

To address your point, if the three numbers seem to be different, there are 3! = 6 different orders in which they could have been placed.

As a result, the solution to the question;

= (2/3)×(1/6)×(1/6)×6

= (2/3)(1/6)

= 1/9.

Therefore, the probability of getting the three consecutive number is 1/9.

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Answer: 13

Step-by-step explanation:

The number of fiction books in the library are 324, as found by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given: There are 5 non-fiction books for every 9 fiction books. Total 130 non-fiction books are there in the library.

To find: number of fiction books.

Finding: By unitary method, For every 5 non-fiction books, there are 9 fiction books.

For every 1 non-fiction book, there are 9/5 fiction books.

For every 130 non-fiction books, there are 9/5 × 130 = 324 fiction books.

Hence, The number of fiction books in the library are 324, as found by unitary method.

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(COMPLETE QUESTION:in a small library there are 5 nonfiction books for every 9 fiction book there are 130 nonfiction book. How many fiction books are there in the library?)

A mean is the average of set of values such that the values hold different levels of importance.

Mean can be defined as the mathematical average of a group or set of numbers.

It is also the most common value in a collection of numbers.

The formula for determining the mean of a group of data is;

Mean = sum of terms/number of terms

An important and distinct property of the mean is the inclusion of every value in a given set of data of the calculation.

Also, both discrete and continuous data are used in determining the mean.

Thus, a mean is the average of set of values such that the values hold different levels of importance.

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Answer: Explanation

Step-by-step explanation:

For #1 first we have to convert all of the fractions to have the same denominator by finding the LCM(Least Common Multiple), which is 60. 1/4=15/60, 1/5=12/60, and 1/3=20/60. Then you add them up and get 47/60. You take that fraction and multiply it by 850 to get about 665.83, which is the estimate.

As for #2, I don't know sorry, I think you can just draw different lengthed lines to show the different distances traveled.

For #3 its 850/9 which is about 94.44

#4 I would recommend stopping through the night because they have about 184 miles to go and since they would only complete about 94 of those miles and would still have to drive tomorrow, they might as well do it all tomorrow.

The equation to find the number of players the team can bring to the tournament is xx = ( 2,143.50 - 888.50 )/62.75 and the number of players the team can bring to the tournament is 20.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal.

Equations express the equality of mathematical expressions by using the equation mark (=).

The total amount raised for the tournament is $2,143.50

The price to rent a bus is $888.50.

The cost of budgeted meals per player is $62.75.

The number of players the team can bring to the tournament is:

xx = ( 2,143.50 - 888.50 ) / 62.75.

xx = ( 2,143.50 - 888.50 ) / 62.75

xx = 1,255 / 62.75

xx = 20

Therefore, the equation to calculate the maximum number of players the team can enter the competition is xx = ( 2,143.50 - 888.50 ) / 62.75.

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The equation of line that passes through the given points in  point-slope form is y - 2 = -4/3( x - 4 ).

Given the data in the question;

Point A(4, 2)

Point B(1, 6)

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 6 - 2 )/( 1 - 4 )

Slope m = ( 4 )/( -3)

Slope m = -4/3

Next, plug the slope -4/3 and point (4,2) into the point slope formula y - y₁ = m( x - x₁ ) and simplify.

y - y₁ = m( x - x₁ )

y - 2 = -4/3( x - 4 )

Therefore, the equation of line that passes through the given points in  point-slope form is y - 2 = -4/3( x - 4 ).

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Check the picture below.

Answer:

g

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

(a) The equation to find x is :  (6x)°  + (x-8)°  = 90°

(b) The degree measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

Complementary angles are two angles whose sum is 90 degree.

Given are two complementary angles ∠1 and ∠2 whose measures are given m∠1 = (6x)° and m∠2 =(x-8)°

From the given figure we can see that sum of  ∠1 and ∠2 is 90°, which means they are complementary.

m∠1 + m∠2 = 90°

And  (6x)°  + (x-8)°  = 90°

Or      6x +x-8 = 90

7x = 90+8

7x= 98

x= 98/7 =14

Then m∠1 = (6x)° = (6*14)° = 84° and m∠2 = (x-8)° = (14-8)° = 6°

Therefore, The equation to find x is (6x)°  + (x-8)°  = 90° and measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

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Step-by-step explanation:

11% = 0.11

the remaining part when subtracting 11% from the whole (100%) is 89%.

89% = 0.89

his after-tax wages are 89% of his total income.

w(h) = 15h × 0.89 = 13.35h

Hence , the coordinate of midpoint of line CD is (17 , 23) .

We have given two coordinate C (24, 18) and D(10, 28) .

Let M be the midpoint of line CD having coordinate (x,y) .

Using midpoint formula , we get

[tex](x,y) = ( \frac{24+10}{2} ,\frac{18+28}{2} )\\\\(x,y) =( \frac{34}{2} ,\frac{46}{2} )\\\\(x,y) =( 17 ,23 )[/tex]

On comparing , we get coordinate (17 , 23) .

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Answer: r=2.62 cm

Step-by-step explanation:

Cylinder Volume: V=πhr^2

179=π(8.3)r^2

179=8.3*3.14*r^2

179=26.062r^2

r^2=6.87

r=2.62 cm

The expression is [tex](x - \sqrt{6} )^{n}[/tex] , n = 1, 2, 3....

Polynomial expression:

A polynomial expression is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

It is given that

x = √6

x - √6 = 0

[tex](x - \sqrt{6} )^{n}[/tex] where n = 1,2,3.....

Therefore the expression of the polynomial given roots is [tex](x - \sqrt{6} )^{n}[/tex] .

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The product should have a 1 significant digit.

When multiplying Scientific notations, the significant figure of the final result must be approximated to the scientific notation that has the least decimal place.

From the question given, if we 4.5160 x 10^3, 2.09 x 107, and 5.8 x 10^3 are multiplied, the product should have 1 significant digits since the least decimal value that occur in question is 1dp

Hence the product should have a 1 significant digit.

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The price that would yield maximum revenue is $260  and maximum revenue is $1,690,000

What is the revenue function?

The fact that total revenue of  the company is the price per purse multiplied by the number of purses sold, means that the revenue modelled function is simply price multiplied by the quantity sold as shown below:

R(x)=P*x

R(x)=Px

R(3000)=$400*3,000

R(3000)=$1200,000

Note for every 500 more purses, the price reduces by $20

R(3500)=$380*3,500

R(3500)=$1,330,000

R(4000)=$360*4000

R(4000)=$1,440,000

R(4500)=$340*4500

R(4500)=$1,530,000

R(5000)=$320*5000

R(5000)=$1,600,000

R(5500)=$300*5500

R(5500)=$1,650,000

R(6000)=$280*6000

R(6000)=$1680,000

R(6500)=$260*6500

R(6500)=$1,690,000

R(7000)=$240*7000

R(7000)=$1,680,000

The total revenue fell at 7,000 purses, which means that the maximum revenue is $1,690,000 at 6500 purses

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Answer:

C. 4.83

Step-by-step explanation:

60/72 = 0.83333333

so the answer is 4.8333333

Probability of an even number product as requested = 7/10 = .7 = 70%

The probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4), and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 even digits = 1*1 = 1. there are thus 6+1 = 7 distinct 2 digit products that result in even numbers from among 10 possible 2 digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%

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The number of number of house holds have pets will be 21450 when 20,735 households do not have pets.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

It is given that the ratio of the households with pets to house holds without pets is 30 to 29 and if 20,735 households do not have pets then it is find the number of number of house holds have pets. It can be find out using the ratio correlation :

That is , 29 is the ratio of house holds without pets ⇒ 20735

1 unit of house holds without pet ⇒ 20735/29 = 715 house hold

Now, the ratio of households with pets  ⇒ 30 x 715 = 21450 house hold

Therefore, the number of number of house holds have pets will be 21450 when 20,735 households do not have pets.

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The two different species of plants will take 5 years to reach the same height.

Given, from the table :

Tree specie A has a:

current height = 38 inches

and its annual growth = 4 inches

Therefore, total height is:

38 + 4x .. eq (1)

Tree specie B has a:

current height = 45.5 inches

and its annual growth = 2.5 inches

Therefore, total height is:

45.5 + 2.5x .. eq (2)

Equate equation 1 and equation 2.

38 + 4x = 45.5 + 2.5x

Subtract the constants.

4x = 45.5 - 38 + 2.5x

4x = 7.5 + 2.5x

now subtract the variables.

4x - 2.5x = 7.5

1.5x = 7.5

x = 7.5/1.5

x = 5

Hence the trees will take 5 years to reach the same height.

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Hi there!

From the given conditions:

[tex]1→1 ⟹1 \times 1 = 1[/tex]

[tex]5→7⟹ 5 \times 7 = 35[/tex]

[tex]8→11 ⟹8 \times 11 = 88[/tex]

[tex]9→4 ⟹9 \times 4 = 36[/tex]

[tex]10 →2 ⟹10 \times 2 = 20[/tex]

Sum = 180, no. of customers = 25

[tex]average = \frac{sum}{no.ofcustomers} [/tex]

[tex] ⟹ \frac{180}{25} = 7.2[/tex]

Therefore, on average, the satisfaction rating of the landscape company was 7.2

Answer:

68 acres per day

Step-by-step explanation:

34 acres per day × 2 days = x

34 × 2 = x

x = 68 acres per day

Hope this helps!

Answer:

68 acres

Step-by-step explanation:

34 acres= 1 day

x=2 days

x=68 acres

they can plant 68 in 2 days

Given the total spent on buying favors = 2.03 $

Let the number of favors she bought = x

let the amount of each favor = y

She bought favors for less than 10 be

x < 10

The amount she spent can be written as  

x * y = 2.03

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The yard is 6 meters wide by use of Pythagoras crossing the diagonal to create a rectangular triangle.

The formula for the Pythagoras theorem is written as c2 = a2 + b2, where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, to generate a Pythagoras triangle, the Pythagoras equation can be used to any triangle with one angle that is precisely 90 degrees.

d² = l² + w²

d = 10

l = 8

Solving for w, the width is

w² = d² - l²

So, we can replace the values with d = 10 and l = 8, to get

w² = 10² - 8²

w² = 100 - 64

w² = 36

w = 6

Hence the width of the yard is 6.

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