A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship. If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?

Answer:

[3, ∞]

Step-by-step explanation:

The area of a triangle whose vertices are r(3, 4), s(6, 2), and t(7, 10) is calculated to be 9.5 units²

Given that,

Vertices are  r(3, 4), s(6, 2), and t(7, 10) which means ,

(x₁,y₁) = (3,4)

(x₂,y₂) = (6,2)

(x₃,y₃) = (7,10)

From formula,

The triangle area

A= 1/2 (|x₁(y₂ -y₃) + x₂(y₂ - y₁) + x₃(y₁ -y₂))

A=1/2(3(2 - 10) + 6(2-4) + 7(4-2))

A = 1/2 (3* -7 + 6* -2 +7* 2 )

A = 1/2 |(-21-12+14)|

A = 1/2 (19)

A = 9.5 units²

area of triangle is 9.5 units² with the given vertices.

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Thus, solving the linear inequalities for y we have

y > 4 - (2/3)x,

y > (3/2)x - 3, and

y ≥ 6x - 6

We have to solve each of the linear inequality for y.

1. The given linear inequality is -

2x + 3y > 12

=> 3y > 12 - 2x

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

2. The given linear inequality is -

3x - 2y < 6

=> -2y < 6 - 3x

=> 2y > 3x - 6

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

3. The given linear inequality is -

4y - 2x ≥ 4x + 3(y-2)

=> 4y - 2x ≥ 4x + 3y - 6

=> 4y - 3y ≥ 4x + 2x - 6

=> y ≥ 6x - 6

Thus, solving the linear inequalities for y we have

y > 4 - (2/3)x,

y > (3/2)x - 3, and

y ≥ 6x - 6

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Salomi's mother's age , represented with algebraic expression is x + 25.

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc).

In other words, algebraic expression is an expression where variables and constant are combined using operations.

Salomi is 25 year younger than her mother.

Therefore,

let

x = Salomi age.

Hence, Salomi mother's age in algebraic expression is as follows:

Salomi mother's age = x + 25

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The percentage of people who filed their taxes during the week of tax day is 10%

I can estimate how many people filed their taxes during the week of April 15th using a percentage of 100 is a/b * 100.

A percentage is a portion of a sum divided into 100 equal parts.

Calculate (Number of persons who submitted their taxes during the week of April 15th / total people who filed their taxes that year) times 100 to get the percentage of people who filed during that week.

Let :

a represents the total number of taxpayers during the week of April 15th.

b represents the total number of taxpayers for that year.

The original equation is reduced to

a/b× 100

As an illustration, 100 individuals submitted their taxes the week of April 15th and

Let's say that year, 1000 persons filed their taxes.

= 100/1000 = 10%

Thus, 10% of Americans submitted their taxes during the week of April 15th, or 100 out of 1,000.

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The value of g = 4π²l/T²

Operators are Mathematical operations that emphasize particular actions like summing up, dividing, and adding multiple times, etc.

In Mathematics, the basic arithmetic operations are Addition, Subtraction Division, and Multiplication.  

The symbols which are used for each operation are

Addition  - (+)

Subtraction  - (-)

Division  - (÷)

Multiplication  - (x)  

Given [tex]l = \frac{gT^{2} }{4 \pi ^{2} }[/tex]  

To get the 'g' value we will use Multiplication and Division

Multiply both sides with 4π²  

=> [tex]4 \pi ^{2} (l )= \frac{gT^{2} }{4 \pi ^{2} }(4 \pi ^{2} )[/tex]  

=> [tex]4 \pi ^{2} (l )= gT^{2}[/tex]  

Divide by T² on both sides

=> [tex]4 \pi ^{2} (l )\frac{1}{T^{2}} = g\frac{T^{2}}{T^{2}}[/tex]

=> [tex]\frac{ 4 \pi ^{2} l }{T^{2}} = g[/tex]

=> [tex]g = \frac{ 4 \pi ^{2} l }{T^{2}}[/tex]  

Therefore,

The value of g = 4π²l/T²

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The formula for T in terms of B and C is T=4B+10C.

How are phrases converted into expressions and equations?

In order to give verbal explanations of mathematical operations:

Find any phrases or key words that denote an operation.

Add the individual processes together to create an expression or equation. Ensure that the sequence of events is maintained.

Let Doughnuts sold in bag be B

Let Doughnuts sold in cartons be C

As given in the question a bag can contain 4 Doughnuts

∴ it is 4B

as cartons can contain 10 Doughnuts

∴ it is 10C

As T is the total number of Doughnuts

∴ the formula is

T=4B+10C

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The combined score for Jodi and Joe is 9-i

Two complex numbers, z₁ = a + bi and z₂ =c +di, can be added by adding the corresponding real and imaginary parts. That is:

z₁+z₂ = (a+c) + (b+d)i

Given: Jodi's score = 5−3i and Joe's score = 4 + 2i

Combined score = 5−3i + 4 + 2i

                           = (5+4) + (-3+2)i

                           = 9-i

Therefore, the combined score is 9-i

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Step-by-step explanation:

mia went shopping. she had $20.00. she bought 1 shirt for $7.50 and a new bracelet for $5.25. how much money does mia have left?​

20 - 7.5 - 5.25 = $7.25 left

[assuming no sales tax]

Answer:

she has 7.25

Step-by-step explanation:

So, Mia has twenty dollars then purchases a shirt which is 7.25 and a bracelet for the price of 5.25

20.00 - 7.50= 12.50-5.25=7.25

Using the concepts of function, we got that to tell how far the turtle has travelled ,my function will be defined as: def distance(x, y) where x and y are the final co-ordinates of turtle.

The turtle module actually provides turtle graphics primitives, in both the object-oriented and the procedure-oriented ways. Because it uses kinter for the underlying graphics, it needs a version of Python installed with Tk support.

Turtle. distance()

This method is actually used to return the distance from the turtle to (x, y) in turtle step units.

Hence, if am going create a new function to tell how far the turtle has travelled. your function will be defined as: def distance(x, y) where x and y are the final co-ordinates of turtle.

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Answer:

good luck

Step-by-step explanation:

Answer:

BANG IT LIKE A CHOLO

Step-by-step explanation:

No the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

In the give question we have to find the octopus can tell the difference between circles and rectangles or not.

From the question;

Circles: 13

Rectangles: 31

Null hypothesis: proportion of circles found = 0.5

Alternate hypothesis: Proportion of circles found > 0.5

Total number of trials is 31+13=44

Since 13 times circle is choosen.

So the probability that octopus chooses circle is

P(C) = Total number of circle/Total number of trials

P(C)=13/44

P(C)=0.295

As probability is 0.295<0.50

So, no the octopus can not differentiate between circles and rectangle and the probability of picking circle is 0.295.

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The sample size will now have to be is 3200.

Given:

the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (e) must be reduced to just 0.025. if the original calculation led to a sample size of 1000.

n = p(1-p)(z/E)^2

800 = 0.5(1-0.5)(z/0.05)^2

800 = 0.5*0.5* z^2/0.0025

800 = 0.25 * z^2/0.0025

800 = 25/100*10000*z^2/25

800 = 1*100*z^2

800/100 = z^2

8 = z^2

z = [tex]\sqrt{8}[/tex]

z = 2.8284

n = p(1-p)(z/E)^2

= 0.25(2.8284/0.025)^2

= 0.25*(113.136)^2

= 0.25*12799.754496

= 3199.938 ≈ 3200

Therefore the sample size will now have to be is 3200.

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According to the Pythagoras theorem, the value of x is 13.8

Pythagoras theorem:

Pythagoras theorem describes that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Given,

Here we have the two right angled triangles with the side values.

Here we have to find the value of x.

In order to find the value of x, we have to find the value of the bisector KM,

So, for that we have to use the concept of Pythagoras theorem,

We can written this one the following type of equation,

=> (12.3)² = (5.4)² + KM²

=> 151.29 = 29.16 + KM²

=> KM² = 122.13

=>  KM = 11.05

Therefore, the value of x is calculated in the same manner,

=> x² = (8.2)² + (11.05)²

=> x² = 67.24 + 122.10

=> x² = 189.34

=> x = √189.34

=> x = 13.76

When we round off this into the nearest tenth the we get the value of x as 13.8.

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When analyzing two quantitative variables the first thing that should be done make a scatterplot.

When comparing two quantitative variables, a scatterplot is the most useful display technique. We plot the variable we consider the response variable on the y-axis and the explanatory or predictor variable on the x-axis.

How do we know which variable is which? The explanatory variable, in general, attempts to explain or predict the observed outcome. A study's outcome is measured by the response variable. One may even consider investigating whether one variable causes variation in another variable; for example, a popular research study found that taller people are more likely to earn higher wages. In this case, the explanatory variable Height would be used to explain the variation in the response variable Salaries.

When summarizing the relationship between two quantitative variables, we must consider the following:

1.Association/Direction (i.e. positive or negative)

2.Form (i.e. linear or non-linear)

3.Strength (weak, moderate, strong)

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Answer:

0.18

Step-by-step explanation:

1005 - 82% = 18%  Divide by 100 to get the decimal answer of 0.18

According to the given expression, the inequality that can model the given situation can be stated as 520 < 400 + 15x.

Since Dan wants to know how many hours he needs to spend walking dogs, let us assume this to be x:

15x + 400

Dan wants to know how many hours he needs to spend walking dogs to earn more than $520 in a week. So the above expression is greater than 520:

15x + 400 > 520

When400 is subtracted from 520, the result is true:

15x > 120

Thus, the first inequality expression can be rearranged as:

520 < 400 + 15x

Thus, the inequality that can model the given situation can be stated as 520 < 400 + 15x.

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The volume of the block after cutting the smaller cubes is:

volume = 56/125 [tex]cm^{3}[/tex]

What is volume?

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies.

The formula to calculate the volume of the cube is given by:

Volume = [tex]a^{3}[/tex], where a is the length of its sides or edges

Length of solid wooden cube= [tex]\frac{4}{5} cm[/tex]

Length of smaller wooden cube= [tex]\frac{1}{3} cm[/tex]

Volume of the large cube = [tex](\frac{4}{3} )^{3}[/tex]

Volume of the large cube = [tex]\frac{64}{125} cm^{3}[/tex]

Volume of the small cube = [tex]\frac{1}{5} cm^{3}[/tex]

Volume of the small cube = [tex]\frac{1}{125} cm^{3}[/tex]

Volume of block after cutting out the smaller cubes is

                = [tex]\frac{64}{125} -\frac{(8)(1)}{125}[/tex]

                = [tex]\frac{64-8}{125}[/tex]

                =[tex]\frac{56}{125}[/tex][tex]cm^{3}[/tex]

Hence, the volume of the block after cutting the smaller cubes is:

volume = 56/125 [tex]cm^{3}[/tex]

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The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

Another example could be kilo gram to gram.

As per the given,

Number of dimes = 276

1 dollar = 10 dimes.

The number of dollars in 276 dimes, is 276/10 = 27.6

So, 27 dollars and 6 dimes.

Hence "The number of dimes in 1 dollar is 10 thus the number of whole dollars that can be made from 276 dimes will be 27 and 6 dimes will leave over".

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Answer:

90 liters

Step-by-step explanation:

It's given in the question!

We will get the solution of the equation g(x) = f(x) by finding the rule for the linear equation g(x) and solving the linear equation, the solution is x = 2.

Here we have two functions, one graphed, which is g(x), and the other defined by a rule:

f(x) = -x + 1

For g(x) we can use the graph to find the rule, notice that this is a linear equation so we can write:

g(x) = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = -3, then:

g(x) = m*x - 3

To find the value of m we can use another point on the graph, for example, (3, 0)

Replacing that we get:

g(3) = 0 = m*3 - 3

3 = m*3

3/3 = m

1 = m

Then g(x) = x - 3

Now we can solve:

g(x) = f(x)

Replacing the functions we get:

x - 3 = -x + 1

Now we can solve this linear equation for x:

x - 3 = -x + 1

x + x = 3 + 1

2x = 4

x = 4/2

x = 2

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Answer:

The average speed is 80km/h.

Step-by-step explanation:

In order to calculate the average speed you have to divide the total distance by the total elapsed time:

Let t represent time (in hours)

t=12:30-11:30=1

Let D represent distance (in kilometers)

D=80

Therefore, since t=/=0:

D/t=80/1=80km/h

And there you have it! Your answer is 80 km per hour.

Answer:

Step-by-step explanation:

Half of the 80 people are women, so divide 80 by 2.

[tex]80/2=40[/tex]

One quarter of that is men.

[tex]40/4=10[/tex]

The rest are children, so:

[tex]40+10=50\\80-50=30[/tex]

There are 30 children, 40 women, and 10 men.

The number of children to men is n:1.

There are 30 children to 10 men, and after simplifying that by dividing by 10, so the value of n is 3, and the ratio is 3:1.

Answer:

3:1

Step-by-step explanation:

Half of the 80 people are women. 80 divided by 2 is 40.

One-quarter of the 40 women are men. 40 divided by 4 is 10.

The total number of men and women is 50, and the rest are children. 50 subtracted from 80 is 30.

There are 40 women, 30 children, and 10 men.

The ratio of children to men is 30:10, which simplifies to 3:1.

Orange County's crime rate is predicted to be 83%. This estimate is based on data from the Orange County Sheriff's Office, which showed that the number of crimes reported per 100,000 residents in the county has been steadily declining over the past few years.

A point estimate for the crime rate in Orange County is = 82.7% = 83%

The predicted number of crimes reported per 100,000 residents in Orange County is

= 100,000 X 0.827

= 82,700

The estimate for the crime rate in Orange County is 83%. However, this is just an estimate and the actual rate could be higher or lower. To get a more accurate estimate, we would need to collect more data.

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The pattern isn't linear as the difference in values is different from 30.

From the information, jezabel had 1,452 subscribers last week and now she had 1,483 subcribers.

The difference will be:

= 1483 - 1452

= 31

It was further stated that every video she posts gains her about 30 new subscribers.

This shows that it isn't linear.

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In the binomial expansion of (2 + 3x)ⁿ, the value of n = 22/5

Binomial expansion is the expansion of the binomial (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ where ⁿCₓaˣbⁿ⁻ˣ is the general term and x = 0 to n

Since we require the expansion of  (2 + 3x)ⁿ, comparing it with the binomial expansion equation above  (a + b)ⁿ.

So, a = 2 and b = 3x

So, the binomial expansion is (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3x)ⁿ⁻ˣ

= ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ

So, the general term of  (2 + 3x)ⁿ = ∑ⁿCₓ2ˣ(3ⁿ⁻ˣ)xⁿ⁻ˣ and the coefficient term is ⁿCₓ2ˣ(3ⁿ⁻ˣ)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15. Then

For the x³ term, xⁿ⁻ˣ = x³

⇒ n - x = 3

⇒ x =n - 3

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₃2ⁿ⁻ˣ(3³) =

Also, for the x⁴ term, xⁿ⁻ˣ = x³

⇒ n - x = 4

⇒ x =n - 4

So, substituting this into the coefficient term, we have

ⁿCₓ2ˣ(3ⁿ⁻ˣ) = ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴)

Now since coefficient of x³ and x⁴ are in the ratio if 8:15, we have that

ⁿCₙ₋₃2ⁿ⁻ˣ(3³)/ⁿCₙ₋₄2ⁿ⁻ˣ(3⁴) = 8/15

ⁿCₙ₋₃/(ⁿCₙ₋₄ × 3)= 8/15

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/15 × 3

ⁿCₙ₋₃/ⁿCₙ₋₄= 8/5

n!/(n - 3)![n - (n - 3)]!  ÷ n!/(n - 4)![n - (n - 4)]! = 8/5

n!/(n - 3)![n - n + 3)]!  ÷ n!/(n - 4)![n - n + 4)]! = 8/5

n!/(n - 3)!3!  ÷ n!/(n - 4)!4! = 8/5

n!/3!(n - 3)! ÷ n!/4!(n - 4)(n - 3)! = 8/5

n!/3!(n - 3)! × 4!(n - 4)(n - 3)!/n! = 8/5

4!/3! × (n - 4) = 8/5

4 × 3!/3! × (n - 4) = 8/5

4(n - 4) = 8/5

Dividing through by 4, we have

(n - 4) = 8/(5 × 4)

(n - 4) = 2/5

Cross-multiplying, we have

5(n - 4) = 2

Expanding the brackets, we have

5n - 20 = 2

5n = 20 + 2

5n = 22

n = 22/5

So, the value of n = 22/5

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Answer:

l = 1

Step-by-step explanation:

v = lwh

8 = l(2)(4)

8 = l8  Divide both sides by 8

1 = l