20 points pls quick and mark brainly

American Eagle Outfitters is advertising 30% off all merchandise.
14A. Zoe wants to buy a sweater that originally costs $40. How much will she save if she buys it on sale? Show your work or explain in words how did you get the answer.

The domain of a relation is the set of all the first elements of the ordered pairs in the relation, and the range of a relation is the set of all the second elements of the ordered pairs in the relation.

So, for the given relation {(5,0),(8,4),(5,2),(-2,4)}, the domain would be {5, 8, -2} and the range would be {0, 4, 2}.

To find the domain, we simply take the first element of each ordered pair and put them in a set. Similarly, to find the range, we take the second element of each ordered pair and put them in a set.

Therefore, the domain of the relation is {5, 8, -2} and the range of the relation is {0, 4,2}.

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The solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.

Two or more expressions with an Equal sign is called as Equation.

We can solve this system of equations using substitution. Solving the second equation for y, we get:

y = 3x - 3

Substituting this expression for y into the first equation, we get:

9x - 3(3x - 3) = 9

9x - 9x + 9 = 9

Therefore, the equation is true for any value of x.

Hence, the solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.

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Step By Step Explanation

Filled jar = ?

How much poured or (x) = 350ml × 8 glasses

=2800 ml

How much left or (y) = 200ml

Capacity = How much poured + How much left

Capacity = x + y

Capacity = 2800 ml + 200 ml

Capacity = 3000ml

Give answer in litres

1 litre = 1000 millilitre

So 3000ml = 3000 ÷ 1000

So 3000 ml = 3 litres

Capacity = 3 litres

The equation that represents a linear function rule for the following set of ordered pairs is  A. y = -3x + 2

We can express the Equation of a linear function, as y = mx + b.

m= slope

b= y-intercept

We can determine the slope (m):

= (change in y)/(change in x )

then we can substitute the values as :

= (-7 -(-4)) / (3 - 2)

= -3/1

= -3

Then thevalue of b can be found through the substituting of  m = -3  into the  equation knowing that  (1, -1) = (x, y)

Then we have;

-1 = [-3(1) + b]

-1 = [-3 + b]

[-1 + 3] = b

b = 2

In this case ,  we can put m = -3 , b = 2

y = mx + b

y = [-3(x) + 2]

Therefore, we have

y = -3x + 2

Hence option A is correct.

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complete question:

Which equation represents a linear function rule for the following set of ordered pairs?

x y

1 -1

2 -4

3 -7

A. y = -3x + 2

B. y = -3x - 2

C. y = -2x + 3

D. y = -2x - 3

The largest possible value x could take given that it must be an integer for x < 2 is 1.

The key distinction between an inequality and an equation is that an inequality describes a connection of inequality between two expressions, whereas an equation expresses equality between two expressions. In other words, an inequality shows that one expression is more or less than the other expression, but an equation shows that two expressions have the same value.

The highest number x might have is 1 if x must be an integer and x 2. This is due to the fact that any number higher than one would break the inequality x 2, and any number between one and two that is not an integer would also violate the stipulation that x must be an integer.

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Carrie can walk at a speed of 3 mph.

To find out how fast Carrie can walk, we can use the formula distance = speed × time. Let's call the speed at which Carrie walks x, and the time it takes her to walk 6 miles t.

Since she can ride 9 mph faster than she can walk, her biking speed will be x + 9. We can set up the following equations:

6 = x × t (for walking)
24 = (x + 9) × t (for biking)

Since the time it takes her to walk 6 miles and bike 24 miles is the same, we can set the two equations equal to each other:

x × t = (x + 9) × t

Simplifying the equation gives us:

x = x + 9

Subtracting x from both sides gives us:

0 = 9

This is not a valid solution, so we need to go back to our original equations and solve for t:

t = 6/x (for walking)
t = 24/(x + 9) (for biking)

Setting these two equations equal to each other gives us:

6/x = 24/(x + 9)

Cross-multiplying gives us:

6(x + 9) = 24x

Distributing the 6 gives us:

6x + 54 = 24x

Subtracting 6x from both sides gives us:

54 = 18x

Dividing by 18 gives us:

x = 3

So Carrie can walk 3 mph.

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The solution is, the value of x is, x = 12.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

from the given figure, we get,

the triangles are similar,

so, we know that, the sides are proportional to each other.

i.e. 8:4 = x: 6

or, x = 8 * 6 / 4

or, x  = 2 * 6

or, x = 12

Hence, The solution is, the value of x is, x = 12.

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Answer:

1162261467

Step-by-step explanation:

Note that this is a geometric sequence.

1,3,9,27
The pattern is to multiply the number by 3 to get to the next term.
a = 1

r = 3

n=20

arⁿ⁻¹ = nth term

You then substitute the values of a,r and n into the nth term:

arⁿ⁻¹=3¹⁹

3¹⁹=1162261467 which is the 20th term of the sequence

Hoped this helped

Answer:

To find the 20th term of the sequence 1, 3, 9, 27, we need to first identify the pattern of the sequence. It appears that each term of the sequence is obtained by multiplying the previous term by 3. This means that the sequence is a geometric sequence with first term (a) = 1 and common ratio (r) = 3.

Using the formula for the nth term of a geometric sequence:

an = a * r^(n-1)

where an is the nth term of the sequence, a is the first term, r is the common ratio, and n is the term number.

Substituting the values we have:

a = 1, r = 3, and n = 20

an = 1 * 3^(20-1) = 1 * 3^19 = 1162261467

Therefore, the 20th term of the sequence 1, 3, 9, 27 is 1162261467.

Step-by-step explanation:

brainliest pls

The value of h is 99.969.

The Esscher Premium Principle is a method of calculating insurance premiums that considers the risk of an event occurring and the potential severity of the loss. The formula for the Esscher Premium Principle is:

Ex = ln(∑eαx Px)/α

Where Ex is the Esscher premium, α is the parameter, x is the loss amount, and Px is the probability of the loss occurring.

In this case, we are given X (3, 0.02), meaning that the loss amount is 3 and the probability of the loss occurring is 0.02. We are also given that the Esscher premium is 300 and the parameter is 1. Plugging these values into the formula, we get:

300 = ln(∑e1(3) 0.02)/1

Simplifying the equation, we get:

300 = ln(0.02e3)

Taking the natural logarithm of both sides, we get:

e300 = 0.02e3

Dividing both sides by 0.02, we get:

e300/0.02 = e3

Taking the natural logarithm of both sides again, we get:

300 - ln(0.02) = 3

Solving for h, we get:

h = (300 - ln(0.02))/3

h = 99.969

Therefore, the value of h is 99.969.

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The statistic that "Richard's Supplies sells more calculators than Joseph's Deals" based solely on the information given is misleading because it compares the total sales of one business for an entire month with the sales of another business for only one week.

It's possible that Joseph's Deals could sell more calculators than Richard's Supplies in a given week or even in the entire month of October, despite the fact that they only sold 30 calculators in the first week but we don't have enough information to compare the sales of these two businesses accurately.

In addition, we don't know if Richard's Supplies and Joseph's Deals are similar businesses with similar customer bases, pricing strategies, and marketing efforts. These factors could also affect their respective sales numbers.

In conclusion, to draw a meaningful comparison between the sales of these two businesses, we would need to gather more data about their sales over a longer period of time and under similar conditions.

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The x-intercepts of y=x2+5x−24 can be determined by solving the equation 0=x2+5x−24. Using the quadratic formula, we can find that x = 6 and x = -4 are the two x-intercepts.

The x-intercepts of y=x2−11x+10 can be determined by solving the equation 0=x2−11x+10. Using the quadratic formula, we can find that x = 5 and x = -2 are the two x-intercepts.
To determine the x-intercepts of the given functions, we need to find the values of x that make y equal to 0. We can do this by factoring the equations and setting each factor equal to 0.

2. y = x^2 + 5x - 24
0 = x^2 + 5x - 24
0 = (x + 8)(x - 3)
x + 8 = 0 or x - 3 = 0
x = -8 or x = 3

The x-intercepts are (-8, 0) and (3, 0).
3. y = x^2 - 11x + 10
0 = x^2 - 11x + 10
0 = (x - 1)(x - 10)
x - 1 = 0 or x - 10 = 0
x = 1 or x = 10

The x-intercepts are (1, 0) and (10, 0).
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Answer:

9

Step-by-step explanation:

7/8 divided by 1/8 is 7

7+2 = 9

Brainliest?

The answer of the number of offers you received are as follow,

1. Mean is equal to 1.96.

2. Standard deviation is equal to 1.17 (rounded to two decimal places) .

1.Mean (or expected value) is represented by E(X)

Formula of the expected value is,

E(X) = ∑xP(x)

Substitute the value from the table we get,

⇒E(X) = (0)(0.19) + (1)(0.12) + (2)(0.38) + (3)(0.16) + (4)(0.15)

⇒E(X)  = 0 + 0.12 + 0.76 + 0.48 + 0.6

⇒E(X)  = 1.96

2. Standard deviation of the number of offers received ,

⇒ Standard deviation 'σ' = √[ Σ(x - E(X))² P(x) ]

Substitute the values from the table we get,

⇒ Standard deviation 'σ'

= √[ (0 - 1.96)² (0.19) + (1 - 1.96)² (0.12) + (2 - 1.96)² (0.38) + (3 - 1.96)²(0.16) + (4 - 1.96)²(0.15) ]

= √[ 1.3728 ]

≈ 1.171665

≈1.17(rounded to two decimal places)

Therefore, the mean and the standard deviation of the number of offers received is approximately 1.96 and 1.17 (rounded to two decimal places) respectively.

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The above question is incomplete, the complete question is:

Suppose you applied for positions at four different companies and let X be the number of offers you received

X      :            0               1               2               3                4

P(x)  :             0.19         0.12           0.38         0.16            0.15

1.  Find the mean

2.  standard deviation

of the number of offers you received. Round your answer to two decimal places

The income tax amount of 6% will be equal to $252 on a salary of $4200.

A number or ratio that can be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent implies.

A percentage is a figure or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A percentage is a figure without dimensions and without a standard measurement.

We must divide the value by the overall value to find the percentage, and then multiply the resulting number by 100.

A tax placed on people or organisations in relation to their income or profits is known as an income tax. Tax rates multiplied by taxable revenue are typically used to calculate income taxes. Tax rates can change depending on the taxpayer's characteristics and sort of income.

The word "income tax" refers to a category of tax that governments levy on income generated by businesses and people under their jurisdiction.

In this question,

Salary amount= $4200

Income tax= 6%

The amount to be paid in income tax= 6% of $4200

                                                             = (6/100)*4200

                                                             = $252

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3 gallons are the starting value determined by the slope-intercept relation.

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.

To determine how much gas is entering his car each second, we must determine the rate of change:

Rise / Run is the rate of change.

Rate of change: (11 - 3 - 11) / (48 - 0)

Change rate: 8/48 = 1/6 gallons

Making use of the slope-intercept relationship:

Y = b(x) + c(slope); c(initial gas amount)

Choose any (x, y) point pair on the table:

(0, 3)

3 = 1/6x + c 3 = 1/6(0) + c\s3 = 0 + c\sc = 3

As a result, the starting point is 3 gallons.

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The function values.

To evaluate the function g(x) = 8 - x / 8 + 7 at the indicated values, we need to substitute the values into the function and simplify.

g(2) = 8 - 2 / 8 + 7 = 6 / 15 = 2 / 5

g(-8) = 8 - (-8) / 8 + 7 = 16 / 15 = 16 / 15

g(1/2) = 8 - (1/2) / 8 + 7 = (15.5) / 15 = 31 / 30

g(a) = 8 - a / 8 + 7 = (15 - a) / 15

g(a - 8) = 8 - (a - 8) / 8 + 7 = (16 - a) / 15

g(x^2 - 8) = 8 - (x^2 - 8) / 8 + 7 = (16 - x^2) / 15

So, the function values are:
g(2) = 2 / 5
g(-8) = 16 / 15
g(1/2) = 31 / 30
g(a) = (15 - a) / 15
g(a - 8) = (16 - a) / 15
g(x^2 - 8) = (16 - x^2) / 15

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Answer:

One possible way to complete the array is:

    8  |  2 0 8

       |

    ------

       |

 2 |  2 6

 5 |  5 2

 1 |  1 7

 6 |  2 0

The answer is 26, so 208 ÷ 8 = 26.

To complete the array, we start by dividing the hundreds digit (2) by 8, which gives 0 with a remainder of 2. We write the remainder (2) in the ones place of the first row. Then we bring down the tens digit (0) and add it to the remainder to get 20. We divide 20 by 8, which gives 2 with a remainder of 4. We write the remainder (4) in the tens place of the second row, and bring down the ones digit (8) to the ones place of the second row. Finally, we add the digits in the second row to get 26, which is the quotient of the division

Step-by-step explanation:

Answer:

Step-by-step explanation:

To graph the equation 3(x - 2) = 5(x + 1), we can first simplify it by expanding the brackets:

3x - 6 = 5x + 5

Next, we can isolate the variable on one side of the equation. We can do this by subtracting 3x from both sides and adding 6 to both sides:

-11 = 2x

x = -11/2

Now we have the x-coordinate of the point where the graph of the equation intersects the x-axis. To find the y-coordinate of this point, we can substitute x = -11/2 into one of the original equations and solve for y:

3(x - 2) = 5(x + 1)

3(-11/2 - 2) = 5(-11/2 + 1)

-33/2 - 6 = -55/2 + 5

-33/2 - 6 + 55/2 = 5

-33/2 + 44/2 = 5

11/2 = 5

The requried combined length of both trains is 900 meters or 900 km.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Let's first convert the given speeds from km/h to m/s to make the calculations easier.

Speed of the first train = 102 km/h = (102 x 1000) m/3600 s = 28.33 m/s

Speed of the second train = 30 km/h = (30 x 1000) m/3600 s = 8.33 m/s

Now, let's consider the relative speed of the two trains since they are moving in the same direction:

Relative speed = Speed of first train - Speed of second train

= 28.33 - 8.33

= 20 m/s

Let's assume that the length of the first train is x m and the length of the second train is y m.

Distance covered by first train in 45 seconds = (x + y) m

Speed of first train = Distance covered by first train / Time taken

= (x + y) / 45 km/s

We know that the speed of the first train is 20 m/s. So, we can write:

20 = [(x + y) / 45]

Solving for (x + y),

x + y = 900 m

Therefore, the combined length of both trains is 900 meters or 900 km.

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The value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

According to the given equation, a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers, we can rearrange the equation to find the value of one of the variables in terms of the others. For example, we can rearrange the equation to find the value of x in terms of the other variables:

x = b+y-a = c+z+1-a

Similarly, we can rearrange the equation to find the value of y and z in terms of the other variables:

y = a+x-b = c+z+1-b

z = a+x-c-1 = b+y-c-1

Now, we can substitute these values into the given matrix to find the value of each element:

[[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]] = [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z+1-c-1]]

Simplifying the matrix, we get:

[[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]]

Therefore, the value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

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A basis for \( \mathbb{R}^{4} \) containing \( v \) and \( w \) is \( \{v, w, e_{1}, e_{2}\} = \{(1,-1,1,-1), (0,1,0,1), (1,0,0,0), (0,1,0,0)\} \).

A basis for \( \mathbb{R}^{4} \) is a set of four linearly independent vectors that span \( \mathbb{R}^{4} \). We are given two vectors \( v=(1,-1,1,-1) \) and \( w=(0,1,0,1) \) that are part of the basis. To find the other two vectors, we can use the standard basis vectors \( e_{1}=(1,0,0,0) \) and \( e_{2}=(0,1,0,0) \) and check if they are linearly independent with \( v \) and \( w \).

First, we check if \( e_{1} \) is linearly independent with \( v \) and \( w \). We can do this by setting up the equation \( a_{1}v + a_{2}w + a_{3}e_{1} = 0 \) and solving for the coefficients \( a_{1}, a_{2}, \) and \( a_{3} \).

\( a_{1}(1,-1,1,-1) + a_{2}(0,1,0,1) + a_{3}(1,0,0,0) = (0,0,0,0) \)

This gives us the system of equations:

\( a_{1} + a_{3} = 0 \)

\( -a_{1} + a_{2} = 0 \)

\( a_{1} = 0 \)

\( -a_{1} + a_{2} = 0 \)

We can see that the only solution is \( a_{1}=a_{2}=a_{3}=0 \), which means that \( e_{1} \) is linearly independent with \( v \) and \( w \).

Next, we check if \( e_{2} \) is linearly independent with \( v \), \( w \), and \( e_{1} \) by setting up the equation \( a_{1}v + a_{2}w + a_{3}e_{1} + a_{4}e_{2} = 0 \) and solving for the coefficients \( a_{1}, a_{2}, a_{3}, \) and \( a_{4} \).

\( a_{1}(1,-1,1,-1) + a_{2}(0,1,0,1) + a_{3}(1,0,0,0) + a_{4}(0,1,0,0) = (0,0,0,0) \)

This gives us the system of equations:

\( a_{1} + a_{3} = 0 \)

\( -a_{1} + a_{2} + a_{4} = 0 \)

\( a_{1} = 0 \)

\( -a_{1} + a_{2} = 0 \)

Again, we can see that the only solution is \( a_{1}=a_{2}=a_{3}=a_{4}=0 \), which means that \( e_{2} \) is linearly independent with \( v \), \( w \), and \( e_{1} \).

Therefore, a basis for \( \mathbb{R}^{4} \) containing \( v \) and \( w \) is \( \{v, w, e_{1}, e_{2}\} = \{(1,-1,1,-1), (0,1,0,1), (1,0,0,0), (0,1,0,0)\} \).

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Therefore , the solution of the given problem of equation comes out to be which is (x, y) = (-60/17, 58/17).

The same letter is frequently used in mathematical formulas to attempt to enforce unity between two claims. Mathematical expression equations, also referred to as assertions, are used to demonstrate the equality of many academic figures. Using y + 6 = 12 like an example, the normalise separates 12 but rather b + 6 in to the two pieces. The relationship between each sign variable and the amount of lines can be identified. A symbol's meaning typically runs counter to itself.

Here,

Elimination is one approach that could be used to solve the problem. So that the component of y in each equation is -12, we can do this by multiplying the first equation by 4 and the second equation by 3:

=> 4(2x + 3y = -6) -> 8x + 12y = -24

=> 3(3x - 4y = -12) -> 9x - 12y = -36

The two formulae combined give us:

=> 8x + 12y + 9x - 12y = -24 - 36

=> 17x = -60

=>x = -60/17

We can find y by substituting x into either equation:

=> 2(-60/17) + 3y = -6

=> 3(-60/17) - 4y = -12

When we simplify each solution, we obtain:

=> -120/17 + 3y = -6

=>-180/17 - 4y = -12

By y in each solution and solving, we obtain:

=> 3y = 174/17

=> y = 58/17

As a result, there is only one solution to the system, which is (x, y) = (-60/17, 58/17).

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Answer:

Step-by-step explanation:

North Dakota is 34 times larger

                 Puerto Rico

North Dakota = 1.83x[tex]10^{5}[/tex]   [tex]Km^{2}[/tex]    

Puerto Rico =  5.33 x [tex]10^{3}[/tex]   [tex]Km^{2}[/tex]  

                       1.83 x [tex]10^{5}[/tex]

                       5.33 x [tex]10^3[/tex]        = 0.34 x [tex]10^2[/tex]

The method for calculating the area of a figure depends on the type of figure.

Here are some common formulas for finding the area of different shapes:

Square: To find the area of a square, you multiply the length of one side by itself: Area = side x side or A = s²

Rectangle: To find the area of a rectangle, you multiply the length by the width: Area = length x width or A = lw

Triangle: To find the area of a triangle, you multiply the base by the height and divide by 2: Area = 1/2 x base x height or A = 1/2 bh

Circle: To find the area of a circle, you multiply pi (3.14) by the radius squared: Area = pi x radius^2 or A = πr^2

Trapezoid: To find the area of a trapezoid, you multiply the average of the bases by the height: Area = 1/2 x (base1 + base2) x height or A = 1/2 (b1 + b2)h

These are just some of the formulas for calculating the area of different shapes. Depending on the figure you're working with, you may need to use a different formula or combination of formulas to find the area.

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The amount of chemical in the tank after 15 minutes is 154.14 grams.

To determine the amount of chemical in the tank after 15 minutes, we need to use the formula for the concentration of a solution:

C = m/V

Where C is the concentration of the solution, m is the mass of the chemical, and V is the volume of the solution.

Initially, the tank contains 12 litres of water and 24 grams of chemical A, so the initial concentration of the solution is:

C0 = 24/12 = 2 grams per litre

The solution flows into the tank at a rate of 4 grams per litre and 4 litres per minute, so the amount of chemical flowing into the tank per minute is:

4 grams per litre × 4 litres per minute = 16 grams per minute

The well-stirred mixture flows out of the tank at a rate of 2 litres per minute, so the amount of chemical flowing out of the tank per minute is:

C × 2 litres per minute = 2C grams per minute

The net change in the amount of chemical in the tank per minute is:

16 grams per minute - 2C grams per minute = 16 - 2C grams per minute

After 15 minutes, the net change in the amount of chemical in the tank is:

(16 - 2C) grams per minute × 15 minutes = 240 - 30C grams

The final amount of chemical in the tank is:

m = 24 + 240 - 30C = 264 - 30C grams

The final volume of the solution in the tank is:

V = 12 + 4 litres per minute × 15 minutes - 2 litres per minute × 15 minutes = 42 litres

The final concentration of the solution in the tank is:

C = m/V = (264 - 30C)/42

Solving for C, we get:

42C = 264 - 30C

72C = 264

C = 264/72 = 3.67 grams per litre

The final amount of chemical in the tank is:

m = C × V = 3.67 grams per litre × 42 litres = 154.14 grams

Therefore, the amount of chemical in the tank after 15 minutes is 154.14 grams.

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Answer: The amount is $43492.35 and the interest is $10992.35.

Step-by-step explanation:

To find amount we use formula:

A = P(1+r/n)^nt

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

In this example we have

P=32,000 , R=6% , N = 1 T= 5 YEARS

After plugging the given information we have

A=32000(1+0.06/1)^1.5

A=32500*1.06^5

A=32500*1.338226

A=$43492.35

To find interest we use formula A=P+I , since A= 43492.35  P =32500  we have:

A=P+I

$43492.35 = 32500+I

I=$43492.35-32500

I=$10992.35

Answer:

-11

Step-by-step explanation:

*The sum of all three angles of a triangle is 180*

So,

80+60

140 + (x + 51) = 180

-140 -140

x + 51 = 40

- 51 - 51

x = - 11

HOPE this helped

Answer: The second and last one

Step-by-step explanation:

The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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The equation (3x⁴z² - 8x⁵)(-6xz⁶) is rewritten without parenthesis as 48x⁶z⁶ - 18x⁵z⁸

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Given the equation:

(3x^(4)z^(2)-8x^(5))(-6xz^(6))

Simplifying gives:

= (3x⁴z² - 8x⁵)(-6xz⁶)

Opening the parenthesis gives:

= -18x⁵z⁸ + 48x⁶z⁶

= 48x⁶z⁶ - 18x⁵z⁸

The equation is equivalent to 48x⁶z⁶ - 18x⁵z⁸

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