Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.
(a) Give the domain and range of the function.
(b)Give an estimate to the nearest hundreds for . Explain how you determined your estimate and tell what means in context of the situation.
(c)Ebony’s bank balance first reached $0 on Day 12. How would you show that information in function notation?
(d)Ebony’s bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know.

Answer:

1/3

Step-by-step explanation:

This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.

5 pages X 60 minutes = 300 pages per hour

It will take 1 hour to print 300 pages on a printer that prints at 5 pages per minute. Do you have enough ink to print 300 pages?

Recall that we can factorize any polynomial as:

where k is a constant and a,b,...n are the root of the polynomial.

Therefore, a polynomial function with the real zeros -3,0, and 3 is:

k can be any constant, therefore, we can set k=1.

Answer:\(x=15\)

Step-by-step explanation:

Angles that are opposite from each other are going to be the same in this case.

Let's plug in 15 into x

\(4(15)+8\\60+8\\68\)

Answer:

is the correct answer.

Step-by-step explanation:

We are given that co-ordinates of D is (-3,8) and F is (5,2).

For finding a point E on the line segment DF dividing it in a ratio 4:1, we can use segment formula.

\(x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}\)

Where \((x,y)\) is the co-ordinate of the point which  

divides the line segment joining the points and in the ratio m:n.

As per the given values  

\(x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2\)

Putting the given values in above formula :

x-co-ordinate of F:

\(x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4\)

y-co-ordinate of F:

\(y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2\)

So, answer is \(E(3.4,3.2)\).

According to the Commutative Property of Multiplication, the product of a multiplication phrase is unaffected by the factors' order.

It is possible to multiply integers, fractions, decimals, exponents, and algebraic equations using the commutative property of multiplication.

The addition and multiplication arithmetic operations are covered by the commutative property. This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or location of the numbers are changed. For instance, 4 + 5 equals 9, and 5 + 4 equals 9.

The commutative property of addition states that the sum is unaffected by the arrangement of the addends. For instance, 4 + 2 Equals 2 + 4 4 + 2 = 2 + 4, plus 2, equals 2, plus 4. 4 + 2 = 2 + 44.

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The required diameter of the spherical gasoline tank is given as 50 feet.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet

Diameter = 2 × r
              = 2 × 25
              = 50 feet

Thus, the required diameter of the spherical gasoline tank is given as 50 feet.

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Answer:

hdvbn

Step-by-step explanation:

nfshvjjnmmnjjmbm

The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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The limit of xlnx when x is tending towards zero is zero.

What is limit in mathematics?

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.

Given limit is:

\(\lim_{x \to 0} x lnX\)

Considering f = x, and g = ln x

The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.

The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as

\(\frac{lnx}{1/x}\)

We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as

The limits

\(\lim_{x \to 0^+} lnx= - \infty\), and

\(\lim_{x \to 0^+} \frac{1}{x}\)

The limits  \(\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}\) exists as:

\(\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0\)

Hence the answer is 0.

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The solution of the compound inequality is x < 3/4 or x >2.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A compound inequality:

4x - 5 < -2 or x + 1 > 3.

Solving inequality,

4x < -2 + 5 or x > 2

4x < 3 or x > 2.

x < 3/4 or x >2.

Therefore, the solution is x < 3/4 or x >2.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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If we have a finite group G and an element x in G, then there must exist a positive power of x which equals its inverse (i.e., x⁻¹ = \(x^{k}\) for some positive integer k).

A finite group is a mathematical object consisting of a set of elements and a binary operation that combines two elements to produce a third. The key feature of a finite group is that the set of elements is finite, meaning it contains only a finite number of elements.

More formally, a finite group is a set G, together with a binary operation * on G, such that:

For any two elements a and b in G, their product a*b is also in G.

The operation * is associative, meaning that for any three elements a, b, and c in G, the product (ab)c is equal to a(bc).

There exists an element e in G, called the identity element, such that for any element a in G, the products ea and ae are both equal to a.

For every element a in G, there exists an inverse element a⁻¹ in G such that the product aa^-1 and a^-1a are both equal to the identity element e.

This statement is saying that if we have a finite group G and an element x in G, then there must exist a positive power of x which equals its inverse (i.e., x⁻¹ = \(x^{k}\) for some positive integer k). This is because if we consider the powers of x, there are only a finite number of possibilities since G is finite. Therefore, at some point, there must be a repetition of a power of x (i.e., \(x^{m}\) = xⁿ for some integers m < n), which means that x^(n-m)\(x^{n-m}\) = 1 (the identity element). Then, we can rewrite x^(n-m-1)\(x^{n-m-1}\) as x⁻¹ and we see that x⁻¹ = \(x^{k}\) for some positive integer k. This statement is important in group theory because it shows that every element in a finite group has a well-defined inverse, which is a key property of groups.

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Answer:

answer

Step-by-step explanation:

step by step explanation

Answer:

the answer is 86°

Step-by-step explanation:

look at the photo

a) The direct variation equation is y = 33x.

b) The customer can pay the company to collect 15 bins.

c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.

A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.

B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:

y = 33x

500 = 33x

x = 500/33

x ≈ 15.15

Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.

C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:

y = 33x + 30

530 = 33x + 30

500 = 33x

x ≈ 15.91

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The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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The equation is given by

a + 3b = 8.50

2a + 2b = 8

And the value of a and b is given by 1.75 and 2.25.

What is an equation and substitution method?

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

Let a and b the cost of sports drink and slice of pizza.

Jim ordered one sport drink and 3 slice of pizza and it cost him 8.50.

Hence, equation become

a + 3b = 8.50

Similarly, for his friend

2a + 2b = 8

a +b = 4

Subtracting these equation we get,

2b = 4.50

b = 2.25

Substitute this value of b in any equation, we will get a = 1.75

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Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

Answer:

12.0625 pounds.

Step-by-step explanation:

To find your answer, divide the number of ounces by 16. The quotient is the number of pounds.

Answer:

See below ~

Step-by-step explanation:

a. Number of outcomes

b. Not red

Answer:YAY

Step-by-step explanation: :)

Answer:

4x+3(3x-4)=1

4x+9x-12=1

13x=13

x=1

Answer:

Here you go :)

Step-by-step explanation:

Answer:

7 1/5

Step-by-step explanation:

2 1/4 * 3 1/5

Change to improper fractions

2 1/4 = (4*2+1)/4 = 9/4

3 1/5 = (5*3+1)/5 = 16/5

9/4 * 16/5

Rewriting

9/5 * 16/4

9/5 * 4/1

36/5

Change back to a mixed number

7 1/5

The scale factor that was used to convert triangle ABC into the image in A ' B ' C ' is 1 / 2.

To find the scale factor, you need to find the length of a side of triangle ABC and then the length of the corresponding side in A ' B ' C '.

The side length we will pick is AB which is:

= 6 - 2

= 4 units

The side length of the other triangle is A' B' :

= 3 - 1

= 2 units

The scale factor is:

= 2 / 4

= 1 / 2

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Answer:

The Answer is x=2

Step-by-step explanation:

Hope this helps!!!!

Answer:

x=2  

Step-by-step explanation:

4x+3=11

4x=11-3      ( subtract 3 on both sides)

4x=8

x=2            ( divide 4 on both sides)

An

Step-by-step explanation:

Cx+y s 100

Answer:

All the inequalities that model the constraints for this situation:

(d) x + y < 200 ;

(e) 0.75 x + 0.50 y ≥ 100

Step-by-step explanation:

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

As, x represent the number of candy bars sold & y represent the number of bags of chips sold.

It is given that,

price for one candy bar =  $0.75

also, price for one dag of chips = $0.50

So, price for 'x' candy bar =  $0.75x

also, price for 'y' of chips = $0.50 y

Is is mentioned in question, the sale of candy bar and bag of chips shoud be atleast $100.  

the First ineqaulity be,

0.75 x + 0.50 y ≥100

(which should the sales of candy baar and dag of chips be equal to 100 dollar or greater than 100 dollar)

Now, the second situation

Again, it is mentioned in the question is number of units (candy bar and dag of chips)  should be not more than 200 units.

the second inequality be,

x+ y < 200

(which shows that number of candy bar and dag of chips should be less than 200 units.)

All the inequalities that model the constraints for this situation

(d) x + y < 200

(e) 0.75 x + 0.50 y ≥100

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