Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
A. how much will be in the account after 4 years?
B. How much will be in the account after 16 years?
C. How many years will it take for the account to contain $2500?
D. How many years will it take for the account to contain $3000?

the percent increase in charges is 33.3%

increase after baggage charges is 55.5%

GIVEN-

price of the ticket initially=​$225

price of the ticket after 1 week=​$300

baggage charge= ​$50

STEPS:

Percentage increase= {(difference)/initial }x 100

difference=final-initial

⇒(300-225)/225 x 100

⇒0.3333 x 100

=33.3%

∴33.3% of the increase in charges

with additional baggage price new ticket=​$350

⇒percentage increase=(350-225)/225 x 100

⇒0.5555 x 100

⇒55.5%

∴55.5% of increase in prices after adding baggage charges.

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The complete question is:

Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Denver was $225. Now the cost is $300. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?

Answer:

C

Step-by-step explanation:

C It makes the line become steeper. When the coefficient in front of x is increased, the slope of the line becomes larger, so the line becomes steeper. The other responses are not correct.

The value of k in order for the ordered pair (-1,k) to be a solution to the function,  f(x) = -x + 2 will be 3.

In mathematics, a function is a rule or an expression that establishes a connection between one variable, known as the independent variable, and another variable known as the dependent variable. It defines the relationship between the two variables, in such a way that for every unique value of the independent variable, there is a corresponding unique value of the dependent variable. Functions are widely used in many areas of mathematics such as algebra, calculus, and trigonometry, as well as in many other fields such as physics, engineering, and economics.

A function can be represented in two ways: graphically and algebraically. The graphical representation of a function is a graph of the function, where the x-axis represents the independent variable and the y-axis represents the dependent variable. A function can be plotted as a set of ordered pairs (x,y) on the coordinate plane. The algebraic representation of a function is an equation that defines the relationship between the independent variable and the dependent variable. The equation can be written in the form of y = f(x) or y = ax + b, where x and y are the variables, and a and b are constants. The graphical representation of a function provides a visual representation of the relationship between the independent and dependent variables, while the algebraic representation provides a way to calculate the output for any given input.

To find the value of k , that satisfies the given equation, we need to substitute the ordered pair (-1, k) the the given equation as follows,

f(-1) = -(-1) + 2

or , k = 1+2

therefore, k =3

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so we know the area if 44 cm², and we also know the "L" is 3 more than twice "W", hmmm what's twice W anyway?  well, just 2W, and 3 more than that?  well 2W + 3, hmmm so

[tex]A=LW ~~ \begin{cases} L=length\\ W=width\\[-0.5em] \hrulefill\\ A=44 \end{cases}\implies 44=LW\hspace{5em}\stackrel{\textit{3 more than twice W}}{L=2W+3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{44=(\underset{L}{2W+3})W}\implies 44=2W^2+3W \\\\\\ 0=2W^2+3W-44 \implies 0=(2W+11)(W-4) \\\\[-0.35em] ~\dotfill\\\\ 0=2W+11\implies -11=2W\implies \cfrac{-11}{2}=W ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 0=W-4\implies 4=W ~~ \textit{\LARGE \checkmark}[/tex]

now, the negative value is a valid value for W, however for this case, the width cannot be a negative number, it must be positive, thus we do away with it, and since L = 2W+3, that means L = 2(4)+3 = 11.

Answer:

Step-by-step explanation:

A VAT (value-added tax) is a consumption tax that is added to the price of goods and services. The VAT rate is typically a percentage of the price of the goods or services.

In order to find the amount the shoe dealer should pay to the company including VAT, we need to know the VAT rate. If the VAT rate is not specified in the problem, it is impossible to determine the exact amount that the shoe dealer should pay.

However, if we assume that the VAT rate is 15%, then the amount of VAT the dealer should pay is 15/100 * 8000 = 1200 birr.

So the total amount the dealer should pay to the company including VAT is 8000 + 1200 = 9200 birr

It's important to note that this is an estimate and the actual amount could be different if the VAT rate is different.

The simplification of the expression −5.55− 8.55c+ 4.35c by combining the like terms is - 5.55 - 4.20c.

Like terms can be defined as terms which has the same variable and power.

For instance,

4a + 5a²

They are not like terms, though they have the same variable a but different power of 1 and 2 respectively.

So,

−5.55− 8.55c+ 4.35c

The like terms are - 8.55c and + 4.35c

−5.55− 8.55c+ 4.35c

= - 5.55 - 4.20c

Consequently, - 5.55 - 4.20c is the simplification of −5.55− 8.55c+ 4.35c.

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All the possible values of each expression is given as an inequality as;

0 < a - b < 4

We are given the inequalities of the domain and range as;

2 < a < 5

1 < b < 2

Thus, we can say that the maximum value of a - b will be the difference between the maximum value of a and the minimum value of b to give;

(a - b)max = 5 - 1

(a - b)max = 4

Similarly, minimum value of a - b will be the difference between the maximum value of b and the minimum value of a to give;

(a - b)min = 2 - 2

(a - b)min = 0

Thus, all possible values would be expressed as;

0 < a - b < 4

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Statistics prove that motorcyclists are B: 35 times as likely as a passenger car occupant to die in a motor vehicle accident.

Compared to the occupants of motor vehicles, motorcycles provide their riders with very little protection from injury. Motorcycles have virtually no ability to absorb the impact from another vehicle; there is the potential for serious injuries or even death for any rider as a result of a motorcycle crash or accident.

Unfortunately, according to statistics motorcycle deaths accounted for 14% of all motor vehicle crash deaths. A motorcyclist is about 35 times more likely to die in an accident compared to passengers in cars.

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Answer: C. Zula can write 4 articles in 10 hours is the best interpretation of the slope of this linear model.

The slope of a linear equation in the form y = mx + b represents the rate of change of y with respect to x. It tells us how much y changes for a one-unit change in x. In this case, the slope of the equation y = 0.4x is 0.

Step-by-step explanation:

Answer:

 [tex]x=-\frac{3}{2}\\[/tex]

Step-by-step explanation:

We must isolate x in this equation. To do that, we can multiply both sides by [tex]\frac{3}{2}[/tex].

[tex](\frac{3}{2})(\frac{2}{3})x=-1(\frac{3}{2})[/tex]

[tex]x=-\frac{3}{2}[/tex]

To find the x coordinate of the vertex, set the inside of the absolute value x equal to 0. In this case, x = 0.

[tex]x = 0[/tex]

Replace the variable x  with 0 in the expression.

[tex]y = |0| + 5[/tex]

Simplify [tex]|0| + 5.[/tex]

The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.

[tex]y = 0+5[/tex]

Add 0 and 5.

[tex]y = 5[/tex]

The absolute value vertex is (0, 5).

The data point 56.7 seconds is an outlier, so we should discard it and measure it again.

The correct option is the last one.

When we have some data, there may be what we call "outliers".

An outlier is a data point that is "away" from the rest of the data points.

For example, if you look at the table, you can see that most values are around 20 seconds, except for one value, which is the middle one and it is:

56.7 seconds.

That point is really far away from all the others on the table, so we can see that it is an outlier, then we should discard it and measure it again.

Thus the correct option is the last one: 56.7 s

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Answer:

The domain of a graph is the possible input values the graph can take.The domain of the graph is: 10,20,30,40,50,60,70,80,90,100

The score (on the x-axis) represents the input values.From the graph, we have:

Minimum score = 10

Maximum score = 100

This means that the domain of the graph is from 10 to 100

From the given options, (d) is correct;

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The simplified exponential notation of the given expression is [tex](2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex].

The given expression is: [tex]12a^{2} -36ab + 27b^{2}[/tex]

An expression in the form of [tex]x^{a} .y^{b}. z^{r}[/tex] is called exponential expression.

We can write the above expression as:

[tex]12a^{2} -36ab + 27b^{2}[/tex]

We know that

[tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]

So,  [tex]12a^{2} -36ab + 27b^{2}[/tex] can be written in the form of [tex](a-b)^{2} = a^{2} +b^{2} -2ab[/tex]

[tex]12a^{2} -36ab + 27b^{2} = (2\sqrt{3}a )^{2} - 2.2\sqrt{3} .3\sqrt{3} +({3\sqrt{3} } b) ^{2}[/tex]

[tex]12a^{2} -36ab + 27b^{2} = (2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex]

Hence, the simplified exponential notation of the given expression is .

[tex](2\sqrt{3}.a - 3\sqrt{3}b )^2[/tex]

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The distance scale between San Antonio and Houston on Vicki's map is 7.3 centimeters. The sane distance in millimeters in millimeters is

Distance measurement is a linear measurement and the unit can be inches, feet, yard, meters, kilometers and so on

In the problem the unit is in centimeters and conversion of centimeters to millimeters is done by the factor 10

Applying the factor of 10 to 7.3 centimeters will to convert it to millimeters and this shown below

= 7.3 * 10

= 73 millimeters

The distance in millimeters is solved to be 73 millimeters

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The total volume of all 4 gumballs: V=3,620 mm³

Gumball is in the shape of a Spherical so we Use the formula for the total volume of a sphere:

Volume of Sphere = (4/3)πr³

r = Radius of Sphere

Plug the given radius into the formula, r =  6mm

Volume of 1 gumball = (4/3)π * 6³

V= 288π  mm³

The total volume of a single gumball will be 288π cubic millimeters.

Because you have 4 gumballs, multiply the total volume of a gumball by 4 to find the total volume for all 4 gumballs.

Volume of 4 gumballs = 4 *  288π

V= 1152π  mm³

In terms of π, the total volume of the 4 gumballs is 1152π cubic millimeters.

Assuming π = 3.14, multiply 1152 and 3.14 together.

1152*3.14= 3,617.28 mm³

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Answer:

[tex]f(-2) = -20[/tex]

Step-by-step explanation:

Plug -2 into the function for x.

[tex]f(x) = 7x - 6[/tex]

For [tex]x=-2[/tex]:

[tex]f(-2) = 7(-2) - 6[/tex]

[tex]f(-2) = -14 - 6[/tex]

[tex]f(-2) = -20[/tex]

In the United States, long-term capital gains and short-term capital gains are treated differently from income tax purposes. Long-term capital gains are gains from the sale of assets that have been held for more than one year, while short-term capital gains are gains from the sale of assets that have been held for one year or less.

The tax rate on long-term capital gains is generally lower than the tax rate on ordinary income, such as wages or salaries. For example, in 2021, the tax rate on long-term capital gains for individuals in the highest income tax bracket is 20%, while the tax rate on ordinary income for those same individuals is 37%. Lower-income individuals may also be eligible for 0% rate on long term capital gains.

Short-term capital gains, on the other hand, are taxed at the same rate as ordinary income. It's worth noting that these tax rates can also be changed by legislation, and can be different at state level as well, So it is best to consult a tax professional for the most up-to-date information on capital gains tax rates and the rules that apply to your specific situation.

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The absolute value equation that can be used to determine Jack's minimum and   is | x + 30| = 10 (third option)

An equation is a mathematical statement that is used to show the equality of two mathematical expressions. An absolute value equation is an equation that is within the absolute value symbols. The absolute value symbols are | |.

The form of the absolute value equation is:

maximum time he spends washing - average time = 10

x - 30 = 10

or

minimum time he spends washing - average time = 10

x - 30 = -10

Putting the two equations above together becomes

|x - 30| = 10

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a) The data modeling in this problem is an exponential function.

b) The function is defined as follows: y = 1.5(2)^x.

c) The rate of change from x = 2 to x = 4 is of 4.

The general format for an exponential function is presented as follows:

y = a(b)^x.

For which the parameters are given as follows:

From the data, when x increases by one, the output y is multiplied by two, hence the rate of change is given as follows:

b = 2.

Hence, when x increases by two, as is the case from x = 2 to x = 4, the rate of change is given as follows:

b² = 2² = 4.

When x = 1, y = 3, hence, applying the recursion of the rate of change, the parameter a is given as follows:

a = 3/2 = 1.5.

Meaning that the function is defined as follows:

y = 1.5(2)^x.

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The minimum y-value after which the exponential function will always be greater than the linear function is y = 4.

How do functions work?

A law relating two dependent and independent variables is known as a function.

An illustration of a linear function is

y =mx+c

and represents the exponential function as follows:

y = aˣ

By looking at the graph, one may identify the lowest y-value after which the exponential function will always be bigger than the linear function.

When y = 4, they are equal, and from that point on, the linear function's value exceeds that of the exponential function.

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The value of the base angles of triangle ABC formed by the given polygon is; 80°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, the number of sides of the given polygon when completed will be 18 sides. Thus, we can say that;

Central angle = 360/18

Central angle = 20°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠B = ∠C = [180 - 20]/2

∠B = ∠C = 80°

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The two types of scatter plots are linear and nonlinear. Linear scatter plots show a linear relationship between two variables, while nonlinear scatter plots show a nonlinear relationship between two variables.

A linear scatter plot is a type of graph that displays the relationship between two variables. In a linear scatter plot, points are plotted on a graph according to their x- and y-coordinates. The points form a line, or a straight line, indicating a linear relationship between the two variables. A linear scatter plot is used when there is a clear and strong positive or negative relationship between the two variables.

Nonlinear scatter plots show a nonlinear relationship between two variables. In nonlinear scatter plots, points are plotted on a graph according to their x- and y-coordinates. The points form a curved or nonlinear line, indicating a nonlinear relationship between the two variables. Nonlinear scatter plots are used when there is an unclear or weak relationship between the two variables, or when the relationship between the two variables is nonlinear.

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Answer:

Whatever has the answer of 80.

Step-by-step explanation:

Observing the geometry and the properties of sides and angles provided in the figure, We can conclude that option 2 is the correct answer. GJ is less than HJ.

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects. A geometer is a mathematician who specializes in geometry. A field of mathematics known as geometry is described as "concerning the measurement, characteristics, and relationships of points, lines, angles, surfaces, and solids." Geometry is a branch of mathematics that deals with points, lines, forms, and surfaces, to put it another way.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

angle GFJ = 60

angle JFH = 62

We know larger angle corresponds to larger sides, So, The side opposite to 62 is larger than of 60.

So, GJ is smaller than HJ.

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Answer:

Step-by-step explanation:

There were 10 different combinations to the multiple choice questions.

Combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

It is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

[tex]C_{n,r} = \frac{n!}{(n-r)! r!}[/tex]

where n = 5

r = 3

[tex]C_{5,3} = \frac{5!}{(5-3)!3!} \\= \frac{5!}{2!3!}[/tex]

= [tex]\frac{5(4)(3!)}{2!3!}[/tex]

= 20/2

= 10 ways

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The surds equation x√40 = x√5 + √10 is resolved into (4√2) / 7  which a and b are 4 and 2 respectively.

A surd equation is a mathematical formula that comprises one or more surds, or irrational numbers, in the form of square, cube, or higher-order roots. Surds, such as √2, √3, 5, etc., are numbers that cannot be expressed as the ratio of two integers. The symbol "√" for them is frequently used.

Because surds are irrational numbers that cannot be stated as a ratio of integers, calculating a surd equation can be more challenging than solving a regular equation. The first step in solving a surd equation is to make the equation as simple as feasible by deleting any surds from any fractions' denominators or numerators. You will then separate the surd on one side of the equation from the numbers on the other side using algebraic manipulation. Once the square root has been eliminated, you can square both sides of the equation to get a polynomial equation that can be solved using conventional algebraic methods.

In the given problem;

x√40 = x√5 + √10

Collect like terms;

x√40 - x√5 = √10

x√(8 * 5) - x√5 = √10

x√(2 * 4 * 5) - x√5 = √10

2x√10 - x√5 = √10

x = (4√2) / 7

The value of a and b are 4 and 2

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Answer:

35/3

Step-by-step explanation:

To find the product of 3 1/3 and 3 1/2, we first need to convert both numbers to fractions with a common denominator.

3 1/3 is equal to 10/3, and 3 1/2 is equal to 7/2.

To find a common denominator, we can find the least common multiple of 3 and 2, which is 6.

Then, we can express both fractions as fractions with a denominator of 6:

10/3 becomes 20/6, and 7/2 becomes 21/6.

Now that both fractions have a common denominator, we can multiply them together:

(20/6) * (21/6) = 420/36

This fraction can be simplified to:

420/36 = 35/3

So, the product of 3 1/3 and 3 1/2 is 35/3.

[tex]3\dfrac{1}{3} \times3\dfrac{1}{2}[/tex]

In order to multiply mixed numbers, you need to convert them into improper fractions.

[tex]3\dfrac{1}{3} \rightarrow\dfrac{10}{3}[/tex]

[tex]3\dfrac{1}{2} \rightarrow\dfrac{7}{2}[/tex]

Multiply:

[tex]\dfrac{10}{3} \times\dfrac{7}{2}[/tex]

[tex]=\fbox{$\dfrac{35}{3} $}or\fbox{11$\dfrac{2}{3} $}[/tex]