How much of the circle is shaded? Write your answer as a fraction in simplest form.
3
7
1
2

The value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

Using the following formula, we can determine the car's value each year:

value = 20000 * [tex](1 - 0.15)^year[/tex]

We're looking for the years where the value exceeds $10,000.

Let's start by determining the car's value after 1 year:

value = 20000 * [tex](1 - 0.15)^1[/tex] = 20000 * 0.85 = 17000

We need to keep lowering the value since it will eventually exceed $10,000 because the value after one year is less than $10,000.

After 2 years:

value = 20000 * (1 - 0.15)² = 20000 * 0.85² = 14525

Still less than $10,000.

After 3 years:

value = 20000 * (1 - 0.15)³ = 20000 * 0.85³ = 12318.75

Since the value has now surpassed $10,000, the car was worth more than $10,000 from year 3 until year 2, or 1 year.

Rounding to the nearest hundredth, the interval is 1 year.

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let's say we have two points A(a , b) and B(c , d) partitioned by a point C, since we're dealing with the MidPoint, C is partitioning AB into two equal halves, so in the ratio of 1 : 1.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(a,b)\qquad B(c,d)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:1} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{1}\implies \cfrac{A}{B} = \cfrac{1}{1}\implies 1A=1B \\\\\\ 1(a,b)=1(c,d) \implies (a~~,~~ b)=(c~~,~~ d) \\\\\\ C=\left( \cfrac{a+c}{1+1}~~,~~\cfrac{b+d}{1+1} \right)\implies \stackrel{ \textit{MidPoint Formula} }{C=\left( \cfrac{a+c}{2}~~,~~\cfrac{b+d}{2} \right)}[/tex]

The cost of printing x business cards can be represented by the linear function C(x) = 0.05x + 20.  The cost of printing 950 business cards is $67.50.

The cost of printing business cards is a linear function, C(x) = mx + b, where C(x) is the cost of printing x business cards, m is the rate at which the cost increases as the number of cards increases, and b is the constant term or the cost of printing zero business cards. In this case, m = 0.05 and b = 20.

The equation C(x) = 0.05x + 20 represents the cost of printing x business cards, where x is the number of cards printed. The term 0.05x represents the cost of printing x cards at a rate of $0.05 per card, and the term 20 represents a fixed cost of $20, regardless of the number of cards printed.

To find the cost of printing 950 business cards, we simply substitute x = 950 into the equation:

C(950) = 0.05 * 950 + 20

C(950) = 47.5 + 20

C(950) = 67.5

Therefore, the cost of printing 950 business cards is $67.50.

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Answer:

2×(a+b)

Step-by-step explanation:

to find the perimeter of a rectangle, we should use this formula

This is my answer so if I am wrong then correct me

The median of the data set is 12.

The mean is 11.29.

Increasing every piece of data by the same value increases the mean and median by the same amount.

The median of the data set is the middle value when the data is arranged in numerical order. To find the median of the data set, we need to arrange the data in increasing order: 9, 10, 11, 12, 12, 13, 34. The median of this data set is 12.

The mean of the data set is the average of all the values. To find the mean, we need to add up all the values and divide by the number of values: (9 + 10 + 11 + 12 + 12 + 13 + 34) / 7 = 11.29.

If every piece of data in the set is increased by 20 after treatment, the new values are 29, 30, 31, 32, 32, 33, 54. The new median is 32 and the new mean is 35.29.

When every piece of data is increased by the same value, the mean and median will increase by the same amount.

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Answer:

[tex]width = \dfrac{75*(5-\sqrt{2}}{23}[/tex]

Step-by-step explanation:

To find the width of the rectangle, divide the area by the length.

      [tex]Width = \dfrac{area}{length}[/tex]

                 [tex]=\dfrac{75}{\sqrt{2}+5}\\\\\\\text{To rationalize, multiply the denominator and the numerator by } \ \sqrt{2}-5[/tex]

              [tex]=\dfrac{75* (5 - \sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})}\\\\\\=\dfrac{75*(5-\sqrt{2})}{5^2 - (\sqrt{2})^2}\\\\\\=\dfrac{75(5-\sqrt{2})}{25-2}\\\\\\=\dfrac{75*(5-\sqrt{2})}{23}[/tex]

Answer:

Let the width of the rectangle be w. Then we have:

[tex]lw = 75[/tex]

[tex]w(\sqrt{2} + 5) = 75[/tex]

[tex]w = \frac{75}{\sqrt{2} + 5}[/tex]

Multiplying both the numerator and denominator by [tex]\sqrt{2} - 5[/tex], we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{(\sqrt{2} + 5)(\sqrt{2} - 5)}[/tex]

Simplifying the denominator, we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{-1}[/tex]

[tex]w = -75\sqrt{2} + 375[/tex]

Therefore, the width of the rectangle is approximately 264.1 cm.

The minimum payment of the credit card will be $40.37.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Daniel's credit card has a minimum monthly payment of 2.78% of the card's balance. If Darryl currently owes $1,452.28.

The minimum payment will be calculated as;-

Minimum payment = ( 1452.28 )  x ( 2.78 / 100 )

Minimum payment = $40.37

Therefore, the minimum amount for the credit card bill is $40.37.

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Answer: 10

Step-by-step explanation:

because

The value of the probability P(z < -2.6) is 0.0046612

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

To calculate the probability P(z < -2.6), we make use of a graphing calculator

Using the above as a guide, we have the following:

P(z < -2.6) = 0.0046612

Hence, the value is 0.0046612

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The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

The infinite series representing ax/a+x can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1[/tex]

The first 5 terms of this series can be calculated as follows:

[tex]Term 1 = (x/(a+x))Term 2 = -(x^2/a^2+2ax+x^2) 4Term 3 = (x^3/a^3+3a^2x+3ax^2+x^3) Term 4 = -(x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4)Term 5 = (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5)[/tex]

The general formula for the infinite series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = (x/(a+x)) - (x^2/a^2+2ax+x^2) + (x^3/a^3+3a^2x+3ax^2+x^3) - (x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4) + (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5) + ...[/tex]

The summation notation for this series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex]

This formula can be used to calculate the sum of the infinite series for any value of x and a.

The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

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M(8)<M(4) means that 8th drive was less expensive than 4th drive.

M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.

The reason for the m(8) is that the model fee for this is nth driver for a certain  day.  this implies M (8) < M (4)

M(8) is Aiden's fee for his 8th drive;

M(4) is Aiden's fee for his 4th drive

In conclusion, Aiden's fee for his 8th drive is greater than his drive for the 4th drive

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The elevation gain from the base of the chairlift to the top is 835.2 m

Consider the following diagram.

The chairlift rises at a constant angle of 37°

i.e., the angle of elevation (∠ACB) = 37°

The length of the chairlift ride is 1,392 m

This means, for right triangle ABC, the length of hypotenuse AC = 1392 m

To find  the elevation gain from the base of the chairlift to the top i.e., the length of side AB.

Consider the sine of angle ∠ACB

sin(∠ACB) = AB/AC

sin(37°) = AB/1392

3/5 = AB/1392

AB = 835.2 m

Therefore, the elvation gain is 835.2 m

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The linear graph represents a proportional relationship, a graph of a line that passes through the points (0, 0) and (0.5, -3).

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the coordinates to find the  linear graph represents a proportional relationship,

we know the equation of a line given by,

y = mx + c

where m is the slope and c is the y-intercept,

to prove the graph the proportional value of the y-intercept should be zero, (0, 0)

when c = 0, y = mx

the equation will proportional,

When the line passes from the origin the equation will be proportional.

Hence option A is correct.

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Its A because if the line passes through the middle of the square is a proportional relationship.

Since the abs. val. graph points down, there has to be a -1 outside the abs val symbol.

Since it's also going through (1,-3) and (-1,-3) instead of (1,-1) and (-1,-1), it's been stretched by a factor of 3.

So y = -3•|x| works.

45.0 units is the required perimeter of triangle XYZ

Triangles are known to be similar if the ratio of the similar sides are equal to a constant. The perimeter is the sum of all the sides of the triangle.

From the given diagram , we need to solve for the value of x first as shown:

9/10 = 14/x

9x = 140

x = 140/9

x = 15.6

Find the required perimeter of XYZ
perimeter = ZY + XY + XZ

perimeter = 15.4 + 14 + 15.6

Perimeter = 45.0 units

Hence the perimeter of triangle XYZ is approximately 45.0 units

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Answer:

x = 3

Step-by-step explanation:

[tex]2x - 9 = -3[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Pizza 4 has the area closest to 450 square inches.

What is an area?

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

To determine the pizza with the area closest to 450 square inches, Dante needs to calculate the area of each pizza. The formula for the area of a circle is A = πr², where r is the radius of the pizza.

Here are the areas of the four pizzas:

Pizza 1: A = π * 10² = 314 square inches

Pizza 2: A = π * 9² = 254.34 square inches

Pizza 3: A = π * 11² = 379.94 square inches

Pizza 4: A = π * 12²  = 452.16 square inches

Out of the four pizzas, Pizza 4 has the area closest to 450 square inches. The area of Pizza 4 is 452.16 square inches, which is only 2.16 square inches greater than 450.

So, Pizza 4 has the area closest to 450 square inches.

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To find the product of all integer divisors of 105 that also divide 14, we need to first find all the divisors of 105 and then find which of those divisors also divide 14.

The divisors of 105 can be found by listing all the positive integers that divide 105 exactly. To do this, we can use a divisibility test for each number up to the square root of 105:

Does 1 divide 105 exactly? Yes, so 1 is a divisor of 105.

Does 3 divide 105 exactly? Yes, so 3 is a divisor of 105.

Does 5 divide 105 exactly? Yes, so 5 is a divisor of 105.

Does 7 divide 105 exactly? Yes, so 7 is a divisor of 105.

Does 11 divide 105 exactly? No.

Does 15 divide 105 exactly? Yes, so 15 is a divisor of 105.

Does 21 divide 105 exactly? Yes, so 21 is a divisor of 105.

Does 35 divide 105 exactly? Yes, so 35 is a divisor of 105.

Since 105 is a composite number, the divisors of 105 can also be found by multiplying pairs of the divisors found above. This gives us the following divisors of 105:

1, 3, 5, 7, 15, 21, 35, 105

Next, we need to find which of these divisors also divide 14. To do this, we can perform a similar divisibility test for each divisor:

Does 1 divide 14 exactly? Yes, so 1 is a divisor of 14.

Does 3 divide 14 exactly? No.

Does 5 divide 14 exactly? No.

Does 7 divide 14 exactly? Yes, so 7 is a divisor of 14.

Does 15 divide 14 exactly? No.

Does 21 divide 14 exactly? No.

Does 35 divide 14 exactly? No.

So, the divisors of 105 that also divide 14 are 1 and 7. To find the product of these divisors, we simply multiply them:

1 * 7 = 7

Thus, the product of all integer divisors of 105 that also divide 14 is 7.

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 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

The distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.

The distance formula is a useful tool in many areas of mathematics and science, such as geometry, physics, and engineering. It can be used to find the distance between two points in any number of dimensions, not just two dimensions as in the coordinate plane In addition, the distance formula can also be used to find the length of a line segment in the coordinate plane, which is just the distance between its endpoints. This can be useful in finding the shortest distance between two points, or in finding the length of a path that connects two points.

The distance formula is a mathematical equation used to find the distance between two points in the coordinate plane. It makes use of the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In the coordinate plane, we can represent each point by its coordinates (x1, y1) and (x2, y2). The distance between the points is then given by the equation:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

For the points (-7,1) and (-7,-5), we can plug in the values into the equation:

distance = sqrt((-7-(-7))^2 + (-5-1)^2) = sqrt(0^2 + (-6)^2) = sqrt(36) = 6

So the distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.

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Answer:

Step-by-step explanation:

this is a simultaneous  equation type. so there are only 2 solutions. one for X and one for Y

Answer: 104

Step-by-step explanation:

To put it simply, let's say 100% is 160 dollars. When Christmas arrived, it was sold with a discount of 35%. This means we deduct 35% from 100% which is 65%. We then find 65% of 160 dollars, which is 104.

Hope that helps, if not, then please reply back :)

Answer:

Step-by-step explanation:

A = bh.

To solve, find factors of seven the fit the description such as 7 and 1.

The length is 7, the width is 6 units less.

So, the width is 1un and the length is 7un.

Answer:

8 / 47 = 0.17021276595 btw u can just use a calculator

Answer:

Below

Step-by-step explanation:

You multiplied the  '4' by 10 to get 40   .....multiply the '1' by 10 the get the second number = 10     this will keep the ratio correct

Answer:

x = 35°

Step-by-step explanation:

The triangle is an isosceles triangle since two sides are formed by the radii of the circle

Therefore m∠C = x°

The angle 70° is the exterior angle of the triangle

Exterior angle = sum of interior angles

70° = x + x = 2x

2x = 70

x = 35°

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}[/tex]

The equation that shows the rate at which she travels is given as r = 300/t

An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between variables and to solve problems by finding the values of unknowns.

An equation is comprised of two expressions separated by an equal sign (=). The expressions can be as simple as a number or as complex as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value of the variable that makes the equation true.

In this problem, we can represent the rate at which we travel by

r = 300 / t

where;

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