A grocery store has increased its prices over time. The price per pound of apples in 2016 was $0.45. Today, the price per pound of apples is $0.85.
What is the equation of the line that would represent the price increase per pound of apples over time?

The changes to the slope and to the intercept of the linear function after the transformation g(x) = f(x) + k, in which k = 2, are given as follows:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

The function f(x) in this problem is given as follows:

f(x) = -2x + 3.

Meaning that it has a slope of -2 and and intercept of 3.

The function g(x) is defined as follows:

g(x) = f(x) + k.

Since k = 2, we have that:

g(x) = f(x) + 2

g(x) = -2x + 3 + 2

g(x) = -2x + 5.

Hence the slope and the intercept are given as follows:

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Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.

Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.

The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.

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Answer:

12

Step-by-step explanation:

11, 11, 13, 13, 12, 13, 11, 12, 10, 13

Put the numbers in ascending (increasing) order.

10, 11, 11, 11, 12, 12, 13, 13, 13, 13

If there is an odd number of numbers, the median is the number in the middle.

There are 10 numbers which is an even number of numbers.

For an even number of numbers, the median is the mean of te two middle numbers.

10, 11, 11, 11, 12, 12, 13, 13, 13, 13

The two middle numbers are 12 and 12.

The mean of 12 and 12 is (12 + 12)/2 = 12

Answer: 12

In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25

The domain and range of the the function are -

Domain → [0, 180]

Range → [600, 1050]

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is that the owners of a recreation area filled a small pond with water in 180 minutes. The pond already had some water at the beginning. The graph {attached below} shows the amount of water (in liters) in the pond versus time (in minutes).

Domain is the set of all possible {x} values. We can write -

Domain → [0, 180]

Range is the set of all possible {y} values. We can write -

Range → [600, 1050]

Therefore, the domain and range of the the function are -

Domain → [0, 180]

Range → [600, 1050]

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Answer:  To solve this problem, we can use the fact that a cubic centimeter of osmium has a mass of about 23 grams and the information provided about the chemist's amount of osmium.

First, we can divide the total mass of osmium by the mass of a cubic centimeter of osmium to find out how many cubic centimeters of osmium the chemist has. The equation would look like this:

2,530 grams / 23 grams/cubic centimeter = 110 cubic centimeters

So, the chemist has approximately 110 cubic centimeters of osmium.

It's worth mentioning that an exact value would require additional information as 23 grams per cc is an approximate value and also any impurities or loss of material in the sample also effect the total mass.

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

here we go~

[tex]\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} [/tex]

[ identity : a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)[/tex]

The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.

The following are the rationales:

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The equation becomes true if we put brackets in the following way:

7x(5 - 2 + 3) = 42

Here we have the expression:

7x5 - 2 + 3 = 42

And we want to find where we need to put brackets in such a way that the equation becomes true.

If we solve the equation as it is, we will get:

7x5 - 2 + 3 = 42

35 - 2 + 3 = 42

36 = 42

Now, let's return to the equation:

7x5 - 2 + 3 = 42

If we put one pair of brackets that includes from the 5 to the 3, we will get:

7x(5 - 2 + 3) = 42

7x(4) = 42

42 = 42

So the equation becomes true.

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If a train travels 283. 8km in 4. 4 hours, the train travels 71km in 1 hour and the train travels 114.5km in 2.5 hours.

Based on the assumption that the train is traveling at a constant speed throughout its journey.

To find the speed the train travels , we divide the total distance by the total time:

speed = 283.8km/ 4.4 hours

speed = 64.5 km/h

To find the distance the train travels , we multiply the speed of the train by the total time:

Distance travelled in 1 hour = 64.5 km/ hour × 1 hour

Distance travelled in 1 hour = 64.5 km

Distance travelled in 2.5 hours = 64.5 km/hour x 2.5 hours

Distance travelled in 2.5 hours = 161.25km

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The constant of proportionality is 9 and equation of the proportion.

is y= 10x.

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.

Given:

As, we know using the Constant of Proportionality

y = kx

or,  k = y/x  where k is Constant of Proportionality.

Then, from the table we have

k = 90/9

k= 10

Thus, y = kx

or, y= 10x

Hence, the equation of the proportion is y= 10x.

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Answer: 4k^7

Step-by-step explanation:

Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.

A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.

The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.

length = 2cm

breadth =3cm

volume = 42 cm³

volume = l*b*h

42 = 2*3*h

h= 42/6 =7cm

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This is a symbol in mathematics that represents "to the power of" or "exponent".

It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.

The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.

Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.

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Answer:16,777,216

Step-by-step explanation:

The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.

What is upper and lower bound of a function?

A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.

Given,

 [tex]f(h) = \frac{48-h}{48}[/tex]

where    f(h) = Percentage of battery left

              h = Hours of cell phone use

Lower Bound of parameter h,

h = 0 ( When percentage is 100%)

f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1

Upper bound of parameter h,

h = 48 (When percentage is 0%)

f(h) = [tex]\frac{48-48}{48}[/tex] = 0

Therefore the upper bound of h is 0 and lower bound of h is 1.

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When the given altitude of the triangle meet at one of the vertices of the given triangle then it represents the option 1. right angled triangle.

As given in the question,

Given is the altitude of the triangle.

Given Condition is :

Altitude of the triangle meet at one of the vertices of the triangle.

⇒ This means altitude is representing the height of the triangle.

Height is always represented by perpendicular line.

⇒One of the side having altitude forms a angle of measure 90°.

⇒Given triangle is right angled triangle.

Therefore, when the altitude of the triangle meet at one of the vertices of the given triangles it represents the option 1. right angle triangle.

The above question is incomplete, the complete question is :

If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is

1) a right triangle

2) an acute triangle

3) an obtuse triangle

4) an equilateral triangle

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Answer:

453

Step-by-step explanation:

To perform long division of 11,778 by 26, we follow these steps:

452

_____

26 ) 11,778

-104

------

157

156

----

21

Therefore, 11,778 divided by 26 is equal to 452 with a remainder of 21.

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The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .

What is a Boolean Expression ?

The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.

Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .

If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .

The given question is incomplete , the complete question is

What is Dual Boolean Expression ?

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The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.

Explanation:

8x + 6+5 - x - 6x - 2

= x + 9.

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The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]

To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.

When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:

[tex]$x = ky^3$[/tex]

where k is the constant of proportionality.

Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:

[tex]$y = \frac{m}{\sqrt{z}}$[/tex]

where m is the constant of proportionality.

Substituting the second equation into the first equation gives:

[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Since the value of x is 3 when z is 12, the equation can be written as:

[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]

Rearranging gives:

[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]

Substituting this value of k into the original equation gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Substituting z as 75 gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]

Simplifying gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]

Therefore, the value of x  when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].

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We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.

We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.

Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent

We must now locate a side opposing the angle A or the hypotenuse.

As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.

Finally, the length of BC is required because it is the side opposite A.

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The complete question should be like:

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

Answer:

Step-by-step explanation:

put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8

b^3=8/125

b=2/5

then the answer is 125*(2/5)^x

The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].

An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.

[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]

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Therefore , the solution of the given problem of surface area comes out to be Felix is required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.

Its surface area is a gauge of the space it takes up overall. A three-dimensional shape's entire environment is considered part of its surface area. Surface area is the total area of a thing. By adding up the faces on each of its six rectangle sides, a cuboid's volume of water can be calculated. The following formula could be used to calculate the dimensions of the box: Surface is the same for 2lh, 2lw, and 2hw (SA). The muti shape's surface area serves as a representation of the entire region.

Here,

Given: One parallelogram-shaped tile has a base of 4 cm and a height of 2 cm.

4 x 2 cm is the area of a single parallelogram-shaped tile.

8 cm2 is the size of one parallelogram-shaped tile.

The total area of the five black and five white tiles is 10 8cm2.

Total tile area is 80cm2 for the 5 black and 5 white tiles.

Felix is therefore required to purchase 10 parallelogram-shaped tiles for an area totaling 80cm2.

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The graph has plotted and attached below

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2x + 3y <12.

Here The graph have plotted and attached below.

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6

8 = 20x

x = 8/20,

simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The complete question is "To find the diagonal  x value by the given equation  16x + 2 = 36x - 6 "

22/154=11/77=1/7

1/7 is the lowest form