Utility from Oranges and Star Fruit. Oranges cost $2 per pound and star fruit costs $5 per pound. Calvin has $26 to spend. If Calvin buys 4 pounds of star fruit and 3 pounds of oranges, how much is his total utility

A graph of the line going through the point (-6, 1) with a slope of -2/3 is shown in the image below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-6, 1) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -2/3(x + 6)  

y = -2x/3 - 4 + 1

y = -2x/3 - 3

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Answer:

a-4

b-3

c-1

Step-by-step explanation:

Answer:

6 days

Step-by-step explanation:

1050 divided by 175 is 6

Answer:

6

6 times 175 equals 1050

y=2x-11 is the equation of line with slope 2 and coordinate (8,5)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is the slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given coordinate is (8,5) and slope is 2

m=2

The slope intercept form for a point

y-y₁=m(x-x₁)

y-5=2(x-8)

y-5=2x-16

y=2x-16+5

y=2x-11

Hence, y=2x-11 is the equation of line with slope 2 and coordinate (8,5)

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Answer:

The situation per week is 30 + 6n

where n is the number of weeks

Range of the function is 18 for the first four weeks of data

Step-by-step explanation:

Here, we are to use an arithmetic sequence for a representation.

The first term here is a which is 30 clients while the common difference of d is 6 new clients per week

So we can write the nth term of the sequence as;

Tn = a + (n-1)d

Tn = 30 + (n-1)6

Tn = 30+ 6n -6

Tn = 24 + 6n

where n is the number of weeks

Now for the second week we shall have a total of a+ d clients = 30 + 6 = 36

For the third we have 24 + 6(3) = 24 + 18 = 42

For the fourth, we have 24 + 6(4) = 24 + 24 = 48

Thus the range mathematically means the difference between the highest and lowest for that four weeks = 48-30 = 18

Answer:

A lawn-mowing company is trying to grow its business. It had 18 clients when they started its business and wants to increase by 4 new clients each week.

Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.

f(x) = 4x + 18; 0 ≤ y ≤ 4

To determine the concentration of the analyte in the unknown using the fit parameters and the linear model, you need to substitute the given signal value into the equation y = mx + b.

In this case, the linear model is represented by the equation y = mx + b, where:

y is the signal value (80.77 in this case),

m is the slope obtained from the regression analysis, and

b is the y-intercept obtained from the regression analysis.

You haven't provided the values of m and b, so I'll use placeholders for now.

Let's assume the slope (m) obtained from the LINEST formula is m = 2.5 and the y-intercept (b) is b = 10.

Substituting these values into the equation:

y = mx + b

80.77 = 2.5x + 10

To find the concentration (x), we can rearrange the equation:

2.5x = 80.77 - 10

2.5x = 70.77

x = 70.77 / 2.5

x ≈ 28.31

Therefore, based on the given fit parameters and the linear model, the concentration of the analyte in the unknown is approximately 28.31 ppm Co2+.

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Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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The required equation function j which is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

As we can see in the graph the functions j and f are similar but the graph of j is 2 units left of f. So, function f(x) has a domain of real number greater than equal to zero, while as the function j is 2 units left of f then its equation is given as  \(j(x)= (x+2)^{1/2}\)  where the domain of j is all real numbers greater then or equal to -2.

Thus, the equation of function j is the transformation of \(f(x)= x^{1/2}\) is  \(j(x)= (x+2)^{1/2}\) .

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In the question the graph is missing, a graph has been added on behalf of the incomplete question.

Answer:

Silurian, Triassic, Jurassic, Tertiary

Step-by-step explanation:

Convert 6.64 so that is is 10\(^8\)

So you'll have 0.664 × 10\(^8\)

Then you can just order them from largest to smallest :)

If it doesn't make sense you can also convert the index notation (the powers with 10) into whole numbers so

2.08 × 10\(^8\) = 2.08 × 100000000 = 208000000

and so on..

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

When we rotate a  Parallelogram PQRS of 90 degrees clockwise about the origin, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.

P(x₁, y₁) ⇒ P'(y₁ , -x₁ )

Q(x₂, y₂) ⇒ Q'(y₂ , -x₂ )

R(x₃, y₃) ⇒ R'(y₃ , -x₃ )

S(x₄, y₄) ⇒ S'(y₄ , -x₄ )

The Greek word "parallelogrammon," which means "bounded by parallel lines," is the source of the English word "parallelogram." Thus, a quadrilateral with parallel lines as its borders is referred to as a parallelogram. The opposing sides of this form are parallel and equal. Each of the three primary varieties of parallelograms—square, rectangle, and rhombus—has distinct characteristics.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposing sides that are parallel for it to be a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both sets of opposite sides are parallel and equal is referred to as a parallelogram.

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Linear equation is the equation in which the highest power of the unknown variable is one. The equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

\(112+25m+45=50+60m\)

Thus the option 4 is the correct option.

Given information;

The saving of the first runner is $112.

The amount of gift card the first runner received is $45 and the saving of each month is $25.

The saving of the second runner is $50.

The amount of second runner save each month is $60.

The number of months it will take for both accounts to have the same amount of money is m.

Linear equation is the equation in which the highest power of the unknown variable is one.

As the saving of the first runner is $112. and the amount of gift card the he received is $45. Also his saving of each month is $25. Thus the money saved by him in m months,

\(=112+45+25m\)

As the saving of the second runner is $50 and the amount he save each month is $60. Thus the money saved by him in m months,

\(=50+60m\)

For the same amount of saving in m months the above two equation must be equal. Therefore,

\(112+45+25m=50+60m\)

Rewrite the equation as,

\(112+25m+45=50+60m\)

Hence the equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

\(112+25m+45=50+60m\)

Thus the option 4 is the correct option.

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Answer:

Linear equation is the equation in which the highest power of the unknown variable is one. The equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

Thus the option 4 is the correct option.

Step-by-step explanation:

Answer:

Part A: He spends an average of $8.50 per day

Part B:  He would save $17 per week

Step-by-step explanation:

The range of values for which x²–2x -3 > 0 is

x < -1 and x > 3

Any equation in algebra that can be written in the standard form where x is an unknown value and a, b, and c are known integers, where a≠0 is a quadratic equation.

By solving the quadratic expression

x²–2x -3 > 0

Find two numbers that is a factor of -3 such that on adding them the answer is -2

that is

(1)(-3) = -3

(1)+(-3) = -2

x² -3x +x -3 > 0

By factorization;

x(x-3)+1(x-3) > 0

(x + 1)(x - 3) > 0

Therefore;

(x+1) > 0 and (x - 3) > 0

x < -1 and x > 3

The range of values for which x²–2x -3 > 0 is x < -1 and x > 3

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Answer:

first one is correct

Step-by-step explanation:

Answer:

The answer is A) the other angles are proportional.

Explanation:

If you already know what 2 of the 3 sides are of each triangle, it only makes sense that the 3rd side would be proportional to those of the 1st triangle.

Answer: The constant of variation, k , is 54

Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.

Answer:

the scale factor is 25, 3000/125 scaled down,

Step-by-step explanation:

you can also explain this with a 25:1 ratio, 25 inches from the original scaled to 1 inch for the photo copy.

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The degree of financial leverage for Foggy Futures Weather Forecasters

is 1.06

Degree of Financial leverage (DFL) = (EBIT) / (EBT)

Earnings Before Interest and Taxes (EBIT) = $750,000

Amount to be given as loan on $1000000

$1,000,000 x 4.5% = $1,000,000 x 4.5/100

= $45000

To find EBT ( Earnings Before Tax),

EBT = EBIT - 45000

       = 750000 - 45000

EBT = 705000

∴ DFL =  (EBIT) / (EBT)

          = 750000/705000

 DFL = 1.06

The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).

Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve

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Answer:

:

Solve:

-X - Y - Z       =-8

- 4X +4Y +5Z=7

2X + 2Z         =4   is the same as x + z = 2.  Thus, z = 2 - x.

Subst. 2 - x for z in the 1st and second equations.

-X - Y - Z       =-8   becomes -x - y - (2 -x) = -8

- 4X +4Y +5Z=7     becomes -4x + 4y + 5(2-x) = 7

Now we have 2 equations in only 2 unknowns.  Let's simplify them!

-x - y - 2 + x = -8               which becomes   -y = -6, or y = 6

-4x + 4y + 10 - 5x = 7       which becomes   -9x + 4y = 7 - 10 = -3

Now substitute 6 for y in this last equation:  -9x + 4(6) = -3, or

                                                                     -9x + 24 = -3, or

                                                                     -9x = - 27 => x = 3

Then x = 3, y = 6 and z = 2 - x, or z = 2-3, or   z = -1.

The solution is (3, 6, -1).  Check it!!

Answer:

Well done

Step-by-step explanation:

Zoomed in

When the person is 42 feet away from the jetski, the sound intensity is approximately 87.1 decibels.

To answer this question, we need to use the inverse square law of sound intensity, which states that the intensity of a sound decreases with the square of the distance from the source.
1. Identify the initial distance (D1) and initial decibel level (L1): In this case, D1 = 12 feet and L1 = 100 decibels.
2. Identify the final distance (D2): In this case, D2 = 42 feet.
3. Calculate the ratio of the initial distance to the final distance: \(R = (D1 / D2)^2\)

\(= (12 / 42)^2\)

\(= (2 / 7)^2\)

\(= 4 / 49.\)
4. Convert the initial decibel level to intensity (I1): The intensity of a sound is proportional to \(10^(L1/10).\)

\(So, I1 = 10^(100/10) = 10^10.\)
5. Calculate the final intensity (I2) using the ratio of distances: I2 = I1 * R

\(= 10^10 * (4 / 49).\)
6. Convert the final intensity back to decibels (L2): L2 = 10 * log10(I2) = \(10 * log10(10^10 * 4 / 49).\)
7. Calculate the final decibel level: L2 ≈ 10 * (10 - log10(49/4)) = 10 * (10 - 1.29)

= 87.1 decibels.

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Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

\(x+8y=190\quad ...(i)\)

\(x+5y=130\quad ...(ii)\)

Aplicando \((i)-(ii)\)

\(8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20\)

Sustituyendo en \((ii)\)

\(x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30\)

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Answer:

Step-by-step explanation:

21

Answer:

The answer is 3

Step-by-step explanation:

I dobt have an explanation, but if u use a calc then u can see that it equals 3/21.

Answer:

44

Step-by-step explanation:

Answer:

$44

Step-by-step explanation:

20% changes to 0.2

$55 x 0.2 = $11 ---> this is the sales discount

$55 - $11 = $44 ---> sale price

Given the data set:

2, 5, 7, 2, 11, 13, 5, 7, 1, 10, 10, 2, 3, 5, 1, 11

Let's find the box plot that correctly displays the data set shown.

For the given square, m∠OKL=45° and m∠MOL=90°.

A square is a regular quadrilateral in Euclidean mathematics because it has four equal sides and four equal angles (right angles, 90-degree angles). It can also be explained as a rectangle with two adjacent sides that are of identical length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and exterior angles are all equal (90°).

In mathematics, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal sections. An angle bisector is a beam that divides an angle into two identical segments of the same length.

Angle bisector points are equally spaced from both angle lines.

Any angle, including acute, obtuse, and right angles, can have an angle bisector traced to it.

In the given square,

The diagonals NL and KM are angle bisectors of ∠K, ∠L, ∠M and ∠N.

Therefore, ∠OKL= 90/2

                  ∠OKL=45°

We know that, in a square, diagonals are equal and bisect each other at right angles.

Therefore, ∠MOL=90°

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