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C. When the independent variable, the number of empanadas, increases by 1, a  dependent variable, the vendor's total pay, increases 5.

what is independent variable ?

An independent variable is a variable in a mathematical equation or relationship that is not affected by any other variables. It is often denoted as "x" and is manipulated or controlled in an experiment or study to observe its effect on the dependent variable.

In the given question,

C. independent variable are the number of empanadas, increases 1, the dependent variable,  vendor's total pay, increases 5.

This can be seen from the given equation: p = 600 + 0.20 x e.

When the number of empanadas sold, e, increases by 1, the total pay, p, increases by:

p = 600 + 0.20 x (e + 1) - 0.20 x e

p = 600 + 0.20

p = 600 + 0.20 x 1

p = 600 + 0.20

p = 600.20

This represents an increase of 5 in the vendor's total pay when the number of empanadas sold increases by 1.

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If principal is $2,658 and rate of interest 9% then the value of  the account balance is approximately $10,253 by using continuous compound interest formula.

Recurring interest is interest calculated on principal plus all interest and other interest. The idea is that lenders always receive interest, not individually at specific times.

The formula for continuous compound interest :

  A=    Peˣⁿ                          

Where,

A =Amount of money  after a certain amount of time

P= principal or the amount of money you start with

e =Napier's number, which is approximately 2.7183

x =Interest rate

n =Amount of time in years.

Use the continuous compound interest formula :

Given  P= 2658

x =9% =   = 0.09

n = 15

e = 2.7183

By using

A=    Peˣⁿ  

A= (2658)(2.7183)⁰°⁰⁹¹⁵

A =10,253 (approximately)

Hence, the value of account balance after 15 years is approximately $10,253

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Therefore, the quotient X is 3 and the remainder Y is 25.

So, X = 3 and Y = 25.

Expression division is a mathematical operation where one expression is divided by another. In mathematics, an expression is a combination of numbers, variables, and operators that represent a mathematical relationship or a value. Division is an arithmetic operation that involves splitting a quantity into equal parts or groups.

So, expression division refers to dividing one mathematical expression by another. For example, if we have two expressions "x + 5" and "3", we can perform expression division by dividing the first expression by the second expression, which would result in the expression "(x + 5) ÷ 3". The result of this expression would be another expression that represents the quotient of the two expressions.

To perform the division of 15h^2 + 10h + 25 by 5h, we need to follow the long division process as shown below:

    ________

[tex]5h | 15h^2 + 10h + 25[/tex]

   [tex]15h^2[/tex]      

    _______

      [tex]10h + 25[/tex]

         [tex]10h[/tex]

         _____

             25

Therefore, the quotient X is 3 and the remainder Y is 25.

So, X = 3 and Y = 25

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Answer:

m = 60.75

Step-by-step explanation:

The angles A and C in the triangle with sides AC = 24, BC = 15, and angle B = 74 degrees are approximately 29.16 degrees and 45.84 degrees, respectively.

To find angles A and C in the triangle, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the included angle.

Let's denote the angles opposite to the sides with lengths 24, 15, and AB as A, B, and C, respectively. Then, the Law of Cosines gives us:

AB^2 = AC^2 + BC^2 - 2ACBCcos(B)

AB^2 = 24^2 + 15^2 - 22415cos(74)

AB^2 ≈ 758.76

AB ≈ 27.54

Now, we can use the Law of Sines, which relates the ratios of the lengths of the sides to the sines of the opposite angles:

sin(A) / AB = sin(B) / BC

sin(A) / 27.54 = sin(74) / 15

sin(A) ≈ 0.4927

A ≈ sin^-1(0.4927) ≈ 29.16 degrees

sin(C) / AB = sin(B) / AC

sin(C) / 27.54 = sin(74) / 24

sin(C) ≈ 0.6863

C ≈ sin^-1(0.6863) ≈ 45.84 degrees

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Answer:

Options B and C

Step-by-step explanation:

First, we have to find out the unit rates

Matte Paint

7.56 ÷ 4

= $1.89 per paint

Glossy Paint

26.16 ÷ 2

= $13.08 per gallon

Paint Brushes

18 ÷ 4

= $4.5 per brush

Now we have to check for each statement.

Option A

If he buys 1 [tex]\frac{1}{2}[/tex] gal on matte paints

1 [tex]\frac{1}{2}[/tex] = 1.5 gal

1.5 × 1.89 = $2.84

So therefor statement A is not true.

Option B

We have to convert quart to gal

1 quart = 0.25 gal

6 quarts = 1.5 gal

1.5 × 13.08 = $19.62

so statement B is true

Option C

They got 2 paintbrushes so we have to mutiply

2 × 4.5=$9

1 gal matte paint

We have to convert gal to pint

1 gal = 8 pint

8 × 1.89 = $15.12

Then we add them

15.12 + 9 = $24.12

Which means statement C is true

Option D

13 pints of glossy paint

$13.08 per gallon

1 gal =8 pint

13 pints = [tex]\frac{13}{8}[/tex] gal

[tex]\frac{13}{8}[/tex] × 13.08 = $21.26

so statement D is not true

That leaves us with Option B and C

The local maximum values of the graph is determined as 3, 4, and 5.

A local maximum value is a point in the domain of a function where the value of the function is greater than or equal to the values of the function at all neighboring points. In other words, a local maximum is a point where the function reaches a peak, but only in the immediate vicinity of that point.

It's important to note that a local maximum need not be the maximum value of the function over its entire domain. There may be other points in the domain where the function attains higher values.

For the given function, the local maximum values are;

{3, 4, 5}.

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The table in the attachment compares the unitary-method prices for cabbage charged by Ed ($0.75 per unit) and other farmers.

Farmer-A:Greater than Ed

Farmer-B:Equal to Ed

Farmer-C:Less than Ed

Farmer-D:Equal to Ed

Unitary technique refers to the process of figuring out the cost of the necessary items. The value of a multiple is typically used to determine the value of one item, and the value of the desired number of articles can subsequently be determined from the value of one. This method primarily uses both division and multiplication.

Considering that Ed fixed the price for 5 pounds of cabbage at $3.75

5 pounds cabbage= $3.75

1 pound cabbage=$3.75  ÷ 5

Unit rate set by Ed = $ 0.75

Charges Set by Farmer-A= $ 0.50 for 1/2 pound

Unit rate set by Farmer-A = $ 0.50 x 2

                                          = $1

Charges Set by Farmer-B= $ 0.75 for 1 pound  

Unit rate set by Farmer-B = $ 0.75

Charges Set by Farmer-C= $ 1.75 for 2 1/2 pound

= $ 1.75 ÷  5/2

Unit rate set by Farmer-C = $ 1.75 x 2/5

=$ 0.70

Charges Set by Farmer-D= $ 6 for 8 pound

 = $ 6 ÷ 8

Unit rate set by Farmer-D = $ 0.75

Based on the above calculation:

Farmer-A charges:Greater than Ed

Farmer-B charges:Equal to Ed

Farmer-C charges:Less than Ed

Farmer-D charges:Equal to Ed

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The correct option is A) 20.2.

What is triangle sum?

The triangle sum is a property of triangles that states that the sum of the interior angles of a triangle is always equal to 180 degrees. In other words, if you add up the measures of the three angles inside a triangle, the result will always be 180 degrees.

Using the given information and the fact that the angles in a triangle sum to 180 degrees, we can find the value of x as follows:

Start by finding the measure of angle K by subtracting the measures of angles A and B from 180 degrees:

K = 180 - A - B

= 180 - 84 - 65

= 31 degrees

Use the law of sines to set up an equation relating the side lengths and corresponding angle measures:

sin(A)/x = sin(K)/17

Substitute the values we know into the equation and solve for x:

sin(84)/x = sin(31)/17

x = sin(84)*17/sin(31)

Using a calculator, we get:

x ≈ 20.2

Therefore, the value of x in the triangle is approximately 20.2.

So, the correct option is A) 20.2.

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Answer:

third

Step-by-step explanation:

both the points are negative therefore they would be in the third quadrant

Answer:

D) 25 : 1

Step-by-step explanation:

[tex]\boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]

Cylinder 1:

         [tex]h_1 = 5 \ cm\\\\r_1 = 3 \ cm[/tex]

Cylinder 2:

           [tex]h_2 = 5 \ cm\\\\r_2 = 15 \ cm[/tex]

[tex]Volume \ of \ cylinder2 : Volume \ of \ cylinder1 = \dfrac{\pi * 15 * 15 * 5}{\pi *3*3*5}[/tex]

                                                                       = 25 : 1

The probability that the dart will hit the circular board and not land on any of the squares is 7/27.

Explain probability

Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is typically expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to analyze and make predictions in various fields, including statistics, finance, science, and engineering, and is essential for decision-making and risk management.

According to the given information

The area of the circular board is π(18)² = 324π square inches. The area of each square is (5)² = 25 square inches, so the combined area of the four squares is 4(25) = 100 square inches.

Therefore, the area on the circular board that the dart can land on and not hit any of the squares is 324π - 100. The probability that the dart will land in this area is the ratio of this area to the total area of the circular board, which is:

(324π - 100) / (π(18)²)

= (324π - 100) / 324π

= 1 - 100/324

= 7/27

So the probability that the dart will hit the circular board and not land on any of the squares is 7/27.

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The equation that represents the mathematical sentence is:

24 + C = 40

Here we start with a mathematical sentence which says that the sum of 24 and Chau's height is 40.

If we define C as Chau's height, then we need to write "the sum of 24 and C is 40"

That is trivial, is the sum of two things equals other one, and we know all of these, then the equation can be written as:

24 + C = 40

Solving it we get:

C = 40 - 24 = 16

That is Chau's height.

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Answer:

1.15

Step-by-step explanation:

To figure out how many miles she walked in 5 days, we can multiply the number from just one day and multiply that by 5 and we will get our answer!

0.23 * 5 = 1.15

Answer:

Step-by-step explanation:

270 counter clockwise = 90 clockwise

This is (x, y) ---> (y, -x).

So R'S'T' will be R'(2, -1), S'(2, -4) and T' = (-3, -2)

The area of rhombus CDEF is approximately 90.3 square units.

What is rhombus?

A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.

We can see that triangle CEF is a right triangle, and we can use the Pythagorean theorem to find the length of CE:

CE² = CF² + EF²

We know that CF = DF/2 = 16.4/2 = 8.2 and that EF = CE/2, so we can rewrite the equation as:

CE² = (8.2)² + (CE/2)²

Expanding and simplifying:

CE² = 67.24 + 0.25CE²

0.75CE² = 67.24

CE² = 89.65

CE ≈ 9.5

Now we can find the length of diagonal DF, which is also equal to 2CE:

DF = 2CE ≈ 19

The area of the rhombus can be calculated as:

Area = (CE × DF) / 2

Area = (9.5 × 19) / 2

Area ≈ 90.3

Therefore, the area of rhombus CDEF is approximately 90.3 square units.

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Answer:

The hypotenuse is 13 cm

The longest leg is 12 cm

The shortest leg is 5 cm

Step-by-step explanation:

Given:

A right triangle

Let's assume, that the longest leg is x, the shortest leg is y and the hypotenuse is z

Let's write 2 equations according to the given information and put them into a system (use the Pythagorean theorem):

[tex]z = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

{√(x^2 + y^2) = x + 1,

{x - y = 7;

Let's make x the subject from the 2nd equation:

x = 7 + y

Replace x in the 1st equation with its value from the 2nd one:

[tex] \sqrt{( {7 + y)}^{2} + {y}^{2} } = (7 + y) + 1[/tex]

[tex] \sqrt{49 + 14y + {2y}^{2} } = 8 + y[/tex]

Square both sides of the equation:

[tex]2 {y}^{2} + 14y + 49 = {(8 + y)}^{2} [/tex]

[tex]2 {y}^{2} + 14y + 49 = 64 + 16y + {y}^{2} [/tex]

Move the expression to the left and collect like-terms:

[tex] {y}^{2} - 2y - 15 = 0[/tex]

a = 1, b = -2, c = -15

Solve this quadratic equation:

[tex]d = {b}^{2} - 4ac = ({ - 2})^{2} - 4 \times 1 \times ( - 15) = 64 > 0[/tex]

[tex]y1 = \frac{ - b - \sqrt{d} }{2a} = \frac{2 - 8}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]

y must be a natural number, since the length of a triangle's side cannot have negative units

[tex]y2 = \frac{ - b + \sqrt{d} }{2a} = \frac{2 + 8}{2 \times 1} = 5[/tex]

We found the length of the shortest leg

Now, we can find the rest of the dimensions:

x = 7 + 5 = 12

[tex]z = \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{144 + 25} = \sqrt{169} = 13[/tex]

Equation for the circle is : (x + 3.2)²+ (y + 3.5)²= 30.25

An equation is a mathematical statement that uses an equals sign to show that two expressions have the same value. Equations are used to solve problems and find the value of unknown variables.

According to the given information :

The equation for a circle with center (a, b) and radius r is:

(x - a)² + (y - b)² = r²

Substituting the given values, we get:

(x - (-3.2))²+ (y - (-3.5))²= 5.5²

Simplifying and squaring out the brackets, we get:

(x + 3.2)² + (y + 3.5)² = 30.25

Therefore, the equation for the circle with center (-3.2, -3.5) and radius 5.5 is:

(x + 3.2)²+ (y + 3.5)²= 30.25

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The Equation for the circle is : (x + 3.2)²+ (y + 3.5)²= 30.25

What is equation?

An equation is a mathematical statement that uses an equals sign to show that two expressions have the same value. Equations are used to solve problems and find the value of unknown variables.

According to the given information :

The equation for a circle with center (a, b) and radius r is:

=> (x - a)² + (y - b)² = r²

Substituting the given values, we get:

=> (x - (-3.2))²+ (y - (-3.5))²= 5.5²

Simplifying and squaring out the brackets, we get:

(x + 3.2)² + (y + 3.5)² = 30.25

Therefore, the equation for the circle with center (-3.2, -3.5) and radius 5.5 is: (x + 3.2)²+ (y + 3.5)²= 30.25

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Best approximation of the mass of an African elephant is 8 ×10³kg

In physics, mass is a fundamental property of matter that measures the amount of substance in an object. It is a scalar quantity that describes an object's resistance to acceleration when a force is applied. Mass is usually measured in kilograms (kg) and can be calculated by dividing an object's weight by the acceleration due to gravity.

Given;

Mass of elephant=8139kg

Dividing the mass by 1000 and multiplying it by 10³, we get

Mass of elephant=8.139 ×10³kg

Estimating the mass of elephant, we get

Mass of elephant=8 ×10³kg

hence, best approximation of the mass of an African elephant is 8 ×10³kg.

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Based on the unbiased samples , 1555 people is the correct response who prefer polar bear

A sample that is sufficiently large and drawn at random qualifies as an unbiased sample. It represents the population, and its outcomes are in line with those of the population1. In contrast, when one or more groups of persons are given preferential screening, a biased sample does not accurately reflect the population.

A biassed sample is one that doesn't fairly represent the entire population. It happens when a statistician adopts a sampling technique where some individuals of the target population have a higher or lower probability of being chosen. Because a biased sample does not accurately represent the community, the validity of a study is at risk.

There are 3380 visitors in total. 46%, 32%, 43%, and 49% of respondents in each category said they preferred polar bears.

There are: persons who favor polar bears overall.

(46% + 32% + 43% + 49%) * 3380 / 100 = 1555.08

When we round to the closest whole number, we obtain:

1555 individuals,

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Answer:

26

Step-by-step explanation:

n+2m                                      m = 12, n = 2

2 + 2(12)

2 + 24

26

Number of Std errors away from 0.12 one need to go = 1.227

Standard deviation (or σ) is a measure of how far the data are from the mean. A low standard deviation means that the data are clustered around the mean, and a high standard deviation means that the data are more scattered. Standard deviation shows how the data are distributed. This is a measure of how far each observation is from the mean.

The variance is the mean squared deviation from the mean and the standard deviation is the square root of that number. Both measures reflect the variability of the distribution, but in different units. The standard deviation is expressed in the same units as the original value (minutes, meters, etc.).

A. for 89%  ; critical z value = 1.227

                                     89% = 0.89

Critical z value = 0.89 × 0.14

                         = 1.227

Therefore number of Std errors away from 0.12 one need to go = 1.227

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The original price of the phone case was $40 according to the given equation.

In mathematics, an equation is a statement that indicates that two expressions are equal. Equations usually consist of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Yes, the equation 9/10 x 0.75C = 27 can be used to find the original price of the phone case.

Here's why:

The initial price of the phone case is represented by C.

It's marked down by 25%, which means the new price is 0.75C (75% of the original price).

You then apply a 10% off coupon, which means you pay 90% of the new price or 9/10 x 0.75C.

The equation 9/10 x 0.75C = 27 represents the final price you paid for the phone case, so we can solve for C to find the original price.

To solve for C, we can first simplify the left side of the equation:

9/10 x 0.75C = 27

0.675C = 27

Next, we can divide both sides by 0.675 to isolate C:

C = 40

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Based on the unit price, the 23.7-ounce bottle is the better buy, since it costs less per ounce than the 10.1-ounce bottle.

What is meant by unit price?

Unit price refers to the cost of one unit of a product or service. It is calculated by dividing the total cost of the item by the number of units and is used by consumers to compare the prices of different products or by businesses to determine their pricing strategies.

What is an ounce?

An ounce is a unit of measurement used to express weight or mass. It is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are commonly used to measure the weight of food, liquids, and precious metals.

According to the given information

To find the unit price for each size of shampoo, we need to divide the cost of each bottle by its size in ounces.

For the 10.1-ounce bottle, the unit price is:

Unit price = cost / size = $2.53 / 10.1 oz = $0.25 per ounce

For the 23.7-ounce bottle, the unit price is:

Unit price = cost / size = $5.48 / 23.7 oz = $0.23 per ounce

So, based on the unit price, the 23.7-ounce bottle is the better buy, since it costs less per ounce than the 10.1-ounce bottle.

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Answer:

[tex]1\frac{3}{5}[/tex] meter is the difference in depths of locations diver dove.

Step-by-step explanation:

Cameron invested $5000 at 14% and $6000 at 7%.

Interest is the amount of money that is paid or earned on a sum of money that has been borrowed or invested. It is usually expressed as a percentage of the original amount, and it can be calculated using various formulas depending on the type of interest and the frequency of compounding.

Let's assume that Cameron invested x dollars in the first account, which earns an interest rate of 14%, and y dollars in the second account, which earns an interest rate of 7%.

According to the problem, the total amount invested was $11,000. So, Equation is

x + y = 11000

We also know that at the end of the first year, Cameron had earned $1120 in interest.

The interest earned on the first account can be calculated as 0.14x, and the interest earned on the second account can be calculated as 0.07y.  

0.14x + 0.07y = 1120

We now have two equations with two unknowns. Here, we will use substitution:

x = 11000 - y

0.14(11000 - y) + 0.07y = 1120

1540 - 0.14y + 0.07y = 1120

0.07y = 420

y = 6000

Substituting y = 6000 into the equation x + y = 11000, we get:

x + 6000 = 11000

x = 5000

Therefore, Cameron invested $5000 at 14% and $6000 at 7%.

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I think it's 3 sorry if I am wrong!!

Answer:222222.333

Step-by-step explanation:

easy just divide

Power leaving the surface is more than power generated in the volume. The power 1.57079633 * 10³² Watt would the star's surface shine into space which is greater in interior. The radius of the star is  6 * 10¹⁰ cm where the power leaving the surface equals the power generated in the interior

a) Power generated in interior = Volume of star * Power generated per unit cc

= (4/3)π (7 * 10⁸)³

= 4.31026512 * 10²⁰ Watt

Power leaving the surface = Surface area * power leaving per unit surface area

= 4π (7 * 10⁸)² * 6000

= 3.69451296 * 10²²

Here, power leaving the surface is more than power generated in the volume.

b) Power generated in interior

= (4/3)π (5 * 10¹²)³ * 3 * 10⁻⁷

= 1.57079633 * 10³² Watt

Power leaving the surface =  Surface area * Power leaving per unit surface area

= 4π(5 * 10¹²)² * 6000

= 1.88495559 * 10³⁰

Hence, 1.57079633 * 10³² power would the star's surface shine into space which is greater in interior.

c) When power generated in volume = Power leaving the surface

= (4/3)πR³ * 3 * 10⁻⁷

= 4πR² * 6000

R = 6000/ 10⁻⁷

= 6 * 10¹⁰ cm

Hence, the radius of the star is  6 * 10¹⁰ cm where the power leaving the surface equals the power generated in the interior.

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