A toy maker needs to make $17,235 per month to meet his cost. Each toy sells for $45. How many toys does he need to sell in order to break even

Answer: Infinitely many solutions

Step-by-step explanation:

On the graph I have attached, you can see the two lines overlap each other. This means the linear equations have an infinite amount of solutions.

The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.

One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.

Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.

Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.

Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.

By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.

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Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).

To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.

f(t) = t, 0 ≤ t ≤ 3

f(t) = 2t - 3, 3 < t ≤ 4

f(t) = 5, 4 < t

Using the Heaviside function uc for the jump at c, we can represent each interval as follows:

f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3

f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4

f(t) = 5uc(t-4), 4 < t

Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)

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Answer:

10km

Step-by-step explanation:

Pythagoras

Formula=[tex]a^2+b^2=c^2[/tex]

[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]

The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.

To plot these lines on a graph, we first need to solve for y in terms of x for each equation.

can plot these lines

[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]

[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]

The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).

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Answer: The correct answer to this problem would be C, or 32/3.

Step-by-step explanation:

The average rate of change in a function is the rate at which one value changes with respect to another value.

Given function: f(x) = 2x² + x + 5 on interval [-2, 2]

Therefore,

Average rate of change = f(2)-f(-2)/2-(-2)

f(2) = 2(2)² + 2 + 5

f(2) = 15

f(-2) = 2(-2)² - 2 + 5

f(2) = 11

Substitute the values,

Average rate = 5-11/2+2

Average rate = 4/4

Average rate = 1

So, the average rate of change is

Leading me to believe option C is correct.

A zero balance in Armando's account can be achieved by subtracting $250 from the account balance. This can be done through a combination of withdrawals and/or transfers out of the account.

Subtracting is a mathematical operation that involves taking one number away from another. It is the inverse of addition, and is represented by the minus sign (-). Subtracting is used to determine the difference between two numbers, or to reduce a number by a given amount. In algebraic terms, subtracting is represented by the equation: a - b = c, where a is the starting number, b is the number to be subtracted, and c is the resulting difference. Subtracting can also be used on fractions, decimals, and other forms of numbers.

For example, Armando could make a $250 withdrawal from the account or transfer $250 to another bank account.

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Answer:

9.5 decimal

espero y te ayude

We have triangle ABC, the length of side AB is 16 inches and the length of side BC is 24 inches, the possible length of the side AC is less than 40 inches

To find the possible length of side AC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side, that is, a + b > c, b + c > a, c + a > b.

Now, for the given triangle ABC:

a = AB = 16 inches

b = BC = 24 inches

c = AC

We know that a + b > c (using the triangle inequality theorem)

16 + 24 > cc < 40

Therefore, By using the triangle inequality theorem, the possible length of the side AC is less than 40 inches.

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The expression for the marginal revenue function is MR(q) = 600r - 7.

The given product's revenue function is R(q) = - 7q + 600qr.

To find an expression for the marginal revenue function, we can use the following steps:

Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).

Step 2: Simplify the expression for MR(q) to record the final result.

In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.

So, we have to differentiate R(q) with respect to q to get MR(q).

The derivative of - 7q with respect to q is - 7.

The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.

MR(q) = dR(q) / dq

= (d/dq)(- 7q + 600r)

= (- 7) + (600r)

= 600r - 7

The equation that represents the marginal revenue function is MR(q) = 600r - 7.

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Answer:

112°

Step-by-step explanation:

Finding the unknown angle in a quadrilateral:

        Sum of all angles of a quadrilateral = 360

                                      a + 49 + 72 + 127 = 360

                                                     a + 248  = 360

                                                                a = 360 - 248

                                                                a = 112°

The best deal for Jack and Jill would be for Jill to offer Jack $10, and for Jack to accept this offer. This would give Jack $9.09 in the future after discounting, and it would give Jill $10 in the future after discounting.

Jack will accept anything positive.

Jill is indifferent between $20 in one year and $16 today (she discounts the future at 20%).

Jack is indifferent between $4 in one year and $3.60 today (he discounts the future at 10%). Note that $16.40 is preferred by Jill to $16 in one year.

Discount refers to the process of reducing the value of future benefits or costs, based on the assumption that people generally prefer immediate benefits to delayed ones. This means that the further into the future a benefit or cost occurs, the less valuable it is considered to be in the present.

Discounting is commonly used in economics, finance, and environmental analysis, where it plays a significant role in determining the present value of future cash flows, investments, and environmental damages. The concept is also used in decision-making, as individuals and organizations often make choices based on their perception of the present value of future outcomes.

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The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.

To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.

We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".

The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.

Differentiating both sides with respect to time, we get:

dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)

We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.

Substituting these values into the formula, we get:

dV/dt = 2π(150)(0.5) + π(150)^2(0)

dV/dt = 47123.74 cubic feet per minute

Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.

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Answer:

x = 20

Step-by-step explanation:

if a line is parallel to a side of a triangle and intersects the other two sides, it divides those sides proportionally.

QR is parallel to ST and intersects the other two sides of the triangle, then

[tex]\frac{PQ}{QS}[/tex] = [tex]\frac{PR}{RT}[/tex] ( substitute values )

[tex]\frac{x}{45-x}[/tex] = [tex]\frac{16}{30-16}[/tex]

[tex]\frac{x}{45-x}[/tex] = [tex]\frac{16}{20}[/tex] ( cross-  multiply )

20x = 16(45 - x)

20x = 720 - 16x ( add 16x to both sides )

36x = 720 ( divide both sides by 36 )

x = 20

The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Answer:

Step-by-step explanation:

you are going to give more info ?????

The point-slope form of the line equation that passes through the points (- 9, - 9) and (- 8, 1) is equals to the y= 10x + 81.

The standard equation of a line is, y = mx + b where m is the slope and b is the y-intercept. This is a very useful form of the linear equation when comparing lines. We have to determine the equation of the line that passes through the points (- 9, - 9) and (- 8, 1). First we determine the value of slope of line. The formula for slope of line that passing through the points (x₁,y₁),(x₂,y₂) is [tex]m = \frac{y_2 - y_1}{x_2- x_1} [/tex]

here, x₁ = -9, y₁ = -9 , x₂ = -8, y₂ = 1, so

[tex]m = \frac{1-(-9)}{-8-(-9)} = \frac{10}{1} = 10[/tex]

The point-slope form for line passing through points (x₁,y₁),(x₂,y₂) is y − y₁ = m(x − x₁)

=> y - (-9) = 10( x -(-9))

=> y + 9 = 10( x + 9)

=> y + 9 = 10x + 90

=> y = 10x + 81

Hence required equation is y = 10x + 81.

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The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer.  If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:

Number of students traveling = 30 x 1/3 = 10  

Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:

Number of students traveling out of the country = 10 x 1/5 = 2

Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.

It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.

In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.

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Answer:

Step-by-step explanation:

Hi there! Just multiply by x and find the value of f=p. Good luck!

Answer: Below :)

Step-by-step explanation:

A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.

The markup is 25% of the cost, which is 0.25 * 500 = €125.

So the total cost of the produce plus markup is €500 + €125 = €625.

Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.

125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.

Therefore, the profit is the markup, which is €125.

B) To find the total income, we add the profit to the total cost:

Total income = €500 + €125 = €625

Answer:

A)  €125

B)  €625

The probability that a student selected randomly owns either a laptop or a car is 85%.

Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?

For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:

P(A) = probability of owning a laptop = 750/1000 = 0.75

P(B) = probability of owning a car = 450/1000 = 0.45

P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35

Now, substituting values into the formula:

P(A∪B) = 0.75 + 0.45 - 0.35= 0.85

Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.

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A statement which is true include the following: C. The functions have opposite slopes.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models one of the function is given by;

y = 4x

mx = 4x

Slope, m = 4.

For the other function, the slope can be calculated as follows;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 4)/(1 - 0)

Slope (m) = -4/1

Slope (m) = -4.

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Answers:

1.2x10

2.72 cubic cm

Answer:

A. Less than

Step-by-step explanation:

Answer:

Cos2a - cot2a/sin2a - tan2a

Step-by-step explanation:

(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).

In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.

8. T (-4,7)             7 units right, 7 units up                      (x-11, y+14)    

9. U (3,-4)               7 units left, 7 units up                         (x+7, y+7)      

10. V (-2,-10)           7 units right, 7 units down                  (x+7, y-7)  

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Answer: The median is 6

Step-by-step explanation: The median is the data value separating the upper half of a data set from the lower half.

Arrange data values from lowest to highest value

The median is the data value in the middle of the set

If there are 2 data values in the middle the median is the mean of those 2 values.

Answer:

Step-by-step explanation:

Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]

                        [tex]= 17.70 \times \frac{3}{2}[/tex]

                       [tex]=\frac{53.10}{2}[/tex]

                      [tex]=\pounds26.55[/tex]

Pay [tex]=11*26.55=\pounds 292.05[/tex]    (I assume you can use a calculator for this)

Solution: [tex]\pounds 292[/tex]