The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better

Answer:

5

Step-by-step explanation:

100% correct

The number of pitchers that she should produce and the price that she should charge in order to maximize profit is 0 and $5, respectively, and the maximum profit is $0.

Given that a retired potter can produce china pitchers at a cost of $5 each. She estimates her price function to be where p is the price at which exactly x pitchers will be sold per week.

The formula for the profit is given by,

Profit = Revenue - Cost

The revenue for selling x pitchers at a price p is xp.

The total cost of producing x pitchers is 5x.

Therefore, Profit [tex]= xp - 5x[/tex]

Profit can be expressed as a function of x using the formulae of the function,

[tex]y = xp - 5x= (p - 5)x[/tex] .............(1)

Now, the number of pitchers that she should produce and the price that she should charge in order to maximize profit can be found by finding the maximum value of the profit function (1).

Let the maximum profit be P. Maximize P with respect to x. To find the maximum of a function of x, we can find its derivative and equate it to zero.

[tex]dP/dx = 0P = (p - 5)x[/tex]

Differentiate P with respect to x again to determine whether it is a maximum or minimum.

[tex]d^2P/dx^2 = -5 < 0[/tex]

Since [tex]d^2P/dx^2[/tex] is negative, the value of P is a maximum.

Substitute the value of x from equation (1) in terms of P to find

[tex]p.P = (p - 5)*P/(p - 5) \\\\p = 5[/tex]

Therefore, the price to maximize profit is $5 and the number of pitchers to produce is,

[tex]x = P/(p - 5) = P/0 =[/tex] undefined

Maximum profit is [tex]P = (p - 5)x = (5 - 5)x = $0[/tex]

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These theories are all true and can be used to demonstrate the congruence of two triangles.

Three straight sides and three angles define the two-dimensional geometric form known as a triangle. It is created by joining three non-collinear plane lines. The three places where a triangle's sides intersect are known as the triangle's vertices, and the line segments that make up the triangle's sides are known as its edges or sides. A triangle's inner angles are always added up to 180 degrees. Triangles can be categorised according to their edges and side lengths.

given

Many triangular congruence theorems exist, and they are all true.

The two triangles are congruent if their two sides and included angles match those of another triangle, according to the Side-Angle-Side (SAS) congruence theory.

The Angle-Side-Angle (ASA) congruence theory states that two triangles are congruent if their included sides and two angles are congruent with one another.

The two triangles are congruent if all three sides of one triangle are congruent with all three sides of the other triangle, according to the Side-Side-Side (SSS) congruence theory.

The right triangles are congruent if their hypotenuses and legs are congruent with those of another right triangle, according to the Hypotenuse-Leg (HL) congruence theory.

These theories are all true and can be used to demonstrate the congruence of two triangles.

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.

Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.

Thus, cost of one jacket = 150/50 = $3.

The jacket lasts 5 years thus for 1 year the equivalent cost is:

3/5 = $0.60.

Now, for the other jacket:

Cost per year is = (80/50) / 2 = $0.80 per jacket per year.

Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

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If a large bag of the same candy has 75 pieces, then the expected average for each color is 15 pieces.

Now, let's apply this concept to our candy problem. If the bag of candy has 75 pieces, we can assume that each color makes up approximately 1/5 or 20% of the total. That means each color should have an equal chance of appearing, with an expected average of 15 pieces per color (75 pieces divided by 5 colors).

However, this is only an expected average. In reality, there may be some variation in the number of pieces of each color that we actually find in the bag. This variation can be caused by a variety of factors, such as the manufacturing process, the mixing of different batches of candy, or even random chance.

To determine which color is likely to appear the most, we can look at the range of variation for each color. If the range of variation for a particular color is higher than the expected average of 15 pieces, then that color is more likely to appear more often than the others. On the other hand, if the range of variation is lower than the expected average, then that color is less likely to appear as often.

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The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.

Given, x^2 + xy + y^2 = 3.

We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).

Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.

Now, we have to form the Lagrange function.

L(x, y, λ) = f(x, y) + λ(g(x, y))

where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)

Now, we have to find the partial derivatives of L with respect to x, y, and λ.

∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)

∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)

∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)

Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.

Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.

Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.

Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.

Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)

Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)

Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.

To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).

After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).

Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

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The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7.

The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7. The repeating section is comprised of 729.

To calculate this, first consider the prime factorization of 727 1,229. 727 1,229 = 17 × 43 × 137.

Since 17, 43 and 137 are all prime numbers, the prime factorization will not yield a power of 10 as a factor. Therefore, the repeating section must have a length of 7 in the decimal representation of 727 1,229.  
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If Yumi bought 13 fish for total then yumi bought 8 zebra fish and 5 neon tetras.

Substitution is a mathematical operation that involves replacing a variable or expression in an equation, function, or formula with another variable, expression, or value.

Let's assume Yumi bought x zebra fish and y neon tetras.

x + y = 13 (equation 1)

2x + 2.3y = 27.5 (equation 2)

Using equation 1, we can solve for one variable in terms of the other:

x = 13 - y

Then, change x in equation 2 to the following expression:

2(13 - y) + 2.3y = 27.5

Simplifying and solving for y:

26 - 2y + 2.3y = 27.5

0.3y = 1.5

y = 5

So Yumi bought 5 neon tetras. To find how many zebra fish she bought, we can substitute y = 5 into equation 1:

x + 5 = 13

x = 8

Therefore, Yumi bought 8 zebra fish and 5 neon tetras.

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A crime reporter's null hypothesis is:H0: The actual number of burglaries per month is 3000.

A null hypothesis is a hypothesis that claims that there is no significant relationship between two variables. The term "null" implies that no effect exists or that the effect is negligible. The null hypothesis is typically utilized in scientific research and experiments. It is also utilized in statistical studies, such as those investigating cause-and-effect relationships or the effects of a treatment or intervention.

The null hypothesis of a crime reporter regarding 3000 burglaries per month is that there is no significant difference between the observed results and what is expected or hypothesized. This is because 3000 burglaries per month is the average, and the null hypothesis aims to verify whether this is the actual result.

Therefore, a crime reporter's null hypothesis is:H0: The actual number of burglaries per month is 3000.

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Answer: If x represents the number of hours that Ryan rides his bike, and y represents the total number of miles that he rides, we can write the equation relating x and y as:

y = 12x + 5

This is a linear equation in slope-intercept form, where the slope is 12 (the rate at which Ryan rides, in miles per hour) and the y-intercept is 5 (the number of miles Ryan has already ridden).

To predict how many minutes it will take for Ryan to ride a total of 60 miles, we can substitute y = 60 into the equation and solve for x:

60 = 12x + 5

55 = 12x

x = 55/12

To convert this to minutes, we need to multiply by 60, since there are 60 minutes in an hour:

x (in minutes) = (55/12) * 60

x (in minutes) ≈ 275

Therefore, it will take Ryan approximately 275 minutes (or 4 hours and 35 minutes) to ride a total of 60 miles.

Step-by-step explanation:

The answer is 250 kilometers. Peter and his mother traveled a total distance of 250 kilometers on their mail delivery.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter is equal to 0.01 kilometers, so 50 kilometers would be equal to 5,000 centimeters. The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

Charltc to Thornton is 1,000 centimeters, Thornton to Avon is 1,500 centimeters, Avon to Ashton is 1,000 centimeters, and Ashton to Charltc is 1,500 centimeters. This gives us a total of 5,000 centimeters, or 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times, since they flew from Charltc to Thornton, then to Avon, then to Ashton, and then back to Charltc). This gives us 250 kilometers, which is the answer to the question.

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Peter and his mother traveled a total distance of 250 kilometers on their mail delivery. The answer is 250 kilometers.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter =  0.01 kilometers,

so 50 kilometers = 5,000 centimeters.

Charlton to Thornton= 1,000 centimeters,

Thornton to Avon= 1,500 centimeters,

Avon to Ashton= 1,000 centimeters,

and Ashton to Charlton= 1,500 centimeters.

Total distance= 1,000+1,500+1,000+1,500

= 5,000 centimeters, or 50 kilometers.

The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times.

=50*5

=250

Since they flew from Charlton to Thornton, then to Avon, then to Ashton, and then back to Charlton.

250 kilometers is the answer to the question.

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Question:

Peter's mother is a pilot. She often makes deliveries near their community. Peter and his mother flew from Charlton to Thornton to make a mail delivery. Then they continued on to Avon and Ashton and returned to Charlton. How many kilometers did Peter and his mother travel in all?

Using simple mathematical operations we know that 4.5 ft of fabric is needed.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, to find the fabric needed:

1 2/7 feet of fabric

Then, 3 1/2 hands will need:

= 9/7 * 7/2

= 9/2

= 4.5 ft of cloth

Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.

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Correct question:

Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?

The theoretical probability for the 1 horned, 1 eyed,  flying, people eater purple is found to be 1/120.

Experimental Probability: Based on actual results rather than mathematical calculations, the experimental probability of an occurrence is the likelihood that the event will actually occur.

Theoretical Probability: Considering that the event is ideal, the theoretical chance that it will occur is the theoretically ideal probability of a specific result. The flaws in the system are not taken into consideration by theoretical probability.

Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.

The given probability are;

Let P(E)  be the theoretical probability  1 horned, 1 eyed,  flying, people eater purple.

Then,

P(E) =  3/4 * 1/5* 2/3* 3/8* 1/2

P(E) =  1/120

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Answer:

  60.5 cm²

Step-by-step explanation:

You want the shaded area of a parallelogram that has a trapezoid shape removed from it.

The area of the parallelogram is the product of its base and height:

  A = bh

  A = (10 cm)(8 cm) = 80 cm²

The area of the trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(5.5 cm +7.5 cm)(3 cm) = 1/2(13 cm)(3 cm) = 19.5 cm²

The shaded area is the area of the parallelogram less the unshaded area of the trapezoid:

  shaded = 80 cm² -19.5 cm² = 60.5 cm²

The shaded part of the figure has an area of 60.5 cm².

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.

Answer:

3 packages

Step-by-step explanation:

61 - 20 * 2 (small grain sandpaper) = $21 remain. The largest grain costs $7, so 21/7 = 3 packages of the largest grain sandpaper was bought.

Hope this helped!

It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.

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[tex]3log5^2 - 2log5^3[/tex] simplifies to 0.

A lοgarithm is a mathematical functiοn that represents the expοnent tο which a given base must be raised tο prοduce a certain value. In οther wοrds, it is a way οf expressing a number in terms οf the pοwer tο which anοther fixed number, called the base, must be raised tο prοduce that number.

Using the pοwer rule οf lοgarithms, we can simplify the lοgarithms inside the expressiοn as fοllοws:

3lοg5² - 2lοg5³ [tex]= log5^{(23)} - log5^{(32)}[/tex]

Using the quοtient rule οf lοgarithms, we can cοmbine the lοgarithms as fοllοws:

[tex]log5^{(23)} - log5^{(32)} = log(5^{(23) / 5^(32)})[/tex]

Simplifying the expressiοn inside the lοgarithm:

[tex]log(5^{(23)}/ 5^{(32)}) = log(5^6 / 5^6) = log(1) = 0[/tex]

Therefοre, [tex]3\log5^2[/tex] - [tex]2\log5^3[/tex] simplifies tο 0.

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Answer:

the chance of a blizzard tommorrow is 5%. write the complement of this event

Step-by-step explanation:

The complement of an event is the event that it does not happen, so the complement of a blizzard occurring tomorrow with a 5% chance is that a blizzard does not occur tomorrow with a probability of:

100% - 5% = 95%

Therefore, the complement event is that there is a 95% chance that a blizzard does not occur tomorrow.

Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.

Step-by-step explanation:

We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].

Now to solve for c

[tex]c-34=21\\[/tex]

add 34 to both sides

[tex]c=55[/tex]

The conic section that formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle

When a plane intersects the central axis of a double-napped cone at a 90° angle, the resulting conic section is a circle.

To understand why this is the case, we can first consider the properties of a double-napped cone. A double-napped cone is formed by rotating a straight line, called the generatrix, around an axis that intersects the line at a fixed point, called the vertex. The resulting surface consists of two parts, each of which is a circular cone.

Now, let us imagine a plane that intersects the central axis of the double-napped cone at a 90° angle. Since the central axis of the cone is perpendicular to the base, the plane must intersect both cones at their widest point, which is also their center. At this point, the cone has a circular cross-section, which means that the plane intersects the cone in a circle.

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Answer:

circle

got it right on edg

Answer:

4

Step-by-step explanation:

count 3 what comes next

Answer:The answer is...... I want you to get it but I will help you solve!!

Step-by-step explanation:

What you want to do first is find out how many points decreased.

28-12=?

Then you will take the number decreased and divide it by the original last season goals 28. The smaller number will get divided by 28.

You will get a .(decimal)??? take that number you get and move the .(decimal) over 2 places to the right(that is because it's a %) and you will have your answer.

The probability of drawing three cards with replacement from a standard deck of 52 cards is 1/416.

The probability of drawing three cards with replacement from a standard deck of 52 cards is to be found when the first card is a club, the second card is a red card, and the third card is the six of hearts.

Here, the Probability of the first card being a club = P(C) = 13/52 = 1/4 [Since there are 13 clubs in the deck of 52 cards]

Probability of the second card being a red card = P(Red) = 26/52 = 1/2 [Since there are 26 red cards in the deck of 52 cards]

Probability of the third card being six of hearts = P(6 of hearts) = 1/52 [Since there is only one six of hearts in the deck of 52 cards]

Therefore, the Probability of drawing three cards with replacement from a standard deck of 52 cards is

= P(C) × P(Red) × P(6 of hearts)= 1/4 × 1/2 × 1/52= 1/416

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The fraction of sweets that does she eat is 7/20

In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.

Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.

So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:

=> 7/20

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After using permutations and combination, There are 1001 groups of 4 people that can answer the 4 different phone lines if all the lines begin to ring at once.

To determine the number of groups of 4 people that can answer the 4 different phone lines, we can use the combination formula, which is:

nCr = n! / (r! * (n-r)!)

where n is the total number of people in the office and r is the number of people needed to answer each phone line.

In this case, n = 14 (the total number of people in the office) and r = 4 (the number of people needed to answer each phone line).

So, the number of groups of 4 people that can answer the 4 different phone lines is:

¹⁴C₄ = 14! / (4! * (14-4)!) = 1001

Therefore, there are 1001 groups of 4 people that can answer the 4 different phone lines if all the lines begin to ring at once.

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Question 7. C (rectangular pyramid)

Question 8. 17 cm

Answer:

Question 7:C rectangular pyramid

Question 8: C 120 in

A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160

Step-by-step explanation: