Alfonso wants to purchase a pool membership for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.

Answer:

To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:

GCF = 2³ * a² * b5 = 8a²b5

To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:

LCM = 2⁴ * a³ * b7 = 16a³b7

So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.

In quadratic functiοn -

          g(x)                                    h(x)                                     d(x)

vertical shift dοwn 3     reflectiοn acrοss the x-axis   vertical shift dοwn 3

hοrizοntal shift left 3     vertical strecht οf 3               hοrizοntal shift right 3

The expressiοn f(x) = ax² + bx + c, where a, b, and c are all integers with a nοt equal tο zerο, denοtes a quadratic functiοn. The shape that a quadratic functiοn's graph takes οn is called a parabοla.

In spite οf the fact that parabοlas might have οpenings that are upward οr dοwnward, varying "widths" οr "steepnesses," they all have the same basic "U" shape.

Quadratic parent: f(x)=x²

The graph is a parabοla with vertex V=(0,0) at the οrigin and οpens up.

When x=1→f(1)=1²→f(1)=1

1) g(x)

The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.

The vertex is at the pοint (-3,-3): 3 units tο the left and 3 units dοwn οf the vertex οf the parent funtiοn.

When x is 1 unit tο the right frοm the vertex g(x)=1

Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:

1.1) vertical shift dοwn 3.

1.2) hοrizοntal shift left 3.

2) h(x)

The graph οpens dοwn, then there is a reflectiοn acrοss the x-axis.

The vertex is at the οrigin (0,0).

When x is 1 unit tο the right frοm the vertex h(x)=-3

Then the transfοrmatiοns were applied tο the quadratic parent functiοn are:

2.1) reflectiοn acrοss the x-axis.

2.2) vertical strecht οf 3.

3) d(x)

The graph οpens up, then there is nοt a reflectiοn acrοss the x-axis.

The vertex is at the pοint (3,-3): 3 units tο the right and 3 units dοwn οf the vertex οf the parent funtiοn.

When x is 1 unit tο the right frοm the vertex d(x)=1

Then the transfοrmatiοns were applied tο the cuadratic parent functiοn are:

3.1) vertical shift dοwn 3.

3.2) hοrizοntal shift right 3.

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The complete question is -

The given graphs show functions which have been transformed from the quadratic parent, f(x) = x2. Determine which transformations were applied to the quadratic parent function to result in each graph.

Therefore , the solution of the given problem of pie chart comes out to be  number of adults who selected math (15) outnumbered the number of minors. (10).

A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.

Here,

for a two-way table: Party A, Party B, and Party C

Men make up 12 8 % of the population while women make up 16 %.

Total            28        15         19

32 ladies make up the group, to start with.

b) 16 female voters plan to support Party A.

            Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.

Total          25         24          31

15 people selected math.

b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).

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Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

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a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.

Answer:

Step-by-step explanation:

In linear equation, value of expression is -5 and 0.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

  -6d + 4a + 5c/5

1)

d = 1 , a = 1 , c = 3

=  -6d + 4a + 5c/5

= -6 * 1 + 4 * -1 + 5 * -3/5

= -6 -4 - 15/5

= -25/5

= -5

2)

 d = -10, a = -5 , c = -8

=    -6d + 4a + 5c/5

= -6 * -10 + 4 * -5 + 5 * -8/5

= 60 -20 - 40/5

 = 60-60/5

  = 0

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The probability of drawing a diamond, then a black card, and then a face card from a standard deck of 52 cards with replacement is 3/104 or 0.028846 .

The probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card is given by the expression, `(13/52) × (26/52) × (12/52)`.

In a standard deck of 52 cards, there are 13 diamonds, 26 black cards (13 clubs and 13 spades), and 12 face cards (4 Jacks, 4 Queens, and 4 Kings).

To calculate the probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card, we use the formula of probability:

`P(E) = n(E) / n(S)`

where, P(E) = Probability of an event

n(E) = Number of favorable outcomes

n(S) = Total number of outcomes

Total number of outcomes = 52

First card will be a diamond

Number of diamonds in a deck of 52 cards = 13

Total number of outcomes after drawing the first card = 52

Probability of drawing a diamond in the first attempt = P(diamond)`= 13/52

Probability of drawing a black card in the second attempt, given that the first card is a diamond= `P(black/diamond)`= (26/52) = `(1/2)`

Probability of drawing a face card in the third attempt, given that the first card is a diamond and second card is a black card= `P(face/diamond and black)`= `(12/52)` = `(3/13)`

Therefore, probability that the first card will be a diamond, the second card will be a black card, and the third card will be a face card`= P(diamond) × P(black/diamond) × P(face/diamond and black) = (13/52) × (1/2) × (3/13)= 3/104`

Therefore, the required probability is 3/104 or 0.028846 rounded to the nearest millionth.

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Nonresponse bias occurs when(D) those responding to a survey or poll differ systematically from the nonrespondents.

Nonresponse bias occurs when individuals who do not respond to a survey or poll differ systematically from those who do respond, resulting in a biased sample. This can lead to incorrect inferences about the population being studied.

Nonresponse bias can occur for various reasons, including lack of interest, inability to participate, or refusal to participate. It is important to understand and address nonresponse bias to ensure the accuracy and reliability of survey or poll results. Strategies such as follow-up contact attempts and incentives can help mitigate nonresponse bias.

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The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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Answer:

m = -9/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, -6) (2, 3)

We see the y increase by 9, and the x decrease by 2, so the slope is

m = -9/2

The probability that a student completed the homework given that they failed the test is 3/8.

Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves the measurement and analysis of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

The concept of probability is used in many fields, such as statistics, physics, finance, and engineering, to make predictions and decisions based on incomplete information. It provides a framework for analyzing situations in which multiple outcomes are possible and assigns a quantitative value to the likelihood of each outcome.

To find the probability that a student completed the homework given that they failed the test, we need to use conditional probability.

Let A be the event that a student completed the homework and B be the event that a student failed the test.

We want to find P(A | B), the probability that a student completed the homework given that they failed the test.

Using the data from the table, we can see that the total number of students who failed the test is 8 (3 who completed the homework and 5 who did not).

Therefore, P(B) = 8/18 = 4/9 (the probability that a student failed the test)

Out of the 8 students who passed the test, 3 also completed the homework, so P(A and not B) = 3/18 = 1/6.

So, P(A | B) = P(A and B) / P(B) = (1/6) / (4/9) = 3/8.

Therefore, the probability that a student completed the homework given that they failed the test is 3/8.

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Answer:

-15

Step-by-step explanation:

4.1.60 - (15) + (-13) = 32

4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15

Answer: FALSE

Step-by-step explanation:

                                   1500 decagram = 15 kg

                                      1 decagram = 0.01 kg

                                       1500 decagram = 1500/0.01 kg

                                                                   = 1500/100 kg

                                        1500 decagram = 15kg  

Answer:

Proofs attached to answer

Step-by-step explanation:

Cant really graph since we don't have access, but here are some pointers.

the solid is really just a right-cylinder missing a chunk.

so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.

Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]

The position of C on the number line is 1/8th position.

A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.

From the given number line, there are total 8 points between 0 to 1

That means, it's fractions of 8.

Location of point C is on the 1st point,

So, position of C on this number line = (1/8) ÷ (1-0) = 1/8

Therefore, In the number line, C is located in the 1/8th place.

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a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

They cover almost equal distances from their starting points:

24 miles ≈ √12²+21² miles

b) They encounter each other.

c) The angle at one vertex measures 30 degrees.

d) e) As shown in the attached picture, it is an almost right triangle.

f) Together, they cover a total distance of 57 miles (12+21+24).

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Answer: 88km is your answer

Step-by-step explanation: We just had this on a test

0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.

0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.

2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.

2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.

Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.

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The correct answer is p=62

Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

Parts-R-Us could be eligible for a $0 bonus if it achieves an on-time performance rate of 94% or more.

The company would have to maintain an order delivery rate of 95% in order to qualify for the bonus. If achieved, the bonus would be as follows: Bonus = 94% * (1 - 100).

The following is the calculation for the bonus:

Bonus = P * (1 - D)

Where:

P represents the proportion of orders that are delivered on time.

D represents the total number of orders placed late.

In the event that Parts-R-Us achieves an on-time performance rate of 94%, the bonus would be as follows:

Bonus = 94% * (1 - 100)

Bonus = $0

If the company only managed to complete its tasks 94% of the time, it will not be eligible for a bonus.

In order to qualify for the maximum bonus, Parts-R-Us would have to maintain an on-time delivery rate of 95%.

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The mean of the sampling distribution will be 3.54. Thus, the correct option is C.

The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.

This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.

The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.

Thus, the correct option is C.

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Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.

The answers to the second question are:

Step-by-step explanation:

Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.

As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.

Second Question Explanation:

1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.

2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.

Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:

         H

        /|

       / |

      /  |

     /   |

    / θ  |

   /____|L

       E

       |

       |

       |

       |

       T

       |

       |

       |

       |

       B

2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).

3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:

         7248

        /|

       / |

      /  | EL

     /   |

    / θ  |

   /____|L

       E

       |10

       |

       |

       |

       T

       | 2

       |

       |

       |

       |

       B

4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:

10/EL = 2/7248

5. Multiplying both sides by EL and dividing both sides by 2, we get:

EL = 7248*5 = 36240 inches

Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).

Step-by-step explanation:

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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Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.

Given,

Number of sacks of potatoes = 30

Mass of each potato = 25

Total weight of Potatoes = 30 * 25

= 750

Number of sacks of carrots = 20

Mass of each Carot = 7.5

Total weight of Carrot = 20 * 7.5

= 150

(The total weight is the weight of potatoes plus the weight of carrots.)

So, total weight = 750 + 150

= 900

The maximum land which Edith can carry safely in the van is 920 kilograms.

∵ 900 < 920

∴ She can use her van safely.

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