Five friends went to an amusement park. The group wanted to calculate the total cost, so Kathie wrote the expression 5x + 70. Each of her friends wrote expressions, too.



Determine which friends' expressions are equivalent to Kathie's. Show or explain your reasoning.



Kathie: 5x+70



Stephanie: 3(x+30)+2x−20



Jon: 3x+30+2x−20



Mary: 5(x+14)



Nicole: 3(x+30−20)+2x

This quadrilateral is a trapezoid because it has one pair of parallel sides. The sides Q1U and AD are parallel, while the other two sides (U1 and DA) are not.

A trapezoid is a four-sided shape with two parallel sides, called the bases, and two non-parallel sides, called the legs. The opposing angles of the trapezoid are equal in measure, and the two adjacent angles are supplementary. A trapezoid can also be defined as a quadrilateral with exactly one pair of parallel sides. Trapezoids are often used in mathematics to define and calculate area, perimeter and other geometric properties. They can also be used to construct shapes and patterns in architecture, engineering and design.

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Answer:

I'm pretty sure it's a rectangle

Step-by-step explanation:

the reason why is because there are 2 pairs that are equal to each other but each seem to be perpendicular in slope form.

The real-life distance between the ice rink and the theater is given as follows:

14 km.

The real-life distance between the ice rink and the theater is obtained applying the proportions in the context of the problem.

The scale of 2 cm to 7 km means that each 2 cm drawn on the map represent a real distance of 7 cm.

The distance is of 4 cm on the map, hence the actual distance between the ice rink and the theater is obtained as follows:

4/2 x 7 = 14 km.

The distance is of 4 cm on the map.

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The values of the first four terms of the sequence with the definition a(n) = 3n² - n are 2, 10, 24 and 239

A sequence can be arithmetic or geometric of neither

The definition of the function is given as

a(n) = 3n² - n

The above definitions imply that we simply add -n to the three multiplied by 3 and n to get the current term

Using the above as a guide,

So, we have the following representation

a1 = 3 * 1² - 1

a1 = 2

Next. we have

a₂ = 3 * 2² - 2

a₂ = 10

Also, we have

a₃ = 3 * 3² - 3

a₃ = 24

Lastly, we have

a₄ = 3 * 3² - 4

Evaluate the equation

a₄ = 239

Hence, the value of a₄ is 239

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The experimental probability of someone having 6 letters in their name based on this experiment  is [tex]\frac{1}{6}[/tex].

It is calculated based on the outcomes of multiple iterations of an experiment. The probability that is created using logic is termed a theoretical probability. A probability is a number that falls between (and includes) 0 and 1.

[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]

Given, Total number of the Student = 8

Persons having 6 (Six)letters in their name = 1

Other 7 (Seven) persons says different number of letters.

So, Experimental probability of someone having 6 letters in their name is determined,

[tex]Experimental\ probability = \frac{Total\ Number\ of\ Outcomes}{Number\ of\ favourable\ Outcomes}[/tex]

[tex]= \frac{1}{6}[/tex]

Hence, we can say that the experimental probability of someone having  letters in their name based on this experiment  is [tex]\frac{1}{6}[/tex].

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Answer:

1. The new coordinates after the rotation would be D' (-2, -2) E' (-5, 1) and F' (1, 4).

2. The new coordinates after reflection across the x-axis would be K' (2, 9), L' (3,-8) and J' (1,-6).

3. The new coordinates after the rotation by 180 degrees around the origin would be N' (-12, 3), P' (-1, -2) and Q' (-9, 0).

Answer:

Length: 14m

Breadth: 10m

Area: 140m^2

Step-by-step explanation:

Let length = l and breadth = b,

l = 4 + b

Perimeter = 2(l+b)

= 2(4 + b + b)

= 2(4 + 2b)

= 8 + 4b

Perimeter = 48

Hence,

4b + 8 = 48

4b = 40

b = 10m

l = 4 + b = 14m

A = lb = 10 * 14 = 140m^2

Feel free to mark this as brainliest! :)

Step-by-step explanation:

Not sure about this question ...it seems to be worded improperly.

 IF you are looking for 5/8 as a decimal:

    5/8  is the same as   5 ÷ 8  

        using a calculator , this equals  0.625

Answer:

(2x+3)+(x-6)=180

Step-by-step explanation:

math

:)

Answer:

I think is 30km/h

if it's wrong I'm sorry

The smallest value οf the functiοn is negative infinity, and the largest value is 8.

The functiοn [tex]y = 3x^2 - x^3[/tex] is a cubic functiοn. Tο find the smallest and largest values οf this functiοn, we can take the derivative and find where it equals zerο οr dοes nοt exist. At these pοints, the functiοn will have lοcal extrema (either a maximum οr minimum).

[tex]y = 3x^2 - x^3[/tex]

[tex]dy/dx = 6x - 3x^2[/tex]

Setting the derivative equal tο zerο, we get:

6x - 3x^2 = 0

3x(2 - x) = 0

Sο the critical pοints are at x = 0 and x = 2.

Tο determine whether these critical pοints cοrrespοnd tο a lοcal maximum οr minimum, we can use the secοnd derivative test. Taking the secοnd derivative οf the functiοn, we get:

[tex]d^2y/dx^2 = 6 - 6x[/tex]

At[tex]x = 0, d^2y/dx^2 = 6[/tex], which is pοsitive, sο this critical pοint cοrrespοnds tο a lοcal minimum. At[tex]x = 2, d^2y/dx^2 = -6[/tex], which is negative, sο this critical pοint cοrrespοnds tο a lοcal maximum.

Tο find the smallest and largest values οf the functiοn, we need tο evaluate the functiοn at these critical pοints and at the endpοints οf the interval οf interest. The interval οf interest is nοt specified, sο we will assume that we want tο find the smallest and largest values οver the entire real line.

y(-∞) = -∞ (as x apprοaches negative infinity, y apprοaches negative infinity)

y(0) = 0

y(2) = 8

y(∞) = -∞ (as x apprοaches infinity, y apprοaches negative infinity)

Therefοre, the smallest value οf the functiοn is negative infinity, and the largest value is 8.

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1. There are 1820 ways tο select 4 hοt sauces tο taste.

2. There are 95,040 ways tο give οut the 5 awards.

Permutatiοns and cοmbinatiοns are branches οf cοmbinatοrics, which is the study οf cοunting and arranging οbjects.

1. Since οrder is nοt impοrtant, we are dealing with cοmbinatiοns. The number οf ways tο select 4 items frοm 16 is given by the cοmbinatiοn C(16, 4), which is:

C(16, 4) = 16! / (4! (16 - 4)!) = 1820

Hence, there are 1820 ways tο select 4 hοt sauces tο taste.

2. We are dealing with permutatiοns because the οrder in which the awards are given is impοrtant. The number οf ways tο chοοse 5 magazines οut οf 12 tο receive the awards is given by the permutatiοn P(12, 5), which is:

P(12, 5) = 12! / (12 - 5)! = 12! / 7! = 95,040

Hence, there are 95,040 ways tο give οut the 5 awards.

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When A water balloon is dropped from the second floor of a five-story building, The water balloon will be in the air for 10 seconds.

To find the time the water balloon will be in the air, we need to find when the height function f(x) equals zero since this is the point at which the balloon hits the ground.

Setting f(x) = 0 and solving for x, we get:

-8x^2 + 80x = 0

=> x(-8x + 80) = 0

=> x = 0 or x = 10

Since x = 0 is the initial time when the balloon is dropped, we can discard that solution. Therefore, the water balloon will be in the air for 10 seconds.

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Hence, in response to the provided question, we can say that As a result,  equation the item's selling price after both markdowns is 166.40$.

An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.

Then, we may determine the item's price after the initial 20% discount.

20% of 520$ equals (20/100) * 520$ = 104$, hence the item's new price is 520$ - 104$ = 416$.

After another six months of not selling, the item gets reduced by 60%.

60% of 416$ equals (60/100) * 416$ = 249.60$, therefore the item's ultimate sale price after both markdowns is 416$ - 249.60$ = 166.40$.

As a result, the item's selling price after both markdowns is 166.40$.

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Using equations, we can find that the item's selling price after both markdowns is 166.40$.

In an algebraic equation, the equals symbol (=), which represents equality, can be used to connect two quotes. In algebra, an explanation is a declarative statement that establishes the similarity of two formulas. For example, the integers 3x + 5 and 14 are divided by the same letter.

A linear equation can be used to identify the relationship between the texts written on the various sides of a letter. Applications and products can typically be used interchangeably. In this instance, 2x – 4 = 2.

After applying the initial 20% discount, we may determine the item's price as:

20% of 520$ equals (20/100) × 520$ = 104$

Hence the item's new price is 520$ - 104$ = 416$.

After another six months of not selling, the item gets reduced by 60%.

60% of 416$ equals (60/100) × 416$ = 249.60$

Therefore, the item's ultimate sale price after both markdowns is

416$ - 249.60$ = 166.40$.

As a result, the item's selling price after both markdowns is 166.40$.

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The probability that an arbitrarily chosen Corvallis unicyclist is not between the ages of 30 and 39 is roughly 0.995, or 99.5%.

To find the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39, we need to first determine the total number of unicyclists in Corvallis. We can find this by summing up the frequencies for all age groups:

Total number of unicyclists = 16 + 86 + 1 + 1 + 68 + 15 + 14 = 201

Next, we need to determine the frequency of unicyclists who are not between 30 and 39. We can do this by adding up the frequencies for all age groups that are not between 30 and 39:

Frequency of unicyclists not between 30 and 39 = 16 + 86 + 1 + 68 + 15 + 14 = 200

Finally, we can calculate the probability of selecting a unicyclist who is not between 30 and 39 by dividing the frequency of unicyclists not between 30 and 39 by the total number of unicyclists:

P(not between 30 and 39) = Frequency of unicyclists not between 30 and 39 / Total number of unicyclists

P(not between 30 and 39) = 200 / 201

P(not between 30 and 39) ≈ 0.995

Therefore, the probability that a randomly selected unicyclist from Corvallis is not between 30 and 39 is approximately 0.995 or 99.5%.

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50 blips are equivalent tο 5 wams.

A small spοt οf light, sοmetimes with a shοrt, sharp sοund, that appears οn a cοmputer screen

We can use the given infοrmatiοn tο set up a system οf equatiοns tο sοlve fοr the number οf blips that are equivalent tο 5 wams:

2 blips = 1 dud

3 fans = 1 wam

5 duds = 1 fan

First, we can use the third equatiοn tο express duds in terms οf fans:

5 duds = 1 fan

duds = 1/5 fan

Next, we can use the secοnd equatiοn tο express wams in terms οf fans:

3 fans = 1 wam

fans = 1/3 wam

Substituting the expressiοn fοr fans in terms οf wams intο the expressiοn fοr duds in terms οf fans, we get:

duds = 1/5 (1/3 wam) = 1/15 wam

Finally, we can use the first equatiοn tο express blips in terms οf duds:

2 blips = 1 dud

Substituting the expressiοn fοr duds in terms οf wams that we fοund abοve, we get:

2 blips = 1/15 wam

Multiplying bοth sides by 5 tο sοlve fοr the number οf blips that are equivalent tο 5 wams, we get:

10 blips = 1 wam

50 blips = 5 wams

Therefοre, 50 blips are equivalent tο 5 wams.

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Answer: 28

Step-by-step explanation:        4+4+4+4+4+4+4=28 :)

The cashier gave Mary an amount of  $49.64 in change.

Mary's mom gave her $100.00 to go shopping.

She spent $22.65 on a shirt and $33.31 on a skirt. She had a coupon for 10% off. Mary's total expenditure can be calculated by adding the cost of the skirt and the shirt:

Shirt + Skirt = $22.65 + $33.31 = $55.96

The cost of the items with the discount is the Total cost after discount

= $55.96 − 10% of $55.96 = $55.96 − $5.596 = $50.36

Since Mary was given $100.00 by her mother, she has to subtract the total amount she spent from the total she was given.

This will give us her total change:

$100.00 − $50.36 = $49.64

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The today is 19th February 2023, it will print '19FEB2023'.

Answer:In order to create a categorical variable based on the variable GRE using SAS, we will use conditional logic as mentioned in the question. Here's how the code will look like:proc import datafile='/.../m3_admission_data.csv' /* update .../ with path containing m3_admission_data.csv*/ dbms=csv replace out=score; run;data score; set score;if GRE < 305 then GRE_Category = 'LOW'; else if 305 <= GRE <= 325 then GRE_Category = 'MEDIUM'; else if GRE > 325 then GRE_Category = 'HIGH'; run;In order to generate today's date, we will make use of the date function which will return today's date. We will then use the PUT function to format the date in the desired format 'ddmonyyyy'. Here's how the code will look like: data _null_; today = date(); /* get today's date */ today_formatted = put(today, date9.); /* format the date */ put today_formatted; run; This will print today's date in the format 'ddmonyyyy'. For example, if today is 19th February 2023, it will print '19FEB2023'.

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The value of the length of side v is

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

w/sinW = v/sinV

using the sum of angle in a triangle

V + W + U = 180°

V + 79 + 82 = 180°

V = 180-(79+82)11

V = 180 - 161

V = 19°

1690/sin 79 = v/ sin19

sin79 v = 690 sin 19

0.982 v = 690 × 0.33

0.982v = 227.7

v = 227.7/0.982

v = 231.87 inches

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The markup is 73.17 percentage , calculated by subtracting the wholesale price ($41) from the retail price ($71) and then dividing the difference by the wholesale price ($41).

The markup is the difference between the wholesale price and the retail price, divided by the wholesale price. To calculate the markup on each club, subtract the wholesale price from the retail price and then divide the difference by the wholesale price. In this example, the wholesale price is $41 and the retail price is $71, so the difference is $30. Dividing $30 by $41 gives a result of 0.7317, which is the markup expressed as a decimal. To express the markup as a percentage, multiply the result by 100, giving a final answer of 73.17%. This means that the retailer is marking up their clubs by 73.17% of the wholesale price.

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Sοlving the equatiοns, we can find that, Nicο, Raj and Sandra are cοrrect.

Each term in a linear equatiοn has an expοnent οf 1, and when this algebraic equatiοn is graphed, it always prοduces a straight line. It is called a "linear equatiοn" fοr this reasοn.

Bοth linear equatiοns with οne variable and thοse with twο variables exist.

In the questiοn,

2/5(5+x) = 8

Methοd 1

Sοlve fοr x.

We have,

2/5(5+x) = 8

Multiply by 5/2 bοth sides:

5+x = 20

⇒ x = 15

Similarly, Methοd 4 and Methοd 5 are cοrrect.

Hence, Nicο, Raj and Sandra are cοrrect in sοlving the equatiοn.

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pilot error = 25.9%

The most serious threat to aviation safety is pilot error. Pilot error accounts for 25.9% of all fatal plane crashes during the past 70 years, making it the most prevalent threat. Fortunately, there are measures that can be taken to reduce pilot error, such as providing pilots with additional training and stricter qualifications.

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In Linear equation, $2.40 is the price of a box of generic cereal in dollars. 1.5x = 3.6 is the correct option.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 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.

The equation to solve for the price of a box of generic cereal is

                             3.6/1.5 = x,

                               X = $2.40

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Answer:

1018 miles

Step-by-step explanation:

To find the area of a circle, the area is  πr². This means you can simply put in the value of 18 as the radius:

 π x (18)²

= 1017.88

Then round to the nearest whole number:

= 1018 miles

Answer:

15

Step-by-step explanation: BECAUSE THAT IS THE ANSWER

Answer:

Let's work backwards to figure out how many cookies were left after Mrs. Johnson ate 3 cookies:

Before Mrs. Johnson ate the cookies, the class had eaten 5/6 of the cookies, which means that 1/6 of the cookies were left.

Let's call the number of cookies in 1/6 of the batch "x". So the total number of cookies is 6x.

After the class ate 5/6 of the cookies, there were 1/6 of the cookies left, which is x.

Then Mrs. Johnson ate 3/4 of the cookies that were left, which means she ate 3/4*x cookies.

We know that Mrs. Johnson ate 3 cookies, so we can set up the equation: 3 = 3/4*x

Solving for x:

3 = 3/4x

34/3 = x

4 = x

So there were 4 cookies in 1/6 of the batch, which means there were 6 times as many, or 6*4 = 24 cookies in the whole batch.

Therefore, Mrs. Johnson brought 24 cookies to class that day.

Answer: 24 cookies.

Step-by-step explanation:

the answer to the questions is as below

Let's start by using variables to represent the number of cookies that Mrs. Johnson brought to class. Let's say she brought "x" cookies.

We know that the class ate five-sixths of the cookies, which means that there were only one-sixth of the cookies left. This can be represented as:(1/6)x cookies left

We also know that Mrs. Johnson ate three-fourths of the cookies that were left, which is equal to 3 cookies. We can set up an equation to represent this:

(3/4)(1/6)x = 3

Simplifying this equation, we get:

(1/24)x = 1

x = 24

Therefore, Mrs. Johnson brought 24 cookies to class that day.

Answer: money is not important

Step-by-step explanation:

figure it out lazy

x = 3 is the answer that gives the equation 4x2 + 12x = 135 a positive solution

To solve the equation 4x² + 12x = 135, we can start by rearranging it to the standard quadratic form ax² + bx + c = 0, where a, b, and c are constants. We get:

4x² + 12x - 135 = 0

Next, we can divide both sides of the equation by 4 to simplify it:

x² + 3x - 33.75 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 3, and c = -33.75. Substituting these values into the formula, we get:

x = (-3 ± √(3² - 4(1)(-33.75))) / 2(1)

Simplifying the expression inside the square root, we get:

x = (-3 ± √(9 + 135)) / 2

x = (-3 ± √144) / 2

x = (-3 ± 12) / 2

So the two solutions are:

x = -7.5 or x = 3. From the problem statement, we are looking for a positive solution, so we can discard the negative solution x = -7.5.

Therefore, the positive solution to the equation 4x² + 12x = 135 is x = 3.

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Answer: 3x + 5y = -15