Matt ate 0.45 of his birthday cake. Convert the amount of cake Matt consumed into a fraction in simplest form.

The length of Mian in inches is 23 and the length of Udon in inches is 11

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is 34 in and Udon is 12 inches shorter than Mian.

Let Mian be represented by M and that of Udon by U,

Therefore, according to question, establishing the equation,

M + U = 34

M - U = 12

Adding both the equations,

2M = 46

M = 23

U = 11

Hence, the length of Mian in inches is 23 and the length of Udon in inches is 11

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Answer:

Step-by-step explanation:

(a) The study is observational type.

(b) Stratified sampling can be used for carrying out this study.

(a) In the given problem, We want to hear students' opinions about the new housing structure and ensure that the survey reflects all students' views equally. The critical thing to note here is that you need to collect opinions. Not the reason behind the opinion. So researchers don't care how the data goes up. So this is an observational study.

(b) In the case of sampling strategy we can use stratified sampling. Stratified sampling refers to a type of sampling technique. In stratified sampling, researchers divide the population into separate groups called strata. A probability sample (often a simple random sample) is then drawn from each group. The same number of samples can be used each year.

Therefore, To make sure the survey equally represents opinions from students from all years (a) the study is the observational type and (b) Stratified sampling can be used for carrying out this study.

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Answer: its 15

Step-by-step explanation:

Answer: The length of a side of a regular pentagon can be found using the formula, side = 2r * sin(π/5), where r is the radius of the circle that the pentagon is inscribed in. Using this formula, the length of a side of the pentagon is approximately 4.08 cm or 40.8 mm (rounded to the nearest mm).

Answer:111

Step-by-step explanation: how to do it:is try

Answer: f(k) = 3k - 5

Step-by-step explanation:

For f(x) functions, you're simply plugging in whatever value is in the parenthesis. For example, if you were asked to find f(1), you would plug in 1 for x.

f(1) = 3(1) - 5 = -2. In this case, you're just plugging in a different variable.

The probability that they are sitting around a round table in age order is 1/12. There are 10 ways for five people to sit in age order.  

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

Five people all of different age are sitting around a round table.

Find the probability they are sitting in age order!

Let's name the 5 people 1, 2, 3, 4, 5.

There are two ways in putting them in the age order, ascending or descending.

There are 10 ways that they are sitting around a round table in the age order.

n(Age order) = 10

The total arrangements for 5 people sitting around a round table is

5! = 1 × 2 × 3 × 4 × 5

5! = 120 ways

n(S) = 120

The probability that they are sitting in age order would be

P(Age order) = n(Age order) / n(S)

P(Age order) = 10/120

P(Age order) = 1/12

Hence, the probability that five people are sitting around a round table in age order is 1/12.

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The number of terms in the algebraic expression 6y + 14 is 2 terms

From the question, we have the following parameters that can be used in our computation:

6y + 14

Consider an expression given as

ax + b

The number of terms in the expression is 2 and the terms are ax and b

Using the above as a guide, we have the following:

6y + 14 has 2 terms

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Complete question

Identify the number of terms and then the resend themselves for each algebraic expression

6y + 14

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{0}{4 +2} \implies \cfrac{ 0 }{ 6 } \implies \text{\LARGE 0}[/tex]

The population growth rate can be calculated using the equation x = x₀ (1+r)ⁿ. The population after 8 years will be 66 frogs.

The population growth is the increase in population after the specified number of years. Lets look into the data which is given.

The initial population is 6 tree frogs.

Population growth percent = 35%    

Rate of growth, r = 35/100 = .35

The population growth is calculated using the equation,  x = x₀ (1+r)ⁿ

     x₀ is  initial population

     r is the rate

    n is the number of years.

x = 6 (1+r)⁸ = 66.19

So the population of frog after 8 years will be 66.

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The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479

According to the question,

we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)

Here,

Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.

And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,

The distribution here is a geometric one, where

P(Y = 3)

= P(Not red light in initial 2 lights) x P(red light in third light)

= [(1 - 0.35)² X 0.35]

= 0.1479

so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.

Note:

mean and variance of this question is not possible to find out.

the complete question ends till the probability to find the first red light on the third day.

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The total cost of Lacey's lesson a function of the number of hours scheduled is [tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex] and this one refers the function.

In math the term called function is known as a correspondence from one value x of the first set A to another value y of the second set B and it relates inputs to outputs.

Here we have know that Lacey pays $15 for each hour of golf lesson and $10 for equipment rental.

And here we have also know that If the lesson is more than 3 hours long she only pays $5 for equipment rental.

Let us consider that x be the amount time she has been taking lessons.

Then the function can be written as,

[tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex]

While we looking into it we have identified that the given situation will create the function.

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After solving, total 360 different executive boards can there be.

In the specified office have one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer.

So there are total 6 members.

The total number of members in executive board = 4

So, the ways of selecting different executive boards = [tex]^{6}P_{4}[/tex]

The ways of selecting different executive boards = [tex]\frac{6!}{(6-4)!}[/tex]

The ways of selecting different executive boards = [tex]\frac{6!}{2!}[/tex]

The ways of selecting different executive boards = [tex]\frac{6\times5\times4\times3\times2!}{2!}[/tex]

The ways of selecting different executive boards = 6 × 5 × 4 × 3

The ways of selecting different executive boards = 360

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To learn more about

The complete question is:

From a committee of 6 members, suppose that each member of the executive board also has a specified office: one member of the executive board is the president, another is the vice president, a third is the secretary, and the last one the treasurer. How many different executive boards can there be?

The length of all a triangle's sides added together yields the perimeter of a triangle.

The length of all a triangle's sides added together yields the perimeter of a triangle.

The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.

perimeter=(length + width)2.

JKL - Delta RST^ prime , RS = 14 ST = 12 , TR = 10 , and LJ = 14 2. ADEF, if triangle DEF sim triangle ABC , AB = 27 BC = 16 CA = 25 , and FD = 15 3

RST perimeter=(length + width)2.

14+ 12+10+14 = 50

triangle ABC

27 + 16 + 25 =68

triangle PQR sim triangle LMN , LM = 16 , MN = 14 , NL = 27 ,

16+14 + 27 = 57

if triangle KTM sim triangle FGH . . FG = 30 GH = 38 , HF = 38

30 + 38 + 38 =106

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Answer: -2

Step-by-step explanation:I'am in a rush right now sorry

Answer: i know what school ur from my school page looks the same (we in CCA) XDD

anyways this question is very vague. but i think its c.

Step-by-step explanation:

again its very vague but i tried i think its c

The length of the line segment is given by the distance equation

D = 7.2 units

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the distance of the line segment between two points be D

Now , the equation will be

Let the first point be represented as P ( 1 , 6 )

Let the second point be represented as Q ( 7 , 2 )

Now , distance between P and Q is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

D = √ ( 1 - 7 )² + ( 6 - 2 )²

On simplifying the equation , we get

D = √ ( -6 )² + ( 4 )²

D = √ ( 36 + 16 )

D = √ 52

D = 7.2 units

Hence , the distance is 7.2 units

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The area of the irregular figure is 65.12 cm².

We know that a shape is said to be irregular if the shape does not fit into any of the known patterns of shape that we have. In this case, we have a kind of shape that is made up of the rectangle and the semi circle.

We know that we can be able to obtain that area of the rectangle by the use of the formula;

A = l * w

A = area

l = length

w = width

We then have;

A = 8 cm * 5 cm

= 40 cm^2

For the semi circle;

A =  (π r²)/2

A = (3.14 (4²))/2 = (3.14*16)/2 = 50.24/2 = 25.12cm²

Total area of the figure = 40 cm² + 25.12 cm² = 65.12 cm²

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The solution of the system of linear equations is :-

x = 6 hours .

y = 330 miles.

Now, According to the question:

Let x be the number of hours that have elapsed since Zac started traveling .

Let y be the number of miles traveled .

We know that,

Speed = Distance / Time.

so,

Speed of Zac = D / T = 123.75 / 2.25 = 55 miles / hour.

Speed of Lynn = D / T = 105 / 1.75 = 60 miles / hour.

then, Distance travelled by Zac in x hours = S * T

y = 55 × x

y = 55x miles

and, Distance travelled by Lynn in (x - 0.5) hours = S * T

y = 60 × (x - 0.5)

y = 60x - 30

Therefore, a system of linear equations that represents the distance each of them has traveled since Zac left on his trip are :-

y = 55x ----------- Eqn.(1)

y = 60x - 30 ------------- Eqn.(2)

Now, putting value of Eqn.(1) in Eqn.(2) , we get,

55x = 60x - 30

60x - 55x = 30

5x = 30

x = 6 hours.

Putting value of x in Eqn.(1),

y = 55 * 6

y = 330 miles.

Hence, the solution of the system of linear equations is :-

x = 6 hours .

y = 330 miles.

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It is given that ABCD is a rectangle. We have to give reasonings for the statements.

What is the rectangle?

A rectangle is a four-sided polygon with four right angles. The opposite sides of a rectangle are equal in length (congruent) and the opposite angles are equal in measure (congruent). The opposite sides are parallel to each other. A rectangle can be defined as a special case of parallelogram where all angles are right angles.

Given: ABCD is a rectangle

Prove: triangle ADC is congruent to triangle BCD

1. Given ABCD is a rectangle

2. By definition of rectangle, opposite sides are congruent (AD is congruent to BC)

3. By definition of rectangle, opposite angles are right angles (angle ADC and angle BCD are right angles)

4. By definition of right angle, adjacent angles are congruent (angle ADC is congruent to angle BCD)

5. By reflexive property, an object is congruent to itself (DC is congruent to DC)

6. By SAS Congruence (Side-Angle-Side), if two triangles have two congruent sides and the included angle congruent, the two triangles are congruent. Since AD=BC and angle ADC= angle BCD, and DC=DC, then triangle ADC is congruent to triangle BCD.

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The equation that can be used to solve for the number of points that Jan scored in the game is:

x + 2x + (x-10) = 70

Given that Jan scored twice as many points as Tritt, we can use the equation

2x = Tritt.

Given that Jan scored ten points fewer than Sarah, we can use the equation

x = Sarah - 10.

Also, we know that the total number of points scored by all three players is 70, so we can use the equation:

x + Tritt + Sarah = 70

If we replace Tritt with 2x and Sarah with x-10, we get:

x + 2x + (x-10) = 70

So the equation that can be used to solve for the number of points that Jan scored in the game is:

3x -10 = 70

We get x = 30, which means Jan scored 30 points in the game.

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The line that is parallel to y = 1/5x + 4, is A. 5 y - x = 6.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.

As mentioned parallel lines will have the same slope so the line that is parallel to y = 1/5x + 4 would have the same slope of 1 / 5.

Converting the first option to slope intercept form gives:

5 y - x = 6

5 y = 6 + x

y = 6 / 5 + x / 5

y = 1.2 + 1 / 5 x

This slope is the same as y = 1/5x + 4 so they are parallel.

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Using subtraction and division operations, the amount you receive for each soup mix sold is $6.

Subtraction and division operations are two of the four basic mathematical operations. The other two are multiplication and addition.

Mathematical operations combine variables, numbers, and mathematical operands to solve mathematical problems.

The number of soup mixes sold = 16

The total sales revenue = 16x + 96

The amount for the company that makes the soup = 16x

The amount that the seller receives = 96 (16x + 96 - 16x)

The amount the seller receives per soup mix = The total revenue received divided by the number of units sold

= 6 (96/16)

Thus, for each soup mix that you sell, you receive $6.

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New weight = 225 x (1 - (16 / 100)) = 225 x 0.84 = 189 pounds.

So, after dieting and exercising, Jim now weighs 189 pounds.

Answer: 189 pounds

Step-by-step explanation:

If he lost 16% of his weight, Jim is now 84% of his original weight.

84% = 0.84

225 x 0.84

189 pounds

Answer: -48x-32

Step-by-step explanation:

The equation that is graphed is (c) y = x² + 2    if x < 1 and y = -x + 2  if x ≥ 1

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

On the graph, we can see that the first curve is a quadratic function,

Also, it has an open circle at x = 1

So, we have:

x² + 2    if x < 1

Next, we have a linear equation with a closed circle at x = 1

So we have:

y = -x + 2 for x ≥ 1

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If the vehicle has 10 gallons of fuel left, it has driven 600 miles.

The term "equation" refers to mathematical statements with at least two terms that contain variables or integers that are equal.

The amount of gas in the tank should be x gallons, and the distance travelled by car should be d miles.

Due to the car's 16-gallon fuel tank

So, 16 - x would be the remaining fuel in the tank.

It gets 85 miles per gallon of gas when travelling on a highway.

⇒ d = (16-x)85

if the tank still holds 10 gallons of fuel

In the equation above, if x = 10, we get

⇒ d = (16-10)85.

⇒ d = (20)85.

⇒ d = 600.

If the vehicle has 10 gallons of fuel left, it has driven 600 miles.

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