A biker travels down the street at 15 m/s. It
takes 60 seconds to travel to the end of the
street. How long was the street?

Yes this question can be proven by mathematical induction

What do you mean by induction in mathematics?

For each and every natural number n, a statement, theorem, or formula can be proved using the mathematical induction technique. By generalizing this into the "Principle of Mathematical Induction," which we would utilize to demonstrate any mathematical assertion.

Here, n ≥ 1

1/1.2 + 1/2.3 + 1/3.4 + .............. + 1/n(n +1)

We employ the idea of Sigma here.

S/1/r(r + 1) { r = 1 to n }

Sigma [1/(r + 1) - 1/(1/r)] { r = 1 to n }

put r = 1 \s1/1 - 1/(1 + 1) = 1 - 1/2

put r = 2 \s1/2 - 1/(2 +1) = 1/2 - 1/3

put r = 3 \s1/3 - 1/(3 +1) = 1/3 - 1/4

........................................................... put r = n 1/n - 1/(n + 1)

after adding

Sigma = [1/(r+1) - 1/(1/r)] {r = 1 to n } = 1 -1/2 + 1/2 -1/3 + 1/3 - 1/4 + ............1/n - 1/(n +1)

= 1 - 1/( n +1) = n/( n +1)

Consequently, 1/1.2 + 1/2.3 + 1/3.4 +... 1/n(n + 1) = n/(n + 1).

so it proved

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1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given,

The community center is 3.1 miles away from Rodrigo's house.

We need to find how far apart are Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

As given, 3 inches : 9.3 miles

1 mile = 3/9.3 inches

1 mile = 0.323 inches.

So let us multiply 3.1 with 0.323

3.1×0.323

1.0013 inches

Hence 1 inch is the distance between Rodrigo's house and the community center on a map with a scale of 3 inches : 9.3 miles

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The probability that the sample mean selling price was more than $210,000 is 0.9772.

The given values are:

The mean selling price(μ) = $215000

Standard deviation(σ) = $25000

The random sample (n) = 100

We have to find the probability that the sample mean selling price was more than $210000.

z-score with z-bar= 210000

z = (x-bar - μ) / (σ/ √n)

 = ( 210000 - 215000) / (25000/ √100)

 = -5000/ 2500

 =-2

Using z-tables, the probability is:

Probability = P[z> -2]

                  = 1 - 0.0228

                  = 0.9772

Therefore the probability is 0.9772.

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The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

Let's check all the options. Then we have

a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have

⇒ 2.449, 2.5, 2.667, order is in ascending form.

b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have

⇒ 2.828, 2.75, 2.667, order is not in ascending form.

c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.9, 2.236, order is in ascending form.

d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have

⇒ 2.6, 2.8, 2.645, order is not in ascending form.

e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.75, 1.732, order is not in ascending form.

The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

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Answer:

i don't know

Step-by-step explanation:

180 students do not take lunch to school.

From the question, we have

Number of students do not take lunch to school= 200-20

=180 students

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The area of the garden is 7 square feet.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions. A rectangle's area (A) is calculated by multiplying its length ('a') by its breadth ('b'). Area of Rectangle is therefore equal to (a× b) square units.

Given,

Width = 3/4

Length = 9 + 1/3

Length = 28/3

Area:

Length × Width

3/4 × 28/3

84/12

7

The area of the garden is 7 square feet.

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Answer:

Answer:

This is in Standard form.  Did you mean scientific form?

1.47 x [tex]10^{-4}[/tex]

Step-by-step explanation:

You move the decimal so that the number is between 1 and 10.  Then since in standard form the number is much less than 1.47, you determine how muhc less my how many places you need to move the decimal to put it back in standard form.  Since you would need to move the decimal 4 places to the left, the exponent would be -4

Answer:

Step-by-step explanation:

to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top

5x(3x)

15x^2 is the area of the blacktop

The “!ield” area is next

12x(7x)

84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same

84x^2-15x^2

69x^2 is the area of the rectangle that is not black top

B- the foundtain we find with the area of circle formula r squared times pi

3x(3x)pi

9x^2pi

Now we just subtract this from the area of the rectangle

69x^2 -9x^2pi is the area

Hopes this helps please mark brainliest

The probability the selected dog is medium and brown by Sarah is 6/49.

Probability = favourable outcome/ total outcome

The table for the given question is attached.

Total dogs owned by Sarah = 7.

Total medium sized dogs = 2.

Total brown coloured dogs = 3

Probability( medium sized ) = 2/7

Probability( brown coloured ) = 3/7

Probability( medium sized and brown coloured ) = (2/7)×(3/7)

Probability( medium sized and brown coloured ) = 6/49

Thus, the probability the selected dog is medium and brown is 6/49.

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Answer:

See below

Step-by-step explanation:

Find slope using two convenient integer coordinates

(-1,4)  and (1, -8) are convenient

  slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) =  12/-2 = -6

the y-axis intercept is -2  ( by looking at the graph)

y = -6x -2      Done.

Step-by-step:

1)Combine multiplied terms into a single fraction

1/7a+ 1/7

1a/7+1/7

2)Multiply by 1

3)Combine fractions with a common denominator

Solution

a+1/7

Hope That helps!

Answer:

Step-by-step explanation:

3 as the x axis and -5 for the y axis

The correct option is c. that is observation is set of recorded values of variables associated with a single entity.

What is observation?

An observation is a case of the data being collected.

For example, if we were collecting data on students in the class, the observations would be each individual student in the class. It could be the student's height, weight, marks scored, etc.

A variable is an attribute or characteristic of the observation we record in our data.

Also an observation in statistics is a value of something of interest measured or counted during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals.

Therefore from the given option c is correct.

Observation is set of recorded values of variables associated with a single entity.

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The researchers include the scenario where subjects wear no bracelet at all are when it comes to mosquitoes, volunteers in each block should live in similar conditions.

An experiment might involve giving a novel drug to rats to see how they respond to learning about it. When you visit a new coffee shop but are unsure of how the coffee will taste, that is an example of an experiment. the act of carrying out a test like that; experimenting. An experiment is a procedure used as part of the scientific method to test a hypothesis. The independent and dependent variables are the two most important variables in every experiment. To investigate the impact of the independent variable on the dependent variable, it is either controlled or altered.

Given,

A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. researchers recruit volunteers for an experiment.

The researchers include the scenario where subjects wear no bracelet at all are:

When it comes to mosquitoes, volunteers in each block should live in similar conditions.

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Answer:

Step-by-step explanation:

slope=change in y over change in x

6-2=4

6--2=6+2=8

-4/-8=1/2

Answer:

VA: x = 1, x = -1

HA: y = 0

x-int: (4, 0)

y-int: (0, 4)

Step-by-step explanation:

x-int:

0 = (x-4)/((x-1)(x+1))

0 = (x-4) because the (x-1)(x+1) are multiplied by 0

4 = x

x = 4

(4, 0)

y-int:

y = (0 - 4)/((0 - 1)(0 + 1))

y = (-4)/((-1)(1))

y = (-4)/(-1)

y = 4/1 = 4

(0, 4)

Answer:

y = [tex]\frac{4}{3}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line

Answer:

Step-by-step explanation:

1. Put Words into Math.

Negative three minus one and two fifths= -3- 1 2/5

2. Solve the math problem

-3-1 2/5= -4 2/5 or   -22/5 in improper fraction

Answer: -4 2/5 or -22/5

Answer:

62%

Step-by-step explanation:

1040-110-145-139=646

646/1040=62%

Answer:

x=[tex]log_{2} 7/9[/tex]

Step-by-step explanation:

4-9×2^x+2+1=0

4-9×2^x+3=0

4+3-9×2^x=0

7-9×2^x=0

7-7-9×2^x=0-7

-9×2^x=-7

9×2^x=7

9×2^x/9=7/9

2^x=7/9

[tex]log_{2} 2^x[/tex]=[tex]log_{2} 7/9[/tex]

x=[tex]log_{2} 7/9[/tex]

An inequality to find the number of batches of rolls Liz can make is 13n/4 ≤ 26 and she cannot make more than 8 batches of rolls.

In order to solve this word problem, we would assign a variable to the number of batches, and then translate the word problem into an algebraic inequality as follows:

Let the variable n represent the number of batches.

Since Liz has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons, we have:

3 1/4 (n) ≤ 26

13n/4 ≤ 26

Cross-multiplying, we have:

13n ≤ 26 × 4

13n ≤ 104

n ≤ 104/13

n ≤ 8.

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Complete Question:

Liz wants to make several batches of biscuits. She has 26 tablespoons of yeast left in the jar and each batch of biscuits takes 3 1/4 -tablespoons. Write and solve an inequality to find the number of batches of rolls Liz can make.

Answer:

===========

Note:

Other sides are 2 and 11. This is not a correct question as sum of two smaller sides (2 + 6) is less than the longest one (11), hence there is no such possible triangle.

The probability that the vertical faces have the same color painted is 0.6875

There are 6 faces on a cube.

Each face of the cube will either be red or blue.

The probability that one face will have red color = probability that the face will have blue color = 1/2

It is given that the cube is placed on a horizontal surface and the 4 vertical faces have the same color.

The painting of the faces of the cube clearly follows a binomial distribution.

Therefore the probability to color the faces of a cube

= P(4 faces are red, 2 faces blue) + P(4 faces are blue, 2 faces red) + P(5 faces blue) + P(5 faces red) + P(All faces blue) + P(all faces red)

For any binomial distribution

ⁿCₓ X pˣ (1 - p)ⁿ⁻ˣ

where

n = no. of sample

x = random variable

p = probability of success

Hence we get

⁶C₄ X 0.5⁴ 0.5²   + ⁶C₄ X 0.5⁴ 0.5²   +    ⁶C₅ X 0.5⁵ 0.5    +   ⁶C₅ X 0.5⁵ 0.5

⁶C₆ X 0.5⁶    +    ⁶C₆ X 0.5⁶

= 15 X 0.015625    +    15 X 0.015625    +    6 X 0.015625    +    6 X 0.015625    +    0.015625

= 0.6875

Therefore we get the probability of having the four vertical faces of the same color to be 0.6875.

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Answer

[tex]60\sqrt{x} 2[/tex]

Step-by-step explanation:

Answer:

StartRoot 60 EndRoot

Step-by-step explanation:

Edge

The required key features of [tex]g(x) = x^{2}[/tex] including domain is (-∞, ∞) (i.e. all real values), range = [0,∞), x-intercept = (0,0), y-intercept = (0,0), interval of increasing = (0,∞) and interval of decreasing = (-∞, 0)

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.

The graphs of quadratic functions are frequently curved or nonlinear. A parabola, a kind of U-shaped curve, is the particular type of curve that makes up the graph of a quadratic function.

Given, [tex]g(x) = x^{2}[/tex]

The graph of the given function is given below:

From the graph,

Domain = (-∞, ∞) (i.e. all real values)

Range = [0,∞)

x-intercept = (0,0)

y-intercept = (0,0)

Interval of increasing = (0,∞)

Interval of decreasing = (-∞, 0)

Hence, these are the required key features of  [tex]g(x) = x^{2}[/tex].

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The probability that there are no counts in a 30 second interval is 0.284

What is probability ?

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.

Given that,

Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.

0.284

P(X < 10 Seconds)  = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284

Therefore, the  probability that there will be no counts in a 30-second period is 0.284.

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Answer:

18$

Step-by-step explanation:

this is so i can reach twenty characters.