Find the difference of 2/7 and 1/21.

The percentage of students age 15 and above travel to school by bus is given as follows:

25.64%.

The percentage is obtained applying the proportions in the context of this problem.

A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.

The total outcomes are given as follows:

195 students 15 and above that travel by bus.

The desired outcomes are given as follows:

195 - 65 - (98 - 18) = 50 students 15 and above that travel by bus.

Hence the percentage is given as follows:

50/195 x 100% = 25.64%.

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The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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The length of PR in the triangle is 229 feet.

To indirectly measure the distance across a river, Savannah stands on one side of the river and uses sight lines to a landmark on the opposite bank. Savannah draws  the diagram below to show the lengths and angles that she measured. Let's find PR, the distance across the river.

Triangle PRE is similar to triangle POC. Therefore, similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Hence,

PR = x

165 / 255 = x / x + 125

cross multiply

165(x + 125) = 255x

165x + 20625 = 255x

165x - 255x = - 20625

-90x = - 20625

divide both sides of the equation by -90

x = - 20625 / - 90

x = 229.166666667

Therefore,

PR = 229 ft

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The measure for x is 1.414 units.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse= 2

angle= 45

Using Trigonometry

cos 45 = B/ H

1/√2 = B/ 2

B = 2/√2

B = √2

Hence, the measure of x is 1.414 unit.

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11/6 is the solution of the equation 4x−1/3 = 7/1.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 4x−1/3 = 7/1

We have to isolate the variable term x by adding 1/3 on both sides

4x=7+1/3

4x=22/3

Divide both sides by 4

x=22/12

22 and 12 are the multiples of 2.

x=11/6

Hence, 11/6 is the solution of the equation 4x−1/3 = 7/1.

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Answer:

the coefficient of 0 indicates that there is no relationship between the two values

the Estimated number of rabbits will be 80 in the year 2016.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given a table of Rabit at a zoo in the table below,

2008 14

2009 24

2010 30

2011         39

2012 45

2013 57

M: 2010.5 M: 34.8333

To estimate the number of rabbits in the zoo in 2016 we need to find the linear equation;

Sum of X = 12063

Sum of Y = 209

Mean X = 2010.5

Mean Y = 34.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = 143.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 143.5/17.5 = 8.2

a = MY - bMX = 34.83 - (8.2*2010.5) = -16451.26667

ŷ = 8.2X - 16451.26667

For x = 2016

y =  8.2* 2016 - 16451.26667

y = 79.933 or 80

therefore, the Estimated number of rabbits will be 80 in the year 2016.

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Complete question:

we can look at this as some exponential growth, now, the page hit 10,000 views in the first day, that is, at the end of the 1st day and the beginning of the 2nd day, so the compounding of 30% will occur only for the next 4 days, that is, the 2nd, 3rd, 4th and 5th days, so we can say starting initially with 10000, how much will it be 4 days later?

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &10000\\ r=rate\to 30\%\to \frac{30}{100}\dotfill &0.3\\ t=\textit{elapsed time}\dotfill &4\\ \end{cases} \\\\\\ A = 10000(1 + 0.3)^{4} \implies A=10000(1.3)^4\implies \boxed{A = 28561}[/tex]

The solution to the given Inequality |2x − 3| ≥ 7 is; x ≤ −2 or x ≥ 5

An absolute value inequality is defined as an expression with absolute functions as well as inequality signs. For example, the expression |x + 4| > 2 is an absolute value inequality containing a greater than symbol.

The absolute value inequality we want to solve is;

|2x − 3| ≥ 7

What this means is;

2x - 3 ≥ -7   or 2x - 3 ≥ 7

Thus;

2x - 3 ≥ -7

Add 3 to both sides to get;

2x ≥ -4

Divide both sides by 2 to get;

x ≤ -2

For 2x - 3 ≥ 7

Add 3 to both sides to get;

2x ≥ 10

Divide both sides by 2 to get;

x ≥ 5

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Answer:

Option D: x ≤ −2 or x ≥ 5

Step-by-step explanation:

i took the test xx

He answers the same number of questions correctly as he answers incorrectly in each round.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

For the pair of equations to be a system of equations, the number of questions answered correctly must equal the number of questions answered incorrectly in each round. Therefore, the equation 5x - 3y = 22 must have the same number of x and y variables, and the equation 10x - 4y = 46 must also have the same number of x and y variables. This is the only condition that must be true for the pair of equations to be a system of equations.

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Answer:

[tex]\dfrac{c}{2}[/tex]

Step-by-step explanation:

We can simplify the given expression by canceling like terms.

Remember that anything divided by itself is 1.

ex:

[tex]\dfrac{2x}{x} = 2 \cdot \dfrac{x}{x} = 2 \cdot 1 = 2[/tex]

Applying this logic to the given expression:

[tex]\dfrac{a}{2b} \cdot \dfrac{bc}{a}[/tex]

↓ simplify multiplication of fractions

[tex]\dfrac{a \cdot bc}{2b \cdot a}[/tex]

↓ rewrite to align like variables

[tex]\dfrac{a \cdot b \cdot c}{a \cdot b \cdot 2}[/tex]

↓ separate out variables that are divided by each other

[tex]\dfrac{a}{a} \cdot \dfrac{b}{b} \cdot \dfrac{c}{2}[/tex]

↓ represent them as 1

[tex]1 \cdot 1 \cdot \dfrac{c}{2}[/tex]

↓ rewrite without unnecessary 1's

[tex]\dfrac{c}{2}[/tex]

To find the time it took Clare to ride 10 miles, we can use the concept of speed, which is defined as distance divided by time. In this case, Clare's constant speed was 15 miles in 72 minutes, so her speed is 15/72 miles per minute.

Using this speed, we can calculate the time it took her to ride 10 miles by dividing the distance by the speed:

Time = Distance / Speed

Time = 10 miles / (15/72 miles per minute)

Time = 10 * 72 / 15 minutes

Time = 43.2 minutes

So, it took Clare approximately 43.2 minutes to ride 10 miles at her constant speed of 15 miles in 72 minutes.

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In selecting 10 students out of the class of 40 students, if 40 names are placed in a hat and 10 names are drawn out of the hat, the type of sample is:

a random sampling.

Random sampling is a type of sampling method where each member of the population has an equal chance of being selected.

In this case, the population is the class of 40 students and the sample size is 10. By randomly selecting 10 names out of a hat, each student has an equal chance of being chosen for the sample.

This ensures that the sample is representative of the entire population, without any bias.

Random sampling is a widely used method for selecting a representative sample from a larger population.

It is important to use random sampling when conducting research or surveys in order to ensure that the results are reliable and accurate.

Random sampling helps to eliminate any potential bias that might be present in the sample if it was chosen through some other method. This is why it is important to use random sampling when selecting a sample from a larger population.

Complete Question:

"To select 10 students out of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. what type of sample is this?"

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The expression that is incorrectly simplified is given as follows:

[tex]\sqrt[4]{9x^4} \times \sqrt[4]{16x^4} = 12x^4[/tex]

The expressions in this problem involve roots, which also can be written as exponents, hence exponential rules such as multiplication of terms with same base and different exponents, along with the power of power rule, are used.

For the first expression, we have that the fourth root can be expressed as an exponent of 1/4, hence:

The coefficients however, stay inside the root, meaning that the result of 12 is false, and the statement is incorrect.

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Answer:

x = 50

Step-by-step explanation:

50 + 2x = 150

2x = 100

x = 50

The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10

The proof of this statement is constructive, as it will provide a way to explicitly construct a positive integer which is equal to the sum of the positive integers not exceeding it.

To prove this, we will use the following formula:

Let n = the positive integer

Let S = the sum of the positive integers not exceeding n

n = 1 + 2 + ... +n-1 + n

S = 1 + 2 + ... +n-1

Therefore, n = S + n

For example, let n = 5. The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10. Therefore, 5 = 10 + 5, which is true. This proves that for any positive integer, n, it is equal to the sum of the positive integers not exceeding it.

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The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."

Converse is a statement obtained by reversing the implication (conditional statement). Simply put, conversion is the opposite of implication. For example, an implication has the formula p→q, then the conversion is the opposite, namely q→p. To understand it better, here is an example conversion.

1 Implication: If Sam is thirsty, then Sam drinks. Conversation: If Sam drinks, then Sam is thirsty.

Implication: If the road is wet, then it rained last night. Conversation: If it rained last night, then the streets are wet.

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From the data analytics of this table, the right statements are A,C and D.

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

Given in the table of students which are watching movies or not

         Yes       No      Total

Boys    6          8          14

Girls     9          7          16

Total    15        15         30

Statement (A): 27% of sampled students are boys who did not watch a movie?

27% of total students = 27 * 30/100

= 810/100

≈ 8 boys

So the statement (A) is true.

Statement (B): 30% of sampled girls watched a movie?

30% of sampled girl = 30 * 16/100

= 480/100

≈ 5 girls

So the statement (B) is false.

Statement (C): 50% of sampled students did not watch a movie?

50% of total students = 50 * 30/100

= 1500/100

= 15 students

So the statement (C) is true.

Statement (D): 57% of sampled boys did not watch a movie?

57% of total students = 57 * 14/100

= 798/100

≈ 8 boys

So the statement (D) is true.

SO that, the right statements are A,C and D.

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4 square 6 in surd form​ is  4√6

A number system is defined as a system of writing to express numbers.

4 square 6 in surd form​

Any number of the form n √a, which cannot be written as a fraction of two integers is called a surd.

4 square 6 in surd form​ is 4√6

Decimal Form is 9.8

Hence, 4 square 6 in surd form​ is  4√6

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Answer:

No, it is not an infinite solution.

Step-by-step explanation:

4x-4=4              

Add 4 to each side

4x=8

Divide 4 on each side

x=2

Answer:

No

Step-by-step explanation:

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.

The length of the candle was 13.5 inches before it was lit.

Let the length of candle in the beginning be c.

Constant rate of change in length of candle=  1.2 inches per hour

Since rate of change is constant so the length of candle can be represented by a linear function [Linear function has constant rate of change.]

Linear function : f(x)= mx+c , where x= independent variable.

m= constant rate of change and c= initial value of function.

Let x = Number of hours after the candle was lit.

Put m=  1.2 , x= 3 and f(x)= 10.5 , we get

c= 13.5

Hence, the length of the candle was 13.5 inches before it was lit.

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Answer:

Step-by-step explanation:

5=19600

10=17200

15=14800

20=12400

it should take about 46 mins to land and the final question should be B

Therefore, a maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

Let the length of the field =  feet

 And the width of the field =  feet

Therefore, area of the rectangular field = Length × Width

                                                             A =  x*y  square feet

Since, length of the fence = 100 feet

And the farmer has to enclose three sides of the rectangle as shown in the figure attached.

Therefore, length of the fence = length + 2(width)

                                               = (x+2y) feet

Hence,  (x+2y)=100

x=100-2y

By substituting the value of 'x' in the expression for the area of the rectangular field.

A=(100-2y)y

A=-2y^2+144y

Find the derivative of the expression with respect to y ,

A'= -4y+100

A'=0

4y=100

y=25

A=-2*625+2500

A=2500-1250

A=1250 square feet

Therefore, maximum area the farmer can enclose with the 144 feet of fencing will be1250 square feet.

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The rate of the machine increased by 0.26% every year.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, On 2078/08/20 A machine was valued at Rs. 20000 whereas its original value was Rs. 17,500​.

Now, From 2023 to 2078 it is (78 - 23) = 55 years.

Therefore,

(20000 - 17500) = (17500×r×55)/100.

2500 = 175×r×55.

2500 = 9625r.

r = 2500/9625.

r = 0.26%.

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The spherical coordinate system is the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2).

A system of coordinates is a set of numbers used to describe the position of a point in space. There are different types of coordinate systems, each with its own advantages and disadvantages.

The spherical shell is the region of space between two spheres with the same center, but different radii. In this case, the center of both spheres is at (4,1,2) and the inner sphere has a radius of 7 while the outer sphere has a radius of 13.

One of the most commonly used coordinate systems for describing spheres is the spherical coordinate system.

To use this system of coordinates to describe the spherical shell, we first need to determine the radial distance for each point in the shell. This distance is between 7 and 13, since the shell lies between the inner and outer spheres.

Therefore, to describe a point in the spherical shell using spherical coordinates, we use the radial distance, polar angle, and azimuthal angle. These coordinates can then be used to plot the spherical shell and understand its geometry and properties.

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In rectangle , The width is 8 and the length is 37.

What is a rectangle ?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.

                              The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

90 = 2(x + 5 + 4x)

90 = 2(5x + 5)

90 = 10x + 10

80 = 10x

x = 8

So the width is 8 and the length is 37.

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The complete question is -

The length of a rectangle is five inches more than four times it’s width. If the perimeter is 90 inches, find its dimensions

Answer:

35 - 8k

Step-by-step explanation:

(24 - 3k) - (5k - 11)

= 24 - 3k - 5k + 11

= 35 - 8k

The initial value of the first investment was M = Rs.12,000,000 and the initial value of the second investment was N = Rs.16,000,000.

Let's assume the initial investment in the first investment be M and the initial investment in the second investment be N.

We know that the annual return from the first investment is 3% of M and the annual return from the second investment is 5% of N.

So, the total annual return (T) is:

T = 0.03M + 0.05N = 1160000

The investor increases his investment in the first investment by 25%, so the new investment in the first investment becomes:

M1 = M + 0.25M = 1.25M

And the new annual return from the first investment becomes:

R1 = 0.03 * 1.25M = 0.0375M

Similarly, the new investment in the second investment becomes:

N1 = N + 0.40N = 1.40N

And the new annual return from the second investment becomes:

R2 = 0.05 * 1.40N = 0.07N

So, the new total annual return (T1) is:

T1 = R1 + R2 = 0.0375M + 0.07N

And the increase in the total annual return is:

410,000 = T1 - T

We have 2 equations with 2 variables (M and N), so we can solve for them.

0.0375M + 0.07N = 0.03M + 0.05N + 410000

Expanding and solving the equation we get:

M = 12,000,000

N = 16,000,000

So, the initial value of the first investment was M = Rs.12,000,000 and the initial value of the second investment was N = Rs.16,000,000.

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If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833. So, the correct option is b .

This is a geometric distribution problem, where we are trying to find the probability of the number of trials (inspections) until the first success (defective board). The probability of success (finding a defective board) on each trial is 0.02 and the probability of failure (not finding a defective board) on each trial is 0.98.

The formula for the probability of exactly k trials until the first success is given by:

P(X = k) = (1 - p)^(k-1) * p

where p is the probability of success and k is the number of trials.

Plugging in p = 0.02 and k = 10, we get:

P(X = 10) = (1 - 0.02)^(10-1) * 0.02 = 0.9833

So the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833.

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