66. Mechanical Engineering A crossed belt connects
a 10-centimeter pulley on an electric motor with a
20-centimeter pulley on a saw arbor (see figure). The
electric motor runs at 1700 revolutions per minute.

(c) Let L be the total length of the belt. Write L as
a function of o, where is measured in radians.
What is the domain of the function? (Hint: Add the
lengths of the straight sections of the belt and the
length of the belt around each pulley.)

The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

The outcome of an event may be known to us or unknown to us. When this happens, we indicate that there is a probability that the event will happen or not.

It is also defined as the ratio of the number of favorable outcomes to the total number of outcomes.

The formula for the probability of an event is given by

P(E) = No of favorable outcomes/ Total No of outcomes ]

Here we have

A basket of fruit contains 4 bananas, 3 apples, and 5 oranges.

Total number of fruits = 4 + 3 + 5 = 12

By the given formula,

Probability of selecting 1 banana = 4/12 = 1/3

Probability of selecting 1 apple = 3/12 = 1/4

Probability of selecting 1 orange = 5/12

The order of the fruits that is given is 1 banana, then 1 apple, then 1 orange

Let's assume that,

We taken 1 banana

=> The probability of selecting one banana = 1/3

After taking one banana, remaining fruits = 12 - 1 = 11

Now we have drawn 1 apple

=> The probability of selecting one apple in 11 fruits = 3/11

After taking one apple remaining fruits = 11 - 1 = 10

=> The probability of selecting one orange from 10 fruits = 5/10 = 1/2

From the above calculations,

The probability of selecting in given order = (1/3)(3/11)(1/2) = 3/66 = 1/22

Therefore,

The probability of selecting one banana, then one apple, then one orange, in that order, from the basket if you are blindfolded is 1/22.

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The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.

The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given series is 15,20,25,30,...,

The common difference is d = 20 - 15 = 5

First term is, 15

The formula can be written as,

an = a₁ + d(n-1)

an = 15 + 5 ( n - 1 )

an = 15 + 5n - 5

an = 10 + 5n

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The test score representing the 3rd decile is 67. So the option a is correct.

In the given question, an achievement exam was given to a population of 1,000 students.

However, a sample of only seven of student scores is listed along with their respective z score and percentile rank in the following table.

TEST SCORE      42        57        67        72        77        87        97

z score              -1.50     -0.75    -0.25     0        0.25     0.75     1.25

percentile rank  10         25        30       45        50       75        95

Using the table information, we have to find the test score representing the 3rd decile.

As we know that the 3rd decile is equal to the 30th percentile.

So that the 3rd decile have the percentile rank = 30

The test score equivalent to percentile rank 30 is 67.

So, the test score representing the 3rd decile is 67. So the option a is correct.

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Answer:

54 is the correct answer

(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

What is solution of the system?

A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

Given:

3(- n + 4) + 5n = 2n ← distribute and simplify left side

- 3n + 12 + 5n = 2n

2n + 12 = 2n ( subtract 12 from both sides )

2n = 2n - 12 ( subtract 2n from both sides )

0 = - 12 ← not possible

This indicates the equation has no solution

Comparing the types of solutions

A n = 3

Indicates that there is only one unique solution to the equation.

B no solutions

This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is

0 = 12

C infinite solutions

This is indicated when you solve the equation and obtain

4 = 4 or - 3 = - 3

Hence,

(A) There is only one solution to the given system.

(B) There is no solution to the given system

(C) There are infinite solutions to the system.

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Answer:

59

Step-by-step explanation:

The total amount of money that Marco has that week would be = $ d + 14.55.

An allowance income is defined as the amount of money an individual earns that can be used to solve their personal needs.

Marco received double payment, an allowance from the mother and from newspaper route.

The total amount of money received from his mother for allowance for that same week = $ d

The amount of money he earned from his newspaper = $14.55

Therefore the total amount of money Marco has that week =$ d + 14.55

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Complete question:

Marco's mom gave him d dollars for his allowance one week. He also earned \$14.55$14.55dollar sign, 14, point, 55 for his newspaper route that week.

How much money does Marco have?

Write your answer as an expression.

Answer:

Step-by-step explanation:

The four options just swap the order, and you should choose them all

Yes, angle 1 is vertically opposite to angle 4 because they are formed due to the intersection of straight lines.

When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.

For example, if two lines intersect and make an angle, say X=55°, then its opposite angle is also equal to 55°. And the adjacent angle to angle X will be equal to 180 – 55 = 125°

In the given figure, ∠AOC and ∠BOD form a pair of vertically opposite angles and similarly ∠AOD and ∠BOC form such a pair. Therefore,

∠AOC = ∠BOD

∠AOD = ∠BOC

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Answer:

37,349

Step-by-step explanation:

month 1

27870 x .05 = 1394

27870 + 1394 = 29264

month 2

29264 x .05 = 1463

29264 + 1463 = 30727

month 3

30727 × .05 = 1536

30727 + 1536 = 32263

month 4

32263 x .05 = 1613

32263 + 1613 = 33876

month 5

33876 x .05 = 1694

33876 + 1694 = 35570

month 6

35570 x .05 = 1779

35570 + 1779 = 37349

Answer:

35,570

Step-by-step explanation:

solution 1 - Multiply by 5%, 6 times. Easter to calculate without a calculator, long process.

1. 27870*1.05= 29,263.5

2. 29263.5*1.05=30726.675

3.repeat

4.repeat

5.repeat

6.repeat

if it's hard for you to multiply by 1.05, you can always divide by 20 or divide by 10 then by 2 (like the below)

1. 27870÷10= 2,787

2. 2787÷2= 1393.5

3. 27870+1393.5 = 29263.5

solution 2 -Fast but probably needs a calculator

1. 27870*1.05^(5)= 35570

1.05 = monthly increase

power of 5 = ^(5) = 6 months - 1 = 5

The linear function expressed by the table is y = -1x + 4.

What is a linear function?

A linear function is a type of mathematical function that represents a linear relationship between two variables, often represented by x and y. The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). Linear functions are also called lines.

To find the equation of the line from a table of values, you can use the slope-intercept form, y = mx + b

where m is the slope and b is the y-intercept

In order to find the slope 'm' we use the following formula:

m = (change in y)/(change in x) = (y2 - y1) / (x2 - x1)

Here,

m = (-2 - 2) / (2 - (-2)) = (-4)/4 = -1

The slope is -1, which means that for every one-unit increase in x there's a corresponding one-unit decrease in y.

To find the y-intercept, you can use one of the points from the table and substitute the x and y values into the equation

y = mx + b

So now we know that m = -1,

plugging the first point (x,y) = (-2,2) in the equation

2 = -2 - b

b = 4

So the equation of the line is y = -1x + 4

Hence, the linear function expressed by the table is y = -1x + 4.

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To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.

To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.

The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.

For example reduce the ratio 225: 125: 25

The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.

If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.

Now divide each number by 5 and see what we get.

225/5: 125/5: 25/5

45: 25: 5

When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.

Now divide each number by 5 again and get a final ratio of 9: 5: 5.

45/5: 25/5: 5/5

9: 5: 1

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Answer:

if its for factor, we have (x+1)(x+5), if its for formula, its x=-1, -5

Step-by-step explanation:

The value of StartFraction P (t) Over A EndFraction for this problem will be 20

Take the value of x that they provide you and plug it into the problem for these kinds of difficulties.

The fraction's numerator is the highest number. It stands in for the entire thing that must be divided.

A fraction's denominator is the value at the bottom. It shows how many equally sized pieces are divided up in the object.

adding 3 to the formula:

6/(3) + 2(3)^2 —> use PEMDAS. Apply the 32 exponents first, followed by left-to-right multiplication and division, and finally addition.

6/x + 2x^2,

when x = 3

=20

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The question the incomplete the full question:

What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?

Answer:

The second part is 0.8 and B. About 1,845 years.

Step-by-step explanation:

:)

The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.​

In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.

Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.

Now, we want to determine whether it is a strong or weak correlation.

The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.

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Answer: A is correct

Step-by-step explanation:

took the test

Answer:

y = 4

Step-by-step explanation:

The triangles are congruent.

8y = 6y + 8

2y = 8

y = 4

Answer:

You need to combine like terms

To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:

log b(x)=logc(x) logc(b)

By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:

log2(x)=log10(x)log10(2)=log(x)log(2)

This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.

The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.

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The likelihood event:

Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

The correct option is A.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Given:

Three softball players discussed their batting averages after a game.

Probability:

Player 1 = six tenths = 6/10

Player 2 = five ninths = 5/9

Player 3 = four sevenths = 4/7

To find better batting averages:

LCM of 10, 9 and 7.

10 = 2 x 5. 9 = 3 x 3, 7 = 7

So, the LCM (10, 9, 7) = 630

Now we have the number of chances are equal for each of the three players.

So, the P(Player 1) = 6/10 = 378/630

P(Player 2)= 5/9 = 350/630

P(Player 3)= 4/7 = 360/630

The Player 1 has better batting average than Player 2 and Player 3.

Therefore, Player 1 is more likely to hit the ball than Player 2 because P (Player 1) > P (Player 2).

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The graph has plotted and attached below

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2x + 3y <12.

Here The graph have plotted and attached below.

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A three-variable system is a system of equations or inequalities involving three variables.

The three variables could refer to any three related quantities, such as a person's age, height, and weight. In a three-variable system, the number of equations is equal to the number of variables, so three equations are needed to solve the system. Each equation in the system will involve all three variables and will be solved through a combination of algebraic manipulation, substitution, and elimination techniques. Once all three equations have been solved, the values of the variables can be found.

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The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.

Check the solution of equation 3x - 9 = 0

3x - 9 = 0

3x = 9

x = 3

Check the solution of equation 4x - 3 = 0

4x - 3 = 0

4x = 3

x = 3/4

Check the solution of equation 5x - 10 = 0

5x - 10 = 0

5x = 10

x = 10/5

x = 2

Check the solution of equation 7x - 49 = 0

7x - 49 = 0

7x = 49

x = 49/7

x = 7

Thus, only 3x - 9 = 0 satisfy the solution x = 3.

Hence, the correct option is A.

--The given question is incomplete, the complete question is

''Which equation has 3 as a solution set?

A. 3x - 9 = 0

B. 4x - 3 = 0

C. 5x - 10 = 0

D. 7x - 49 = 0''--

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The 40th term of the sequence  aₙ = - 24 - 3n is - 144.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, A sequence is represented by the explicit formula aₙ = - 24 - 3n.

We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.

Therefore, To find a₄₀, we'll simply replace n with 40.

So, a₄₀ = - 24 - 3(40).

a₄₀ = - 24 - 120.

a₄₀ = - 144.

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Answer:

2.46

Step-by-step explanation:

Answer:

[tex]A=283.528736986[/tex]

Step-by-step explanation:

The formula for the area of a circle is:

[tex]A=\pi \times r^2[/tex]

Remember that the radius is half the diameter, we are given the diameter which is 19, which means we need to find the radius:

[tex]d=19[/tex]
[tex]19\times\frac{1}{2} =9.5[/tex]
[tex]r=9.5[/tex]

Substitute and solve:

[tex]A=\pi \times9.5^2[/tex]
[tex]9.5^2=9.5\times9.5=90.25[/tex]
[tex]\pi \times90.25=283.528736986[/tex]
[tex]A=283.528736986[/tex]

Since the question doesn't say to round the area is "283.528736986."

Hope this helps.

the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one

How do you find the value of log base 2?

Properties of Log Base 2

Multiply two numbers with base 2, then add the exponents. Divide two numbers with the base 2, subtract the exponents. Power Rule: Raise an exponential expression to power and multiply the exponents.

Use the change-of-base formula:

since we know that natural log and log with base 10 are different

So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:

Hence ,  the value of log2 base 2 is 1 because if base and logrithm value is same then it is always one

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Answer:

c) m <2 =m <3

Step-by-step explanation:

since the angles 2 and 3 are equal then they should be alternate angles

then c and d are parallel lines

Based on the provided information, the APR is 71.4%.

Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by

APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100

The finance terms in the given case is $29.99 per week for 73week. Hence,

Total amount paid = 29.99*73 = $2,189.27

Loan principal = $1,095

Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27

Fees = 0 (as it not mentioned in the question)

Number of days in loan terms = 73*7 = 511 days

Substituting the values in the formula,

APR = ((1094.27/1095)/511) * 365 * 100

APR = 71.4%

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