The requried inequality to determine the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
The normal body temperature for an adult horse is 100 degrees F, but it can vary by as much as 1.2 degrees.
Let x be the average temperature of the horse,
100 - 1.2 ≤ x ≤ 100 + 1.2
98.8 ≤ x ≤ 101.2
Thus, the requried inequality determines the range of body temperature is given as 98.8 ≤ x ≤ 101.2.
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How do I solve for the fourth line
Answer:
y = -8/3x + 73/4
Step-by-step explanation:
A line perpendicular to the 3rd equation has a slope that is the negative inverse of the other line. It also has the same y-intercept (b) because it is forming a square.
Therefore, the equation of the 4th line is:
y = -8/3x + 73/4
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. • The equation that relates Runner #2’s distance (in miles) with time (in minutes) is `t=8. 5d`. Find the slope/rate of ch
If the equation that relates the Runner 2’s distance (in miles) with time (in minutes) is [tex]t=8.5d[/tex] then the slope/rate of change of Runner 2 is 8.5 minutes for 1 mile .
The three runners are training for the marathon ,
The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is ⇒ [tex]t=8.5d[/tex] ,
to cover the distance of 2 miles Runner2 will take [tex]t= 8.5 \times 2[/tex] minutes ;
So , [tex]t=17[/tex] minutes ;
the first point will be (2,17) .
and to cover the distance of 4 miles the runner 2 will take [tex]t= 8.5 \times 4[/tex]
So , [tex]t=34[/tex] minutes ;
the second point will be (4,34) .
we have to find the rate of change/slope of runner 2 ,
that can be written as : [tex]Slope = \frac{34-17}{4-2}[/tex]
On simplifying ,
we get ;
[tex]Slope = \frac{17}{2}[/tex] ;
So , [tex]Slope = 8.5[/tex].
Therefore , the rate of change of Runner 2 is 8.5 .
The given question is incomplete , the complete question is
Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is "t = 8.5d". Find the slope/rate of change of Runner 2 ?
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Which describes why digital signals are a more reliable way to encode and transmit information than analog signals? Multiple choice question. Noise builds up on digital signals only when the signals travel long distances. Noise is easily filtered out without damage to the original signal because only one of two values is expected. Noise is easily filtered out without damage to the original signal because a narrow range of values is expected. Noise does not build up on digital signals when they are transmitted, unlike analog signals.
The solution is Option B.
Noise is easily filtered out without damage to the original signal because a narrow range of values is expected
What are digital signals?A digital signal encodes data as a sequence of discrete values. A digital signal can only have one value from a finite set of possible values at any given time. A signal which is a discrete function of time, i.e. non-continuous signal, is known as digital signal. Digital computers and digital phones are some of the examples of digital signals
The three types of digital signals are
Continuous-Time/Analog Signal
Discrete-Time Signal
Digital Signal
Given data ,
The digital signals are a more reliable way to encode and transmit information than analog signals
Because , while transmitting information through digital signals , they have less interference over long distances and digital signals offer better clarity
The digital devices only record pieces of sound waves, not full waves.
Now , Analog technology stores information as sound waves; digital technology stores it as strings of ones and zeroes.
Hence , noise is easily filtered out without damage to the original signal because a narrow range of values is expected
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Hello can someone help me with this please
Answer:
Below
Step-by-step explanation:
x - 6 = 12 add 6 to both sides of the equation
x - 6 + 6 = 12 + 6 simplify
x = 18
3x-1 = 11 add 1 to both sides of the equation
3x -1 + 1 = 11 + 1
3x = 12 now divide both sides by 3
3x/3 = 12 / 3 simplify
x = 4
Identify the place value of the underlined digit.
1) 0.9838.47
3) 145.58
4) 0.005
5) 31.0643
The place value of the following underlined digit are as follows:
0.983 = hundredths.8.47 = hundredths.145.58 = tens.0.005 = tenths.31.0643 = unit.What is a place value?In Mathematics, a place value can be defined as a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.In this scenario, the underlined digit 8 in "0.983" has a place value of hundredths because it is located 2 places after the decimal point. Additionally, the underlined digit 4 in "145.58" has a place value of tens because it is located 2 places before the decimal point.
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Complete Question:
Identify the place value of the underlined digit.
1) 0.983
2) 8.47
3) 145.58
4) 0.005
5) 31.0643
What is the degree of the polynomial √ 3?
The degree of the polynomial √3 is 1.
What is polynomial?Polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponents of variables. Polynomials are often used to solve problems in algebra, geometry, calculus and other branches of mathematics.
A polynomial is an expression made up of variables, constants, and exponents.
A polynomial is said to have a degree when the highest degree of any of its terms is known.
The degree of a polynomial is determined by the highest exponent of a given term. In the case of √3, the exponent is 1, making the degree 1.
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Which variation is represented by this situation:
Lisa and Maria are at a convention. There is enough food at the convention to feed 300 attendees for 4 days. If 400 people attend the convention, how long will the food last?
If 400 people attend the convention,
the food will last for 3 days.
What is inverse proportion?Two quantities a and b are said to be in inverse proportion if an increase in quantity a, there will be a decrease in quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant. Sometimes, it is also known as inverse variation.
That is, if ab = k, then a and b are said to vary inversely. In this case, if b1, b2 are the values of b corresponding to the values a1, a2 of a, respectively then a1 b1 = a2 b2 or a1/a2 = b2 /b1
Given,
Food for 300 people will Last for 4 days.
Attending people = 400
Let the food for 400 will last for x days.
According to the question,
300 × 4 = 400 × x
x = 300 × 4 /400
x = 3
Hence, the food will last 3 days,
if 400 people attend the convention.
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Using the graph below with the following point find the length of the two diagonals to determine if TUVW is a rectangle or not T(-5,0) U(7,3) V(9,-6) W(-3,-9)
The lengths of each diagonal are given as follows:
[tex]TV = \sqrt{232}[/tex][tex]WU = \sqrt{244}[/tex]As the lengths are different, the polygon TUVW is not a rectangle.
How to obtain the diagonals?The diagonal length is obtained using the formula for the distance between two points, presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
The first diagonal is TV, and the length is given as follows:
[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]
The second diagonal is WU, and the distance is given as follows:
[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]
A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.
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Park rangers plan to expand the area of a park to 506 square miles. Currently, the length of the park is 18 miles and the width is 17 miles. They want to extend the length and the width by the same number of miles. If they are successful, what will the new dimensions of the park be? Explain and I need this before tomorrow
As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
We know the area of a rectangle is (length×width).
Given, Park rangers plan to expand the area of the park to 506 square miles.
Currently, the park has an area of (18×17) = 306 square miles.
Therefore, The amount of square miles they need to increase is (506 - 306)
= 200 miles.
Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.
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Jean Junction is selling jeans at 15% off the regular price the regular price is $25 per pair what is the discount amount
Answer:
15% off means take $3.75 off the regular price
Step-by-step explanation:
$25(0.15) = $3.75
$25 - $3.75 = $21.75 sale price
Required:
a. For the balance sheet, identify how each transaction affects total assets, total liabilities, and total equity. For the income statement, identify how each transaction affects net income.
b. For the statement of cash flows, identify how each transaction affects cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities.
WHAT AM I MISSING?!?!
The answers for the two questions is described below:
a. The balance sheet is a financial statement that shows a company's assets, liabilities, and equity at a specific point in time. Each transaction will affect one or more of these categories in different ways:
An increase in assets will increase total assets.
An increase in liabilities will increase total liabilities.
An increase in equity will increase total equity.
The income statement is a financial statement that shows a company's revenues, expenses, and net income over a specific period of time. Each transaction will affect net income in different ways:
An increase in revenues will increase net income.
An increase in expenses will decrease net income.
b. The statement of cash flows is a financial statement that shows the cash flows from operating activities, investing activities, and financing activities over a specific period of time. Each transaction will affect one or more of these categories in different ways:
An increase in cash from operating activities will increase cash flows from operating activities.
An increase in cash from investing activities will increase cash flows from investing activities.
An increase in cash from financing activities will increase cash flows from financing activities.
It is important to note that it can be complex to classify some transactions into one category or another, and it may require more context of the specific transaction and the company's operations.
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Cheese pizza was preferred by 40 students pepperoni pizza was preferred by 28 based on the results how many of the 340 students can be expected to prefer cheese pizza?
The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Cheese pizza = 40 students
Pepperoni pizza = 28
The ratio of cheese and Pepperoni pizzas.
= 40:28
= 10:7
Now,
Cheese pizza = 10x
Pepperoni pizza = 7x
The number of expected students who prefer cheese pizza.
= (10x)/(17x) x 340
= 10/17 x 340
= 10 x 20
= 200
Thus,
The number of expected students preferring cheese pizza is 200.
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Use the given confidence interval to find the margin of error and the sample mean
(12.7, 19.5)
The margin of error and the sample mean of the confidence interval are given as follows:
Margin of error: 3.4.Sample mean: 16.1.How to obtain the margin of error and the sample mean of the confidence interval?The confidence interval is defined as follows:
(12.7, 19.5).
The definition of a confidence interval is that it is obtained as the sample mean plus/minus the margin of error.
Hence the sample mean is calculated as the mean of the bounds of the interval, hence:
(12.7 + 19.5)/2 = 16.1.
The margin of error is calculated as the absolute value of the difference of each bound from the sample mean, hence:
|19.5 - 16.1| = |12.7 - 16.1| = 3.4.
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Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Answer:
Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Step-by-step explanation:
ind the Average Rate of Change of the table below for the interval 0 < x < 4
The average rate of change is equivalent to 2.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the table as shown below -
[x] : 0 1 2 3 4
[y] : -2 -3 1 3 6
The rate of change in the interval 0 < x < 4 is -
AROC = (6 + 2)/(4 - 0)
AROC = 8/4
AROC = 2
Therefore, the average rate of change is equivalent to 2.
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If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of h[f(5)]
Answer:
29
Step-by-step explanation:
The area of the triangle is no more than 30 square inches. Right and solve inequality that represents a.
(HELP ASAP!)
The answer is a ≤ 30.
An inequality is a mathematical expression that compares two values or expressions using an inequality operator. In this case, the inequality would be a ≤ 30. This means that the area of the triangle must be less than or equal to 30 square inches.
This can be solved by finding the area of the triangle. To do this, we need to know the lengths of the sides of the triangle. Suppose we have sides p, q, and r. Then the area of the triangle can be found using the formula:
a = 1/2 × b × h
where q is the base of the triangle and r is the height. To ensure that the area of the triangle is no more than 30 square inches, the inequality must be satisfied. That is, 1/2 × b × h ≤ 30. This inequality can be rewritten in terms of the side lengths by substituting 1/2 × q × r for h. This gives us a ≤ 30.
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Find the sum of the interior angles of a nonagon.
A. 140°
B. 1,620°
C. 1,260°
D. 1,450°
The sum of the interior angles of a nonagon (a 9-sided polygon) is 1,450°.
1. The interior angles of a polygon can be calculated by subtracting 2 from the number of sides, then multiplying the result by 180°.
2. For a nonagon (a 9-sided polygon), the calculation is
(9-2) × 180° = 1,450°.
The sum of the interior angles of any polygon can be calculated using the formula
(n-2) × 180°,
where n is the number of sides of the polygon. This formula works because the sum of the interior angles of any polygon is always equal to (n-2) times the measure of a single interior angle. For a nonagon, a 9-sided polygon, the calculation is
(9-2) × 180° = 1,450°.
This means that the sum of the interior angles of a nonagon is 1,450°.
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fraction bigger than 2 out of 5 and smaller than 2 out of 3. When i divided numerator by denominator , it will be 0.533.
The fraction that is bigger than 2/5 and smaller than 2/3 is 8/15.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3, 1/5 is a fraction.
We have,
Let the fraction be a/b.
2/5 < a/b < 2/3
Now,
a/b
= (2/3 + 2/5) / 2
= (10 + 6) / 30
= 16/30
= 8/15
= 0.533
Thus,
The fraction is 8/15.
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A school is selling cookies as a fundraiser. Each box contains 10 cookies. Each student can sell 17 boxes of cookies. How many cookies can 11 students sell
11 students could sell 1870 cookies.
Explain about the expressions?A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.
Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.
An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.
= 10 X 17
= 170 X 11
= 1870
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Solve for x.
2x = 25-3x
Simplify your answer as much as possible.
x
=
3 0.8
X
Ś
[tex]2x = 25-3x[/tex]
Simplify:
[tex]2x=-3x+25[/tex]
Add 3x to both sides:
[tex]2x+3x=-3x+25+3x[/tex]
[tex]5x=25[/tex]
Divide both sides by 5:
[tex]\dfrac{5x}{5} =\dfrac{25}{5}[/tex]
[tex]\fbox{x = 5}[/tex]
The histogram shows the ages of passengers riding in a tour van. How many passengers are under 45 years of age? Enter your answer as a number, like this: 42
Answer:
12
Step-by-step explanation:
3 + 4 + 5 = 12
You know that 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77. You also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91. How much does a ticket in Virginia cost?
The cost of one ticket in Virginia is $8
What is a system of linear equations?A System of Linear Equations is when we have two or more linear equations working together.
Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.
To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,
Let V represents the cost in Virginia that of in Maryland be M
Therefore,
4v+5m = 77.......(i)
8v+3m = 91........(ii)
Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]
(8v+10m = 154) - (8v+3m = 91)
7m = 63
m = 9
Put m = 9 in eq(i)
4v+5(9) = 77
4v = 77-45
4v = 32
v = 8
Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.
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find four consecutive odd integers such that 4 times the sum of the first and third is 4 larger than 4 times the fourth
The four consecutive odd integers = 15, 17, 19, 21
What are integers ?Positive, negative, and zero are all examples of integers.
The Latin word "integer" signifies "whole" or "intact."
As a result, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers.
This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.
According to our question-
First digit: x
Second digit: x + 2
Three-digit number Equals x + 4
Fourth digit: x + 6
The difference between the opposite of the third and the first two sums up to 55.
x + x + 6 = -(x + 4) + 55
x + x+6 = (-x - 4) + 55
2x + 6 = -x + 51
assemble similar terms
2x + x = 51 - 6
3x = 45
x = 15
Therefore,
First digit: x = 15
Second digit: 15 + 2 + x = 17
Third number: 15 + 4 + 4 = 19
Fourth digit: x+6 = 15+6 = 21
The four odd numbers in a row equal 15, 17, 19, and 21.
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1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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What is the nature of roots of quadratic equation x^2 =- 2x 1?
The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
x² = -2x + 1
transform it into the standard form:
x² + 2x - 1 = 0
Calculate the discriminant:
D = 2² - 4 (-1) = 8
Since D > 0, the roots are two distinct real roots.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation x² = -2x + 1?
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Type the correct answer in the box. Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of the circle measured in inches is modeled by the function , where s is time in seconds. The area of the spill when seconds is square inches.
The area of the oil spill is 2.924π square inches.
What is the radius of the circle?
Any line segment connecting a circle's center to its perimeter is considered a circle's or sphere's radius, and in more recent usage, their length is also considered. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."
Here, we have
The radius of the circle of oil spread is modeled by the function r = ∛s where s = time in seconds.
The area of the oil spill A = πr²
= π(∛s)²
So, we need to find the area of the oil spill when s = 5.
So, A = π(∛s)²
A = π(∛5)²
A = π(1.7099)²
A = 2.924π square inches.
Hence, the area of the oil spill is 2.924π square inches.
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H)
how many five- card hands are possible that contain at least three kings?
==========================================================
Explanation:
We'll break things up into cases. The phrasing "at least 3" means "3 or more".
We either will have 3 kings or 4 kings.
----------------------------------------------
Case A) There are exactly 3 kings.
Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.
Put another way: there are 4 ways to leave a certain king out of the hand.
Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128
To recap, we found
4 ways to pick the three kings1128 ways to pick the other two cards that aren't kingsThat gives 4*1128 = 4512 ways to have case A happen.
----------------------------------------------
Case B) There are exactly 4 kings
4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.
Overall there are 1*48 = 48 ways to have case B play out.
----------------------------------------------
There were 4512 ways to have case A happen, and 48 ways to have case B happen.
These cases are mutually exclusive to allow us to simply add the counts:
4512+48 = 4560
This is why the final answer is 4560
a form of reasoning called is the process of forming general ideas and rules based on your experiences and observation
A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.
What is the Induction?The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.
The action or process of inducting someone to a position or organization.
We have given that,
A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.
As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.
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Kyle puts all of his craft beads into a bag. Exactly 1/3 of the beads are blue and 5/16 are red. What is the unit rate of blue beads to red beads in Kyle's bag?
The unit rate of blue beads to red beads in Kyle's bag is 1(1/15).
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
Blue beads = 1/3
Red beads = 5/16
The unit rate of blue beads to red beads.
= 1/3 ÷ 5/16
= 1/3 x 16/5
= 16/15
= (16/15) / 1
= 1(1/15) / 1
Thus,
The unit rate is 1(1/15).
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