Thus, the value displayed by Point K is roughly 373.
What is the name of the numerical line?A number line in mathematics is a continuous straight line with numerals spaced equally apart along that line. Some stories will have a defined beginning and conclusion. We refer to these as closed number lines.
The distance between 367 and 377 can be split into five equal portions because the number line has 5 increments. Two components make up each section.
So, starting at 367, we must move 2 units to the right for each component until we reach Point K in order to determine the number represented by Point K.
We arrive at 369 by adding 2 units to the right of 367. From 369, we deduct another 2 units to arrive at 371. Following the same pattern, we arrive at 373, 375, and ultimately 377.
Point K is closest to 373 because it lies between 373 and 375. Thus, the value displayed by Point K is roughly 373.
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b The equation of a curve is y = ax + b/√x where a and b are constants. The equation of normal to the curve at (4, 12) is 3y + 2x-44. Find the value of each of the constants a and A. 16
the value of a is 7/6 and the value of b is 0.
What is normal and tangent to a curve?The tangent is an immediate line that simply touches the curve at a given point. The regular is an immediate line this is perpendicular to the tangent. the slope of any line perpendicular to a line with slope m is the terrible reciprocal −1/m.
Given a curve y = ax + b/√x.
with the constant value of a and b.
First, we need to find the derivative of the curve y = ax + b/√x in order to find the gradient of the tangent to the curve at any given point. We can use the quotient rule to differentiate the equation:
dy/dx = a - (b/2)x^(-3/2)
Now we can find the gradient of the tangent to the curve at the point (4, 12) by substituting x = 4 into this equation:
dy/dx = a - (b/2)4^(-3/2) = a - b/16
The gradient of the normal to the curve at this point is the negative reciprocal of the gradient of the tangent, so:
-1/m = -(a - b/16)
We know that the equation of the normal is given by:
3y + 2x = 44
We can use this to substitute in y in terms of x:
y = (44 - 2x)/3
Now we can substitute this into the expression for -1/m:
-1/m = -(a - b/16) = -(dy/dx) = -(a - b/2x^(3/2)) = -(a - b/2(4)^(3/2))
-1/m = -(a - b/8)
Simplifying this equation, we get:
1/m = a - b/8
Substituting the value of m = -3 into this equation (because the gradient of the normal is -3), we get:
-1/3 = a - b/8
Multiplying through by 8, we get:
-8/3 = 8a - b
We also know that the curve passes through the point (4, 12), so we can substitute this into the equation for the curve:
12 = 4a + b/2
Multiplying through by 2, we get:
24 = 8a + b
Now we have two equations in two variables:
-8/3 = 8a - b
24 = 8a + b
Adding the two equations together, we get:
56/3 = 16a
Dividing through by 16, we get:
a = 7/6
Substituting this into one of the equations, we get:
24 = 8(7/6) + b
b = 0
Therefore, the value of a is 7/6 and the value of b is 0.
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what is the area of these shapes . step by step pls beed today before school
In the figure below, m < 1=79° and m < 2 = 53°. Find m < KJL.
Applying the angles addition postulate, m<KJL = 132°.
What is the Angles Addition Postulate?The Angles Addition Postulate is a fundamental property of angles in geometry that explains how to find the measure of an angle that is formed by two adjacent angles. According to this postulate, the measure of the larger angle, which is formed by two adjacent angles, is equal to the sum of the measures of the two smaller adjacent angles.
Given the following:
m <1 =79°
m<2 = 53°
Thus, we have:
m<KJL = m<1 + m<2
Substitute:
m<KJL = 79 + 53
m<KJL = 132°
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The angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure of m∠KJL = 132°.
How to evaluate for the angle measure of m∠KJLWe can observe that the angles m∠1 and m∠2 are between the angle m∠KJL hence the sum of the two angles m∠1= 79° and m∠2 = 53° will give the measure of m∠KJL as follows:
m∠1 + m∠1 = m∠KJL
79° + 53° = 132°
m∠KJL = 132°
Therefore, the angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure m∠KJL = 132°
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What is the conversion of 65 kilos in pounds?
The conversion of 65 kilos in pounds is equivalent to approximately 143.3 pounds.
Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.The approximation we use for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb. To convert from kilogram to pound, we multiply by 2.2. To convert from pound to kilogram, we divide by 2.2.
To convert 65 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.
Therefore,65 kilograms = 65 x 2.20462 pounds= 143.3003 pounds (rounded to 4 decimal places)
So, 65 kilograms is equivalent to approximately 143.3 pounds.
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Josiah invested $96,000 in an account paying an interest rate of 3. 5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?
Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, the value of the account will reach $153,400 after 9 years.
How long would it take, to the nearest year, for the value of the account to reach $153,400?To calculate this, we can use the formula for the future value of a single sum invested with an inverted interest rate compounded continuously.
Future Value = Present Value × (1 + r)n
Where:
Present Value = 96,000r = 3.5% expressed as a decimal, 0.035n = number of yearsWe can solve for n to find out how many years it will take to reach $153,400.
153,400 = 96,000 × (1 + 0.035)n
153,400/96,000 = (1 + 0.035)n
Taking the natural log of both sides and simplifying:
ln(153,400/96,000) = n × ln(1.035)
n = ln(153,400/96,000)/ln(1.035)
n ≈ 8.99
To the nearest year, it will take 9 years for the value of the account to reach $153,400.
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A surveyor needs to determine the height of a
large grain silo. He positions his transit 65 m from
the silo and records an angle of elevation of 52º.
If the height of the transit is 1.7 m, determine the
height of the silo, to the nearest metre.
The height of the silo, to the nearest meter is, 84.9 m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A surveyor needs to determine the height of a large grain silo.
And, He positions his transit 65 m from the silo and records an angle of elevation of 52º.
Now, By the given condition we can formulate;
tan 52° = x / 65
x = 83.2 m
Here, the height of the transit is 1.7 m,
Thus, The height of the silo, to the nearest meter is,
83.2 + 1.7 m
84.9 m
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What is the value of 2/2 to the power of -3
PLEASE HELP OF YOURE GOOD AT GEOMETRY! DUE TOMORROW. THANK YOU SO MUCH.
The coordinates of Room 1314 are given as follows:
(2, 13).
How to obtain the coordinates of room 1314?We are going to label the rooms are follows:
Room 1305: X.Room 1324: Y.Room 1314: Z.Then the coordinates of Room 1314 are obtained applying the proportions in the context of the problem.
Room 1314 is located five-sevenths of the distance from Room 1305 to Room 1324, hence the equation is given as follows:
Z - X = 5/7(Y - X).
Then the x-coordinate is obtained as follows:
x + 8 = 5/7(6 + 8)
x = 10 - 8
x = 2.
The y-coordinate is obtained as follows:
y + 2 = 5/7(19 + 2)
y + 2 = 15
y = 13.
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Calculator
What is value of x?
Enter your answer in the box.
The value of x is 10
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
The large triangle is divided into 2 similar triangles
The ratios of corresponding sides are equal
8/12 = x+4/2x+1
=> 8( 2x+1) = 12( x+4 )
=> 16x+8 = 12x+48
=> 16x-12x = 48-8
=> 4x = 40
=> x= 40/4 = 10
The value of x is 10
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Please Help Me!! Will Mark Brainliest!! :)
Jeff has a sack full of marbles. Each time he picks one out, he puts it back into the sack before drawing another. In his sack there are 5 red marbles, 6 yellow marbles, and 8 blue marbles. Find the following probabilities.
c. If two marbles are drawn, what's the chance they are both the same color?
d. If two marbles are drawn, what's the chance they are NOT the same color?
The solution of the given problem of probability comes out to be P(not same color) = 236/361.
What precisely does the probability method suggest?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.
Here,
There are three cases to consider:
Case 1: both marbles are red
Case 2: both marbles are yellow
Case 3: both marbles are blue
The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):
P(red and red) = (5/19) × (5/19) = 25/361
Similarly, the probability of drawing two yellow marbles is:
P(yellow and yellow) = (6/19) × (6/19) = 36/361
And the probability of drawing two blue marbles is:
P(blue and blue) = (8/19) × (8/19) = 64/361
So, the probability of drawing two marbles that are the same color is:
P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)
P(same color) = (25/361) + (36/361) + (64/361)
P(same color) = 125/361
d.
There are three cases to consider:
Case 1: one marble is red and one marble is yellow
Case 2: one marble is red and one marble is blue
Case 3: one marble is yellow and one marble is blue
The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):
P(red and yellow) = 2 × (5/19) × (6/19) = 60/361
Similarly, the probability of drawing one red marble and one blue marble is:
P(red and blue) = 2 × (5/19) × (8/19) = 80/361
And the probability of drawing one yellow marble and one blue marble is:
P(yellow and blue) = 2 × (6/19) × (8/19) = 96/361
So, the probability of drawing two marbles that are not the same color is:
P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)
P(not same color) = (60/361) + (80/361) + (96/361)
P(not same color) = 236/361
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A landowner recently sold a large plot of land. The sale decreased his total acreage by 12%. Let v be the original acreage. A. Write two equivalent expressions that represent the new acreage. B. Use the expressions to describe another way to find the new acreage
A. Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new average directly using:
x = 0.88v (using the second expression )
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.
For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.
Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.
A. Let x be the new acreage after the sale. Then we have:
x = v - 0.12v (12% decrease means 0.12v decrease from v)
x = 0.88v (Simplify by factoring out v)
So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:
x = v - 0.12v (using the first expression above)
x = 0.88v (simplify)
x = (1 - 0.12)v (factor out v)
x = 0.88v (simplify)
Alternatively, we can calculate the new average directly using:
x = 0.88v (using the second expression above)
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Answer:A.Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B.Another way to find the new average directly using:x = 0.88v (using the second expression )What is expression ?In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.A. Let x be the new acreage after the sale. Then we have:x = v - 0.12v (12% decrease means 0.12v decrease from v)x = 0.88v (Simplify by factoring out v)So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:x = v - 0.12v (using the first expression above)x = 0.88v (simplify)x = (1 - 0.12)v (factor out v)x = 0.88v (simplify)Alternatively, we can calculate the new average directly using:x = 0.88v (using the second expression above)
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how many tbsp is 3/8 cup
Answer:
6 US tablespoons
Step-by-step explanation:
what is 190pounds in kg?
190 pounds is approximately equal to 86.1826 kg ( rounded to four decimal places )
To convert 190 pounds to kg, we can use the following formula:
1 pound = 0.453592 kg
The conversion factor is 0.453592
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The mass in kg = conversion factor × The mass in pounds
Substitute the values in the equation
The mass in kg = 0.453592 × 190
Multiply the numbers
= 86.1826 kg ( rounded to four decimal places )
Therefore, 190pounds is 86.1826 kg
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How is press fit calculated?
Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.
Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.
Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.
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what is 115000 minutes to hours?
The value of minutes can be converted to hours by dividing the value of minute by 60 so 115000 minutes means 1916.66 hours.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
With the help of our conversion tools, you can convert 115000 Minutes to Days (min to d). Use the direct conversion formula below to convert 115000 min to d.
115000 min = 79.861111111111 d.
Also, you can change 115000 Minutes into other Time (common) units.
We will create an equation to convert 115000 minutes to hours, then utilise the equation to perform the conversion. Since there are 60 minutes in an hour, we can construct our equation as follows:
Hours = Minutes / 60
In the equation above, we may convert 115000 minutes to hours by substituting 115000 minutes, giving the following result:
115000 / 60 = Hours
1916 2/3 hours divided by 115000 minutes is 1916.66667 hours.
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Express the negations of the proposition using quantifiers and in English "There is a student in
this class who has never seen a computer"
The negation of the proposition posed the statement is:
"Every student in this class has seen a computer."
What is the express the negations of the proposition using quantifiers and in English "There is a student in this class who has never seen a computer"?The negation of the proposition "There is a student in this class who has never seen a computer" can be expressed using quantifiers as follows:
∀ x ∈ S, ∃ y ∈ C (x has seen y)
This means "For all students x in the class S, there exists a computer y in the set of computers C such that x has seen y."
In English, the negation of the proposition can be expressed as "Every student in this class has seen a computer."
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A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 5 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 2:8?
4 cm
10 cm
16 cm
64 cm
Answer:10 cm
Step-by-step explanation:
Answer:B 24 cm
Step-by-step explanation:
Find integer matricesA,Bnot multiples of each other such thatNul(A)=Nul(B)andCol(A)=Col(B)
A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).
To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:
A = [1 0 0; 0 1 0; 0 0 0]
B = [1 1 0; 0 0 0; 0 0 0]
The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).
The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).
We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.
Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).
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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?
select the correct answer. an observatory is 150 feet high. when a person is standing in the observatory looking at an island, the angle of depression is . what is the approximate horizontal distance from the observatory to the island? the picture shows a right-angled triangle. the length of the opposite side is 150 ft. a dotted horizontal line (observatory) touches the top vertex. the angle of the left vertex (island) and the outer angle of the top vertex is 25 degrees. a. 322 feet b. 166 feet c. 70 feet d. 355 feet
Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
We can use trigonometry to solve this problem.
Let's call the horizontal distance from the observatory to the island "x".
Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -
tan(25) = opposite / adjacent
tan(25) = 150 / x
Solving for x, we get -
x = 150 / tan(25)
Using a calculator, we find that -
x ≈ 322 feet
Therefore, the horizontal distance value is 322 feet.
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Answer:
Step-by-step explanation:
Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
We can use trigonometry to solve this problem.
Let's call the horizontal distance from the observatory to the island "x".
Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -
tan(25) = opposite / adjacent
tan(25) = 150 / x
Solving for x, we get -
x = 150 / tan(25)
Using a calculator, we find that -
x ≈ 322 feet
Therefore, the horizontal distance value is 322 feet.
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how much is 12 oz in milliliters
The Volume 12 oz on converting to millimeter is equivalent to 354.9 milliliters .
The Ounces (oz) is a unit of volume which is used in the US customary system of measurement.
The Milliliters (mL) is a metric unit of volume.
We have to convert 12 ounces to milliliters, we need to use a conversion factor.
⇒ 1 fluid ounce (oz) is = 29.5735 milliliters (mL).
So , to convert 12 ounces to milliliters , we write :
⇒ 12 ounces × 29.5735 mL/ounce = 354.882 mL ≈ 354.9 mL .
Therefore , 12 ounces is approximately equal to 354.9 milliliters.
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what is symbolab derivative calculator?
Symbolab is the best derivative calculator that solves first derivatives, second derivatives, higher order derivatives, one point derivatives, partial derivatives, implicit derivatives, derivatives with definition and more.
Symbolab Derivative Calculator is free online tool for calculating derivatives of functions. It allows users to input the equations and then calculates the derivatives of those equations for the user. This tool is useful for students and professionals who need to calculate derivatives quickly and accurately.
The calculator supports a variety of mathematical functions, including exponential, polynomial, logarithmic and trigonometric functions. It also allows users to graph derived functions. The calculator is easy to use and can also save users time and effort. It can also be used to check the correctness of the derivative of a function.
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What is 12.5% expressed as a fraction in lowest terms
Answer:
25 / 2
Step-by-step explanation:
12.5% = 125 / 10 ( simplify the fraction with 5 )
= 25 / 2
Is F continuous if F is differentiable?
what is long division polynomials calculator
A long division polynomials calculator is an online tool used to perform polynomial long division for dividing polynomials.
A long division polynomials number cruncher is an internet based device that performs polynomial long division, a strategy used to separate one polynomial by another. This cycle is like long division with numbers, yet rather than partitioning by single-digit numbers, it includes separating by a polynomial of at least one terms. The interaction includes partitioning the most extensive level term of the profit by the most extensive level term of the divisor, then increasing the divisor by the remainder and taking away the outcome from the profit. The subsequent articulation is the rest of the division. The interaction is then continued involving the rest of the new profit, until the level of the rest of not exactly the level of the divisor. An internet based long division polynomials mini-computer robotizes this interaction, permitting clients to enter the profit and divisor polynomials and get the remainder and remaining portion. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to partition polynomials for computations and critical thinking.
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if you sell 15 items for $360 each and make 22%commission, how much do you earn in total ?
Answer:
1,188
Step-by-step explanation:
15x360=5,400
5,400-22%=4212
5,400-4,212=1,188
A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 318?
The probability of selecting the integer 318 is 0
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
Sample space = 1 to 50
The integer 318 is not in the range of integers that the random number generator can select from (1 to 50).
Hence, the required probability of selecting the integer 318 is 0.
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37 dollars an hour is how much a year
The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.
Number of dollars in one hour is equal to 37 dollars.
Relation between year and hour .
1 year = 12 months
1 month = 31, 30 or 28 days
Total number of days in a year = 365 days
Number of hours in 1 day = 24 hours
Number of hours in 365 days = ( 365 × 24 ) hours
= 8760 hours
In 1 hour = 37 dollars
⇒ 8760 hours = ( 37 × 8760 ) dollars
⇒ 8760 hours = ( 324,120 ) dollars
⇒ 1year = ( 324,120 ) dollars
Therefore, the number of dollars in a year is equal to 324,120 dollars.
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give an example of fractions that you would copare by finding commen denominators, and an example of fractions you would compare by finding common numerators?
how to make a mixed fraction into an improper fraction
Answer:
Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.
For example, suppose you want to convert the mixed number to an improper fraction. First, multiply 3 by 5 and add 2:
(3 · 5) + 2 = 17
Use this result as your numerator, and place it over the denominator you already have.
Place this result over the denominator:
This method works for all mixed numbers. Furthermore, if you start with the fractional part reduced, the answer will also be reduced.
Step-by-step explanation:
Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns $15 for each thirty-minute session and $25 for each sixty-minute session.
If she earned $230 this past weekend and had x thirty-minute sessions and x-2
sixty-minute sessions, what is the value of x?