The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
What is trignomentry ?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of triangles and to solve problems involving angles and distances in two-dimensional space.
sin(π/6)cos(π/2) - cos(π/60)sin(π/2)
The first term in the expression, sin(π/6)cos(π/2), can be simplified as follows ,
sin(π/6) = √(3)/2, cos(π/2) = 0
so sin(π/6)cos(π/2) = (√(3)/2) * 0 = 0
The second term in the expression, -cos(π/60)sin(π/2) , can be simplified as follows ,
sin(π/2) = 1, cos(π/60) = sqrt(3)/2 - 1/2
so -cos(π/60)sin(π/2) = -(sqrt(3)/2 - 1/2) * 1 = -sqrt(3)/2 + 1/2
Now we can substitute the simplified values back into the original expression ,
0 - (-sqrt(3)/2 + 1/2)
and combining like terms, [tex]\frac{1-\sqrt{3} }{2}[/tex],
Hence , The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .
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9 ft
cft
12 ft
Pls help me
The third side of the right angle triangle is x = 15 ft.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
We have to find the measure of third side of given right triangle.
The two sides of right triangle are 9 ft and 12 ft.
Let the side of third side is x.
By using the Pythagoras theorem,
(9)^2 + (12)^2 = x^2
81 + 144 = x^2
225 = x^2
x = 15
Hence, the third side of the right angle triangle is x = 15 ft.
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Carolyn makes and sells necklaces. The material to make each necklace costs$3. 20 Last week she made 12 necklaces and wants to make a total profit of $54Using the equation 12(X-3. 20) = 54 Carolyn determined that she will make a profit of$7. 70 on each necklace. Which error did Carolyn make?
Carolyn made an error in her calculation. She failed to take into account the cost of labor and overhead in her equation.
Her equation only accounted for the cost of materials, not the cost of labor and overhead. The equation should have been: 12(X-3.20) + Cost of Labour and Overhead = 54. This would have given her a more accurate calculation of the profit per necklace.
In addition, Carolyn did not account for other factors such as marketing, shipping, and taxes, which could also affect the total profit. If she had taken into account these other costs, she would have been able to better calculate her profit margin on each necklace. By not accounting for these costs, Carolyn could have underestimated her profit margin, leading to an inaccurate calculation.
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Conditional statements: MELTS IN YOUR MOUTH , NOT IN YOUR HAND!
Converse:
Inverse:
Contrapositve:
dont forget to use If and Then
If something melts in your mouth and not in your hand, then it must be something that has a low melting point.
Converse,Inverse and Contrapositve
If it melts in your hand, then it does not melt in your mouth.Inverse: If it does not melt in your mouth, then it does not melt in your hand.Contrapositive: If it does not melt in your hand, then it does not melt in your mouth.This could be something like chocolate, marshmallows, or even butter.The inverse of this statement is if something does not melt in your mouth but does in your hand, then it must have a high melting point.This could be something like metal or plastic. The contrapositive of this statement is if something does not melt in your hand, then it will not melt in your mouth either.This could be something like a rock or a piece of ice. All of these statements apply when discussing the melting temperature of different materials. Therefore, when it comes to melting, it all depends on the temperature of the material and whether it is safe to put in your mouth.To learn more about Converse,Inverse and Contrapositve refer to:
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in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4. if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1. how many more white beans are there than kidney beans?
As per the unitary method, the amount of white beans are there than kidney beans are 30.
The term unitary method is known as a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
Here we have given that in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4.
And we also know that if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1.
Here we have consider that let the number of pinto beans be x and that is the number of white beans will be x + 30
In which means the total number of beans in the jar will be written as,
=> x + x + 30 = 2x + 30
Here we know that the Total ratio is calculated as,
=> 5 + 4 = 9
In order to find the number of pinto beans then it can be calculated as,
=> ratio of pinto beans / Total ratio X Total number of beans
Which can be written as.
=> (2x + 30) = x
When we simplify this one then we get the value of x as,
=> x = 30.
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If 5m= 7n, what is the ratio of n to m?
Answer:
the ratio of n to m is 5 : 7
5m = 7 n
n : m = 5 : 7
31. Grace solved the equation 2 1/2y = 5/8. Her steps for the solution are shown in the table but are all mixed up. Write her steps I. The correct order on the right side of the table
The correct steps in the solution of the fraction are;
Step 1 ; 2 1/2y = 5/8Step 2 ; 5/2 y = 5/8Step 3 ; y = 5/8 . 2/5Step 4 ; y = 10/40 or 1/4What are the steps in the solution?We know that when we talk about a fraction what we mean is just a part of a whole. There are some steps that we would need in the solution of the question and the steps have not been arranged in the proper order in the image that is attached here.
The task that we have then is to be able to arrange the steps that we need to take in the proper order and as such, we are going to have that;
Step 1 ; 2 1/2y = 5/8
Step 2 ; 5/2 y = 5/8
Step 3 ; y = 5/8 . 2/5
Step 4 ; y = 10/40 or 1/4
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Question 9(Multiple Choice Worth 1 points)
(02.05 MC)
What are the vertex and range of y = x + 21-6?
O(-2,-6); -6 ≤ y ≤0⁰
O(-2,-6); -
O(2,-6): -6 ≤ y
O(2,-6); -
The vertex and range of y = |x + 2| - 6 are: A. (-2, -6); -6 ≤ y < ∞.
What is an absolute value function?Generally speaking, the vertex points of an absolute value function occurs when the absolute values are equal to zeros. Therefore, we would equate the x-values of this absolute value function to zero as follows;
y = |x + 2| - 6
|x + 2| = 0
x + 2 = 0
x = -2
When x = -2, the value of y for this absolute value function is given by;
y = |x + 2| - 6
y = |-2 + 2| - 6
y = 0 - 6
y = -6
Therefore, the vertex is (-2, -6).
Since |x + 2| ≥ 0, we would add -6 to both sides of the inequality in order determine the range as follows;
|x + 2| - 6 ≥ -6
y = f(x) ≥ -6
Therefore, the range of this absolute value function is defined for all real numbers that are greater than or equal to -6 i.e -6 ≤ y < ∞.
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Complete Question:
What are the vertex and range of y = |x + 2| - 6?
the probability of randomly picking out a book of poetry from a bookshelf is 3 over 10. what are the odds in favor of choosing a book of poetry?
3:7 are the odds in favor of choosing a book of poetry
given that
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. [note 1] [1] [2] The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half
the probability of randomly picking out a book of poetry from a bookshelf is 3/10
now, we need to find what are the odds in favor of choosing a book of poetry
P(poerty) = 3/10
P(non-poerty) = 1 - 3/10 = 7/10
number of odds = P(poerty) /P(non-poerty)
= 3/10/7/10
= 3/7
= 3:7
3:7 are the odds in favor of choosing a book of poetry
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andrew buys 8 pounds of apples for $12.00. he wants to know and use the unit rate of the cost per pound. true or false: using the unit rate of the cost per pound, do 5 pounds of apples cost $7.50?
The unit price for the apples is $1.5 per pound. The statement is true.
Now, According to the question:
How to calculate the Unit rate of the cost per pound?
8 pounds of Apple costs $12
The unit rate is
8= 12
1= x
We can write, by cross - multiply
8x = 12
x= 12/8
x= 1.5
Hence, the unit rate of the cost per pound is $1.5
And, 5 pounds of apples cost $7.50
cross multiply,
5× 12/8
60/8 = 7.50
5 pounds of apples = 7.50
Hence, The unit price for the apples is $1.5 per pound. The statement is true.
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the seller of a loaded die claims that it will favor the outcome 6. we don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. our p-value turns out to be 0.03. which conclusion is appropriate? explain. a) there's a 3% chance that the die is fair. b) there's a 970/0 chance that the die is fair. c) there's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.
It is plausible to assume that the die is fair because there is a 3% possibility that a loaded die might randomly yield the outcomes that we saw.
The appropriate conclusion is that there is a 3% chance that a loaded die could randomly produce the results we observed. We tested this hypothesis by rolling the die 200 times and our p-value turned out to be 0.03. This means that there is only a 3% chance that the results we observed could have been produced randomly by a loaded die, so it is reasonable to conclude that the die is fair. This is because a p-value of 0.03 is considered to be statistically significant, which indicates that the results we observed are unlikely to have been due to chance. Therefore, we can conclude that the seller's claim that the die will favor the outcome 6 is likely false.
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A sales person works 40 hours per week at a job where she has two options for being paid option as an hourly wage of $20 option B is a commission rate of 10% on weekly sales how much does she need to sell this week turn the same amount with the two options
write 6x^5/8 in radical form
the radial form is, 6 times the eight root of x to the fifth power.
What is radical form?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
here, given that,
6x^5/8
now,
the radial form is,
6 times the eight root of x to the fifth power.
Hence, the radical form is, 6 times the eight root of x to the fifth power.
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Ryan is saving for his college tuition. he has $2,500 in a savings account that pays 6.25% annual interest. how much money will ryan have in his account in 6 years?
The amount of money Ryan will have in his account in 6 years is $3668.71.
How is the Exponential Compound Interest calculated?Compound interest is calculated using the exponential formula y = P(1+r)ⁿ. P is for "Present" or Principal value; r stands for interest rate; n stands for time (in years), and y stands for future value after the amount compounds annually
Given:
Principal Amount = $2500
Rate of interest = 6.25%
Time = 6 years
The exponential equation can be given as:
y = P(1+r)ⁿ where n is the number of years.
y = 2500(1 + 0.0625)ⁿ
The money Ryan will have in his account in 6 years can be calculated as by putting n's value as 6 years.
y = 2500(1 + 0.0625)⁶
y = $3668.71
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which angles must be less than 146 degrees? please list both angles and support your answer by stating the theorem that will support your conclusion.
Any two angles whose sum is 146 degrees must both be less than 146 degrees. This can be supported by the Triangle Sum Theorem, which states that the sum of the measure of the interior angles of a triangle is 180 degrees.
The Triangle Sum TheoremThe Triangle Sum Theorem states that the sum of the measure of the interior angles of a triangle is always 180 degrees. Therefore, if two angles add up to 146 degrees, then both of those angles must be less than 146 degrees. This is because the remaining angle must make up the difference to reach the total of 180 degrees.
For example, if two angles measure 80 degrees and 66 degrees, then the third angle must measure 34 degrees in order to sum up to 180 degrees.Therefore, any two angles whose sum is 146 degrees must both be less than 146 degrees.
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How many solutions can a system of 3 linear equations have?
A system of 3 linear equations can have 0, 1, or an infinite number of solutions.
A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.
If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.
If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.
If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.
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greatest common factor of 8,18 and 70
find the roots of the factored polynomial. (x 1)2(x 2) write your answer as a list of values separated by commas.
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
what are polynomial ?A polynomial is a mathematical expression that solely uses additions, subtractions, multiplications, and powers of positive integer variables. It is composed of coefficients and uncertainty. A single indeterminate x polynomial is indicated by the expression x2 4x + 7. In mathematics, a polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is a statement in mathematics involving variables and coefficients. The only operations that can be included in an expression are addition, subtraction, multiplication, and non-negative integer exponents. These formulas are known as polynomials.
given
(x - 5)(x + 2) = 0
Using the 0 product property:
Case 1
x - 5 = 0
x = 5
Case 2
x + 2= 0
x = -2
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
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if two sides of a triangle have lengths 13.2 and 21.5, what must the third side length be less than?
If two sides of a triangle have lengths 13.2 and 21.5, then the third side length be less than 34.7.
When a triangle's two sides are given lengths of 13.2 and 21.5, we must determine what the third side's length should be.
The sum of the lengths of any two sides of a triangle can always be more than the length of the third side.
The length difference between any two triangle sides will never be greater than the length of the triangle's third side.
13.2 and 21.5 add up to 34.7, and their difference equals 8.3.
The above condition must not be violated, and the length of the third side must be greater than 8.3 and less than 34.7.
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(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
The solution is Option C.
The equation of line is given by y = -2x + 58
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 2 , 54 )
Let the second point be Q ( 5 , 48 )
The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 54 - 48 ) / ( 2 - 5 )
On simplifying the equation , we get
Slope m = 6 / -3
Slope m = -2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 54 = -2 ( x - 2 )
On simplifying the equation , we get
y - 54 = 2x + 4
Adding 54 on both sides of the equation , we get
y = -2x + 58
Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )
Hence , the equation of line is y = -2x + 58
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The area of a rectangle is rectangle 28 ft2 . Determine the dimensions of the rectangle if the width is 3 less than the length.
Answer:
4ft by 7 ft
Step-by-step explanation:
4*7=28 and 7-4=3 so the dimensions are 4ft by 7ft
The dimensions of the rectangle are 7 ft by 4 ft.
What is the area of the rectangle?
The area of a rectangle is defined as the product of the length and width.
Let x be the length of the rectangle.
The width of the rectangle is 3 less than the length, so the width can be represented as x-3.
The area of a rectangle is the length multiplied by the width, so:
Area = Length * Width
Area = x × (x-3)
Area = x² - 3x
We know that the area of the rectangle is 28 ft², so we can set the equation equal to 28 and solve for x:
x² - 3x = 28
x² - 3x - 28 = 0
Now we can use the quadratic formula or factoring method to find the solutions of x:
x = (3 ± √(3² - 41-28))/(2*1)
x = (3 ± √(9+112))/2
x = (3 ± √121)/2
x = (3 ± 11)/2
x = -4 or 7/2
The dimensions of the rectangle can't be negative, so the only valid solution is x = 7/2, which means the length of the rectangle is 7/2 ft and the width is (7/2 - 3) ft = -1/2 ft.
The width can't be negative, this answer is incorrect. So we have to check the other solution x = 7.
Therefore, the dimensions of the rectangle are 7 ft by 4 ft.
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An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. talk and the initial velocity of the ball is 40 ft per sec. The height s of the hall in feet is given by the equation s=-2.7t^2 + 40t+6.5 , where the number of seconds after the ball was thrown. After how many seconds in the ball 22ft above the moons surface?
Answer:
Step-by-step explanation:
Using the given equation, we can solve for t when s is equal to 22.
22 = -2.7t^2 + 40t + 6.5
Subtracting 6.5 from both sides, we get:
15.5 = -2.7t^2 + 40t
Adding 2.7t^2 to both sides, we get:
18.2t^2 = 15.5 + 40t
Subtracting 40t from both sides, we get:
18.2t^2 - 40t = 15.5
Dividing both sides by 18.2, we get:
t^2 - 2.2t = 0.855
Factoring, we get:
(t - 1)(t - 0.855) = 0
Setting each factor equal to 0 and solving, we get:
t = 1 and t = 0.855
Therefore, the ball will reach a height of 22ft after 1 second and 0.855 seconds.
(2x + 5y) * 3/x = ?
Answer:
(6x + 15y) / x
Step-by-step explanation:
(2x + 5y) * 3/x =
3 * (2x + 5y) / x =
(3 * 2x + 3 * 5y) / x ==> distribute 3 to 2x and 5y
(6x + 15y) / x ==> simplify
Last month the average price of gas was $2.20 per gallon. This month, the average price has increased by 75%. What is the average price of gas per gallon this month?
The average price of gas per gallon this month is
(don't forget $)
The average price of gas per gallon this month: $3.85 per gallon.
Define the term percentage increase?The degree, intensity, extent, or value of a variable can change to a greater or lesser extent as measured by percent rise and percent decrease. By comparing the original (or before) as well as final (or after) amounts in accordance with a predetermined formula, the figures are derived.For the stated question-
Average price of gas last month = $2.20 per gallon.
Percentage increase = 75%.
75% of 2.20 = 75*2.20 / 100
= 1.65
Average price of gas this month = $2.20 + $1.65 per gallon
= $3.85 per gallon
Thus, the average price of gas per gallon this month: $3.85 per gallon.
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use the row of numbers shown below to generate 12 random numbers between 01 and 99. 78038 18022 84755 23146 12720 70910 49732 79606 Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.
The formula to generate random numbers between 01 and 99 is (number*99/max_number)+1.
For the first number in the row, 78038, the calculation would be (78038*99/78038)+1 = 99.
For the second number in the row, 18022, the calculation would be (18022*99/78038)+1 = 25.
For the third number in the row, 84755, the calculation would be (84755*99/78038)+1 = 68.
For the fourth number in the row, 23146, the calculation would be (23146*99/78038)+1 = 17.
For the fifth number in the row, 12720, the calculation would be (12720*99/78038)+1 = 9.
For the sixth number in the row, 70910, the calculation would be (70910*99/78038)+1 = 89.
For the seventh number in the row, 49732, the calculation would be (49732*99/78038)+1 = 56.
For the eighth number in the row, 79606, the calculation would be (79606*99/78038)+1 = 97.
The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.
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how many -digit positive integers can be formed if the digits in odd positions (counting the rightmost digit as position ) must be odd and the digits in even positions must be even and positive?
The numbers that can be formed using the condition is [tex]20^n[/tex]
When a positive integer has n digits and the first digit is 2, all of the digits are prime, the probability that any two successive digits added together are prime is. Numbers from the set {1,3,5,7,9} must be used in the n odd locations, and numbers from the set {2,4,6,8} must be used in the n even spots.
We cannot include 0 in even positive integers because it is neither positive nor negative.
Order matters and repetitions are permitted.
So, here we are
possibilities are
[tex]5^n \times 4^n =20^n[/tex]
where n is the integral value
Therefore, the number of positive integers with digits and the specified restriction is [tex]20^n[/tex]
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type the coordinates of the images s', r' , t' for each of the following points under the translation defined by (x,y) (x+4,y-5)a) S(7,14) b) R(-8,-1) c) T(h,k) a) 5(7,14)--(Type an ordered pair) b) RI-B, -1)--(Type an ordered pair) c) Th.)--T(Type an ordered pair)
So, the coordinates of the images S', R', T' under the translation are (11,9), (-4,-6) and T'(h+4,k-5) respectively.
a) For the point S(7,14), we are given the translation defined by (x,y) -> (x+4, y-5). This means that for any point (x,y), we add 4 to the x-coordinate and subtract 5 from the y-coordinate to find the image of that point. Applying this transformation to the point S(7,14) gives us the image point S'(7+4, 14-5) = S'(11,9). So the coordinates of the image S' is (11,9)
b) For the point R(-8,-1), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point R(-8,-1) gives us the image point R'(-8+4,-1-5) = R'(-4,-6). So the coordinates of the image R' is (-4,-6)
c) For the point T(h,k), we are given the same translation defined by (x,y) -> (x+4, y-5). Applying this transformation to the point T(h,k) gives us the image point T'(h+4,k-5).
Here h and k are variables and we can't say the coordinates of image point T' without specific values of h and k. But we can say the transformation of point T as T'(h+4,k-5)
So, we have found the coordinates of the images S', R', T' under the translation defined by (x,y) -> (x+4, y-5) as (11,9), (-4,-6) and T'(h+4,k-5) respectively.
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Alexandra is fishing from a small boat. A fish swimming at the same depth as the hook
at the end of her fishing line is 5 meters away from the hook. If Alexandra is 13 meters away
from the fish, how far below Alexandra is the hook?
Answer:
12 m
Step-by-step explanation:
Here's a picture to show the problem.
boat
--------------------------------------------
~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~
\-----------Alexandra ---------/ surface of the water
|\
| \
| \
| \
d | \ 13 m
| \
| \
| \
| --- rt < \
hook -----|------------------------------ fish
5 m
There is a right angle at the hook. We have a right triangle with leg d, the distance we need to find, leg 5 m, and hypotenuse 13 m.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = √144
b = 12
Answer: 12 m
In scientific notation, we use powers of ______ to express very large or very small place values. Example: Look at this large number: 2,540,000.
We write numbers in scientific notation as the product of ____________ parts.
➔ The first part, called the first ________________, is a number between ______ and ______. ➔ The second part is a ____________ of ______.
To get the first factor, move the ________________ ________________ in the standard notation so there is just one ________________ number to the ___________ of the decimal point.
Answer:
see attached
Step-by-step explanation:
You want to fill in the blanks to complete the description of writing a number in scientific notation.
Scientific notationA number written in scientific notation can be described as a coefficient times a power of ten (2nd attachment). Different terminology is used by different authors to describe these parts.
Sometimes the entire coefficient is also called the "mantissa." Sometimes, the term "mantissa" is used to refer to the fractional part of the coefficient, the digits to the right of the decimal point. Your curriculum calls the coefficient the "first factor."
The power of ten is chosen so that the first factor is always a number greater than or equal to 1, but less than 10.
The power of 10 has an exponent, also called the "characteristic". Your curriculum calls the combination of base (10) and exponent the "second factor." The exponent is equal to the exponent of the place value multiplier of the most-significant digit when the number is written in standard form (3rd attachment).
DescriptionThe filled-in description is shown in the first attachment. You will notice that its wording helps you fill in the blanks. It asks you how many parts there are to the number, then refers to them as the "first part" and the "second part." It asks you what the parts are called, then refers to the first one as the "first factor."
The given example in scientific notation is ...
[tex]2.54\times10^6[/tex]
The exponent of 6 corresponds to the 6 little left-arrows in the figure in your problem statement. It is the power of 10 that represents "millions," the place-value multiplier of the most-significant digit of the number two million five hundred forty thousand.
Elena is designing a logo in the shape of a triangle. She wants the logo to have an area of 12 square inches. She draws bases of different lengths and tries to compute the height for each base. Write an equation that Elena can use to find the height, h, for a base that is b inches long.
An equation that Elena can use to find the height 'h' is h = 24/b.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a triangle is (1/2)×base×height.
Given, Elena is designing a logo in the shape of a triangle having an area of 12 square inches.
Therefore,
(1/2)×base×height = 12.
b×h = 12×2.
b×h = 24.
So, Elena can use the following equation to get the height 'h',
h = 24/b.
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The following data represents the age of 30 lottery winners. Given the frequency distribution for the data
Solving the provide question, we can say that frequency distribution 70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).
what is frequency distribution?In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution.
Here,
A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data.
The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9,
70 years or older is 0.1333, 4/30, or 13.3% younger than 40 years old is 8/30, 0.2666, or 0.4000. (there are 12 under 50 out of 30 altogether).
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The complete question is "The following data represents the age of 30 lottery winners .Given the frequency distribution for the data,
Each column (left to right) is as follows: Age, Frequency, Relative Frequency, Cumulative Relative Frequency
[20,29] 1 0.0333 0.0333
[30,39] 7 0.2333 0.2666
[40,49] 4 0.1333 0.3999
[50,59] 5 0.1667 0.5666
[60,69] 9 0.3 0.8666
[70,79] 3 0.1 0.9666
[80,89] 1 0.0333 0.9999
What is the frequency of lottery winners of age between 19 and 40?
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