Answer: 1
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}lg\frac{25}{4} -2lg\frac{4}{5} +lg\frac{320}{125}=\\\\lg\sqrt{\frac{5^2}{2^2} } -lg(\frac{4}{5})^2+lg\frac{5*64}{5*25}=\\\\lg\sqrt{(\frac{5}{2})^2 } -lg\frac{4^2}{5^2} +lg\frac{64}{25}=\\\\[/tex]
[tex]lg\frac{5}{2} -lg\frac{16}{25}+lg\frac{64}{25} =\\\\ lg\frac{5}{2}+lg\frac{64}{25} -lg\frac{16}{25} =\\\\lg\frac{5*64}{2*25} -lg\frac{16}{25}=\\\\ lg\frac{5*2*32}{2*5*5}-lg\frac{16}{25}= \\\\lg\frac{32}{5}-lg\frac{16}{25}=\\\\lg\frac{32*25}{5*16}=\\\\lg\frac{16*2*5*5}{5*16} =\\\\lg(2*5)=\\\\lg10 =\\\\1[/tex]
The data set represents the number of students per faculty member for 20 public colleges 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 20 15. Use five classes.
The median and mode of the data set is
median =16mode =15This is further explained below.
What are the median and mode?Generally, median = value of [tex]$\left(\frac{n+1}{2}\right)^{\text {th }}$[/tex] the position
- the value of [tex]$\left(\frac{20+1}{2}\right)^{\text {th }}$[/tex] the position
= value of the position
= value of [tex]$10^{\text {th }}$[/tex] position +0.5 (value of 10^th position - value of 9th position)
Arranging the data below.
8,10,13,15,15,15,15,15,16,16,16$, $17,18,19,20,20,21,29,28,30
median =16+0.5(16-16)
median =16
mode = { value of maximum frequency }
mode =15
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The data set represents the number of students per faculty member for 20 public colleges 13 15 15 8 16 20 28 19 18 15 21 23 30 17 10 16 15 16 2[tex]$(10.5)^{\text {th }}$[/tex]0 15. Use five classes.
What is the median and mode of the data
If ST 13 and RT = 46, find RS. Use the number line below.
R
RS=
(Type an integer or a decimal.)
CODO
So
The length of the line segment RS is 33 ;By considering the line segment RT of length 46 units and line segment ST of length 46 units.
Given a line segment RT of length 46 units and line segment ST of length 46 units and asked to find the length of line segment RS.
Given the number line RT;
RT=RS+ST
⇒46=RS+13
⇒RS=33
The length of line segment RS is 33 units.
Therefore,The length of the line segment RS is 33 ;By considering the line segment RT of length 46 units and line segment ST of length 46 units.
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You are solving a measurement problem where the numbers 4.514 x 10^−3, 3.09 x 10^7, and 2.80 x 10^3 are multiplied. How many significant digits should the product have?
The significant digits from the product of the values are 7
What are significant digits?It is important to note the following;
Non-zero digits are always significantZeros between two significant digits are also significantGiven the values;
4.514 x 10^−33.09 x 10^72.80 x 10^3Let's find the product
4.514 x 10^−3 × 3.09 x 10^7 × 2.80 x 10^3
39. 055128 × 10^-3 + 7 + 3
39. 055128 × 10^7
The significant digits are 7
Thus, the significant digits from the product of the values are 7
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Which of the following describes the end behavior of the function f(x) = root(x, 3) - 4 as approaches infinity ?
Answer:1) An operator is missing in your statement. Most likely the right expression is:
Step-by-step explanation:
2x
f(x) = -------------
3x^2 - 3
So, I will work with it and find the result of each one of the statements given to determine their validiy.
2) Statement 1: The graph approaches 0 as x approaches infinity.
Find the limit of the function as x approaches infinity:
2x
Limit when x →∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
3 - 3/∞ 3 - 0 3
Therefore the statement is TRUE.
3) Statement 2: The graph approaches 0 as x approaches negative infinity.
Find the limit of the function as x approaches negative infinity:
2x
Limit when x → - ∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
3 - 3/(-∞) 3 - 0 3
Therefore, the statement is TRUE.
4) Statement 3: The graph approaches 2/3 as x approaches infinity.
FALSE, as we already found that the graph approaches 0 when x approaches infinity.
5) Statement 4: The graph approaches –1 as x approaches negative infinity.
FALSE, as we already found the graph approaches 0 when x approaches negative infinity.
Solve inequality.
9 a<45
To solve the inequality, divide both sides by 9. The solution is a < 5 or (∞, 5)
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
9a < 45
Notice that the variable, a, is already isolated on the left side. Divide both sides by 9: (Note that the inequality sign is not flipped since 9 is a positive number)
9a : 9 < 45 : 9
a < 5
Using the interval notation, the solution is (∞, 5)
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Two students calculated the area of a polygon in the coordinate plane using different strategies. Explain the two methods. Which method do you prefer and why?
From the two methods to find the surface area, the method used by student 2 is most desirable as the smaller regular objects are easily interpreted to solve.
What is the area of the composite figure?
We want to find the area of the irregular composite polygon figure. Now, there are two ways to do this which are;
1) To divide the internal part of the irregular polygon into regular shapes and find the respective areas and add up to get the total area.
2) To inscribe the irregular polygon into a regular shape like a rectangle or square, Then divide into regular shapes the external parts of the irregular polygon that share boundary with the bigger regular shape. Then add up the areas and subtract from the area of the big regular shape.
Now, looking at the two options to find the surface area, the method used by student 2 is most desirable as the smaller regular objects are easily interpreted to solve.
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Which domain would allow the inverse of y =cos(x)
The inverse of y = cos(x) could be a function in domain (A) [0, π].
What are domain and range?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f(x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value. To obtain the domain and range, simply solve the equation y = f(x) to determine the values of the independent variable x. To calculate the function's range, simply express x as x=g(y) and then find the domain of g(y).So, domain of y =cos(x):
The inverse cosine function has a domain of [1,1] and a range of [0, π].Therefore, domain (A) [0, π] would allow the inverse of y = cos(x) to be a function.
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The complete question is given below:
Which domain would allow the inverse of y = tan(x) to be a function?
A) [0, π]
B) [0, 2π]
C) (-∞, ∞)
D) [-π/2, π/2]
82.156-41.31-29.16 (Estimated)
Answer:Your answer would be 11.686
Step-by-step explanation:Please give brainliest if right.
Answer:
The answer is or, should be 11.686
the product of negative six and a number is thirty
Answer:
-6n = 30
Step-by-step explanation:
Solve inequality.
-b/5 ≥ -6
To solve the inequality, multiply both sides by (-5). The solution is b ≤ 30 or (∞, 30]
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
-b/5 ≥ -6
Notice that the variable, b, is already isolated on the left side. Multiply both sides by (-5) and flip the sign of the inequality ( since we multiply it by a negative number):
-b/5 . (-5) ≤ -6 . (-5)
b ≤ 30
Using the interval notation, the solution is (∞, 30]
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a certain european automobile has a gas mileage of 19 km/l. what is the gas mileeage in miles per gallon
The gas mileage in miles per gallon = 44.690mi/gal.
What is a vehicle's mileage?A vehicle's mileage is the number of miles it can drive solely on a single gallon or liter of fuel. They are ready to pay up to $500 more for fuel-efficient vehicles. 3. a noncountable noun.
How can I figure out my mileage?Subtract the original tachometer reading from either the new one to get the miles traveled first from the trip odometer. Divide the distance traveled by the number of gallons used to fill the tank. As a result, your car's overall kilometers per gallon yield for that driving period will be calculated.
According to the given data:1 km = 0.621371 mi
1 L = 0.264172 gal
calculating that the amount of gas mileage in miles per gallon by multiplying with distance and gas used per miles.
19 km/L = (19*0.621371)/0.264172 mi/gal
= 44.690 mi/gal
the gas mileage in miles per gallon = 44.690mi/gal.
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Complex numbers
I need help!
Answer:
1. i
2. -1
Step-by-step explanation:
what is the slope intercept form of y=-3x+1
Answer:that is the slope intercept form
Step-by-step explanation: slope intercept form is y=mx+b
Determine if the function ƒ(x) = 3x5 – 9 is even, odd, or neither.
A) Neither odd nor even
B) Odd
C) Not enough information given
D) Even
Please help!!
The function f(x) = 3[tex]x^{5}[/tex] -9 given in the question is neither an even function nor an odd function
The function f(x) = 3[tex]x^{5}[/tex] -9 cannot be an even function because the exponential power is not in the multiples of 2 and there is second step to check whether the function is even function or not if f(x)= f(-x) but this cannot be checked here because it proved not be an even function in the first step itself
The function f(x) = 3[tex]x^{5}[/tex] -9 is odd function only if -f(x) = f(-x)
so lets check f(1)= 3([tex]1^{5}[/tex]) -9 = 3-9 = -6
now f(-1) = 3(-[tex]1^{5}[/tex]) -9 =-3-9=-12
and -f(1) = 6
Hence the function given in the question is neither an even function nor an odd function
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Please help with all answers on this. And please explain how you got those answers!!!
8) The part shared by vector BC and vector CB is called the magnitude of the line segment.
9) (a) Another name for ∠C is ∠ACB.
(b) ∠ADF and ∠BDC are two angles with point D as the vertex.
(c) Another name for ∠1 is ∠FBD.
(d) Another name for ∠2 is ∠FDB.
8) There are two vectors : vector BC and vector CB.Both the vectors have the same magnitude, i.e., length, but opposite directions to each other.Hence, the vector BC and vector CB have a common magnitude, which is equal to the length of the line segment joining the points B and C.9) According to the given figure,a) The angle ∠C is formed using line segments CA and CB. So, another name for ∠C is ∠ACB.b) ∠ADF and ∠BDC are two angles with point D as the vertex.c) The angle ∠1 is formed using line segments BF and BD. So, another name for ∠1 is ∠FBD.d) The angle ∠2 is formed using line segments DF and DB. So, another name for ∠2 is ∠FDB.To learn more about angles, visit :
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Brandon wants to ride his bicycle 21 miles this week. He has already ridden 6 miles. If he rides for 5 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Equation: 5x+6=21
Solve: 5x+6=21
-6= -6
5x=15
5x/5 = 15/5
x =3
Answer: x = 3
Using proportions, it is found that he would have to ride his bike 3 miles a day to meet his goal.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
He has already ridden the bike for 6 miles, and needs to run 21 - 6 = 15 miles in 5 days, hence the average is given by:
x = 15/5 = 3 miles a day.
He would have to ride his bike 3 miles a day to meet his goal.
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8 divided by $3.09 round to the nearest cent
Answer: $0.39
Step-by-step explanation:
3.09/8=
0.38625=
0.38625=$0.39
Can someone help??????
Answer:
rotate 180
Step-by-step explanation:
because you can try it urself
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-3y = -x - 7
Answer:
spam question
not able to answer
Step-by-step explanatio
mark me
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Trent wants to buy 2 packs of trading cards for 3 dollars each. The trading card packs that Trent normally buys tend to come in packs of 6, 10, 12, or 15 cards. After selecting 2 packs, Trent found that the first pack of cards cost 25 cents per card, and the second pack cost 30 cents per card. Trent uses this information to write the equations below in order to compare c, the number of cards in each pack. There are cards in the first pack, and there are cards in the second pack. The first pack has more cards than the second pack.
A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers (numerals) only. This ultimately implies that, a numerical data refers to a type of data set consisting of numbers (numerals) rather than words.
Based on the information provided, the number of cards (c) in each pack can be modeled by the following mathematical expression (equation):
Note: 100 cent is equal to 1 dollar.
First pack: 0.25c = 3
Second pack: 0.3c = 3
Now, we can determine the number of cards (c) in the first pack as follows:
0.25c = 3
c = 3/0.25
Number of cards, c = 12 cards.
For the second pack, we have:
0.3c = 3
c = 3/0.3
Number of cards, c = 10 cards.
Therefore, there are 12 cards in the first pack, and there are 10 cards in the second pack.
Difference = First pack - Second pack
Difference = 12 - 10
Difference = 2 cards.
In conclusion, the first pack has 2 more cards than the second pack.
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Solve the equation. − 3 ( 3 − 4 x ) = 5 ( x − 1 ) + 7 ( x + 2 ) Show each step you used to solve the equation. Determine whether the equation has one solution, no solution, or infinitely many solutions. Explain your reasoning.
Answer:
0=18
Step-by-step explanation:
-3(3 - 4x) = 5(x - 1) + 7(x + 2)
-3( -4x + 3) = 5(x - 1) + 7(x + 2)
Find the quotient of The quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.. Write the final answer in scientific notation.
6 x 1048
6 x 1024
6 x 100
6 x 10−48
The quotient of the given problem using laws of exponents is; 6 * 10⁰
How to use the law of exponents?
We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.
This is;
(30 * 10⁻²⁴)/(5 * 10⁻²⁴)
Now, we can break this down into like terms to get;
(30/5) * (10⁻²⁴/10⁻²⁴)
= 6 * 1
Now, 1 can also be written as;
10⁰ = 1
Thus, the solution of the given problem is; 6 * 10⁰
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Valeria bought a 9 foot length of ribbon from which she wants to cuut 2/3 foot pieces how many pieces can she cut what will be the length of the leftover pirece of ribbon?
The number of pieces she can cut is 13 and the length of the leftover piece of ribbon is 1/3 feet, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given:
Total length of ribbon = 9 feetLength of each piece of ribbon = 2/3 feetTo find: Number of pieces of ribbon cut and length of leftover pieces.
Finding:
Let x be the number of pieces of ribbon that can be cut.
Then, according to question, by basic algebra:
2x/3 = 9
=> x = [tex]\frac{27}{2}=13\frac{1}{2}[/tex]
That is, the number of pieces of ribbon that can be cut are 13
The leftover length of ribbon is then given by:
9 - 13 (2/3) = 9 - (26/3) = 1/3
That is, the leftover length of ribbon is 1/3 feet.
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Rays DA and DC are perpendicular. Point B lies in the interior of {angle]ADC. If m[angle]ADB = (3a + 10) degrees and m[angle]BDC = 13a degrees, find a, m[angle]ADB, and m[angle]BDC
Applying the definition of the angle formed by perpendicular lines, the measures are:
a = 5
m<ADB = 25°
m<BDC = 65°
What is the Angle Formed by Perpendicular Lines?When two lines intersect perpendicularly at a point, they form a right angle, which is equal to 90 degrees.
Thus, angle ADC is a right angle. Therefore, angles ADB and BDC are complementary angles. This means that:
m<ADB + m<BDC = 90°
Substitute
3a + 10 + 13a = 90
16a + 10 = 90
16a = 90 - 10
16a = 80
16a/16 = 80/16
a = 5
m<ADB = (3a + 10) = 3(5) + 10 = 25°
m<BDC = 13a = 13(5) = 65°
Thus, applying the definition of the angle formed by perpendicular lines, the measures are:
a = 5
m<ADB = 25°
m<BDC = 65°
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1/3y^2+2/3y+1 is it a polynomial function
Answer:
yes it is
Step-by-step explanation:
because it has the leading power of x as 2
A small insect viewed through a convex lens is 1.8 cmcm from the lens and appears 2.5 times larger than its actual size. part a what is the focal length of the lens?
Answer:
4.50
Step-by-step explanation:
There's 2 total decimal places in both numbers.
Ignore the decimal places and complete the multiplication as if operating on two integers.
1 8
× 2 5
___________________
+ 9 0
+ 3 6
___________________
= 4 5 0Rewrite the product with 2 total decimal places.
Answer = 4.50
Therefore:
1.8 × 2.5 = 4.50
The archery club competed in a tournament. Each archer shot 6 arrows in 5 minutes.
The numbers of arrows in the inner ring of the target, or bull’s-eye, are recorded in
the table. Which archer had an average rate that can be represented as a terminating
decimal?
Answer:
Step-by-step explanation:
Answer
the number of arrow in inner ring is i don't know
Stepby-step explanation:
reflection across y = x
(2,-2)
(3,-5)
(-2,-4)
About how many times greater is the number
8.4493E13 than the number 7.994E-2 when
displayed on a calculator?
The number of times the number 8.4493E13 isgreater than the number 7.994E-2 when displayed on a calculator is 1.05696E15.
How do we use division to get the number times a number is greater than the other?8.4493E13 = 84,493,000,000,000
7.994E-2 = 0.07994
The number of times the number 8.4493E13 isgreater than the number 7.994E-2 can be obtained by dividing 8.4493E13 by 7.994E-2 as follows:
Number of times greater = 8.4493E13 / 7.994E-2 = 84,493,000,000,000 / 0.07994
Number of times greater = 1,056,955,216,412,310
When displayed on a calculator, we will have:
Number of times greater = 1.05696E15
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approximately 60% of mathematics students do their homework on time. in a class of 100 students, what is the mean, variance, and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution? answer choices rounded to the nearest whole number
The mean of distribution will be 60, standard deviation will be 5 and variance will be 24
Given,
The total number of students (n)= 100
The probability of students, completing their homework on time (p)= 60%
= 60 / 100
= 0.6
According to the binomial distribution,
mean = np
= 100 × 0.6
= 60.
Variance = np× (1 - p)
= 100 × 0.6 × 0.4
= 24
Standard deviation = [tex]\sqrt{variance}[/tex]
= [tex]\sqrt{24}[/tex]
= 4.89 or 5
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