Properties of Logarithms are as follows: Product Property, Quotient Property, Power Rule, Change of base rule, Reciprocal Rule, Natural logarithmic Properties and Number raised to log property.
The properties of the logarithms are used to expand a single log expression into multiple or compress multiple log expressions into a single one. Seven logarithmic properties are as follows:
Product Rule : [tex]log_{a}mn = log_{a}m + log_{a}n[/tex]
Quotient Rule : [tex]log_{a}\frac{m}{n} = log_{a}m - log_{a}n[/tex]
Power Rule : [tex]log_{a}m^{n} = n* log_{a}m[/tex]
Change of base rule : [tex]log_{a}m = \frac{log_{n}m}{log_{n}a}[/tex] Where [tex]m, n, a[/tex] are positive integers and [tex]n\neq 1, a\neq 1[/tex]
Reciprocal Rule : [tex]log_{a}m = \frac{1}{log_{m}a}[/tex] where [tex]m,a[/tex] are positive integers other than 1.
Natural logarithmic Properties: [tex]ln(mn) = ln(m) + ln(n)[/tex]
[tex]ln\frac{m}{n} = ln(m) - ln(n)[/tex]
[tex]ln(m^{n}) = n* ln(m)[/tex]
The number raised to log : [tex]a^{log_{a}m} = m[/tex]
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3 3 Carl had 7 litres of juice in a container. He poured of the total quantity into 4 15 similar bottles. How many mililitres of juice does each bottle contain?
1000 milliliter make up one liter. Therefore, we can multiply the volume by 1000 to get the value in milliliter for any liquid capacity expressed in liter.
What is a milliliter?Knowing the relationship between the two units will make converting between liter and milliliter simple. Both liters and milliliter are measurements of a liquid's volume. The basic measure of liquid capacity is the liter.
The liquid volume can also be measured in milliliter, centiliters, and kiloliters. All of these units have different values from one another.
Similar to milliliters, liters also denote volume, however, one liter is equivalent to one thousand milliliters (1 L = 1000 mL). The formula below can be used to translate a value from liters to milliliter:
1000 milliliter make up one litre. Therefore, we can multiply the volume by 1000 to get the value in milliliter for any liquid capacity expressed in liters.
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What is the factored form of 4x² 9?
After taking the common, the factored form of [tex]4x^2-9[/tex] is (2x+3)(2x-3).
In the given question, we have to find the factored form of [tex]4x^2-9[/tex].
The following is how we factor the GCF out of a polynomial:
(1) Determine the polynomial's GCF for each term.
(2) Present each term as the GCF and another factor's product.
(3) To factor out the GCF, use the distributive property.
To solve this question we use the formula [tex](a^2-b^2) = (a+b)(a-b)[/tex]
We can write [tex]4x^2-9[/tex] as
[tex]4x^2-9[/tex] = [tex](2x)^2-(3)^2[/tex]
[tex]4x^2-9[/tex] = (2x+3)(2x-3)
Hence, the factor form of [tex]4x^2-9[/tex] is (2x+3)(2x-3).
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The complete question is:
What is the factored form of [tex]4x^2-9[/tex]?
A set of sweater prices are normally distributed with a mean of 58 5858 dollars and a standard deviation of 5 55 dollars. What proportion of sweater prices are between 48. 50 48. 5048, point, 50 dollars and 60 6060 dollars?.
The proportion of sweater prices falling between 48.50 dollars and 60 dollars can be found by calculating the area under the normal curve for the two endpoints which is 78.38%
This can be calculated using the z-score formula, which is defined as
(x-μ)/σ, where x is the value of interest, μ is the mean, and σ is the standard deviation.
For 48.50 dollars, the z-score is
(48.50-58)/5.5 = -1.454545.
For 60 dollars, the z-score is
(60-58)/5.5 = 0.363636.
Using a z-table, the proportion of sweater prices between 48.50 and 60 dollars is 0.7838, or 78.38%.
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Which operation must be done on both sides of the given equation in order to solve them 1 8x =24?
What is the image of (3, 3) after a dilation by a scale factor of centered at the origin
The image point of (3, 3) is (3/n, 3/n).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given point (3, 3).
Let n be the scale factor.
The image of (3, 3) after dilation,
by a scale factor of n centered at the origin will be,
= (3/n, 3/n).
= (3/n, 3/n).
Therefore, (3/n, 3/n) is the image point.
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write a scientific national 6.3×10^3
The scientific notation 6.3 × 10³ can be written as 6300 in regular notation
Scientific Notation is a way of writing big and small numbers very easily. It is also known as the Standard form in Britain. It is used when a number can be multiplied by a power of 10.
When we write a scientific notation, it has two parts.
Only the digits are written with decimal points put after the first digit.The digits are followed by ×10 to a power (eg 10² or 10³) that shows how many places exactly we should move our decimal point to get the actual number.In the question instead of writing 6.3 × 10³, we can also write 6.3 × 10^4 which is easy to type but means the same.
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The complete question will be:
How is the Scientific Notation 6.3 × 10³ can be written as regular notation?
21
What is the area of the shaded region?
sq units
= 7 sq units
Answer: 7 sq units
Step-by-step explanation:
I'm pretty sure that this is right
the length of a rectangular is one less than twice the width. Find the length + width, if the perimeter is 40
Answer:
[tex]\huge\boxed{\sf Length = 13, \ \ Width = 7}[/tex]
Step-by-step explanation:
Let the length of rectangle be x and width be y.
Condition # 1:x = 2y - 1 --------------(1)
Condition # 2:2x + 2y = 40
Take 2 as a common factor2(x + y) = 40
Divide both sides by 2x + y = 40/2
x + y = 20 -----------(2)
Put Eq. (1) in Eq. (2)2y - 1 + y = 20
2y + y - 1 = 20
3y - 1 = 20
Add 1 to both sides3y = 20 + 1
3y = 21
Divide both sides by 3y = 21/3
y = 7Put y = 7 in Eq. (1)x = 2(7) - 1
x = 14 - 1
x = 13So,
Length = 13Width = 7[tex]\rule[225]{225}{2}[/tex]
Kellan burns 348
calories in 3 hours. How
long will it take her to
burn 870 calories?
Answer:
7.5 Hours
Step-by-step explanation:
Given:
Kellan burns 348 calories in 3 hours.
Question:
How long will it take her to burn 870 calories?
Solve:
Since, it given that KelIan burns 348 calories in 3 hours. Then we need to find how much KeIlan burns per hour.
To do that, divide the calories by the hours.
Thus, 348 divided by 3 which equals 116.
Now knowing that KeIlan burns 116 per hour will help us know how much hours it would take to burn up 870 calories.
To do that,
We have to divide 870 by 116 which equals 7.5.
Hence, it would take 7.5 hours to burn 870 calories.
RevyBreeze
After completing your analysis of the rating system, you determine that any rating greater than or equal to 3. 75 points can be considered a high rating. You also know that chocolate and tea considers a bar to be super dark chocolate if the bar's cocoa percent is greater than or equal to 80%. You decide to create a new data frame to find out which chocolate bars meet these two conditions. Assume the first part of your code is: best_trimmed_flavors_df <- trimmed_flavors_df %>% you want to apply the filter() function to the variables cocoa. Percent and rating. Add the code chunk that lets you filter the new data frame for chocolate bars that contain at least 80% cocoa and have a rating of at least 3. 75 points.
The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.
filter(cocoa.percent >= 80, rating >= 3.75)
1. Start by creating a new data frame called best_trimmed_flavors_df that uses the trimmed_flavors_df data frame
2. Use the %>% operator to pipe the trimmed_flavors_df data frame into the new data frame
3. Use the filter() function to filter the new data frame for chocolate bars with at least 80% cocoa and a rating of at least 3.75 points
The code creates a new data frame that filters for chocolate bars that contain at least 80% cocoa and have a rating of at least 3.75 points.
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What is the example of SAS congruence?
The SAS congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
First, let's take two triangles ABC and DEF. If the side lengths of both triangles are the same (AB = DE, AC = DF) and the included angle (angle A) is the same in both triangles (angle A = angle D) then the two triangles are congruent. This is known as the SAS congruence.
To prove the SAS congruence, we can use the Law of Congruent Triangles. This law states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
To prove this, we can use the Side-Angle-Side Postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
This means that if the side lengths of both triangles are the same (AB = DE, AC = DF) and the included angle (angle A) is the same in both triangles (angle A = angle D) then the two triangles are congruent. This is known as the SAS congruence.
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Question 3 of 10
What is the solution to the system of equations?
-5
y = 3x + 1
5.
-5.
OA. (-2, 1)
OB. (1, -2)
OC. (-2,-1)
OD. (-1,-2)
5
y=-2x-4
Option D: The solution of the system of equation is (-1,-2)
What is System of Equation ?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
The equations are :
y = 3x + 1 ⇒ y - 3x = 1 (i)
y = -2x -4 ⇒ y + 2x = -4 (ii)
Subtracting (i) from (ii) we get ,
2x +3x = -4 -1
⇒ 5x = -5
⇒x = -1
for x = -1
y = 3x + 1 = 3*(-1) + 1 = -2
The solution of the system of equation is (-1,-2)
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Select the statements that are true based on the following given information. D = {x | x is a whole number} E = {x | x is a perfect square < 36} F = {x | x is an even number between 20 and 30} The expression D ∪ E = E. E ∪ (D ∩ F) is {25}. F ⊂ D (E ∩ F) is the empty set. Set E is infinite.
The statements that are true based on the following given information is F ⊂ D (E ∩ F) is the empty set.
What is a set?You should understand that a set is the collection of different items or numbers to form a group.
The given parameters that will help us to understand what a set is is given below
D = {x | x is a whole number}E = {x | x is a perfect square < 36}F = {x | x is an even number between 20 and 30}The elements of these sets are given as follows
D= {1,2,3,4,5,6,7,8,9, ...}
E= {4,9,16,25}
F= {20,22,24,26,28,30)
D ∪ E = {1,2,3,4,5,,,,,9......16....25...) ≠ E
Also
E∪(D∩F) =
First find (D∩F) =
(D∩F) = but E∪(D∩F) = Ф
Also, F ⊂ D (E ∩ F)
E∩F = Ф and F⊄E
Therefore it is an empty set
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What is the domain and range of a logarithmic function f/x LOGB X?
The domain of the function [tex]f(x) = log_{b} x[/tex] is (0, ∞) and the range of the function is (-∞, ∞) which means that all real numbers is the range for the given function.
The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.
Given, [tex]y = log_{b} x[/tex]
To calculate the domain of given function we put argument greater than 0
[tex]x > 0[/tex]
Now we have to express the domain in the form of interval
Domain = (0, ∞)
Now put the domain in logarithmic expression to get range:
∴ Range = (-∞, ∞)
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Wednesday was 5 degrees warmer than Tuesday.
What was the temperature on Wednesday?
Answer: The temperature on Wednesday is 5 degrees hotter than Tuesday
Step-by-step explanation:
all numbers with an absolute value greater than 3 but less than 7
The solution of the statement is,
⇒ - 6, - 5, - 4, - 4, 5 , 6
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The algebraic statement is,
''All numbers with an absolute value greater than 3 but less than 7''.
Now,
The mathematical expression of the given statement is,
⇒ 3 < |x| < 7
Thus, All the possible values are;
⇒ |x| = 4, 5, 6
⇒ x = - 6, - 5, - 4, - 4, 5 , 6
Thus, All the solution of the given statement is,
⇒ x = - 6, - 5, - 4, - 4, 5 , 6
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Factorise : 625² − 121² by using suitable identity
Answer:
(625 - 121)(625 + 121)
Step-by-step explanation:
625² - 121² ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
then
625² - 121²
= (625 - 121)(625 + 121) ← in factored form
The Hendricksons are in charge of bringing treats for 505050 football players. They brought 333 coolers of popsicles and 222 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat
If the Hendricksons are in charge of bringing treats for 505050 football players. The statement that best predicts how many football players will get a popsicle is: C. There will be exactly 30 football players who get a popsicle.
How to find the football players that will get a popsicle?First step is to find the total cooler
Total cooler = 3+2
Total cooler = 5
Since play we have 3:2 type of color
Hence,
Number of player with popsicles = 3/5 × 50
Number of player with popsicles = 30
Number of player with sandwiches = 2/5 × 50
Number of player with sandwiches = 20
Therefore the correct option is C.
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The complete question is:
The Hendricksons are in charge of bringing treats for 50 football players. They brought 3 coolers of popsicles and 2 coolers of ice cream sandwiches. Each player is going to randomly select a cooler from which to get their treat. Which statement best predicts how many football players will get a popsicle? Choose 1 answer:
A. There will be exactly 20 football players who get a popsicle.
B. There will be close to 20 football players but not exactly 20 who get a popsicle.
C. There will be exactly 30 football players who get a popsicle.
D. There will be close to 30 football players who get a popsicle but not exactly 30 who get a popsicle
Multiply.
15x(1/3)
A)1/45
B)1/5
C)5
D)45
Answer:
5
Step-by-step explanation:
15/3 = 5
Answer:
c. 5
Step-by-step explanation:
15 ×1/3
= 5
note: three goes into fifteen 5 and goes into itself 1 living 5 .
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
1
1
a.
b.
c.
d.
y = f(x+3)
y = f(x-3)
y + 3 = f(x)
y-3 = f(x)
Answer:
The red graphed equation is f(x) = y + 3
Step-by-step explanation:
The red graph is +3 units greater than the black graph.
Red = f(x)+3
The nomenclature is confusing, but if we say the black graph is given by y, the red graph would be y+3. This looks like c, although is is not clear what f(x) refers to.
See the attached worksheet.
Lucía and Quinn train for a bike race. Lucía bikes 46 miles in 240 minutes.
Quinn bikes 51 miles in 5 hours. Who bikes at a faster rate? Show your work
Answer:
Lucia has a faster rate.
Step-by-step explanation:
Lucia's unit rate
46/4 = 11.5 240 minutes is the same as 4 hours 240/60
Lucia can travel 11.5 miles in 1 hour.
Quinn's unit rate:
51/5 = 10.2
Quinn can travel 10.2 miles in 1 hour
Answer:Lucia is faster
Step-by-step explanation:
speed= distance / time Lucia:46miles /240
What is the volume of each cylinder?
The cylinder's capacity is 1.25 x [tex]10^{5}[/tex] and 3.28077× [tex]10^{5}[/tex] its radius and height are indicated in the illustration, accordingly.
what is volume ?The area contained by an object's limits in three-dimensional space is referred to as its volume. Another name for it is an object's capacity. The quantity of space a 3-dimensional item occupies is another way to quantify volume. A vessel's liquid content is measured in standard units and is known as the liquid measurement. Additionally, we call it the vessel's "volume" or "capacity." Both the juice bottle and the infant milk bottle have milliliter measuring marks.
given
a) r = 20 cm
h = 100 cm
V = [tex]\pi r^{2}h[/tex]
V = [tex]\pi * 20^{2} * 100[/tex]
= 1.25 x [tex]10^{5}[/tex]
b) d = 118 m = 118 / 2 = 59 m
h = 30 m
V = [tex]\pi r^{2}h[/tex]
V = [tex]\pi * 59^{2} * 30[/tex]
= 3.28077× [tex]10^{5}[/tex]
The cylinder's capacity is 1.25 x [tex]10^{5}[/tex] and 3.28077× [tex]10^{5}[/tex] its radius and height are indicated in the illustration, accordingly.
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Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make copper balls that have a radius of 6 in. If copper costs $0.75 per in^(3), how much will the copper cost to make one ball? Use 3.14 for \pi , and do not round your answer.
The cost of making the ball is $678.24.
What is the cost of the ball?
We are told in the question that Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make copper balls that have a radius of 6 in. If copper costs $0.75 per in^(3).
Now we have to obtain the volume of the ball. Let us recall that the ball has the shape of a sphere hence volume of a sphere is;
V = 4/3πr^3
V = 4/3 * 3.14 * (6)^3
V = 904.32 in^3
The cost of the ball is; 904.32 in^3 * $0.75
= $678.24
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I NEED HELP ASAP what is -5/9 divided by (-1/3)?!
answers choices
- 5/27
- 1 2/3
- - 1 2/3
- 1 1/3
I hope you’re having an amazing day! :)
The simplified form of the expression -5/9 ÷ -1/3 is 1 2/3.
What is -5/9 divided by (-1/3)?Given the expression in the question;
-5/9 ÷ -1/3
To divide a fraction by another fraction, multiply by its reciprocal.
Hence;
-5/9 × -3/1
Note that; - × - = +
5/9 × 3/1
Multiply 5 and 3
( 5 × 3 ) / 9
15 / 9
Cancel out the common factor of 3
5/3
Convert the improper fraction
5/3
1 2/3
Therefore, the result is 1 2/3.
Option B) 1 2/3 is the correct answer.
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q17 ANSWER FOR 20 POINTS
Answer:
18√3
Step-by-step explanation:
To simplify the expression 2√48 + 5√12, you can first simplify each of the terms inside the parentheses. The square root of 48 is equal to 4*√3, so you can rewrite the first term as:
2√48 = 2*(4√3) = 8√3
The square root of 12 is equal to 2*√3, so you can rewrite the second term as:
5√12 = 5*(2√3) = 10√3
Now that you have simplified the terms inside the parentheses, you can add them together to get:
(8√3) + (10√3) = 18*√3
So, the simplified expression is equal to 18*√3
Solve the following equation:
|2x-5|=|7x+10|
The x values after solving the equation |2x - 5| = |7x + 10| are -3 and [tex]\frac{-5}{9}[/tex].
As per the given data, the given equation is:
|2x - 5| = |7x + 10|
Here we have to solve the given equation.
Which means we have to find the value of x.
|2x - 5| = |7x + 10|
Remove the mod on either side of the equation.
When we remove mod ± should be added to another side of the equation.
We get:
2x - 5 = ± (7x + 10)
When it is positive, we get:
2x - 5 = (7x + 10)
7x - 2x = -5 - 10
5x = -15
x = -3
When it is negative, we get:
2x - 5 = - (7x + 10)
2x - 5 = -7x - 10
2x + 7x = -10 + 5
9x = -5
x = [tex]\frac{-5}{9}[/tex]
Therefore the values of x are -3 and [tex]\frac{-5}{9}[/tex].
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The Golden Gate Bridge in San Francisco is approximately 8,980 feet long. a model of the bridge is made in a scale of 1 inch to 100 feet. how long is the model of the bridge?
898 inches
90 inches
8.98 inches
89.8 inches
Based on a scale factor of 1 inch to 100 feet, the length of the model of the bridge is equal to: D. 89.8 inches.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as bridges, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Mathematically, the scale factor of a geometric object can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure).
Substituting the given parameters into the scale factor formula, we have the following;
Length of model bridge = 8980/100
Length of model bridge = 89.8 inches.
In this context, we can reasonably infer and logically conclude that the model bridge's length is equal to 89.8 inches.
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Combine and simplify the following radical expression.
The radical value of the expression is 144⁵/³
What is a radical expression?You should be aware that a radical expression is defined as any expression containing a radical (√) symbol.
The given expression to be ex[pressed is
(2∛12)(3∛2)
To express this, we multiply two two brackets together to have
6∛24
Taking the cube root of 24 we have
6¹ * 24¹/³
Applying the multiplication law of indices we have
144⁵/³
In conclusion this is to say that the radical expression is 144⁵/³
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Fill in the blank divide data sets in fourths. divide data sets in fourths. Outliers Z-scores Quartiles С Ranges answer(s) and then click Check Answer. Clear All All parts showing
Quartiles divide data sets in fourths.
In statistics, a quartile is a specific kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.
Quartiles (Quartiles are the most prevalent percentiles. Data sets are divided into quadruples, or four equal sections, by quartiles. The bottom 25% of the data are separated from the top 75% by the first quartile, abbreviated Q1. The first quartile therefore corresponds to the 25th percentile. The second quartile, or Q2, separates the bottom 50% of the data from the top 50%; it is corresponding to the median or 50th percentile. The third quartile, or Q3, which corresponds to the 75th percentile, separates the bottom 75% of the data from the top 25%.
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In an arithmetic sequence, the first term is $100$ and the fourth term is $76$. What is the value of the first term that is less than $0$
The value of the first term that is less than 0 is -4
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
Where a₁ is the first term in the sequence, d is the common difference between terms, and n is the position of the term that we are trying to find.
If in an arithmetic sequence, the first term is 100 and the fourth term is 76, then the common difference is
aₙ = a₁ + (n - 1)d
76 = 100 + (4 - 1)d
76 = 100 + 3d
3d = 76 - 100
3d = -24
d = -8
Solve for aₙ that is less than 0.
aₙ = a₁ + (n - 1)d
aₙ = 100 + (n - 1)(-8) < 0
100 - 8n + 8 < 0
8n > 108
n > 13.5
a₁₄ = 100 + (14 - 1)(-8) = -4
Therefore, the value of the first term that is less than 0 is -4.
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