Using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.
What is a normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
The characteristics of normal distributions are as follows: Bell-like in its symmetry.
The distribution's mean and median, which are both at its center, are equal.
68 percent of the data, or approximately, falls within one standard deviation of the mean.
So, the formula is used to determine the Z score for a data point x in a normal distribution:
Z = z - mean/standard deviation
Now, use the formula to calculate the z value as follows:
Z = z - mean/standard deviation
Z = 25 - 16/6
Z = 9/6
Z = 3/2
Z = 1.5
Therefore, using the normal distribution formula, we know that the z score that is equivalent to 25 is 1.5.
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if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?
8 ounce of yellow color required.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
if you mix 3 ounces of blue paint and 2 ounces of yellow paint.
So, we have the composition ratio as 2:3
Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.
Thus, yellow = 2/5 x 20= 8 ounce
Blue= 3/5 x20 = 12 ounce
Hence, 8 ounce of yellow color required.
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In January and February of this year, the store made $2,500 from sales of accessories and services. a. Let x represent the amount the store will make from sales of computer products from March through December. Write an equation (slope-intercept form) that represents the predicted amount y that the store will make from sales of accessories and services x for the entire year. Y = 0.05x+2,500 b. If Enrique predicts sales from accessories and services for the entire year will be $5,000, use your equation to determine how much money must be made from computer product sales from March through December. Just your answer by showing our work on explaining our thinking
The equation that represents the predicted amount y that the store will make from sales of accessories and services x for the entire year is y = 0.05x + 2500
As it is given that Enrique can make extra money from the sales of services and accessories for computer products sold by his store and the store makes x dollars selling computer products, he predicted to the store will make 0.05x dollars ($0.05) from selling accessories.we consider x to be dollars of selling computer products, in the month of January and February of this year, the stored made $2,500 from sales of accessories and services.
so the linear equation will be : y = 0.05x + 2500
If sales from accessories and services for the entire year will be $5,000, then the equation will be :
y = 0.05x + 5000
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At Master Street Elementary School
there are 22 classrooms. If there are
30 students in each classroom, how
many students are there in the entire
school?
660 or it may not be that because only said that theres 22 classrooms. So yeah ;)
30 x 22 = 660 its just multiplication
what is the domain and range for a parabola with the equation y=x^2-x-2
The quadratic equation y = x² - x - 2 has a domain with all real numbers and a range with all values equal to or greater than - 9 / 4.
How to determine the domain and the range of the parabola
The domain of a function is the set of values of x that belongs to the functions and the range of the function corresponds to its set of values of y. In this case we find the definition of a quadratic equation, of which we must determine its domain and range. A brief manner to determine them is modifying the function by deriving its vertex form:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.First, write the quadratic equation:
y = x² - x - 2
Second, modify the equation into its vertex form:
y + 1 / 4 = x² - x + 1 / 4 - 2
y + 9 / 4 = x² - x + 1 / 4
y + 9 / 4 = (x - 1 / 2)²
The domain of all quadratic functions is all real numbers and the range of the quadratic function y = x² - x - 2 is y ≥ - 9 / 4 as the vertex constant is greater than zero.
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Five friends divid three bags of apples equally between them. Write the division represented in this situation as a fraction.
The fraction when five friends divide three bags of apples equally between them is 3/5.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Therefore, the fraction when five friends divide three bags of apples equally between them will be:
= Number of apple / Number of friends
= 3/5
The fraction is 3/5.
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let x represent the full length of a certain species of newt. assume that x has a normal probability distribution with mean 110.6 inches and standard deviation 4.9 inches. you intend to measure a random sample of n
If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.
Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.
Sampling distribution of the sample mean:
using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.
The standard deviation of the population is σ = 3.1 and the sample size is n =103, people
The standard deviation σ/√n= 3.1/√103 =0.31.
As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.
x-bar ≈ N (216, 0.31)
μ_{x-bar} = 216
σ_{x-bar} =0.31
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(complete question)
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.
you toss a fair coin 9 times. find the probability of no more than 8 heads given that at least one toss resulted in heads.
On tossing a fair coin 9 times, the probability of no more than 8 heads where at least one toss is heads would be 511/512.
What is Probability?The possibility of an event happening is gauged by probability. Many things are difficult to forecast with absolute confidence. We can only anticipate the likelihood of an event occurring using it. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.
How to solve?
total number of possibilities on tossing a coin 9 times= 2^9
number of ways to get all heads = 1/2^9
number of getting at most 8 heads = number of ways of getting one tail
= 1 - 1/2^9
=511/512
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the chi-square goodness of fit test assesses whether the observed counts of a categorical variable .
The chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
The chi-square fit test of goodness assesses whether the proportions of a category or individual outcome in a sample follow a hypothetical proportion population distribution.
In other words, if you take a random sample, the observed proportions follow the values suggested by theory.
Analysts often use the goodness-of-fit chi-square test to determine whether the proportions of categorical results are equal. Alternatively, the analyst can specify the proportions to include in the test.
Alternatively, this test can assess whether observed results follow a discrete probability distribution, for example, Poisson distribution.
As a hypothesis test, the chi-square test of goodness can be used to infer the entire population based on a sample.
Thus, it is true that the the chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
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the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 5.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. the mean wait time was calculated to be 5.61 minutes. assuming the population standard deviation is 2.50 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 5.00 minutes with a 98% level of confidence?
In this case, the standard error would be standard error = 2.50 / sqrt(41) = 0.342 and the z-score would be z = (5.61 - 5.00) / 0.342 = 1.71
What is the z-score value?A z-score value is the numerical measured value of the relationship of a value to the mean of a group of values and it is measured in the terms of standard deviations from mean value.
What is the formula to measured the z-score value?The z-score is measured by formula z=(x- μ)/ a where x is the raw score, μ is the population mean and a is the population standard deviation. So to calculate z-score, we subtract the population mean from the raw score and divide it by the population standard deviation.
standard error = population standard deviation / sqrt(sample size)
standard error = 2.50 / sqrt(41) = 0.342
Next, you would need to calculate the z-score for the observed mean wait time of 5.61 minutes.
z = (observed mean - population mean) / standard error
z = (5.61 - 5.00) / 0.342
z= 1.71
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If the experiment called for the temperature of the liquid to change by -3\4°c each hour, what would the temperature be at noon? Explain.
The temperature of the liquid at noon would be of:
-2.25ºC.
What is the linear function?The linear function in this problem is defined in the slope-intercept format, as follows
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change of the temperature.b is the y-intercept, representing the initial temperature.The values of these coefficients are given as follows:
m = -3/4, b = 0.
Then the function that gives the temperature in x hours after 9 A.M. is of:
y = -3/4x.
Noon is three hours after 9 A.M., hence the estimate is given as follows:
y = -3/4(3) = -9/4 = -2.25ºC.
Missing InformationThe problem states that the initial temperature is of 0ºC at 9 A.M.
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the weights for newborn babies is approximately normally distributed with a mean of 5.6 pounds and a standard deviation of 1.2 pounds. consider a group of 1100 newborn babies: 1. how many would you expect to weigh between 4 and 7 pounds? 2. how many would you expect to weigh less than 6 pounds? 3. how many would you expect to weigh more than 5 pounds? 4. how many would you expect to weigh between 5.6 and 8 pounds? hint: do not round until you get your final answer.
The answer to the parts for the given standard deviation are 859, 629 , 308, 477.
What is standard deviation?
Standard Deviation may be a live that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists
Main body:
1 )
mean=5.6
sd=1.2
total number 1000 find number weight between 4 to 9 pounds
z=x-mue/sd
⇒ 4-5.6/1.2=-1.6/1.2 =-1.33
z value by table = 0.09176
⇒z=7-5.6/1.2=1.4/1.2 = 1.666
z value by table =0.95154
effective value 0.95154 -0.09176 = 0.8598
number of children =1000 x 0.8598=859.8
babies expect to weigh between 4 and 7 pounds are 859.
2)
less than 6 pounds
z=6-5.6/1.2=0.4/1.2=0.333
z value by table = 0.62930
number of children born less than 7 pounds =0.62930 x 1000=629.3
means 629 children less than 6 pounds
3)
more than 5 pounds
z=5-5.6/1.2= -0.6/1.2= -0.5
z value as per table -0.5 = 0.30854
number of children born 1000 x 0.30854=308.5
number of children born more than 5 pounds are 308
4)
weight between 5.6 to 8 pounds
z=5.6-5. 6/1.2=0/1.2 =0
value of z by table 0.5
z=8-5. 6/1.2=2.4/1.2 = 2
value of z by table 0.97725
0 value will be 0.97725-0.5000=0.4772
number of children born between 5.6 to 8 pounds=0.4772 x 1000 = 477.2 means 477.
Hence the value are as follows
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Write an equivalent expression by distributing the "-" sign outside the parentheses: 8.2r - (-7s− 1)
Answer:
8.24 + 7s + 1
Step-by-step explanation:
You negate everything in the parentheses, so --7s and --1, which turns into 7s and 1.
How would you solve this?
The irregular hexagon has an area of 147 square units. (Correct choice: A)
How to find the area of an irregular polygon
In this problem we have an irregular hexagon that is the result of subtracting a small rectangle from a great rectangle. Likewise, the area of this hexagon is the result of subtracting the area of the small rectangle from the area of the great rectangle. From geometry we know that the area formula for the rectangle is:
A = w · h
Where:
A - Area of the rectangle, in square units.w - Width of the rectangle, in units. h - Height of the rectangle, in units.Now we proceed to determine the area of the irregular polygon:
A'' = A - A'
A'' = 13 · 12 - 3 · 3
A'' = 156 - 9
A'' = 147
The area of the irregular hexagon is equal to 147 square units.
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Which expression is equivalent to x 6 – 16x 2
Answer:
Below
Step-by-step explanation:
x^6 -16x^2 = x^2 ( x^4 - 16 ) is one possibility
( you didn't include choices)
A local charity has put together 20 care packages for
people. Each package contains $15 worth of goodies
and $2.50 per food satchel added to it. If the charity
spent $800 on the care packages how many food
satchels were in each package? Write and solve an
equation for this scenario.
Answer:
The equation is 15x + 2.50y = 800, where x is the number of care packages and y is the number of food satchels. Solving for y, we get y = 32. Therefore, each package contained 32 food satchels.
Step-by-step explanation:
the number of golf balls in tigers golf bag (y) after x rounds of golf is represented by the equation y=-3x+28 what is the meaning of the value of "-3" in the context of this situation? question 8 options: tiger loses 3 balls each round. tiger begins with 3 balls in his golf bag. tiger finishes with 3 balls in his bag. tiger adds 3 balls to his bag each round.
Question 8 options:
Tiger begins with 3 balls in his golf bag.
Tiger finishes with 3 balls in his bag.
Tiger adds 3 balls to his bag each round.
The value of "-3" in the context of this situation is "tiger loses 3 balls each round".
The correct answer option is option A
How to determine the parameters in an equation?y = -3x + 28
Where,
The number of golf balls in tigers golf bag = yRounds of golf = xNumber of balls lost each round = -3For instance, if the tigers played 8 rounds of golf,
The number of golf lost = - 3x
= -3(8)
= -24
Then,
The number of golf balls in tigers golf bag,
y = -3x + 28
= -3(8) + 28
= -24 + 28
= 4 golf balls.
Therefore, the situation can be solved using equation and determining the parameters of the equation.
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Answer:
Tiger begins with 3 balls in his golf bag.
Step-by-step explanation:
:)
The diameter of a cylindrical water tank is 11 ft, and Its height is 8 ft. What is the volume of the tank?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
11 ft
8 ft
Answer:
760ft
Step-by-step explanation:
Use the formula: πr^2h where r = radius(diameter/2) and h = height
radius: 11/2 = 5.5
pi: 3.14
Height: 8
3.14*5.5^2*8
= 759.88
Rounded: 760 ft
FILL IN THE BLANK. In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that _____.
If the slope of a basic regression analysis—in which y is the dependent variable and x is the independent variable—is positive, then there must be a positive correlation between x and y.
What is regression analysis?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A statistical technique that demonstrates the link between two or more variables is regression analysis. The approach examines the connection between a dependent variable and independent variables, often represented in a graph. A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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A factory make heet of metal that are 1/2 of an inch thick. If a worker at the factory make a tack of 10 of the heet, how many inche thick will the tack be
We know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.
What do we mean by mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).
So, we know that:
Each sheet is 1/2 inch thick.
The worker prepares a stack of 10 sheets.
Then, calculate the thickness of the tack as follows:
1/2 * 10
1 * 5
5 inches
Therefore, we know that the stack of 10 sheets will be 5 inches thick using simple mathematical operations.
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(1 point) from a group of 8 men and 7 women a committee consisting of 4 men and 3 women is to be formed. how many different committees are possible if
There are 1365 different committees that are possible if a group of 3 men refuses to serve together.
Given that,
From an 8 men, 7 woman group A committee made up of four men and three women will be created.
If all prerequisites are met, a total of committees could be formed.
⁸C₄ x ⁷C₅= 70 x 21= 1470
Three males now reject serving in unison.
As a result, in the event that they serve simultaneously, a combination is= ⁵C₄ x ⁷C₅= 5 x 21= 105
Therefore, a combination that could be used in the event that they don't work together is = 1470- 105= 1365
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In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of a?a = 3a = 8a = 18a = 33.
A linear function with a rate of change of +5 is depicted in the table as m = 13 + 5 = 18.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
We will discover what a linear function is in this article, along with information on its graph, domain, and range.
Additionally, we will learn how to recognize a linear function and how to calculate its inverse.
According to our question-
The graph in the table shows a linear function.
The linear function's general equation is y = ax+b, where a denotes slope and b denotes a constant.
Finding the equation of the linear function at x = 3 y = 13 and at x = 5 y = 23 13 = 3a+b by utilizing the first and third points from the table (1)
23 = 5a+b → (2) find a and b by resolving (1) and (2)
Consequently, a = 5 and b = -2; y = 5x – 2
After then, the equation of y = y = 5*4-2 = 18 was changed by substituting x = 4 in it.
m = 18
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PLEASE HELP QUICK THIS IS DUE IN 5 MINUTES!!!
Find the surface area of a cube with side lengths of 2 meters.
Use the formula SA= 6s², where s =side lengths (This is algebra)
A: 10 square meters
B: 64 square meters
C: 144 square meters
D: 24 square meters
Answer:
The answer is d: 24 square meters
The Terra family sold its heavily wooded land to
a lumber company for $350,000 at a rate of $700
dollars per acre. If the property averages 8 trees
per acre, which of the following is closest to the
number of trees on the land?
A.
63
B. 500
C. 3,500
D. 4,000
E. 5,608
Answer:
B
Step-by-step explanation: It is very simple. All you have to do is to do 350 000 divided by 700 which gives you 500. That's your answer!
The volume of a rectangular prism is with height x + 2. Using synthetic division, what is the area of the base?.
The solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.
What is synthetic division?Synthetic division, which is frequently used to determine a polynomial's zeros, is described as a streamlined method of dividing a polynomial with another polynomial equation of degree 1. Comparatively easier to calculate than the long division method, this division method is carried out manually.
we know that the volume of a rectangular prism as where V is volume ,A is area ,H is height
Now, we are given
V=[tex]2x^{3}+9x^{2} -8x-36[/tex]
h=x+2
now, we can find A
V=A*h
A=V/h
now, we can plug it
[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2}[/tex]
now, we can use synthetic division method
so, we can write it as
A=[tex]\frac{2x^{3}+9x^{2} -8x-36}{x+2} = 2x^{2} +5x-18[/tex]
So the area of base=[tex]2x^{2} +5x-18[/tex]
Therefore ,the solution to this question is [tex]2x^{2} +5x-18[/tex] which is area of base of rectangular prism.
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9/10 times 0.5 in fraction form
Answer:
9/20
Step-by-step explanation:
(9/10)*(1/2)
(9/20) times
Answer: tis answer would be 9 over 20
Step-by-step explanation:
Why does the following equation have no solutions? 5-4x-7-10x=-8x-4-6x-10
There are no solutions to linear equations of the following equation
5-4x-7-10x=-8x-4-6x-10, because if they have the same variable term but different constant values on opposite sides of the equation.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation.
The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Given equation is ,
5-4x-7-10x=-8x-4-6x-10
-14x-2=-14x-14
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
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The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Mason is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 10,125(1.83)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.
r (number of years) 1 2 3 4
g(r) (amount in dollars) 9,638 18,794.10 36,648.50 71,464.58
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer.
(a) The amount will be increasing by 83%.
(b) Part B's account has a higher percentage change in money over the preceding year than Part A's account.
A part or quantity in every hundred is defined as a percentage. It's a fraction having a denominator of 100. The percentage difference is the change in the value of a quantity over time expressed as a percentage difference. Percentage Change is a term used to describe the growth or decrease in a quantity expressed in percentages.
Find:
Whether the amount is increasing or decreasing over the years and which is experiencing a greater change.
From the given equation,1.831>1 , this shows that money in account A is 83% more, compared to its previous year. The amount will be increasing by 83%.
Part B:
The change in each consecutive term is 94%. This shows that the consecutive term is multiplied by 94% the previous year's amount. As a result, Part B's account has a higher percentage change in money over the preceding year than Part A's account.
Hence we get the required answer.
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4% of what number is 1.48?
well, is really "x", which oddly enough is the 100%, but we also know that 4% of "x" is 1.48, hmmm what the heck is "x"?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 1.48& 4 \end{array} \implies \cfrac{x}{1.48}~~=~~\cfrac{100}{4} \implies \cfrac{ x }{ 1.48 } ~~=~~ 25\implies x=37[/tex]
Given log_5 2≈0.4308 and log_527≈2.0478, evaluate the expressions. Note: you must use the given values and not values obtained from a calculator for those logarithms.
log_5 3
log_5 (27/50)
The solutions to the logarithm equations are;
1) Log₅3 = 0.6826
2) Log₅(27/50) = -0.383
How to solve logarithm Equations?
There are different rules of logarithm such as;
Product rule which is; Log a + Log b = Log (ab)
Quotient rule which is; Log a - Log b = Log(a/b)
Power rule which is; Log aˣ = x log a
We are given that;
Log₅2 = 0.4308
Log₅27 = 2.0478
We know that 27 = 3³. Thus;
Log₅27 = Log₅3³
Using power rule, we have;
Log₅3³ = 3Log₅3
Thus;
Log₅27 = 3Log₅3 = 2.0478
1) We want to solve Log₅3
We have;
3Log₅3 = 2.0478
Thus;
Log₅3 = 2.0478/3 = 0.6826
2) Log₅(27/50)
Using quotient rule, we have;
Log₅27 - Log₅50
This can also be expressed as;
Log₅3³ - Log₅ (25 * 2)
= 3Log₅3 - [2Log₅5 + Log₅2]
= 2.0478 - 2 - 0.4308
= -0.383
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Help fast due soon
Given: AC = CB
CD Bisects AB
Prove: AADC= ABDC
What are the statements and reasons
Answer:
Step-by-step explanation:
Given: AC = CB
CD Bisects AB
Prove: ΔADC= ΔBDC
AC≅CB Given
AD ≅ DB are congruent because of the segment bisector theorem.
DC≅DC reflexive property
ΔADC≅ ΔBDC SSS theorem