The change of base formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.
The change of base formula is a mathematical formula that allows you to convert a logarithm with one base to a logarithm with another base. The formula states that for any logarithm base b and any positive number x: log_b(x) = (log_c(x)) / (log_c(b)), where c is any base.
One way to prove this is to use the properties of logarithms:
log_b(x × y) = log_b(x) + log_b(y)log_b(xⁿ) = n × log_b(x)Using these properties, we can write log_b(x) as:
log_b(x) = log_b([tex]c^{(log_c(x))}[/tex])
log_b(x) = log_b([tex]c^{(log_c(x))}[/tex]) / log_b(c¹)
log_b(x) = log_c(x) / log_c(b)
Therefore, the change of base formula is proven.
To learn more about change of base formula visit: https://brainly.com/question/2141478
#SPJ4
Ten cards numbered 1-10 are placed in a hat.What is the probabiliy of randomly drawing a card with an even number then a card with a number equal to five if the firdt card iis replaced
Answer:
1/ 20
Step-by-step explanation:
Given :
Cards = {1,2,3,4,5,6,7,8,9,10}
Even number = {2,4,6,8,10}
Probability (drawing an even number) :
Number of even / total. Number of cards
5 / 10 = 1/2
Card with number, 5 :
P(card numbered 5) = 1/10
Since they are independent events :
P(even number) * P(card numbered 5)
1/2 * 1/10 = 1/20
in an assignment and need help with this question
Please help, and plz don't be saying this is the right answer if u dont know for sure.
Answer:
135 degrees
Step-by-step explanation:
(8x-7)+(12x+57)=180
combine like terms
20x+50 = 180
subtract 50 on both sides
20x = 130
divide by 20
x = 130/20
x = 13/2
x = 6.5
cpq = 12x+57
cpq = 78 + 57
cpq = 135
Which statement best describes the domain of the function represented in the graph?
Given:
The graph of a function.
To find:
The correct statement for the domain of the given function graph.
Solution:
Domain is the set of x-values for which the function is defined or it is the set of input values.
From the given graph it is clear that it is a linear function with end points (1,2) and (9,14).
So, the given function is defined for [tex]1\leq x\leq 9[/tex]. Here 1 and 9 are including in the set of x-values.
Therefore, the correct option is C, i.e., [tex]1\leq x\leq 9[/tex] or x between 1 and 9, inclusive.
Find the equation of the linear function represented by the table below in slope-intercept form.
Answer: The equation is y = 3x + 3
Step-by-step explanation:
Rewrite the equation 2x + 3y = 6 in slope-intercept form.
3y = -2x + 6
y= -2x+6
y= - 2/3 x+2
y = 2x+6
Simplify the expression -2.2f+0.5f-13-3
Answer:
-1.7f - 16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
-2.2f + 0.5f - 13 - 3
Step 2: Simplify
Combine like terms (f): -1.7f - 13 - 3Combine like terms (Z): -1.7f - 16I need help on this.. And I will give you a BRANILIST if you the first one with the right answer
Answer:
0.1
Step-by-step explanation:
(9,4) (5,1) [tex]\frac{y_{2} y_{1} }{x_{2} x_{1} }[/tex], plug in the numbers, [tex]\frac{(1)(4)}{(5)(9)}[/tex]= [tex]\frac{4}{40} or \frac{1}{10}[/tex], to write it as a decimal, you divide the numerator by the denominator, 0.1
PLEASE HELP!!
Find the 14th term of the sequence: 2,4,8,16...
Answer:
16384
Step-by-step explanation:
You have to find 2 to the 14th power (that's the rule)
Hope that helps!
I NEED HELP PLEASE ASAP, It's due soon.
Which series of transformations will create similar but not congruent figures? (1 point)
O reflection and translation
O reflection and dilation
O reflection and rotation
O rotation and translation
If you don't know let someone who does answer
Answer:
I thik O rotation and translation
the pythagorean theorem states that a^2 + b^2 = c^2 If A and B represent the length of the legs of a right triangle and C represents the length of the hypotenuse. Find the length of the hypotenuse Is the length of the legs are 9cm and 12cm.
Answer:
25 or 50 points is that if 25 or 20 im not
Answer:
The hypotenuse equals 15cm
A six-sided Fair number cubis rolled 100 times as part of an experiment. The frequency of the role of the number 3 is 20. W hich statement about rolling a 3 is correct
Answer:
The Theoretical probability is 1/6.
The experimental probability is 1/5
Step-by-step explanation:
Given
Rolls: 100
Outcome of 3 : 20
Required
Which of the options is true (See attachment for options)
From the attachment, we understand that the question requires that we calculate the experimental and theoretical probability.
The experimental probability (E) is calculated as thus:
[tex]E = \frac{Outcomes}{Total\ Rolls}[/tex]
[tex]E = \frac{20}{100}[/tex]
[tex]E = \frac{1}{5}[/tex]
The theoretical probability (T) is calculated as thus:
A cube has 6 faces, one of which is the face 3.
So, T is:
[tex]T = \frac{n(face\ 3)}{n(Total)}[/tex]
[tex]T = \frac{1}{6}[/tex]
Hence, C is true
Solve for x Round to the nearest 100th if needed.
x/13 + 18 = 49
Answer:
2.4
Step-by-step explanation:
X=49-18/13
X=31/13
X=2.38
Please help
(10 points)
A bill for dinner at a restaurant is $98.87. A 15% tip for the server is added
to the bill. What is the total amount of the bill?
A $100.37
B $109.26
$113.70
D $113.87
TIMED!!
PLEASE HELP!!
WILL give brainliest
Answer:
easy third one also plz give heart
Step-by-step explanation:
i just know
please please please help asap
Answer:
∠ UVX = 126.8°
Step-by-step explanation:
∠ WVS and ∠ UVX are vertical angles and congruent, then
∠ UVX = 126.8°
Samuel Morse determined that the percentage of t's being used in the English language in the 1800's was 9%. A random sample of 600 letters from a current newspaper contained 48 t's. Test the claim that the proportion of t's has changed in modern times, using the current newspaper data and a significance level of 0.05
Answer:
There is insufficient evidence to indicate that the population proportion of t’s in modern newspaper is different from 0.09. The result is not statistically significant
Step-by-step explanation:
H0 : p0 = 0.09
H1 : p0 ≠ 0.09
Sample size, n = 600 ; α = 0.05
Decision region
Zstatistic < Zcritical ; reject H0
P = 48 / 600 = 0.08
Zstatistic = (p - p0) ÷ sqrt((p0(1 - p0)) /n)
Zstatistic = (0.08 - 0.09) ÷ sqrt(0.09(0.91))/600)
Zstatistic = - 0.01 /0.0116833
Zstatistic = - 0.856
Zcritical at 0.05, = - 1.96
Zstatistic > Zcritical
-0.856 > - 1.96
Hence, we fail to reject the Null
what is 3 + 7 -90+180
Answer:
100
Step-by-step explanation:
3+7=10
-90+180=90
10+90=100
Someone help please
help and ill give extra (60 points)
Answer:
1) substitution method
2) zero
Step-by-step explanation:
because it has no solution as the variables cancle out eachother.
FAST!!
Select ALL the correct answers.
With which information can you construct more than one triangle?
the measurements of two angles
the measurements of two angles and the length of the included side
the measurements of all the angles
the lengths of two sides and the measurement of the included angle
Answer:
a b and d
Step-by-step explanation:
Answer:
the measurements of two angles
the measurements of two angles and the length of the included side
the lengths of two sides and the measurement of the included angle
Step-by-step explanation:
Graph the following equation:
Graph f(x)= -2^x-2
Answer:
Step-by-step explanation:
I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe
Answer:
1 4/6 inches
Step-by-step explanation:
10/6= 1 4/6 inches
Hope it helps!!
Jana has $10. She wants to buy a bottle of nail polish for $9.50. The sales tax is 7%. Does she have enough money?
Answer:no, she would be 17 cents short
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
Compute the tax =
9.50 * 7% = 9.5 * .07 or 66.5 cents.
Since she only has $10, she does not have enough money.
Can someone help me please
Answer:
X=3-(y/2)=8
Step-by-step explanation:
suppose the numbers is X
3 less than half the product of a number is 8
X= 3- (y/2)=8
If 80 = y, then y = 80
Answeryes
Step-by-step explanation:
A Lamborghini is worth $700,732 if the tax of this car is 5% what would be the full price?
The length of a rectangle is 5 centimeters more than the width.
The area of the rectangle is 36 square centimeters.
What is the length?
Answer:
Length is 4 centimeters
Step-by-step explanation:
4 x (4 + 5)
4 x 9
36
The area of a square field is (49m^2 - 42m + 9) square units. find the dimensions of the field. ( STEP BY STEP EXPLANATION)
Answer:
(7m−3)(7m−3)
Step-by-step explanation:
Factor 49m2−42m+9
49m2−42m+9
=(7m−3)(7m−3)