Answers
Answer:
[tex]\displaystyle log_\frac{1}{2}(64)=-6[/tex]
Step-by-step explanation:
Properties of Logarithms
We'll recall below the basic properties of logarithms:
[tex]log_b(1) = 0[/tex]
Logarithm of the base:
[tex]log_b(b) = 1[/tex]
Product rule:
[tex]log_b(xy) = log_b(x) + log_b(y)[/tex]
Division rule:
[tex]\displaystyle log_b(\frac{x}{y}) = log_b(x) - log_b(y)[/tex]
Power rule:
[tex]log_b(x^n) = n\cdot log_b(x)[/tex]
Change of base:
[tex]\displaystyle log_b(x) = \frac{ log_a(x)}{log_a(b)}[/tex]
Simplifying logarithms often requires the application of one or more of the above properties.
Simplify
[tex]\displaystyle log_\frac{1}{2}(64)[/tex]
Factoring [tex]64=2^6[/tex].
[tex]\displaystyle log_\frac{1}{2}(64)=\displaystyle log_\frac{1}{2}(2^6)[/tex]
Applying the power rule:
[tex]\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}(2)[/tex]
Since
[tex]\displaystyle 2=(1/2)^{-1}[/tex]
[tex]\displaystyle log_\frac{1}{2}(64)=6\cdot log_\frac{1}{2}((1/2)^{-1})[/tex]
Applying the power rule:
[tex]\displaystyle log_\frac{1}{2}(64)=-6\cdot log_\frac{1}{2}(\frac{1}{2})[/tex]
Applying the logarithm of the base:
[tex]\mathbf{\displaystyle log_\frac{1}{2}(64)=-6}[/tex]
Related Questions
Which is the upper left quadrant on the coordinate plane?
A coordinate plane.
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answers
Answer:
the upper left Quadrant is Quadrant II
Answer:
its Quadrant IV
Step-its Quadrant by-step explanation:
find the area in square inches of a rectangle with a length of 5 inches and a width of 3 5/6 inches
Answers
Answer:
19 1/6 in^2
Step-by-step explanation:
just do multiplication bruv
Which of the following is an example of an independent variable?
A. graph
B. output
C. input
D. rule
Answers
Answer:
C is an independent variable
Step-by-step explanation:
The input is the number you feed into the expression
Between x=2 and x=3, which function has the largest average rate of change?
Answers
Answer:
I believe it would be C
Step-by-step explanation:
Janie ordered 12 packs of glitter. There were 25 packs of glitter in each pack. How many packs of glitter did Janie order?
Answers
Answer: 300
Step-by-step explanation: 25 multipled by 12 is 300
Answer: I think its 300
Step-by-step explanation: Because if you multiply 12 by 25 you would get 300.
I need these answers quick please!! I will mark brainliest if they are correct! Hurry please (:
Answers
Okay I'll go as fast as I can!!
1.) 0.05
2.) -0.007
3.) 0.028
4.) 0.125
5.) 2.333
6.) 0.272
7.) -0.6
8.) 0.086
9.) 0.642
10.) 0.296
11.) 0.068
12.) 0.814
13.) 2.08
14.) 3
15.) 0.093
16.) -0.185
I am so sorry! I dont know what 17 and 18 are. I feel bad but I hope you can figuar it out!
How would you describe the correlation in the data? Explain your reasoning. (2 points).
Answers
Answer:
How would you describe the correlation in the data? Explain your reasoning. (2 points)
Step-by-step explanation:
The product of a number and -5 is equal to twice the number subtracted from 9. What is the number?
Answers
Answer:
4.5
Step-by-step explanation:
i think that is the answer
Find the slope of the line that passes through each pair or poin
Answers
Answer:
The slope is 1/5
Step-by-step explanation:
I need help answering this
Answers
Answer:
True
Step-by-step explanation:
The angles <wax and <yau are vertical angles and has same measurement.
3 If the perimeter and sum of two sides of triangle are 24 em and 17 cm then calculate the length
of third side 2]
Answers
Answer:
answer is 42 cm
Step-by-step explanation:
explained
16 ÷ 47 = ?
47 ÷ 9 = ?
47 ÷ 7 = ?
47 ÷ 5 = ?
47 ÷ 3 = ?
47 ÷ 2 = ?
Answers
#1: 0.3404255319
#2: 5.2 repeat
#3: 6.714285714
#4: 9.4
#5: 15.6 repeat
#6: 23.5 repeat
I am not 1,000 percent sure that this is right. If it is not then please tell me! Hope this helped if it was correct!
A cake recipe calls for 3/4 cup of flour for every 1/3 teaspoon of baking powder. What is the unit rate of cups per teaspoon?
Answers
Answer:
i just looked it up and i saw 57 so i think thats it
Step-by-step explanation:
Answer:
9/4
Step-by-step explanation:
Clare buys an item with a normal price of $24, but saves
$6 by using a coupon. For what percentage off is this
response coupon?
y response
Answers
Answer:
25% off
Step-by-step explanation:
6 is 1/4 of 24
1/4=25%
What is the exact value of sin(105°)?
Answers
Answer:
0.9659258263
0.9659 when rounded to two decimals
0.966 when rounded to three decimals
0.97 when rounded to two decimals
Step-by-step explanation:
Answer:
305
Step-by-step explanation:
105°
+ 200°
305°
The lifetime of a computer can be modeled by an exponential random variable with an expected lifetime of 900 days. 1. Find the probability that the computer will function for more than 2000 days.2. Find the probability that the computer will function for more than 2000 days, given that it’s still working after 500 days.
Answers
Answer:
1. 0.108368
2. 0.188876
Step-by-step explanation:
Let X be the exponential random variable that represents the lifetime of a computer.
i.e. [tex]X\sim Exp(0.001)[/tex]
The probability that the computer will function more than 2000 days can be computed as follows:
P(X > 2000)
: [tex]f_X(x) = \lambda e^{-\lambda x[/tex]
P(X > 2000) = 1 - P(X< 2000)
P(X > 2000) = exp(-2000/β) = e⁻²²
P(X > 2000) = 0.108368
2.
By applying conditional probability;
[tex]P(X>2000 \bigg | X>500) =\dfrac{P(X>2000 \ \cap \ X>500)}{P(X> 500)}[/tex]
[tex]P(X>2000 \bigg | X>500) =\dfrac{P(X>2000 )}{P(X> 500)}[/tex]
[tex]P(X>2000 \bigg | X>500) =\dfrac{0.108368 }{0.57375}[/tex]
[tex]\mathbf{P(X>2000 \bigg | X>500) =0.188876}[/tex]
A company orders 9 boxed lunches from a deli for $115.20. If each boxed lunch costs
the same amount, what is the unit cost of each boxed lunch?
Answers
Answer:
12.80
Step-by-step explanation:
115.20 divided by 9
Answer:
7 =7.45x
Step-by-step explanation:
Peyton invested $690 in an account paying an interest rate of 5.6% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 8 years?
Answers
Answer:
$1,080.
Step-by-step explanation:
Given that Peyton invested $ 690 in an account with an annual interest of 5.6% compounded monthly, and that he kept said money in his account for 8 years without withdrawing or adding any amount, to obtain the final amount of money that said account would have after 8 years. years of investment, the following calculation must be made:
8 x 12 = 96
X = 690 x (1 + 0.56) 96
X = 1,078.85
Thus, after 8 years of investment, the amount that Peyton's account will have will be $ 1,078.85, that is, $1,080 rounded to the nearest ten dollars.
Answer:
$1,080.
Step-by-step explanation:
Given that Peyton invested $ 690 in an account with an annual interest of 5.6% compounded monthly, and that he kept said money in his account for 8 years without withdrawing or adding any amount, to obtain the final amount of money that said account would have after 8 years. years of investment, the following calculation must be made:
8 x 12 = 96
X = 690 x (1 + 0.56) 96
X = 1,078.85
Thus, after 8 years of investment, the amount that Peyton's account will have will be $ 1,078.85, that is, $1,080 rounded to the nearest ten dollars.
want free HEREeeeeeeeeeeeeeeeee
Answers
Answer:
thanks
Step-by-step explanation:
Answer:
thanks
Step-by-step explanation:
284 + 0 = 284 is an example of which property
Answers
Answer:
Addition propriety
Step-by-step explanation:
Answer:
thats wrong
Step-by-step explanation:
thats not right
WRONG ANSWERS ONLY, who is this anime character? You must actually answer the question though.
Answers
Answer:
I think it may be Naruto
Step-by-step explanation:
Assume the random variable x is normally distributed with mean μ = 80 and standard deviation σ = 4. Find the indicated probability.
P(x < 72) = _____ (round to four decimal places as needed).
Answers
Answer:
0.2278
Step-by-step explanation:
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation
z => 72 - 80/4
= -2
Probability value from Z-Table:
P(x ≤ 72) = P(x = 72) => P(x < 72)
0.02275
Approximately =>0.2278
The probability of the calculated value is " 0.0227501", its calculation can be defined as follows:
Normal distribution calculation:Mean [tex](\mu)= 80\\\\[/tex]
Standard Deviation [tex](\sigma)= 4[/tex]
Since we know that
[tex]\to Z_{\text{score}} =\frac{x-\mu}{\sigma} \\\\[/tex]
a)[tex]x = 72[/tex]
[tex]\to \frac{72-80}{4}=\frac{-8}{4}= -2[/tex]
so,
[tex]P(x < 72) = P(z < -2) =0.0227501[/tex]
PS: you have to refer z score table to find the final probabilities.
Find out more about the p-value here:
brainly.com/question/14723549
Question 1
7
Find the coordinates of the image of the point (3,1) when it is reflected across the line y = 6.
O (3,7)
O (3. - 1)
O (3, 11)
O (3.-5)
Answers
Answer: Chowder
Step-by-step explanation: Chowder is the answer for this question because the equation form of chowder will explain. If you do not understand the Chowder Equation Theorem, simply search it up and you will be provided with knowledge of what to do. (x, y + 6)
It’s 3,11
What is the missing length in the right triangle?
Answers
Answer:
I would assume that s is also 5 because its an isosceles triangle. This leaves the hypotenuse side, which would be 7.07. To find a missing side when you have two sides, you can use the Pythagorean theorem, which is [tex]a^{2} +b^{2} = c^{2}[/tex]. The longest side will always represent c, so when you plug in a and b squared, you will get 50 in total. To get c by itself, you just need to square root it. I hope that made sense!
Domain and Range of the graph
Answers
you are driving at a constant speed of 75 mph. how far will you drive in 4 hrs
Answers
Answer:
300miles
Step-by-step explanation:
If you are driving 75 miles per hour, and you need to know how many miles you will have drive in 4 hours. Multiply 4 by 75 to get 300.
75mi 4 hr
____ x___ = 75mi x 4 = 300miles
1 hr y
PLEASE HELP ME
A pyramid has a row of 100 blocks in the first row, 96 blocks in the
second row, and 92 blocks in the third row. (A) Write an explicit rule to
model the number of blocks in the nth row of the pyramid. (B) Use the rule
to find how many blocks are in the 17th row.
Answers
Answer:
3196
Step-by-step explanation:
A. You Add all the blocks.
B. Then you multiply 17 x your answer then you get your answer.
How do I find matrices
Answers
Likewise for b, and for c.
Sum them up, but remember the minus in front of the b.
Sry it look like that but anyways please hurry
Answers
Answer:
1. subtract by 12 on both sides
2. Divide both sides by -8
Step-by-step explanation:
a bank is offering 2.5%simple interest in a saving account. if you deposit 5000, how much interest would you earn in one year
Answers
Answer:
$125
Step-by-step explanation:
.025(5000)= 125
