Answers
Answer:
x=8
Step-by-step explanation:
log4( x-6) +log4(x) = 2
We know that loga + log b = log (ab)
log4( x-6)(x) = 2
Raise each side to the base of 4
4^log4( x-6)(x) = 4^2
( x-6)(x) = 16
Distribute
x^2 -6x = 16
Subtract 16 from each side
x^2 -6x-16 = 0
Factor
(x-8) (x+2) =0
Using the zero product property
x-8=0 x+2 =0
x=8 x=-2
Checking, we cannot have the log of a negative number so -2 is not a solution
Answer:
x = 8
Step-by-step explanation:
log4(x - 6) + log4(x) = 2
log4[(x - 6) × x] = 2
x² - 6x = 4²
x² - 6x - 16 = 0
x² - 8x + 2x - 16 = 0
x(x - 8) + 2(x - 8) = 0
(x + 2)(x - 8) = 0
x = 8, -2
Log of negative numbers do not exist, so x is only 8
Related Questions
How many factors does 12 have
Answers
Answer:
6 if you count 1 and 12
Step-by-step explanation:
1*12
6*2
3*4
(1,12,3,4,6,2)
2 negatives make a positive**
(-12,-1) (-1,-12) (-3,-4) (-4,-3) (-6,-2) (-2,6)
In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answers
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?
Answers
Answer:
2 divided
Step-by-step explanation:
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY
Answers
Answer:
E 39
Step-by-step explanation:
x+6 = 45
Subtract 6 from each side
x+6-6 = 45-6
x = 39
10 X 5/11=
just multiplication get it right and get brainlyest
60pts or whatever it narrows it down to
Answers
The answer is 4.55
When you divide 5 by 11 you will get 0.45454545454 than when you multiply these numbers by 10 you will get 4.54545454545 and then the rounded answer is 4.55.
Answer: 4.54
Step-by-step explanation:
Find the arc length of a partial circle with a radius of 5
Will mark brainlist! pleaseeee
Answers
Answer:23.55
Step-by-step explanation:
radius=r=5
Φ=360-90
Φ=270
π=3.14
Length of arc=Φ/360 x 2 x π x r
length of arc=270/360 x 2 x 3.14 x 5
Length of arc=0.75 x 2 x 3.14 x 5
Length of arc=23.55
Answer:
23.55 units
Step-by-step explanation:
Hope this helps!
A box below needs to be painted.
How many square inches of paint will be needed to cover the entire surface?
A
80/12 in2
B
61/9 in2
C
49/5 in2
D
77/55 in2
Answers
Answer: c
Step-by-step explanation:
Answer:B
Step-by-step explanation:
Which line is parallel to y = 1/2x -5
Answers
Answer:
Any line with a slope of 1/2 would be parallel to that line.
Step-by-step explanation:
A line is parallel when the slopes are the same, causing the situation where the lines will never intercept. The line in the question has a slope of 1/2, so a parallel line must have that same slope.
Sally wants to fill ten 8-inch tea glasses. How much tea does she need?
A) 80 ounces
B) 40 ounces
C) 80 cubic inches
D) Not enough information to answer
Answers
Answer
I believe C considering cubic mass
Answer:
D
Step-by-step explanation:
A boat sailed 560 km in 8 hours. It took three hours to travel
the first 150 km. What was its average speed for the
remaining journey?
km/h
Answers
Step-by-step explanation:
150 km in 3 hours
= 150 ÷ 3 = 50km/h
Remaining distance = 560 - 150 = 410
Remaining hours = 8 - 3 = 5
Then average speed = 410 ÷ 5 = 82 km / h
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answers
Answer:
⅓ m/s
Step-by-step explanation:
Area of a square is:
A = s²
Take derivative of both sides with respect to time:
dA/dt = 2s ds/dt
Given that dA/dt = 6 m²/s and s = 9 m:
6 m²/s = 2 (9 m) ds/dt
ds/dt = ⅓ m/s
The Formula of the area of a square: A = bh or A = s^2
Solution:
~Take derivative of both sides
da/dt = 2s * ds/dt
~Use given values (6m^2/s and 9m)
6 = 2(9) * ds/dt
~Simplify
1/3m/s = ds/dt
Best of Luck!
e is 5 more than d.
fis 7 less than d.
a) Write an expression for e in terms of d.
Answers
Answer:
C
Step-by-step explanation:
Answer:
e = d + 5
Step-by-step explanation:
e = d + 5
f = d - 7
Solve for e means write as e = ...d
and this is already there...
You can not write it more compact then this.
If you try, you will notice you finally end with the initial equation which you started with, or you endup with something which is obviously very true like
e = e or d = d.
what is the cube root of 1
Answers
Answer:
1.
Step-by-step explanation:
∛1= 1.
It can also be seen as:
1×1×1= 1.
9x-3=87 what is the anwser
Answers
Answer:
x=10
Step-by-step explanation:
9x-3=87
add 3 to both sides
9x=90
divide by 9 on both sides
x=10
Answer:
x=10
Step-by-step explanation:
9x-3=87
you add 3 to both sides
9x-3(+3)=87(+3)
which equals
9x=90
90/9= 10
answer:
x =10
I hope this helped!
What’s the volume of the pic
Answers
Answer:
100[tex]\pi[/tex] cubic cm
Step-by-step explanation:
The volume of a cone can be represented by the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]. Since we know the radius is 5, all we need to find id the height. To do that, we can use the Pythagorean theorem, and see that the height is equal to 12. Plugging the numbers into the formula gives us:
[tex]V =\frac{1}{3} \pi (5^{2}) (12)[/tex]
[tex]V = 100\pi[/tex]
HOPE THIS HELPED! :)
The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour. Write a function b(t) that would represent this relationship after t hours. Use this function to determine how many bacteria would be in the dish after 10 hours and write it only as a number without units.
Answers
Answer:
[tex]B(t) = 1150*(2)^{t}[/tex]
After 10 hours: 1,177,600
Step-by-step explanation:
The number of bacteria after b hours is given by the following equation:
[tex]B(t) = B(0)(1+r)^{t}[/tex]
In which B(0) is the initial number of bacteria and r is the rate that it increases.
The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.
This means that [tex]B(0) = 1150, B(1) = 2*1150[/tex]
So
[tex]B(t) = B(0)(1+r)^{t}[/tex]
[tex]2*1150 = 1150(1+r)^{1}[/tex]
[tex]1 + r = 2[/tex]
[tex]r = 1[/tex]
So
[tex]B(t) = 1150*(2)^{t}[/tex]
After 10 hours:
[tex]B(10) = 1150*(2)^{10} = 1177600[/tex]
1,177,600 bacteria after 10 hours.
A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is true. Let p ˆ be the proportion in a sample of 100 such ABC batteries. What is the probability that this sample proportion is within 0.05 of the population proportion.
Answers
Answer:
78.88% probability that this sample proportion is within 0.05 of the population proportion
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this question:
[tex]p = 0.8, n = 100[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
What is the probability that this sample proportion is within 0.05 of the population proportion.
This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.
X = 0.85
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944.
X = 0.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a pvalue of 0.1056.
0.8944 - 0.1056 = 0.7888
78.88% probability that this sample proportion is within 0.05 of the population proportion
Which equation has the solution x = 12?
(A
4x + 3 = 45
B
5x - 8= 68
2x - 5=29
3x +6=42
Answers
Answer:
D). last one
Step-by-step explanation:
a. 4x+3=45
4x=42
x=10.5 (incorrect)
b. 5x-8=68
5x=76
x=25.2 (incorrect)
c. 2x-5=29
2x=34
x=17 (incorrect)
d. 3x+6=42
3x=36
x=12
please ASAP , giving BRAINLIEST if correct.
Answers
Answer:
B. -3(4x + 1) (x - 4)
Step-by-step explanation:
Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).
However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answers
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.
Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places
Answers
Answer:
Hence, Stacy will spin 6, 8.33 times out of her n = 50 attempts.
Step-by-step explanation:
Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.
We will estimate the number of times that she spins a 6 as the expected value of this random variable.
Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.
Then , in this case, with n=50 and p=1/6 we expect to have number of times of having a 6, which is 8.33.
the stained glass below shows bilateral symmetry. The two overlapping squares are congruent. What is the area of the window?
Answers
Answer:
116.82 square inches
Step-by-step explanation:
The overall shape is that of a 10-inch square with four triangles attached. Each of those is an isosceles right triangle with leg lengths of 2.9 inches.
The area of the four triangles is ...
total triangle area = 4(1/2)(2.9 in)(2.9 in) = 16.82 in²
The area of the 10-inch square is ...
square area = (10 in)² = 100 in²
Then the total window area is ...
window area = 16.82 in² +100 in²
window area = 116.82 in²
Given: circle k(O), m AB = 120° m∠BCA = (x+60°) Find: x
Answers
Answer:
x=0
Step-by-step explanation:
<BCA is half of arc BA or half of 120 which is 60.
do the math, and then x has to be 0 degrees
The median and mode of this set of data (23,13,17,11,11)
Answers
Answer:
Mode: 11
Median: 13
Answer:
(23, 13, 17, 11, 11):
Median: 13
Arithmetic mean: 15
Geometric mean: 14.380735416546
Harmonic mean: 13.848764056076
Mode: 11
Standard deviation: 4.5607017003966
Variance: 20.8
Mean Absolute Deviation: 4
Range: 12
Interquartile range: 9
Lower quartile: 11
Upper quartile: 20
Quartile deviation: 4.5
Population size:5
A slot machine has 3 dials each dial has 30 positions one of which is jackpot. To win jackpot all three dials must be in jackpot position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot
Answers
Answer:
3/90
Step-by-step explanation:
1 slot is 1/30
2 slot is 1/30
3 slot is 1/30
this gives you that 3/90 when you had them
Answer:
D) 1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Step-by-step explanation:
will mark the branliest to first one who answers
Answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)
An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?
Answers
Answer:
696.265 inches
Step-by-step explanation:
Radius = 27/2 = 13.5
2 semicircles + 2 lengths
(3.14 × 13.5²) + 2(62)
696.265 inches
Answer:
696
Step-by-step explanation:
perform the following operations on matrices (1 8 0 7) (7 6 7 4) = ( )
Answers
Answer:
[tex]\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}1&8\\0&7\end{array}\right]\left[\begin{array}{cc}7&6\\7&4\end{array}\right]=\left[\begin{array}{cc}(1)(7)+(8)(7)&(1)(6)+(8)(4)\\(0)(7)+(7)(7)&(0)(6)+(7)(4)\end{array}\right]\\\\=\left[\begin{array}{cc}63&38\\49&28\end{array}\right][/tex]
Each element of the product matrix is the dot product of the corresponding row in the left matrix and the corresponding column in the right matrix.
For example, the element at row 2, column 1 of the product is [0 7]·[7, 7], the dot product of row 2 of the left matrix with column 1 of the right matrix.
_____
Many calculators, spreadsheets, and web sites can do this tedious math for you.
which number when rounded to the nearest hundredth is 37.62
Answers
Answer:
Answer: B
Step-by-step explanation:
The number given is 37.62. So, by rounding to the nearest hundredths the number becomes 37.612 and this can be determined by using the rules of rounding off to the nearest hundredths.
Given :
Number - 37.62
The following steps can be used to round off any number to the nearest hundredth:
Step 1 - In the thousandths place value analyze that digit to round off a decimal.
Step 2 - If the value is 5 or more than 5 in the thousandth place then the digit is increased by 1 which is at the hundredth place and in the thousandth place digit and thereafter becomes zero.
Now, the number given is 37.62. So, by rounding to the nearest hundredths the number becomes 37.612.
Therefore, the correct option is B) 37.612.
For more information, refer to the link given below:
https://brainly.com/question/2096984
Drag each tile to the correct box. Not all tiles will be used.
Arrange the equations in the correct sequence to find the inverse of f(x) = y = 3x / 8 + x
Answers
Answer:
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the function
[tex]f(x) = \frac{3 x}{8+x}[/tex]
Given function is one-one and onto function
Hence f(x) is bijection function
[tex]y = f(x) = \frac{3 x}{8+x}[/tex]
now cross multiplication, we get
( 8+x)y = 3 x
8 y + x y = 3 x
8 y = 3 x - x y
taking Common 'x' we get
x (3 - y) = 8 y
[tex]x = \frac{8 y}{3-y}[/tex]
Step(ii):-
The inverse function
[tex]x = \frac{8 y}{3-y} = f^{l}(y)[/tex]
The inverse function of x
[tex]f^{l}(x) = \frac{8 x}{3-x}[/tex]
Final answer:-
Inverse of f(x)
[tex]f^{l} (x) = \frac{8 x}{3-x}[/tex]
