Since log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b) for any logarithm base, we have
[tex]\dfrac{\log_x(64) + \log_x(4) - \log_x(8)}{\log_x(1024)} = \dfrac{\log_x\left(\dfrac{64\times4}8\right)}{\log_x(1024)} = \dfrac{\log_x(32)}{\log_x(1024)}[/tex]
Then using the change-of-base identity, we have
[tex]\dfrac{\log_x(32)}{\log_x(1024)} = \log_{1024}(32)[/tex]
But we also know that 2¹⁰ = 1024 and 2⁵ = 32, so we can back up slightly and instead write
[tex]\dfrac{\log_x(32)}{\log_x(1024)} = \dfrac{\log_x(2^5)}{\log_x(2^{10})} = \dfrac{5\log_x(2)}{10\log_x(2)}[/tex]
Then the logarithms cancel and you're left with 5/10 = 1/2.
there was a vote at a local school to determine a new logo. You are told 7% of the students wanted to keep the old logo, and that 7% represents 1,400 students at the school. how many students are at the school?
Step-by-step explanation:
Let the number of students be x,
Now,
7% of x = 1400
or, 7/100 X x = 1400
or, x = 1400 x 100
—————
7
or, x = 140000/ 7
or, x = 20000
Thus, there are 20,000 students
5.89 to the nearest 10th
Answer:
5.9
Step-by-step explanation:
Did you mean rounding?
8 is in the tens place, and 9 is in the hundreds place. If the number in the hundreds place is greater than the number in the tens place, the tens place moves up by 1.
So 5.89 becomes 5.9
Which of the following shows the prime factorization of 72 using exponential notation?
Answer:
2^3 .3^2
Step-by-step explanation:
if 2×2×2 = 8
and 3×3=9 then 8×9=72
Answer:
2³ × 3²
Step-by-step explanation:
Repeatedly divide by 2 until finish, then divide by 3
72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9 , then
9 ÷ 3 = 3
3 ÷ 3 = 1 ← finish when 1 is reached
Then
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Can someone help me with these? Pls Answer ill mark Brainliest
Answer:
ok
Step-by-step explanation:
ok
Maggie's brother is 11 years younger than three times her age. The sum of their ages is 41.
How old is Maggie?
Maggie is_______ years old
Answer:
Maggie is 13 years old.
Step-by-step explanation:
The explanation is attached.
Laske arvo,kun a=2. a^4
Hey there!
a^2
= 2^4
= 2 * 2 * 2 * 2
= 4 * 4
= 16
Therefore, your answer is: 16
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
g(x)=
Write a relationship for a function whose g(x) values are 2 more than five times the principal square root of x.
Lets do
2 more than five times the square root of x[tex]\\ \sf\longmapsto g(x)=5\sqrt{x}+2[/tex]
Lets take an example
[tex]\\ \sf\longmapsto g(4)=5\sqrt{4}+2[/tex]
[tex]\\ \sf\longmapsto 5(2)+2[/tex]
[tex]\\ \sf\longmapsto 10+2[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
Simplify attachment below
Answer:
Simplifies to:
5.991339a^5b^3
What is the y intercept?
The yintercept is (0,0)
The reason why is because that is the place that intersects the y axis.
You solve an equation by finding the value that is?
The _____ measures the variation in the dependent variable that is explained by variables other than the independent variable in simple regression analysis .
a. total sum of squares
b. sum of squares error
c. sum of squares within
d. sum of squares regression
Find the first 8 multiples of 92
Answer:
92, 184, 276, 368, 460, 552, 644, 736, 828, 920
Step-by-step explanation:
hope this helps :D
brainliest appreciated
Deductive reasoning
Deductive reasoning is a basic form of valid reasoning. Deductive reasoning, or deduction, starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion, according to California State University.
HOPE IT HELPS ✨
The angle measures 42°, 50°, 130°, and 138° are written on slips of paper. You choose two slips of paper at random.
What is the probability that the angle measures are supplementary? Enter your answer as a fraction.
WILL MARK YOU BRAINLY
Answer:
1/3Step-by-step explanation:
Combination of pairs of paper slips:
4C2 = 4!/(2*2) = 6A pair of 50 with 130 and 42 with 138 are the two pairs of supplementary angles.
The probability is:
P(supplementary pair) = 2/6 = 1/3Step-by-step explanation:
slips=2Angles=4Apply combination
4C_24!/((4-2)!2!)4!/2!2!24/46P(supplementary)
2/61/333.33%What is the HCF of 25, 45
Answer:
5
Step-by-step explanation:
25 = 5 x 5
45 = 5 x 9
Hey there!
25: 1, 5, & 25
because: 5 * 5 = 25 & 1 * 25 = 25
45: 1, 3, 5, 9, 15, 45
because: 1 * 45 = 45, 3 * 15 = 45, & 5 * 9 = 45
Common factors: 1 & 5
The bigger number of those two is 5
Therefore, your possible answer is: 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Set theory Need answers quick
Answer:
4. {2,4,6,8}
5. [(-2, -1), (1, 8)}
9. {0, 2}
Step-by-step explanation:
The intersection of the given sets is the set that contains elements common to all of the given the sets.
Question 2
5 pts
Which of the following subtraction problems show a difference of 12.93?
Select TWO that apply.
51.639 - 38.709
146.8 - 17.5
136.8 - 122.87
18.63 - 5.7
Answer:
51.639-38.709
18.63-5.7
Step-by-step explanation:
Hope it helps...
The distance between the points (a, b) and (c,d) is
Need Help? Read It
Submit Answer
Viola Dr
Unfortunately there's not much we can say other than
[tex]\text{distance} = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\\text{distance} = \sqrt{ (a-c)^2+(b-d)^2}\\\\[/tex]
If we knew the numbers that replace a,b,c,d, then we could compute the actual numeric distance.
PLEASE HELP ME!!! Ror what values of k will the relation not be a function S={(2-|k+1|, 4), (-6, 7)}
Answer:
Step-by-step explanation:
The relation S is note a function when
2 - |k+1| = -6
Because when they are equal we have two points (-6,4) and (-6,7) in S which implies that -6 is related to two different values.
Now solving
2 - |k+1| = 6
2 - |k+1| = 6
2 - 6 = |k+1|
-4 = |k +1|
But absolute value always non negative, so there is no such k.
Find the greatest common factor of 30 and 105. 3 15 30 5
Answer:
15
Step-by-step explanation:
factorise your numbers
1x 30
2x 15
3x10
etc
go through all the numbers up till there isnt any more numbers then find the largest and common one between the two numbers
An angle measures 85.2° less than the measure of its complementary angle. What is the measure of each angle?
Answer:Complementary angles are two angles whose sum is 90 degrees.
Let x represent one of the angles.
The other angle which is 84.2 degrees less would be x - 84.2.
Using this, we can write an equation.
x + (x-84.2) = 90.
Combine like terms: 2x - 84.2 = 90
Add 84.2 to both sides of the equation.
2x = 174.2
Divide by 2: x = 87.1
and x - 84.2 would equal 2.9. to check: does 87.1 + 2.9 = 90? yes.
Step-by-step explanation: Thats as close as its gonna it i think
Create a scale drawing of the Colombian flag with a scale of 2 cm to 1 ft
There are 450 students in my high school. 39 students are taking AP
statistics and 86 students are taking AP calculus. 12 students are
taking both AP statistics and AP calculus. If a student were to be
selected at random from the whole school, what is the probability of
the student chosen taking only AP statistics? Give your answer as a
decimal.
The probability that a student will be picked from a AP statistics class is 0.06
What is Probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 is certainty
Probability = sample space / total possible outcome
the total possible outcome is 450 students
the number of students that take AP statistics alone = 39- 12= 27students
therefore probability of choosing from AP statistics= 27/450= 0.06
learn more about probability from
https://brainly.com/question/24756209
#SPJ1
A fruit basket weighing a total of 15 lbs. contains three types of fruit: apples, oranges, and pears. The apples weigh 4 1/2 lbs. The oranges weigh twice the amount the apples weigh, and the pears weigh the rest. Which of the following expressions could be used to find the weight of the pears?
Answer Choices:
A) (4 1/2+4 1/2 *2) - 15
B) 15 - (4 1/2*2)
C) 15 - (4 1/2+4 1/2 *2)
D) 15 - (9*2)
Help appreciated
Answer:
B is most likely the answer
Step-by-step explanation:
4 1/2 * 2= 9 so 15-9= 6
Pears weight is 6 Ibs and
4 1/2 *2 would make the most sense
Cual es el exceso de 150 sobre 76?
Answer: The answer is 74
Need help with these
Answer:
CNot clearAACStep-by-step explanation:
1) 2x + 246 = 360° (Vertically opposite and angle at a point)
2x = 360 - 246
2x = 114°
x = 114 / 2
x = 57°
3) Since <ABD is a right angle (i.e its sum is 90°)
<CBD = 90° - 75° = 15°
5) <1 = <2 (Vertically opposite angles are equal)
12x + 3 = 10x + 15
12x - 10x = 15 - 3
2x = 12
x = 6
Therefore,
<2 = 10(6) + 15
<2 = 75°
Maths log question please help- image attached
Answer:
a = 2 and b = -1.
Step-by-step explanation:
We want to show that the equation:
[tex]\displaystyle \log_{2} \left( y + 1\right) - 1 = 2\log_{2} x[/tex]
Can be rewritten as:
[tex]\displaystyle y = ax^2 + b[/tex]
Where a and b are integers.
Note that:
[tex]\displaystyle 1 = \log _{2} 2[/tex]
Hence:
[tex]\displaystyle \log_{2} \left( y + 1\right) - \log _2 2= 2\log_{2} x[/tex]
From logarithmic properties:
[tex]\displaystyle \log_2 \left(\frac{y+1}{2}\right) = 2\log_2 x[/tex]
Likewise:
[tex]\displaystyle \log_2 \left(\frac{y+1}{2}\right) = \log_2 x^2[/tex]
For the logs to be equivalent, the inner equations must be equivalent. Hence:
[tex]\displaystyle \frac{y+1}{2} = x^2[/tex]
Simplify:
[tex]\displaystyle y = 2x^2 - 1[/tex]
In conclusion, a = 2 and b = -1.
7y -2 = 26 help me please
Y=
Answer:
y = 4
Step-by-step explanation:
7y -2 = 26
+2 +2
----------------
7y = 28
---- -----
7 7
y = 4
Hope this helped.
does anybody know this
Step-by-step explanation:
The equation used to determine the amount of radioactive material left is
[tex]A = A_0(2)^{-t/HL}[/tex]
We are have the following given quantities:
t = 30 seconds
[tex]A_0[/tex] = 50 grams
HL = 6 seconds
Plugging these into our equation we get
[tex]A = (50\:\text{grams})(2)^{-(30s/6s)}[/tex]
[tex]\:\:\:\:= (50\:\text{grams})(0.03125)[/tex]
[tex]\:\:\:\:= 1.56\:\text{grams}[/tex]
Please Help! I will give you a lot of points if you do!
--This is Hindu-Arabic math so you have to use their number system
Answer:
47
Step-by-step explanation:
According to the number system 7 lines and 12 dots, a line is 5 and a dot is 1
you do 5*7+12 which is equal to 47
So the answer is 47,
Hope this helps!
First look at the chart and then convert each symbols to their respective numbers
[tex]\\ \tt\longmapsto 6+14+13+4+0+10[/tex]
Now add[tex]\\ \tt\longmapsto 20+17+10[/tex]
[tex]\\ \tt\longmapsto 37+10[/tex]
[tex]\\ \tt\longmapsto 47[/tex]
