Answer:
2
Step-by-step explanation:
using the rules of logarithms
logx + logy = log(xy)
logx - logy = log ([tex]\frac{x}{y}[/tex] )
log[tex]x^{n}[/tex] ⇔ nlogx
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
3log2 + log200 - log16
= log 2³ + log200 - log16
= log8 + log200 - log16
= log(8 × 200) - log16
= log1600 - log16
= log ([tex]\frac{1600}{16}[/tex] )
= log100
let [tex]log_{10}[/tex] 100 = n , then
100 = [tex]10^{n}[/tex] = 10²
thus value of expression is n = 2 , that is 2
[tex]2 \cdot 1[/tex]Answer:
Equal to 2
Step-by-step explanation:
1. Apply log rule: [tex]alog_c(b) = log_{c}(b^a)[/tex]
[tex]3log_{10}(2) = log_{10}(2^3)[/tex]
[tex]= log_{10}(2^3) + log_{10}(200) - log_{10}(16)[/tex]
2. Apply log rule: [tex]log_c(a) + log_c(b) = log_c(ab)[/tex]
[tex]log_{10}(2^3) + log_{10}(200) = log_{10}(2^3 \cdot 200)[/tex]
[tex]= log_{10}(2^3 \cdot 200) - log_{10}(16)[/tex]
[tex]2^3 \cdot 200 = 1600[/tex]
[tex]= log_{10}(1600) - log_{10}(16)[/tex]
3. Apply log rule: [tex]log_c(a) - log_c(b) = log_c(\frac{a}{b})[/tex]
[tex]log_{10}(1600) - log_{10}(16) = log_{10}(\frac{1600}{16})[/tex]
Divide the numbers: [tex]\frac{1600}{16} = 100[/tex]
[tex]= log_{10}(100)[/tex]
Rewrite 100 in power - base form: [tex]100 = 10^2[/tex]
[tex]= log_{10}(10^2)[/tex]
4. Apply log rule: [tex]log_a(x^b) = b \cdot log_a(x)[/tex]
[tex]log_{10}(10^2) = 2log_{10}(10)[/tex]
[tex]2log_{10}(10)[/tex]
5. Apply log rule: [tex]log_a(a) = 1[/tex]
[tex]log_{10}(10) = 1[/tex]
[tex]= 2 \cdot 1 = 2[/tex]
On Tuesday, recess began at 11:43. The students got back to their class at 12:04. How long were they at
recess?
Answer:
They were out side for 21 minutes
Step-by-step explanation:
you just add 11:43 and add 21 minutes to it and you get 12:04
(I.5)
Write the sentence as an equation.
148 is equal to 12 minus z
Type a slash ( / ) if you want to use a division sign.
Answer:
the verbal sentence so it is easier to translate. ... 12 equals p divided by. 4 n. 2. +. 12. = p. ÷. 4. 4. Half of j minus 5 is the sum of k and 13.
Step-by-step explanation:
Solve the following expression when
p = 15
P + 4
_
3
Answer:
49/3 or 16.33...
Step-by-step explanation:
15 + 4/3.
15/1 + 4/3
45/3 + 4/3.
ANSWER: 49/3
9. You roll a standard number cube (with 6 sides) 8 times. The results are 5, 1, 2, 4, 6, 3, 5, 5
a. What is the experimental probability of rolling a 5 on a standard number cube?
b. For 40 rolls of the number cube, predict the number of rolls that will result in a 5 based on your experiment.
Answer:
a) we have 5 there 3 times so answer is 3/8
b)
for 8 times rolling 3 times 5 we have
for 40 times rolling will 15 times 5
Step-by-step explanation:
a) we have 5 there 3 times so answer is 3/8
b)
for 8 times rolling 3 times 5 we have
for 40 times rolling will 15 times 5
Assuming that Dave’s marginal tax bracket is 25%, but how much did his federal taxes declined this year if he contribute 7000 to his retirement account?
The marginal tax bracket of Dave shows that the amount of the federal tax is $28000.
How to compute the tax?Let the federal tax be represented by x.
From the information, Dave’s marginal tax bracket is 25%, and he contributed 7000.
Based on the information, the amount will be:
25% of x = 7000
0.25 × x = 7000
0.25x = 7000
x = 7000/0.25
x = $28000
In conclusion, the amount is $28000.
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0.6 × 0.8 = ___ I need help with this question KNOW!!!!!!
ANSWER = 0.48
HOPE IT HELPS :)
Answer: 0.48
Step-by-step explanation:
6 x 8 = 48
we add those decimals back in which would be 0.48
Which is greater -8.5 or -15
Answer:
-8.5
Step-by-step explanation:
this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.
Find the quotient and the remainder of
64−133+32+3−12
-------------------------------
−2
Answer:
Below
Step-by-step explanation:
64-133+32+3-12= -46
-46/2= -23
There is no remainder
Please help me thank u!
Answer:
The odds of drawing a heart are 13:52
Explanation: A standard deck of card contains 52 card. There are 4 types of playing cards: clubs, diamonds, hearts and spades. Every type of them has 13 cards. How do u know that? Well just divide 52 by 4 and then you get 13.
Estimate how many times larger 5x10^8 is than 24x10^6?
A) 10 times larger
B) 20 times larger
C) 50 times larger
D) 100 times larger
Answer:
20times bc u times 5 by 10 then divide 8 u get 6.2
Need Help Confused give explanation please and thanks
Which point is located at (–0.50, –1.25)?
Point
Answer:
Hopefully, this helps you!!
:3
Here's a graph!
Have a great day!!
[tex]Sokkachan[/tex]
Answer:
Point W
Step-by-step explanation:
What is the equation of the line that passes through the point (3, 5) and has a slope
of -1/3
Answer:
[tex]Y=-\frac{1}{3} + 6[/tex]
Hope This Helps! :) Please Mark Brainliest!
a cart is pushed 40 meters against 45 newtons of friction = how much work done
Answer:
-1.8 kJ
Step-by-step explanation:
Given
Displacement = 40 metersForce against = 45 NSolving
W = F x SW = - 45 x 40W = -1800 J = -1.8 kJAnswer:
2250 J
Step-by-step explanation:
Work done is given by the formula :
work done = force × distance
Substituting values given gives us:
Work done = 45 × 40
Work done = 2250 J
You deposit $1500 in an account earning 3.5% interest compounded monthly.
a. a. How much will you have in the account in 20 years?
b. b. How much interest will you earn?
Answer:
Answer:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
Step-by-step explanation:
Standard equation of a circle: \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2
\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2
Now substitute the point (-7, 5) into the equation to find r²:
\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2
\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2
\sf \implies 149=r^2⟹149=r2
Final equation:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
Sample question.....asajs
Answer:
Bob
Step-by-step explanation:
Answer:
..............................
The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.
The actual roots ordered from least to greatest are?
The actual roots of the function P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45 are its real roots
The actual roots ordered from least to greatest are -3 and 3
How to determine the actual roots?From the complete question, the polynomial function is:
P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45
Expand the above equation
P(x) = x^4 - 4x^3 + 5x^2 - 9x^2 + 36x - 45
Factorize the equation
P(x) = x^2(x^2 - 4x + 5) - 9(x^2 - 4x + 5)
Factor out x^2 - 4x + 5
P(x) = (x^2- 9)(x^2 - 4x + 5)
Express x^2 - 9 as a difference of two squares
P(x) = (x + 3)(x - 3)(x^2 - 4x + 5)
The expression (x^2 - 4x + 5) cannot be factorized.
So, we have:
P(x) = (x + 3)(x -3)
Equate to 0
(x + 3)(x -3) = 0
Expand
x + 3 = 0 or x - 3 = 0
Solve for x
x = -3 or x = 3
Hence, the actual roots ordered from least to greatest are -3 and 3
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Answer:
answer in picture
Step-by-step explanation:
Felix buys five vests for $22 each, three pairs of shoes for $50 each, and six hats for $17 each. What is the mean amount that he spent?
A. $34.62
B. $32.81
C. $25.86
D. $22
Answer: C
Answer:
$ 25.86 is the answer
Step-by-step explanation:
The average weight of an adult black bear is 4.35 x102 pounds.
This is 15 times as much as Shaneen's dog weighs.
What is the weight of Shaneen's dog?
Answer: B (2.9 x 10)
Step-by-step explanation: (4.35 x 10^2)/15 = 29 = 2.9 x 10
What is the next fraction in this sequence? Simplify your answer 1/52 1/26 1/13 2/13
Answer:
4/13
Step-by-step explanation:
The pattern is that every number is multiplied by 2 starting at 1/52. To find the next fraction in the sequence, multiply 2/13 by 2:
[tex]\frac{2}{13} (\frac{2}{1} )=\frac{4}{13}[/tex]
4/13 is our final simplified answer
I hope this helps!
Which function is the inverse of f(x) = -5x -4?
Answer:
f−1(x)=x5+45
Step-by-step explanation:
please help me
and please show good answers
Answer:
1st one is 0.021
2nd one is 0.009
the last question is 0.015 tho
Answer:
for the first one it will be 0.021
the second one it's 0.009
and for the third one it will be 0.015
If Jo's misc. expenses rise by 1/3 and she starts paying for a phone that is $49 per month, how much less will she have towards next years holiday it all other expenses and her wage and bonus stay the same?
The amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.
Original payment for the phone
The initial amout that Jo paid for the phone is calculated as follows;
amount per month = ($49) / (1 + ¹/₃)
amount per month = ($49) / (1.333)
amount per month = $36.76
For 1 year (12 months), = $36.76 x 12 = $441.12
Amount paid now$49 x 12 = $588
Amount she will have less towards next year= $588 - $441.12
= $146.88
Thus, the amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.
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a tree diagram represents an experiment consisting of two trails.
P(A and D) = [?]
Answer:
0.3
Step-by-step explanation:
Start at the beginning, follow the branch to A and then the branch to D (see attached annotated diagram).
When calculating the probability of an event AND another event, multiply the probabilities.
P(A and D) = 0.5 x 0.6 = 0.3
If prices increase at a monthly rate of 0.1%, by what percentage do they increase in a year?
Answer:
Step-by-step explanation:
Since the prices increase at a monthly rate of 0.1% per month. To find the percentage do they increase a year, we need to convert 0.1% to a decimal.
So here how we do it. We put 0.1 percent on the numerator because it a small number which is what we want over 100 like this:
[tex]\frac{0.1}{100}[/tex]
Now when plugging this into your calculator you get:
0.001
.So what do we do with this number?
We now times it by 12 like this:
0.001 x 12 which gives us:
0.012
So we can convert this back to a percentage by moving the decimal by 2 places to the right which gives us 1.2%.
Another way we could of done this without doing the long way to figure it out is by multiplying 0.1 times 12 which still gives us 1.2%
HELP PLEASE!!!
Worth 1 point
Giving 30!!
PLS HELP
I'LL GIVE BRAINLEIST IF CORRECT!!
Answer:
^EKF and^HKI
Step-by-step explanation:
Because they are vertically opposite angles
Approximately how many
years would it take for an
investment of $1,000 to grow
to $1,500 with a simple
interest rate of 8%?
Answer:
6.25 years
(6 years 3 months)
Step-by-step explanation:
Simple interest formula
A = P(1 + rt)
where:
A = final amountP = principalr = interest rate (in decimal form)t = time (in years)Given:
A = $1,500P = $1,000r = 8% = 0.08Substitute given values into the formula and solve for t:
⇒ 1500 = 1000(1 + 0.08t)
⇒ 1500 = 1000 + 80t
⇒ 500 = 80t
⇒ t = 6.25 years
Solve the proportion.
3x/10=3/2
In order to solve a proportion, you should cross-multiply:-
[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]
Multiply 3x times 2 and 10 times 3:-
[tex]\bf{6x=30}[/tex]
Divide both sides by 6:-
[tex]\boxed{\bf{x=5}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Please help me
10 points
answer:
127.2345in²
explanation:
attached
--
if this helped, please consider giving brainliest !
There was 1/2. Of a cake left over from Hannah’s birthday party when she and her sister came home from school the next day they ate 2/3 of the left over cake for a snak. How much of the whole cake did the girls eat
Answer:
1/3
Step-by-step explanation:
This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.
