Rewrite the logarithm log8(2) as an exponential expression then find the value of the logarithm
Answer:
exponential expression:
8ᵇ = 2
log8(2) = 0.333333333 or 1/3
Answer:
log8(2) = 1/3
Step-by-step explanation:
I don't know if they mean this by an exponential expression but:
set x = log8(2), then
8^x = 8^(log8(2))
By logarithmic properties:
8^x = 2.
notice that 8 = 2^3.
By exponential properties:
8^x = (2^3)^x = 2^(3x)
So 2^(3x) = 2 = 2^1.
Comparing exponents gives:
3x = 1 <=> x = 1/3.
So log8(2) = 1/3.
What is 39/20 written as decimal ?
Answer:
1.95
Step-by-step explanation:
if you can buy 3 loaves of bread for $5 how many loaves can you buy for $12
Answer:
You can buy 6 because it cost 2.50 for 1 loaf
Step-by-step explanation:
Solve for a
-3=a+4
I need some help today
HELP ASAP (1O BRAILY/POINTS FOR ANSWER)
What is the value of x in the solution of the system?
x + y = 3
y = -6x + 3
Step-by-step explanation:
x + y = 3 ---------------- eqn 1
y = -6x + 3 ------------- eqn 2
Substitute y for -6x + 3 in equation 1
x + -6x + 3 = 3
x - 6x + 3 = 3
-5x + 3 = 3
Collect like terms
-5x = 3 - 3
-5x = 0
Divide both sides by -5
x = 0
Hope this helped!
Step-by-step explanation:
x + y = 3 ---------------- eqn 1
y = -6x + 3 ------------- eqn 2
Substitute y for -6x + 3 in equation 1
x + -6x + 3 = 3
x - 6x + 3 = 3
-5x + 3 = 3
Collect like terms
-5x = 3 - 3
-5x = 0
Divide both sides by -5
x = 0
Help help help help help help pls
Answer:
a.) 36
b.) 18
c.) 27
Step-by-step explanation:
Well happy New Year everyone. I've been thinking about the upcoming year "2021" and found something interesting. Reduced to its prime factors it becomes 43*47. Yes, it resolves into 2 CONSECUTIVE 2 digit prime numbers, which does NOT happen that often. The last time this occurred was in 1927 (41 * 47). However these are NOT consecutive prime numbers. (There's another prime number between 41 and 47). If we go back to 1763 (41 * 43), it resolves into two 2-digit CONSECUTIVE primes AND they are TWIN primes (prime numbers with a difference of 2).
And now, here's the question: Can anyone find some interesting factorizations of upcoming years? For example, the year 2033 = 19*107 and the year 2041 = 13*157. In each case the factors are less than 10. Obviously, this is not THE most vital question, so don't spend too much time on it. (Although I've been told that a solution will finally bring about World Peace!!! ) LOL
Answer:
As 2021 and 1927 does not have any product of primes
HCF and LCM of 2020 and 1926 is shown below
Step-by-step explanation:
2020 = 2^2 × 5 × 101
1926 = 2 x 3^2 x 107
2 is the HCF
2 x 2 x 3 x 3 x 5 x 101 x 107 = 1945260
1945260 is the LCM
2022 and 1928 both have product of primes and their HCF and LCM is
1949208 is the LCF and 2 is the HCF
1949208 - 1945260 = 3948
3948/2 = 1974
2022-1928 = 94
2020 - 1926 = 94
1974/94 = 21
and brings us back to our year again.
Happy New Year to you.
a hotel with 75 rooms has 45 for doubles and 30 singles. singles can be booked in any room, but reservations for two or more people must be booked in double rooms. what inequalities represents this situation?
Answer:
y = 75 - x
Step-by-step explanation:
From the question, we are given variables, and then we can see that
when x = 75 then y = 0
when x = 30 then y = 45
Finding the difference, we have
slope(m) = (45 - 0) / (30 - 75)
slope(m) = 45 / -45
slope(m) = -1
Next, we use the calculated m, to find b, using the formula
y = mx + b
0 = -1 * 75 + b
0 = -75 + b
b = 75
And finally, to get the needed equation, we say that
so y = mX+c
So that
y = -1 * x + 75
y = -x + 75
or y = 75 - x
Robert pays $32.04 for 6 student tickets to the basketball game. What is the cost of each student ticket?
Answer:
$5.34
Step-by-step explanation:
Step-by-step explanation:
$5.34
hope it helps!
......
Help me out here pleaseeeeee
Answer:
C
Step-by-step explanation:
If U is the set of all multiples of 3 less than 20, and M={3,12,18}, find Mc (the complement of M). Express your answer as a set in the roster form: i.e. {a,b,c...}.
Answer:
Step-by-step explanation:
U={3,6,9,12,15,18}
M={3,12,18}
M'={6,9,15}
The answer is,
U={3,6,9,12,15,18}
M={3,12,18}
M'={6,9,15}
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
here. given that,
U is the set of all multiples of 3 less than 20,
i.e. U={3,6,9,12,15,18}
and M={3,12,18},
Mc (the complement of M),
i.e. M'={6,9,15}.
Hence, we get, U={3,6,9,12,15,18} , M={3,12,18} & M'={6,9,15}.
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A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
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Answer all of these
18% of 34
27% of 81
85% of 74
54% of 90
33% of 360
TOPIC
62% of 75
4% of 56
6% of 140
© 12% of 625
5% of 134
Finding a Percent of a
90% of 44
9% of 17
48% of 20
70% of 69
2% of 800
Some doctors recommend that no more than 30% of a
person's daily calones come from fats. Following this
recommendation. If you eat 2,400 calones in a day, what
is the maximum number that should come from fats?
When training for a fight Rocky tries to maintain a heart
rate that is 80% of his maximum heart rate, Rocky has a
resting heart rate of 60 and a maximum heart rate of
175 beats per minute. What is his training heart rate?
mbe
Answer:
18% of 34 = 6.1227% of 81 = 21.8785% of 74 = 62.954% of 90 = 48.633% of 360 = 118.862% of 75 = 46.54% of 56 = 2.246% of 140 = 8.412% of 625 = 755% of 134 = 6.790% of 44 = 39.69% of 17 = 1.5348% of 20 = 9.670% of 69 = 48.32% of 800 = 16-------------------------------------
30% of 2400 = 720 calories--------------------------------------
80% of 175 = 140 beats per minuteIn order from less complex to more complex, which level of organization is directly after tissue?
PLEASE HELP!! It’s urgent!! I will mark brainliest
Answer:
a,c,d
Step-by-step explanation:
Answer:
the answer is F, C, A
Which of the following expressions is equivalent to the expression 42+90?
A. 6(7+14)
B.6(7+15)
C.7(6+12)
D.6(36+84)
Answer:
B
Step-by-step explanation:
6(7+15)
= 6(7) + 6(15)
= 42 + 90
:D it helps!
Find the x-intercept and y-intercept of the line given by the equation below. Then graph the line.
x + y = 2
X-intercept:
y-intercept:
For exercises 16-18 , trace each figure and draw its rotated image
Help me please I don’t know it
9 = 40 + 13
Helpppppp I need it due today
Its is equal to 9x6=53 Goodluck
Tamara draws a tile from a bag and records the results. The bag contains tiles labeled with the letters, W, A, T, E, R, M, E, L, O, and N. Based on this information, which statement is true?
Answer:
These are the statements. I need help to
Step-by-step explanation:
She is 1.5 times less likely to draw a vowel than a consonant.
She is 1.5 times more likely to draw a vowel than a consonant.
She is twice as likely to draw a consonant as a vowel.
Drawing a vowel and a consonant are equal likely.
-5b = -20 b= need help with homwork
Answer:
b = 4
Step-by-step explanation:
you must divide both sides of the equation by -5 to get b by itself. division cancels out multiplication but also keeps both sides equal
b = -20/-5
b = 4
when a load of 5 pounds is placed on a spring, its length is 6 inches, and when a load of 9 pounds is placed on the spring, its length is 8 inches. what is the average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds? give units on your answer
Four inches every four and a half pounds
The average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.
What is average?It is a measure of how much the function changes per unit, on average, over the given interval.
We have,
5 pounds loaded on a spring:
The length of the spring is 6 inches.
9 pounds loaded on a spring:
The length of the spring is 8 inches.
The average rate of change in the length of the spring as the load varies:
= (8 - 6) / (9 - 5)
= 2 / 4
= 1 / 2
= 0.5 inches per pound
Thus the average rate of change of the length of the spring as the load varies from 5 pounds to 9 pounds is 0.5 inches per pound.
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If it takes 3 gallons of gas to go 60 miles, how many gallons of gas does it take to go 440 miles at the same rate?
Answer:
it would take 22 gallons of gas
Step-by-step explanation:
3 divided by 60
that’s the amount of gas per single mile
then that number times 440 (number of miles you wish to go).
Please Help! Will mark brainliest!
Directions; Write a system of equations for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
A golfer completed 18 holes with a total of 79 strokes. On each hole, he met par, which was either four or five each time. How many holes were played in four-strokes?
Answer:
11
Step-by-step explanation:
Let a= times he hit 4 par
Let b = times he hit 5 par
a+b=18 => 4a+4b = 72
4a+5b=79
b=79-72=7
So a = 11
answer:
18 = 4a + 5b = 79, b = 79 - 72 = 7 → 11 holes
i hope this helps ♡♡♡
Find the distance between a point (-7,-19) and a horizontal line at y = 3 .
The line is horizontal so the x value of the dot doesn’t matter because the x is a horizontal location.
The vertical distance would be the y value to the line.
-19 to 0 would be 19 and from 0 to 3 is 3
Total distance is 19 + 3 = 22
The answer is 22
Mike and Joe each receive money for their lunch. Mike receives $100 and spends $3 each day on his lunch. Joe receives $20 and then an additional $5 each day. Joe saves his
money and does not buy lunch. How many days will it take for Mike and Joe to have the same amount of money?
Solve for the variable in the proportion below. Type the number only. Your answer should be a whole number.
2/4 =5/x
x =
Solve for the complimentary angle b
Answer:
b = 38
Step-by-step explanation:
The two angles form a 90 degree angle so they add to 90
b+52 = 90
Subtract 52 from each side
b+52-52 =90-52
b = 38
Answer:
38
Step-by-step explanation:
90-52=38
and the little box indicates it's a right angle which is 90 degrees
A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?
Answer:
4/9
Step-by-step explanation:
simplify if you ned
d to
n(s) = 9
n(e) = 6
p(e) = 6/9 = 2/3
Step by step explanation
1. n(s) = Number of sample space
2. n(e) = Number of events
here , question asks to find the probability of marbles that are not blue , that means
red and green so n(e) = 6
3. p(e) = probability