Answer:
10log10(3)abc
The equivalent expression for the log function log3(a^5bc^2) is 5log3a+log3b−2log3c
Logarithmic functionsLogarithmic functions are expressed as the inverse of exponential functions.
Given the logarithmic expression
log3(a^5bc^2)
Since product are written in form of addition, hence;
log3(a^5bc^2) = log3(a^5) + log3(b) + log3(c^2)
The power will be carried to the back of the log function;
log3(a^5bc^2) = 5log3(a) + log3(b) + 2log3(c)
This gives the equivalent expression for the log function log3(a^5bc^2)
Learn more on logarithmic expression here: https://brainly.com/question/25710806
which term in the quotient of this expression contains an error?
Answer:
The + 78 :- it should be + 60.
Step-by-step explanation:
Long division:-
x - 3 )4x^4 - 6x^3 + 0x^2 + 6x + 3 ( 4x^3 + 6x^2 + 18x + 60 <--- Quotient.
4x^4 - 12x^3
6x^3 + 0x^2
6x^2 - 18x^2
18x^2 + 6x
18x^2 - 54x
60x + 3
60x - 180
183
I’ll mark brainliest
Answer:
[tex]\text{A. }y=1.30x+1.50[/tex]
Step-by-step explanation:
The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.
For any exponential function of the form f(x) = a · b^x where b≠0, what is the y-intercept of the graph of f(x)?
(0,a)
(1,0)
(a,0)
(0,1)
Answer:
1) (0,a)
Step-by-step explanation:
f(0) = a. b^0 = a. 1 = a
=> (0,a)
Find the surface area of the
prism.
Answer:
Area of front and back = 2 * 2 * 5 = 20 cm^2
Area of sides = 2 * 3 * 4 = 24 cm^2
Area of top and bottom = 2 * 4 * 5 = 40 cm^2
TOTAL area = 84 cm^2
Step-by-step explanation:
Find the distance between A(-3, 2) and B(5, -1).
will mark brainliest
Answer:
(x, y) = (-2,-5)
Step-by-step explanation:
Multiply the first equation by 3,and multiply the second equation by 1.
3(3x+y=−11)
1(4x−3y=7)
Becomes:
9x+3y=−33
4x−3y=7
Add these equations to eliminate y:
13x=−26
Then solve13x=−26for x:
13x=−26
13x
13
=
−26
13
(Divide both sides by 13)
x=−2
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
3x+y=−11
Substitute−2forxin3x+y=−11:
(3)(−2)+y=−11
y−6=−11(Simplify both sides of the equation)
y−6+6=−11+6(Add 6 to both sides)
y=−5
Answer:
x=−2 and y=−5
As shown in the diagram below, AABC - A DEF, AB=14, BC=4, DE=7, and EF = X
D
14
B
4
С
E
X
F
What is the length of EF?
А
28
B
14
2
4
Answer:
EF=4
Step-by-step explanation:
vì diện tích bằng nhau và bằng 28 áp dụng công thức tính diện tích
identify the angle type, then find the value of x
9514 1404 393
Answer:
acute anglex = 25Step-by-step explanation:
The angle shown is 75°. It is less than 90°, so is an acute angle. (The diagram is misleading in that respect.)
__
The two marked angles are vertical angles, so have the same measure.
3x° = 75°
x = 25 . . . . . . . . divide both sides by 3°
1. A drama club earned $662.50 from a production where 85 adult tickets were sold and 65
student tickets were sold. An adult ticket costs $2.50 more than a student ticket. Which
system of equations can be used to find a, the cost of an adult ticket, and s, the cost of a
student ticket?
Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44
Step-by-step explanation:
Let the cost of adult ticket be 'x' and cost of student ticket be 'y'
From the question, the equations formed are:
[tex]662.5=85x+65y[/tex] .....(1)
[tex]x=2.5y[/tex] ......(2)
Putting value of 'y' from equation 2 to equation 1:
[tex]662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44[/tex]
Now, solving for 'x', we get:
[tex]x=2.5(2.44)=\$ 6.1[/tex]
Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44
libreng puntoss
yeeah
PA BRAINLIEST
Which is the graph of an even monomial function?
Answer:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
please help quick!!!
The circle above has a radius of 7 cm. What is the area of the circle
Answer:
153.86 cm²
Step-by-step explanation:
Area circle = πr²
Area = 3.14 * 7²
Area = 3.14 * 49
Area = 153.86
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which drink has more sugar per fluid ounce? 50 POINTS
There is a mound of g pounds of gravel in a quarry. Throughout the day, 200 pounds of gravel are added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,400 pounds of gravel.
Write the equation that describes the situation. Then solve for g.
Answer:
g + 200 - 2*600 = 1400
g = 2400 pounds
Step-by-step explanation:
g + 200 - 2*600 = 1400
g + 200 - 1200 = 1400
g - 1000 = 1400
g = 2400
Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 67 and standard deviation 10 when given to third graders. Sixth graders have mean score 86 and standard deviation 9 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)
(a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.) a = b = (b)
Do the same for the sixth-grade scores.
a =
b =
(c) David is a third-grade student who scores 79 on the test. Find David's transformed score.
Nancy is a sixth-grade student who scores 79. What is her transformed score?
Who scores higher within his or her grade? Nancy or David
Answer:
a.) a = -34 and b = 2
b.) a = -91.11 b = 2.22
c.) David scored 124, nancy scored 84.27
David scored higher
Step-by-step explanation:
for those in the 3rd grade
mean u = 67
s = 10
we used the z formula
[tex]z=\frac{x-u}{s}[/tex]
[tex]z=\frac{x-67}{10}[/tex]
we have the new score
u = 100
s = 20
we use this formula [tex]z*s+u[/tex]
[tex][\frac{x-67}{10} ]20\\[/tex] + 100
multiply through by 20
[tex][\frac{20x-1340}{10} ] +100[/tex]
dividing the bracket by 10
= [tex]2x-134+100[/tex]
= [tex]2x-34[/tex]
from this solution above,
a = -34 and b = 2
b.)
we solve for those in the 6th grade
u = 86
s = 9
[tex]\frac{x-86}{9}[/tex]
for new score,
y = 100
s = 20
[tex][\frac{x-86}{9} ]20+100[/tex]
[tex]2.22x-191.11+100\\= 2.22x - 91.11[/tex]
from this solution
a = -91.11
b = 2.22
c.) if David scored 79
[tex]= 2(x)-34[/tex]
= 2(79) - 34
= 158 - 34
= 124
if nancy scored 79
= 2.22(79) - 91.11
= 175.38 - 91.11
= 84.27
from these scores we can see that David scored higher in his grade
A rectangle is 9 inches long and 3x inches wide. The value of the perimeter (in inches) is equal to the value of the area (in square inches).
Find x
Answer:
3
Step-by-step explanation:
The perimeter of the rectangle is equal to the doubled sum of the sides, and the area is equal to the product of the sides. So we have the following equation
Express the shaded area as a fraction, a decimal, and a percent of the whole.
Fraction:
Decimal:
Percent:
Answer:
3/10 30%.3
hooe its write
help me please geometry!!
Find the missing side length.
Set up a ratio:
16/12 = 28/?
Cross multiply:
16? = 12 x 28
16? = 336
Divide both sides by 16:
? = 336/16
? = 21
Help me asap!!pleaseeee
Answer:
a
Step-by-step explanation:
yes
The ratio of winners to losers was 7 to 5. If the total number of winners and losers was 1260, how many more winners were there than losers?
Answer:
210
Step-by-step explanation:
7:5
First add the ratios
7+5=12
Put each ratio over the denominator 12 then multiply each by the total
7/12×1260= 735
5/12 × 1260 = 525
To find how many more winners than losers
735-525= 210
I’ll mark you as brainliest
Step-by-step explanation:
1) -5n+10n
= 5n
2) -x-9+2x-10
= 2x-x-9-10
= x-19
3) -5(x-10)-x
= -5x+50-x
= -6x+50
4) 9-5(1-7x)
= 9-5+35x
= 35x+4
5) y^2-x
= 3^2-2
= 9-2
= 7
Do the remain questions by yourself, you can do it!
A research team conducted a study showing that approximately 30% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 30 businessmen, all of whom wear ties, what are the following probabilities?
a. at least one tie is too tight
b. more than two ties are too tight
c. no tie is too tight
d. at least 18 ties are not too tight
Answer:
a) 0.9998
b) 0.9979
c) 0.7
d) 0.9155
Step-by-step explanation:
P( people who wear their ties tightly ) = 0.3
P( people who do not wear their ties tightly ) = 1 - 0.3 = 0.7
sample size ( n ) = 30
Given that the events are independent and there are only two outcomes we will apply Binomial distribution
a) P( at least one tie is too tight )
P ( x ≥ 1 ) = 1 - P ( x < 1 ) = 1 - P ( x = 0 )
= 1 - 0.00002 = 0.9998 ( excel function: 1 - BINOMDIST(0,30,0.3,0) )
b) P( more than two ties are too tight )
P ( x > 2 ) = 1 - P ( x ≤ 2 ) = 1 - BINOMDIST(2, 30, 0.3, 1 )
= 1 - 0.002113178
= 0.9979
c) P ( no tie is tight )
P ( x = 0 ) = 0.7
d) P( at least 18 ties are not too tight ) i.e. ( P = 0.7 )
P ( x ≥ 18 ) = 1 - P( x ≤ 17 )
= 1 - BINOMDIST ( 17, 30, 0.7, 1 )
= 1 - 0.08447006
= 0.9155
Dan's car depreciates at a rate of 7% per year.
By what percentage has Dan's car depreciated after 6 years?
Give your answer to the nearest percent.
Answer:
20%
Step-by-step explanation:
Given that
The car is depreciated at a rate of 7% per year
We need to find out the percentage when the car is depreciated after 6 years
So,
Since the car is depreciated by 7% so we can say it can be 0.93 times in a year
Now after 6 years, it would make
= 0.93^3
= 0.80
So, the percentage is
= 1 - 0.80
= 0.20
= 20%
Help me please and thank you
Answer:
A
Step-by-step explanation:
Solution is in this picture.
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200. Construct a 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200.
Answer:
The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200.
This means that [tex]n = 150, \pi = \frac{60}{150} = 0.4[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.3216[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.4784[/tex]
The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).
Suppose that the logons to a computer network follow a Poisson process with an average of 3 logons per minute. (a) What is the mean time between logons (in minutes)
Answer:
The mean time between logons is of 0.3333 minutes.
Step-by-step explanation:
Poisson process with an average of 3 logons per minute.
This means that the time between logons follows an exponential distribution, which mean is given by:
[tex]E(X) = \frac{1}{\lambda}[/tex]
For this question, we have that [tex]\lambda = 3[/tex], and thus:
[tex]E(X) = \frac{1}{\lambda} = \frac{1}{3} = 0.3333[/tex]
The mean time between logons is of 0.3333 minutes.
Which of the following are mutually exclusive events?
A. An athlete being 5 feet tall and 6 feet tall
B. A student belonging to the chess club and the math club
C. A person having brown eyes and brown hair
D. A teacher teaching English composition and English literature
Answer: A
Step-by-step explanation: Ape x
What is the density of this object? (A sphere)
9514 1404 393
Answer:
about 0.299 kg/m³
Step-by-step explanation:
Density is the ratio of mass to volume.
ρ = M/V
ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³
Given: x - 6 ≤ 1. Choose the solution set.
Answer:
x<7
Step-by-step explanation:
See image below:)