Answers
Answer:
Third option is correct. The value of given expression is 4.
Step-by-step explanation:
The given expression is
[tex]log_381[/tex]
The given expression can be written as
[tex]log_3(3\times 3\times 3\times 3)[/tex]
[tex]log_3(3^4)[/tex]
According to the property of logarithm expression,
[tex]log_a(a^b)=b[/tex]
Using this property of logarithm expression, we get
[tex]log_3(3^4)=4[/tex]
Therefore the value of given expression is 4 and option third is correct.
The value of the expression log₃(81) is 4.
We have,
The value of log base 3 of 81 can be found by asking the question: "To what power must 3 be raised to obtain 81?"
In this case, the answer is 4, because 3 raised to the power of 4 equals 81.
i.e
[tex]3^4[/tex] = 81
Therefore,
The value of the expression log₃(81) is 4.
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Related Questions
A bank runs a contest to encourage new customers to open accounts. In the contest, each contestant draws a slip representing a different reward—$5, $3, or $x—from a jar. At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x.
If the expected value of the first draw from the jar is $5.8, the value of x is__
At one point in the contest, the jar contains 3 slips for $5, 7 slips for $3, and y slips for $x. If the expected value on the next draw is $6, the value of y is __
Answers
We'll use x = 9 from part 1.
Again let,
A = event that the $5 reward is drawn
B = event that the $3 reward is drawn
C = event that the $x reward is drawn (x is some positive number)
We can update event C to say
C = event that the $9 reward is drawn
The probabilities change to
P(A) = 3/(10+y)
P(B) = 7/(10+y)
P(C) = y/(10+y)
where y is some positive whole number. It represents the number of slips in jar C
The net values are
V(A) = 5
V(B) = 3
V(C) = x = 9
Like before, multiply the probabilities and net values to get
P(A)*V(A) = (3/(10+y))*5 = 15/(10+y)
P(B)*V(B) = (7/(10+y))*3 = 21/(10+y)
P(C)*V(C) = (y/(10+y))*9 = (9y)/(10+y)
The results add up to
[ 15/(10+y) ] + [ 21/(10+y) ] + [ (9y)/(10+y) ]
(15+21+9y)/(10+y)
(36+9y)/(10+y)
That last expression is the expected value. The expected value is also given to be 6, so set the two expressions equal to each other and solve for y.
(36+9y)/(10+y) = 6
36+9y = 6(10+y)
36+9y = 6(10)+6(y)
36+9y = 60+6y
9y-6y = 60-36
3y = 24
3y/3 = 24/3
y = 8
The statement "y slips of $x" turns into "8 slips of $9" since x = 9 and y = 8.
A circular city park has a sidewolk directly through the rmiddle that is 111- feet long. I each bag of fertilizer covers 50 square feet, then determine how many bags of tertilizer the Parks and Recreation department needs to use to cover the circular park. Ignore oll the sidewalks around and through the park.
Answers
.. A = (π/4)d^2
.. = (π/4)*(111 ft)^2 ≈ 9676.9 ft^2
The number of bags of fertilizer required will be
.. (9676.9 ft^2)*(1 bag)/(50 ft^2) = 193.5 bags
Parks & Rec needs to use 193.5 bags of fertilizer to cover the park.
_____
No doubt, P&R has half a bag left over from a previous use of fertilizer in the park, so they will not have to purchase a whole bag to cover the fraction.
the average airspeed velocity of an unladen European swallow is approximately 24 miles per hour at this rate how many hours will it take to swallow to fly from Appin to Glen Coe about 18 Miles??
Answers
[tex]x = \frac{18}{24} = 0.75 [/tex]
So, it would take him:
[tex]0.75(60) = 45[/tex]
So, it will be 45 mins.
1.The sales tax rate in a certain state is 8%. How much would you pay in total for a taxable item that costs $25.25?
2.Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?
3.Jim bought a fishing rod for $42. This price was 70% of the original price. What was the original price?
4.An auctioneer sold items totaling $42,000. If her rate of commission was 7%, what was her income from commissions?
5.At a local hardware store, Ms. Jones learned that 1 would cost her $.50, 12 would cost $1.00, and the price of 144 would be $1.50. What was Ms. Jones buying?
6.People sometimes use credit cards to purchase items they can’t afford to pay for at the moment of purchase. If you’re one of these people, you should know that the monthly finance charge on credit purchases is based on percent. Let’s say you have an outstanding balance of $800 on your credit card. The credit card company charges 1.6% per month. What finance charge will you have to pay for one month?
Answers
P = r x b
where: P = Percentage (Portion)
r = rate
b = base amount
1. Your given for number 1 is as follows:
rate = 8%
Base amount = $25.25
You are looking for how much you would pay in total. First you need to find out how much your going to pay in taxes, based on the base amount. To get that, you need to convert the rate in its decimal form by dividing it by 100.
rate = 8/100 = 0.08
Next you need to find how much you will pay in taxes, you can do that by using the formula:
P = r x b
= 0.08 x $25.25
= $2.02 This is how much you will pay in taxes.
To get the total amount you will pay, just add it to the original price:
$25.25 + $2.02 = $27.27
2. Your given will be:
p = 20
b = 25
r = ?
All you have to do is input what you know in the formula:
P = r x b
20 = r x 25
Transpose the 25 to the other side of the equation to get the rate and divide:
20/25 = r
0.8 = r
For this case it is asking for the rate in percent, all you need to do is multiply your computed rate by 100% and you will get 80%.
3. If your given would be:
P = $42.00
r = 70%
b = ?
Base is the unknown here, because you are looking for the original price. So we put this into our equation again:
$42.00 = 0.70 x b
Transpose the 0.70 to the other side of the equation again and divide:
$42.00/0.70 = $60.00
The original price was $60.00
4. The given would be:
P = ?
r = 7% or 0.07
b = $42,000
We are looking for how much he got, or the portion he got, so we are looking for the percentage. Input what you know into our formula:
P = 0.04 x $42,000
= $2,940.00
6. Your given would be as follows:
P = ?
r = 1.6% or 0.016
b = $800
You are looking for how much you would pay in finance charge, or the portion that will be added, based on your base amount so you will be looking for the percentage. Input your given into the formula:
P = 0.016 x $800
= $12.80
As for number 5, that is a trick question. The prices are different and no matter what formula you will use, you will not come up with a mathematical sound answer. Consider the situation, what can you buy in local hardware store that has 1, 12, and 144? The answer is HOUSE NUMBERS.
2. 80%
3. $60
4. $2,940
5. Ms. Jones was buying house numbers. Her house number was 112144. Each separate number would cost $.50. Therefore, the number 1 would cost $.50, the numbers 1 and 2 (12) would cost $1.00, and the numbers 1, 4, and 4 (144) would cost $1.50.
6. $12.80
Which simplified equation is equivalent to the equation shown below?
4x+x-3-9+4x=6
a.5x-8=6
b.-3x=6
c. 9x-12=6
d. 8x-12=6
Answers
9x-12=6
Answer C
We need to group the like terms and combine like terms to get the simplified equation.
[tex] 4x+x-3-9+4x=6\\ \\ Step \; 1: \; Group \; like\; terms\\ \\ 4x+x+4x-3-9=6\\ \\ Step \; 2: \; Combine \; like\; terms\\ \\ 9x-12=6 [/tex]
Conclusion:
Option C is the right answer !!
which of the following is equivalent to the polynomial below
Answers
1. to find the roots of the equation (D=-36):
[tex] \left[\begin{array}{ccc}x=5+6i\\ x=5-6i\end{array}\right[/tex]
2. to simplify the polinom:
x²-10x+61=(x-(5-6i))(x+(5+6i))
Answer: 1
Create a system of linear equations that has the solution (3,5)?
Answers
Answer:
x + 2y = 133x - y = 4Step-by-step explanation:
I find it easiest to write the equations in standard form, as above. You just need to pick numbers for the x- and y-coefficients, then see what the left-side evaluates to. I wanted the x-coefficients to be different, and one of the y-coefficients to be negative. (The x-coefficients need to be positive when the equation is written in standard form.)
_____
Check
3 +2·5 = 3 +10 = 13 . . . first equation works
3·3 -5 = 9 -5 = 4 . . . . . second equation works
The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm. What is the actual distance between Los Angeles and San Francisco?
Answers
this is answer
Step 1: Let us assign variable for the unknown that we need to find.
' x ' be the actual distance between Los Angeles and San Francisco
Step 2: Set up an equation based on the given statement "The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm."
[tex] \frac{distance \; in \; cm}{distance\; in\; miles}=\frac{1}{35}=\frac{10.8}{x} \\ \\ Cross \; Multiply\\ \\ 1 \cdot x = 35 \cdot 10.8\\ \\ x = 378 [/tex]
Conclusion:
The actual distance between Los Angeles and San Francisco is 378 miles.
1.Write equatios to represent the distances the family drove on the given days.
2. construct a math argument to explain why your answer to 5 is correct.
3. How can you check that your answer is reasonable?
Answers
i think this is correct because you need morning and evening combined to know a exact answer.
you can check this by calculating you equations and u will end up with Wednesday as the longest amount of miles
Phillip flips a coin, rolls a standard number cube, and randomly chooses a shape from the list below. Find the probability that the coin will show tails, the cube will show an odd number, and a red shape will be chosen. 1/6 1/2 None of these 1/12 1/8 HELPPP PLZ TODAY!!!!
Answers
Answer:
thx for pts
Step-by-step explanation:
HELP ME ANSWER THIS QUESTION!
Boyd (B) is trapped in a soccer training circle. Albert (A) and Carlos (C) kick the ball to Boyd in rotation. Determine how far Boyd needs to kick the ball to Carlos if he is located in the center of his training circle and Carlos is located at the outer rim.
Answers
AB = 19+x
BC= x
AC= 30
From the picture we can see that side AB is hypothenuze. We are given number 19 as part of length of that hypothenuze. Other part is equal to distance from center to edge of circle. This length is same as side BC.
We will use Pythagorean theorem to solve this:
[tex] (AB)^{2} = (BC)^{2} + (AC)^{2} \\ (19+x)^{2} = x^{2} + 30^{2} \\ 361+38x+ x^{2} = x^{2} +900 \\ x^{2} - x^{2} +38x=900-361 \\ 38x=539 \\ x=14.2yard[/tex]
which word phrase represents the following expression r ÷ 6 ?
Answers
Answer : The correct phrase used is, r is divided by 6.
Step-by-step explanation :
We are given an expression :
r ÷ 6
The word used for subtraction operation is 'less'.
The word used for multiplication operation is 'times'.
The word used for division operation is 'divided by'.
Thus, the verbal sentence for given equation is, r is divided by 6.
The percentage of high school students who drink and drive stood at 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.† (a) find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where t = 0 corresponds to the beginning of 20
Answers
1) The linear function : f(t) = -0.72t + 17.5
2) When t = 14 the value is 7.42
Part A
For this case we have the following information given:
t= 2001 (0) f(0)= 17.5%
t= 2011 (10) f(10)= 10.3
Slope= [tex]\frac{10.3-17.5}{10-0}[/tex]
10.3 = -0.72*10 +b
b= 10.3 +10*0.72
= 17.5
Then the equation is:
f(t) = -0.72t + 17.5
Part B
For 2015 the value of t = 2015-2001
= 14
Substitute in function,
f(14)= -0.72×14 + 17.5
= 7.42
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Complete question:
The percentage of high school students who drink and drive was 17.5% at the beginning of 2001 and declined linearly to 10.3% at the beginning of 2011.†(a) Find a linear function f(t) giving the percentage of high school students who drink and drive in year t, where t = 0 corresponds to the beginning of 2001.f(t) = (b) If the trend continued, what was the percentage of high school students who drank and drove at the beginning of 2015? %
To find the linear function that represents the percentage of high school students who drink and drive in a given year, we can use the slope-intercept form of a linear equation. We can determine the slope and y-intercept by using the given data points. The linear function is f(t) = -0.82%t + 17.5%.
Explanation:To find a linear function f(t) giving the percentage of high school students who drink and drive in year t, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the percentage of students who drink and drive, and t represents the year. We know that at the beginning of 2001 (t=0), the percentage was 17.5%, and at the beginning of 2011 (t=10), the percentage was 10.3%. Using this information, we can find the slope (m) and the y-intercept (b) of the linear function.
Step 1: Calculate the slope (m):
m = (y2 - y1) / (t2 - t1) = (10.3% - 17.5%) / (10 - 0) = -0.82% per year.
Step 2: Substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b). Using the point (0, 17.5%):
17.5% = -0.82%(0) + b
b = 17.5%.
Therefore, the linear function f(t) is: f(t) = -0.82%t + 17.5%.
In which situation is the original price bigger? (A) after a 5% discount the price was $190; (B) after a 10% discount the price was $180; (C) after a 20% discount the price was $170; (D) after a 30% discount the price was $140.
Answers
Answer:
C
Step-by-step explanation:
Calculate each one of them to see which one is highest:
a)190/.95 = 200
b) 180/.9 = 200
c)170/.8 = 212.5
d)140/.7 = 200
8. The U.S. population was 309 million in 2010. If the U.S. had had the same firearm death rate as Australia in 2010, how many firearm deaths would the U.S. have expected to have that year? Australia’s population was 22.3 million people in 2010. Australia had 236 firearm deaths in 2010. (round to the nearest person)
Answers
As per linear equation, in 2010 the expected firearm death U.S. had is 3270.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
Australia’s population was 22.3 million people in 2010.
Australia had 236 firearm deaths in 2010.
Therefore, portion of Australian population had firearm deaths is
[tex]= \frac{236}{22.3(10)^{6} } \\= 0.000011[/tex]
The U.S. population was 309 million in 2010.
Therefore, the expected firearm deaths in U.S. in 2010 was
[tex]= (309) (10^{6}) (0.000011)\\= 3270.13\\= 3270[/tex]
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what is the word form and the expanded form of 427.968?
Answers
400 + 20 + 7 + .900 + .060 + .008
I hope this helps!
The word form is four hundred twenty-seven and nine hundred sixty-eight thousandths, and the expanded form is 400 + 20 + 7 + 0.900 + 0.060 + 0.008
The number is given as: 427.968
To expand, we make use of the addition arithmetic operator.
So, we have:
[tex]\mathbf{427.968 = 400 + 20 + 7 + 0.900 + 0.060 + 0.008}[/tex]
Hence, the expanded form of 427.968 is 400 + 20 + 7 + 0.900 + 0.060 + 0.008
In the expanded form above, we have the following numbers:
400 - Four hundreds.20 - Twenty.7 - Seven.0.900 - Nine tenths.0.0600 - Six hundredths.0.008 - Eight thousandths.Combine the above words to give four hundred twenty-seven and nine hundred sixty-eight thousandths.
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1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.
Answers
A (0,0,0)
B (0,5,0)
C (3,5,0)
D (3,0,0)
E (3,0,4)
F (0,0,4)
G (0,5,4)
H (3,5,4)
a.) The prism is reflected over the xz-plane.
Reflection Point P(x,y,z) over the xz-plane is P'(x,-y,z):
Reflection P(x,y,z) over the xz-plane → P'(x,-y,z)
Reflection A(0,0,0) over the xz-plane → A'(0,-0,0) = A'(0,0,0)
Reflection B(0,5,0) over the xz-plane → B'(0,-5,0)
Reflection C(3,5,0) over the xz-plane → C'(3,-5,0)
Reflection D(3,0,0) over the xz-plane → D'(3,-0,0) = D'(3,0,0)
b.) The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
Translation P'(x,-y,z) 2 units back, 3 units left, and 1 unit up is P''(x-2,-y-3,z+1):
Translation P'(x,-y,z) → P''(x-2,-y-3,z+1)
Translation A'(0,0,0) →A''(0-2,0-3,0+1) = A''(-2,-3,1)
Translation B'(0,-5,0) →B''(0-2,-5-3,0+1) = B''(-2,-8,1)
Translation C'(3,-5,0) →C''(3-2,-5-3,0+1) = C''(1,-8,1)
Translation D'(3,0,0) →D''(3-2,0-3,0+1) = D''(1,-3,1)
How to start the problem off. (substitution)
Answers
A triangle has one 60 degree angle and one 20 degree angle. The third angle in the triangle must be
a.acute
b.obtuse
c.commplementary
d.straight
Answers
3/4,19/20,1/6,3/5,8/15 what is lcd
Answers
.. 4 = 2^2
.. 5
.. 6 = 2*3
.. 15 = 3*5
.. 20 = 2^2*5
is 2^2*3*5 = 60
The lowest common denominator is 60.
Can you answer this one for my plz I need before Monday ty
Answers
.. -x^2 -4x +1
.. = -(x^2 +4x) +1
.. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square
.. = -(x +2)^2 +5
The vertex is (-2, 5).
The axis of symmetry is x = -2.
Which triangle is it ?
Answers
we know that
sin(30°)=0.5 cos(30°)=√3/2
sin(60°)=√3/2 cos(60°)=0.5
sin(60)=BC/AC=5√3/10=√3/2-------------- is ok
cos (60)=AB/AC=5/10=0.5---- is ok
sin(30)=BA/AC=5/10=0.5-------------- is ok
cos (30)=BC/AC=5√3/10=√3/2-------------- is ok
if angle B is 90°
then
AB²+BC²=AC²------------> 5²+(5√3)²=10²=(25+75)=100------------- > is ok
the solution in the attached figure
What is the following product? 3 sqrt d x 3 sqrt d x 3 sqrt d
Answers
Answer: the first option, d.
Step-by-step explanation:
If the APY of a savings account is 3.2%, and if the principal in the savings account was $2400 for an entire year, what will the balance of the savings account be after all the interest is paid for the year?A. $2400
B. $2406.24
C. $2600
D. $2476.80
Answers
Answer:
The answer is $2476.80 Apex
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
x=
Answers
3x + 50 = 6x - 10
3x - 6x = -10 - 50
-3x = -60
x = 20
The answer is x=20.
The length of a rectangle if the length is twice the size of the width increased by one
Answers
The length of a rectangle if the length is twice the size of the width increased by 1 is it one of the following answers:
A) l= 2w-1
B) l= 2w+1
C) l= 3w
D) none of the choices given
Let
l--------------> length of a rectangle
w-------------> width of a rectangle
we know that
if the length is twice the size of the width increased by 1
l=2w+1
the answer is the option B) l= 2w+1
The answer should be a fraction
Answers
4y2/5y3..
now apply the exponent rule, which is : xa /xb = 1/ xb-a
so...y2/y3 = 1/ y3 - 2 = 1/y
ANSWER : 4/5y
The correct answer to your question is... [tex] 2^{3} y^{5} [/tex]
Evidence:
Step 1: Simplify [tex] y^{2} [/tex]/5
( 40 multiplied by [tex] y^{2} [/tex]/5 multiplied by [tex] y^{3} [/tex] )
Step 2: [tex] y^{2} [/tex] multiplied by [tex] ^{3} [/tex] = y(2 + 3) = [tex]y^{5} [/tex]
So the correct answer is... [tex] 2^{3} y^{5} [/tex]
I hope this helped! : )
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Evaluate g(n-5) if g(x)=x^2-6/2x
Answers
g( n-5) = ( [n-5]^2 -6) / 2(n-5)
= ( n^2 -10n +25 -6 ) / 2(n-5) or ( n^2 -10n +25 -6 ) / (2n-10)
Your Answer
I did foil first and got n^2-10n+25
then did 25-6 to get 19.
so n^2-10n+25 is on top.////// should have been n^2 -10n +19
and the bottom is 2(n-5) so I distributed the 2 and got 2n-10
so n^2-10n+25
2n-10
= (n^2 -10n +19) / 2(n-5)
Answer: We want to evaluate g(x) in x = n -5, where g(x) = (x^2-6)/2x
then, doing it step by step: [tex]g( n- 5)= \frac{(n-5)^{2} - 6 }{2*(n-5)}= \frac{(n^{2} - 2*5*n + 25) - 6 }{2n - 10} = \frac{n^{2} - 10n + 19 }{2n - 10}[/tex]
where i used that (a - b)^2 = a^2 -2ab + b^2
So the correct option is C.
which expressions are polynomials
A) 20x^2
B)20x^2/y
C)20x^2+y^1/2
Answers
The explanation is shown below:
1. The polynomials can't have:
- Fractional exponents.
- Variables in the denominator.
2. As you can see, the option B) 20x^2/y has the variable "y" in the denominator, Therefore, it is not a polynomial.
3. The option C) 20x^2+y^1/2 has a fractional exponent, so it is not a polynomial.
The answers are : 20x^2 and 20x^2 + y^1/2
I just took the test I promise those are the correct answers.
Suppose given an isosceles triangle with a leg measuring 5 in. Two lines are drawn through some point on the base, each parallel to one of the legs. Find the perimeter of the constructed parallelogram.
Answers
Let ΔABC be isosceles triangle with legs AB=BC=5 in. Draw an arbitrary point D on the base AC and spend two lines DE and DF such that DE || BC and DF || AB.
You get the parallelogram BFDE.
1. Consider ΔAED. This triangle is isosceles, because ∠ADE≅∠ACB as corresponding angles at parallel lines. The legs of this triangle are AE=ED.
2. Consider ΔDFC. This triangle is isosceles, because ∠FDC≅∠BAC as corresponding angles at parallel lines. The legs of this triangle are DF=FC.
3. Find the perimeter of parallelogram BFDE.
[tex]P_{BFDE}=BF+FD+ED+BE.[/tex]
Since AE=ED and DF=FC, you have that
[tex]P_{BFDE}=BF+FC+AE+BE=AB+BC=5+5=10\ in.[/tex]
Answer: 10 in.