The value of the expression log₃9 is 2.
The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.
Log a to the base b can be written as- log a/ log b.
Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a
Here, we are given a logarithmic expression- log₃9
We can expand this as-
log₃9 = log 9/ log 3
= log [tex]3^{2}[/tex]/ log 3
= 2 log 3/ log 3
= 2
Thus, the value of log₃9 is 2.
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Thang decided to borrow $2000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 7%.How much interest will Thang pay?
The amount that Thang would pay in interest is $420 based on the loan of $2000 and simple interest of 7%
What is simple interest?
The simple interest on the loan is determined as the amount borrowed multiplied by the interest rate of 7% and as well multiplied by the number of years it takes for the loan to be repaid
I=PRT
I=simple interest payable by Thang=unknown
P=principal=amount borrowed=$2000
R=interest rate=7%
T=number of years before the loan is repaid=3
I=$2000*7%*3
I=$420
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5 x 3 x 45 x 67 x 34 x 98 x 19 x 1009
Answer:
2.8888722e+12
Step-by-step explanation:
calculator
Create an equation equivalent to x - y = 3 by multiplying each term on both sides by any number you choose.
Step-by-step explanation:
you can plus for obtain a multiply
5×-2y=3
A cylinder has a diameter of 16 feet
and a height of 5 feet. What is the
volume of the cylinder??
Answer:
V = 1,005.31ft³
Step-by-step explanation:
V = [tex]\pi[/tex][tex](\frac{d}{2} )^{2}[/tex]h
V = [tex]\pi[/tex][tex](\frac{16}{2} )^{2}[/tex](5)
V = 1,005.30965ft³
Step-by-step explanation:
diameter is 16 feet
height is 5 feet
For you to find the volume you have to know the
formula for finding it
the formula is πr^2h
π=22/7,
r=radius=16/2=8
h=height=5
πr^2h
22/7 x 8^2 x 5
22/7 x 64 x 5
22/7 x 320
=1005.71 feet^3
Write an equation for the number of miles y it travels in x hours how many miles will it travel in 3
The equation for the given statement is y=3x.
The given equation is the number of miles y it travels in x hours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We need to find the number of miles travelled in 3 hours.
Now, using the formula Distance = Time × Speed
y = 3x
Therefore, the equation for the given statement is y=3x.
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The duck pond game at the capital has a pool whit 75 toy ducks twenti-five of these duck are marked undemeant
Let us organize the information first. The game consists in picking up a numbered duck. Let us denote the number of the duck as xx. The possible prizes are
1≤ x≤ 60 consolation prize
60 ≤ x ≤ 70 stuffed duck
70≤ x ≤ banana
We have 75 possible numbers equally likely to select, and 1111 outcomes where we win the stuffed duck
60, 61, 62, 63, 64, 65, 66, 67, 68, 69 and 70
Therefore, the probability of winning a stuffed duck is
p(60 ≤ x ≤ 70) = 11/75= 0.146
The event of not winning a duck or a banana is that of winning the consolation prize, that is, picking a number 1 ≤x ≤ 60.
Those are 59 equally likely to occur outcomes. Then we have
c= 59/75= 0.786
To check whether this result is right, we can use the complementary events law. That is, the probability of not winning a duck or a banana is 11 minus the sum of the probabilities of winning a duck or a banana. Mathematically this is
p (1 ≤ x ≤ 60) = 1-(p (60≤x≤70)+p(70≤x≤75)
p (1≤ x ≤ 60) = 0.786
which is a desired result.
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Which graph represents y-³√x?
Answer:
There wasn't an image put to choose which graph it would be.
Step-by-step explanation:
Which expression is equivalent to -3[4*-0.50]?
–12x – 1.50
–12x + 1.50
–12x – 2.50
–12x – 3.50
In given expressions no one is equivalent to the expression -3 [4 × -0.50]
Given,
The expression : -3 [4 × -0.50]
We have to find the expression equivalent to the above expression from the given options.
Solve the expression:
-3 [4 × -0.50] = -3 × -2 = 6
Now we can solve the expressions given in the options:
1) -12 × -1.50 = 18
Not equal to the given expression
2) -12 × 1.50 = -18
Not equal to the given expression
3) -12 × -2.50 = 30
Not equal to the given expression
4) -12 × -3.50 = 42
Not equal to the given expression
So, we can conclude that, there is no equivalent expression in the options for the expression -3 [4 × -0.50]
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Solve each equation. Check your answers.
2 ln 2 x²=1
After solving the equation 2 x² the value of x is equal to 1 [tex]\sqrt{1/2}[/tex]
we are asked to find x in 2x² = 1
⇒ 2x² = 1
⇒ x² = 1/2
⇒ x = [tex]\sqrt{1/2}[/tex]
So, x is equal to [tex]\sqrt{1/2}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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HELP PLS WILL GIVE BRAINLIST
Answer:
AB + BC + AC a. segment addition postulate
2x+6x+8 = 32 b. substitution property of equality
8x + 8 = 32 c. Combine like terms
8x = 24 d. subtraction property of equality
x = 3 e. division property of equality
PLS HURRY DUE A HOUR AGO
1. Show an example of two numbers that are additive inverses.
Step-by-step explanation:
Greetings !
Definition:-In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite, sign change, and negation.
For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0. Similarly, the additive inverse of a − b is −(a − b) which can be simplified to b − a. The additive inverse of 2x − 3 is 3 − 2x, because 2x − 3 + 3 − 2x = 0.
Hope it helps!!!
A figure is multiplied by a scale factor of 1/3. Did the figure get smaller or larger? How do you know?
I will give Brainiest answer
Answer:
Smaller
Step-by-step explanation:
If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
The dot plot shows predictions for the winning time in the 200 meter sprint. the winner finished the race in 22.2 seconds. what is the greatest percent error among the predictions?
The greatest percent error among the predictions time of the race is: 3.15 %
Although part of your question is missing, you might be referring to this dot plot that shows the predictions for the winning time (see image attached)
To solve this exercise, we have to apply the percentage formula:
Error (%) = [(prediction time – real time) / real time] * 100
Information about the problem:
Prediction time= 22.9 secondsreal time =22.2 secondsError (%) =?Applying the percentage formula, we have:
Error (%) = [(prediction time – real time) / real time] * 100
Error (%) = [(22.9 seconds – 22.2 seconds) / 22.2 seconds] * 100
Error (%) = [(0.7 seconds) / 22.2 seconds] * 100
Error (%) = 0.0315 * 100
Error (%) = 3.15 %
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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HELP HELP HELPP i'll mark brainliest
Solve for x: 3( + 1) − 7( − 1) = 3(2 − 4)
Answer:
10 = -6
Step-by-step explanation:
Answer:
X = - 39
Step-by-step explanation:
x divided by 3x 1 - 7(-1)=3(2-4)X(1/3)+7-3(-2)X times 1/3 +7+-3 x2x/3+7-6x+21/ 3 = -6x+21 + (-3)6X +21 = -3x6x+21 = - 18(x+21) + (-21)= -18 +(-21)X+21-21= - 18-12ANSWER: x+3x7/3 = - 6
Hope this helps u : )
Calculate the sample standard deviation of the data shown. Round to two decimal places. X 18 11 12 15 13 22 26 sample standard deviation =
please help me out it's due in 10 minutes
Answer: The SD is 5.589
Step-by-step explanation:
Help, the Question is attached.
the box select is:
Right triangle
Not a right triangle.
The triangle with lengths 6cm, 8cm and 10cm are right triangles.
What are right triangles?A right triangle is a polygon with three sides. It is a triangle in which the sum of the square of the two sides is equal the square of the longest side. The sum of the angles in a right triangle is 180 degrees. One of the angle in a right triangle measures 90 degrees.
According of the Pythagorean Theorem, a triangle is a right triangle if the sum of the square of the two sides is equal the square of the longest side.
The Pythagorean Theorem: a² + b² = c²
where:
a = lengthb = basec = hypotenuse6² + 8² = 10²
36 + 64 = 100
The triangle is a right triangle because it means the parameters set forth by the Pythagorean Theorem.
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the height of a house is 52 ft. a tree beside the house is 7 ft more than twice as tall. what is the height of the tree? enter your answer in the box. ft
Answer: 111 ft tall. Thats a big tree!
Step-by-step explanation: if its seven more than two times the height of the house, do 52 X 52 + 7 which equals 111 ft.
Peter says the least common multiple of 4 and 6 is 24, Do you agree or disagree? Explain.
Answer:
I Disagree with Peter, the explanation is down below.
Step-by-step explanation:
I disagree because to find the least common multiple or the LCM, you need to first list the first several multiples of each number. So, because the numbers are 4 and 6, I would write:
4 - 4, 8, 12, 16, 20, 24, 28, 32
6 - 6, 12, 18, 24 30, 36, 42, 48
The next step would be to find the same multiples in the list. If there are no same multiples, then I would keep on adding multiples.
If we look at the list, the first numbers that we see that are the same are 12 and 12.
12 would be the LCM, not 24.
If the two numbers were 24 and 12, then the LCM would have been 24, but in this case, the LCM is 12. So that is why I disagree.
Hope this helped! :D
Have a wonderful day!~~
Use the Change of Base Formula to evaluate each expression.
log₂9
The value of the expression log₂9 after using change of base theorem is 3.17.
Given that the expression be log₂9.
We are required to find the value of the expression by finding the value of log values.
Change of base formula is basically used in a situation where we have to solve the log values with different bases at one time. It says that
[tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex].
The expression is log₂9.
We know that [tex]log_{b}a[/tex]=log a/log b.
log₂9=log 9/log 2
Now,we have to use the values of log in the above expression.
=0.9542/0.3010
=3.17
Hence the value of the expression log₂9 after using change of base theorem is 3.17.
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If principal=p,rate of interest=R and time=T,then write the formula to find the compound amount
It is given that P = principal, R = rate of interest and T = time
Formula to find compound interest is:
A = P(1 + R/100)^T
where A = amount received after n years
P = principal amount invested
R = rate of interest
T = time for which the amount is invested
The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.
It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.
Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.
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Find the slope of the line passing through the points (-4, 6) and (3, -8).
11
3 08
X
Undefined
Ś
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-4)}}} \implies \cfrac{-14}{3 +4}\implies \cfrac{-14}{7}\implies -2[/tex]
solve inequality and graph on number line
3|14-m|>18
Answer:
Hey Rey
Step-by-step explanation:
[tex] \mathsf{\red{m∈( - ∞, \: 8)U(20,∞)}}[/tex]
Answer:
Hey Rey ...
Step-by-step explanation:
[tex]\mathsf{\blue{m∈( - ∞, \: 8)U(20,∞)}}[/tex]
A charge of $8.99 is automatically deducted from Ari's bank account each
month for a live TV streaming service. What is the change in Ari's bank
account after 6 months for this service?
Ari loss 53.94% of his account balance for this live tv streaming service.
Given,
The charge for a live tv streaming service that is automatically deducted from Ari's bank account each month = $8.99
This deduction continues for 6 months.
We have to find the change in Ari's bank account after 6 months for this service.
Charge for 1 month = 8.99
Charge for 6 months = 6 × 8.99 = 53.94
That is if Ari had $100 in his account, now after 6 months 53.94% deducted for the tv streaming service charge.
Now, he has an account balance:
100 - 53.94 = 46.06
In terms of amount, he has an account balance of $46.06.
In terms of percentage,
Ari lost 53.94% from his account balance and now he has 46.06% account balance.
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what is the sum of all the positive integers from sqrt(14 to sqrt(80
Sum of all the positive integers from √14 to √80=30
Definition of a perfect square-A number system that can be stated as the square of a specific number from the same system is called a perfect square.Assume that N may be expressed as the product of x and x = x²,if x is a perfect square of a number N. Square roots can be used to understand this in another way. We compute the square root of a given number to determine if it is a perfect square or not. The supplied number is a perfect square if the square root is a whole number.However, if the square root value is not a whole number, the given number is not a perfect square.Now according to given question we have to find sum of all the positive inetegers between √14 to √80
√14=3.74165 & √80=8.94427Positive integers between 3.74-8.94 are 4,5,6,7 & 8Sum of 4+5+6+7+8=30∴Sum =30
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what is the least common denominator of 3/4 and 1/10
Answer: 20
Step-by-step explanation:
3/4= 15/20
1/10=2/20
The following data shows the scores Gina obtained on 12 IQ tests:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
The box plot represents the data:
box plot has minimum value equal to 74, lower quartile equal to 83, median equal to 86.5, upper quartile equal to 92.75 and maximum value equal to 99
Which of the following is shown incorrectly in the box plot?
Median
Lower quartile
Upper quartile
Maximum value
The maximum value of the data is being incorrectly shown by the box plot diagram.
We are given the data:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
We are also given the box plot diagram of the data which shows that:
Minimum value of the data = 74
Lower quartile = 83
Median quartile = 86.5
Upper quartile = 92.75
Maximum value = 99
We need to tell which is the wrong interpretation among these.
We can see that, the maximum value of the data is only 93 and not 99.
So, that is the wrong representation by the box plot.
Therefore, we get that, the maximum value of the data is being incorrectly shown by the box plot diagram.
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or
On Saturday mornings, Madelyn volunteers at the hospital where her mother works. One Saturday, she answers phone calls at the information desk while the receptionist is away. Then she spends 40 minutes delivering flowers to patients' rooms. In all, Madelyn volunteers at the hospital for 90 minutes that day.
Which equation can you use to find the amount of time t that Madelyn answers phone calls?
Answer:
90-50=40 so she answers phone calls for 50 min
Step-by-step explanation:
A ship captain is attempting to contact the deep sea diver in the maximum range for communication is 50 meters will he be able to communicate with the diver based on their current positions? Explain.
Using the distance between two points, it is found that the distance between the positions of the ship and of the diver is greater than 50 meters, hence the ship captain will not be able to communicate with the diver based on their current positions.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Looking at the graph, the positions of the ship and of the diver are given as follows:
Ship: (8,8).Diver: (48, -36).Hence, applying the formula presented at the beginning of the explanation. the distance is given by:
[tex]D = \sqrt{(48 - 8)^2+(-36-8)^2}[/tex]
D = 59.6.
The distance between the positions of the ship and of the diver is greater than 50 meters, hence the ship captain will not be able to communicate with the diver based on their current positions.
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What value correctly fills in the blank so that the expressions are equivalent?
32 + 72 = blank x (4 + 9)
4
8
12
13
Answer: The answer is 8 because you add 32 + 72 and get 104 x and then 4 +9 = 13 then you divide 104 divided by 13 = 8
Answer:
8, because you add 32 and 72, which will get 104x and then 4+9 which is 13 then you divide 104 divided by 13 = 8
Step-by-step explanation:
hope this helps!
What is the value of the expression 8^2+3\times78
2
+3×7 ?
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ 8² + 3 × 78² + 3 × 7
Simplify the expression, then we have
⇒ 8² + 3 × 78² + 3 × 7
⇒ 64 + 3 × 6084 + 21
⇒ 85 + 18252
⇒ 18337
The value of the expression 8² + 3 × 78² + 3 × 7 will be 18337.
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