The value of the logarithmic expression log(10³ x) is 3 + log(x).
The opposite of exponential functions is logarithmic functions. The exponential function y = aˣ has the inverse, [tex]x=a^{y}[/tex]. The exponential equation [tex]x=a^{y}[/tex] is defined as being identical to the logarithmic function y = logₐ x.
The properties of logarithm are:
Product rule: logₐ (mn) = logₐ m + logₐ n
Quotient rule: logₐ (m/n) = logₐ m – logₐ n
Power rule: logₐ (mn) = n( logₐ m )
Consider the logarithmic expression,
a = log ( 10³ x )
Using the property of logarithm:
logₐ ( mn ) = logₐ m + logₐ n
Then,
a = log( 10³ x )
a = log( 10³ × x)
a = log( 10³ ) + log( x )
By using the property of logarithm:
logₐ mⁿ = n( logₐ m )
So,
a = 3( log 10 ) + log( x )
a = 3 + log ( x )
Therefore, log( 10³ x ) = 3 + log ( x ).
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for exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to the lines. y
Your question was incomplete. Please refer the content below:
For Exercises 17 And 18, Find The Acute Angle Between The Given Lines By Using Vectors Parallel To The Lines.
y = x , y = 2 x + 3
The acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.
We are given the lines:
y = x
y = 2 x + 3
The formula for finding the angles between two vectors is given by:
cos θ = u · v / | u | | v|
We know that (0,0) and (1, 1) lies on the line y = x.
Now, vector u for the line y = x will be:
u = (1,1) - (0,0) = {1, 1}
(0,3 ) and (1, 5) lies on the line y = 2 x + 3
Similarly, vector v will be equal to:
v = (1, 5) - (0, 3) = {1, 2}
cos θ = {1, 1} · {1, 2} / √1 + 1 √1 + 4
cos θ = 1 + 2 / √10
cos θ = 3 / √10
θ = cos⁻¹ ( 3 / √10)
θ = 18.4349°
Therefore, the acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.
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Charlie, Beth, and Miguel all babysit kids in their neighborhood. The table shows the number of hours and amount each of them earn last night. If each person babysits for five hours next weekend, which person will earn the most money? Use a coordinate plane if needed to solve.
Answer:
Step-by-step explanation: well first their is int a chart but bye reading the question i think is is Beth.
i hope this helped.
Ginny Brown hoped her crops would get 3 3/4 inches of rain this month. The newspaper said the area received 3.8 inches of rain. Was that more or less than Ginny hoped for? By how much?
Answer:
More, by 0.05 or [tex]\frac{1}{20}[/tex] inches more.
Explanation:
Find out if the amount of rain was more or less by subtracting the desired outcome from the real outcome. If the answer comes out as positive then the amount of rain was more and if the answer is negative, it was less.
Workout:
[tex]\sf real \ outcome - desired \ outcome[/tex]
[tex]3.8 - 3\dfrac{3}{4}[/tex]
[tex]3.8 - 3.75[/tex]
[tex]0.05[/tex]
Hence, The rain was more than ginny expected by 0.05 inches more.
In an arithmetic sequence, the 10th term (a10) is 30 and the common difference is 2
. What is the 1st term (a₁)?
Based on the calculations on this arithmetic sequence, the value of the first term is equal to -8.
What is an arithmetic sequence?An arithmetic sequence can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Given the following data:
Tenth term (a₁₀) = 30.
Common difference = 2.
Substituting the given parameters into the formula, we have;
10 = a₁ + (10 - 1)2
10 = a₁ + (9)2
10 = a₁ + 18
a₁ = 10 - 18
First term, a₁ = -8.
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Julio is paid 1.3 times his normal hourly rate for each hour he works over 29 hours in a week. last week he worked 44 hours and earned $456.32
The hourly rate is $9.40 per hour.
How to calculate the hourly rate?It should be noted that in this case, Julio works for 44 hours which mean 15 hours more than 29 hours.
He gets 1.3 times rate for this 15 hours and normal rate for the first 29 hours. Then the salary he would get should be: 29x + 1.3x(15)= 29x + 19.5x= 48.5x
Julio gets $456.32 which was 48.5 times of his hourly rate. The hourly rate would be:
= $456.32 /48.5
= $9.40/hour
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Julio is paid 1.3 times his normal hourly rate for each hour he works over 29 hours in a week. last week he worked 44 hours and earned $456.32.
Calculate the hourly rate.
a clydes dale drinks about 120 gallons of every 4 days at this rate how many gallons of water does a clydsdale drink in 28 days
The gallons of water that a clydsdale drink in 28 days will be 840 gallons.
How to calculate the gallons?It should be noted that Clyde's dale drinks about 120 gallons of every 4 days. Therefore, the gallons Frank in a day will be:
= 120 / 4
= 30 gallons
Therefore, the gallons drank for 28 days will be:
= 30 × 28
= 840 gallons.
Therefore, the gallons of water that a clydsdale drink in 28 days will be 840 gallons.
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A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute? __ kilometer(s) per minute
Answer:
15 minutes=1km
1 minute=?
(15m:m)×1km
minutes cancel minutes
15×1km=15km
An item costs $480 before tax, and the sales tax is $14.40.
Find the sales tax rate. Write your answer as a percentage.
7/4 to 4 is the same as x to 32
Answer:
14
Step-by-step explanation:
7/4:4 = x:32
x = 32(7/4) / 4 = 14
PLEASE PLEASE PLEASE ANSWER !!!
What is the equation of the given line?
x = 0
y = -2
x = -2
y = -1
Answer:
y = -1
Step-by-step explanation:
→ First determine which axis the line passes through
y
→ Find which point the line passes through
-1
→ Equate both variables
y = -1
need help !! Please somebody help
Answer:
The bottom Option
Note:
Due to my sus vibes from your questions, this is the last one I am answering from you. this is basic and easy if you read it.
Sebastian has 100$ he spits it to four of his friends how much does sebastian give?
Answer: $25 to each friend
Step-by-step explanation: 100 divided by 4 = 25
ASAP!!! PLEASE HELPPP!!Write an equation for the following sentence, then solve for the unknown value.
3 times the difference of a number and 8 is less than 15.
Answer:
3(x - 8) < 15
Step-by-step explanation:
3(x - 8) < 15
3x - 24 < 15
3x < 39
x < 13
now we’ll look at what happens when we take the average of four normal draws (sample size is 4), and do that 100 times (number of trials is 100), so we get 100 means of four normals. first consider the theoretical quantities. question 6: for the sampling distribution of the mean of four standard normals, what are its theoretical mean and its standard deviation?
The theoretical mean and standard deviation is 22 and 38 respectively
np>5 and n(1-p)>5 for normal approximation
p=0.77
np>5 n×0.77>5=6.49
n(1=0.77)>5
n>5/0.23
n=21.7
The standard error of the mean for a sample size of 153 is 25 . In quest to reduce the SE of the mean in half(to 12.5 )
Standard error of sample maean is se=sd/sqrt n
se=sd/sqrt 153
Taking four times of sample size we get 4×153=612
The required sample size is 612
The mean of an infinite population is 73 and a standard deviation of 38 . The sample size of 121 is taken randomly from the given population. The SE of the sample mean equals:
standard error of the sample mean =38/sqrt121=3.4545
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Sebastian started watching a movie at 17:30 (5:30 pm).
The movie was 1 hour and 54 minutes but partway through he paused it for 15 minutes.
What was the time when he finished the movie?
Give your answer using the 24 hour clock.
I need help with this question!
the angle measures less than 90°, thus, the correct classification is acute.
Which is the correct classification for the angle ∠JML?
First, let's define the possible angles that we have here:
Obtuse: With a measure larger than 90° and smaller than 180°Acute: With a measure between 0° and 90°Right: With a measure of 90°Straight: With a measure of 180°.Notice that the angles HML and LMK should add up to 180°, then we can write:
∠HML + ∠LMK = 180°
132° + ∠LMK = 180°
∠LMK = 180° - 132° = 48°
Now we can see that:
∠JML = ∠JMK + ∠LMK
∠JML = 41° + 48° = 89°
So the angle measures less than 90°, thus, the correct classification is acute.
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the area of a certain state is 840000 square miles. what is this area in scientific notation?
1. 8.4x10.-4
2. 84x10.-3
3. 84x10.3
4. 8.4x10.5
please help
Answer:
4. 8.4×10^5
Step-by-step explanation:
The exponent of ×10 is the amount of places that you move the decimal. When the exponent is negative, you move the decimal to the left and when it is positive, you move it to the right. Number 1 and 2 are wrong right away because they move the decimal to the left which is not what we want. Number 3 is wrong because there are not enough 0's when we move the decimal. So, option 4 is correct. I hope this helps!
Ted is a freshman attending a 4-year college. He has been approved for an $8.000 subsidized federal loan at 4.29% for 10 years. How much will the U.S. Department of
Education subsidize in interest costs during his 4.5-year non-payment period?
Answer:
12.17634
Step-by-step explanation:
Answer: $1,544.40
Step-by-step explanation: It just is
Using the diagram and the given angle measure to find the other three angle measures
Based on the given.
If [tex]m∠2 = 59°[/tex]
Then, [tex]m∠4 = 59 °[/tex]
(reason: vertically opposite angles are equal)
If [tex]m∠4 = 59 °[/tex]
Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]
(reason: angles on a straight line = 180°)
If [tex]m∠1 = 121°[/tex]
Then, [tex]m∠3 = 121°[/tex]
(reason: vertically opposite angles are equal)
Therefore:
[tex]m∠1 = 121°[/tex]
[tex]m∠3 = 121°[/tex]
[tex]m∠4 = 59 °[/tex]
See attached image for the placement of the values.
I don’t really understand how to get this one :/
in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
How to identify the transformation?
Here the parent function is:
f(x) = x^2
And the transformed function is the one graphed in the lower right side of the given image.
Notice that the y-intercept of the transformed function is y = 600.
The x-intercepts are x = -10 and x = 30
Then the polynomial is something like:
y = a*(x + 10)*(x - 30)
Using the fact that the y-intercept is y = 600, then:
600 = a*(0 + 10)*(0 - 30) = a*-300
600/-300 = a = -2
The transformed function is:
g(x) = -2*(x + 10)*(x - 30)
Expanding that:
g(x) = -2( x^2 + 10x - 30x - 300)
Completing squares we get:
g(x) = -2*( x^2 - 20x - 300)
= -2*(x^2 - 2*10*x - 300)
Now we can add and subtract 100, so we get:
-2*(x^2 - 2*10*x - 300 + 100 - 100)
-2*( (x - 10)^2 - 400)
Finally, expanding that:
g(x) = -2*(x - 10)^2 + 800
Writing it in function notation, we get that the transformed function is:
g(x) = -2*f(x - 10) + 800
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large pies cost $5, and small pies cost $2. if 45 pies were sold for $120, how many small pies were sold ?
Answer:
35 small pies
Step-by-step explanation:
Framing system of linear equations and solving:Let the number of large pies be 'l' and
The number of small pies be 's'.
Total pies sold = 45
⇒ l + s = 45 ------------(I)
l = 45 - s -------(II)
Cost of 45 pies = $120
Cost of 1 large pie = $5
Cost of 'l' large pies = 5*l = 5l
Cost of 1 small pie = $2
Cost of 's' small pie = 2*s = 2s
5l + 2s = 120 --------------(III)
Solving : substitution method
Substitute l = 45 -s in equation (III)
5*(45 - s) + 2s = 120
5*45 - 5*s + 2s = 120
225 - 5s + 2s = 120 {Combine like terms}
225 - 3s = 120
-3s = 120 - 225 {Subtract 225 from both sides}
-3s = -105
s = -105 ÷ (-3) {Divide both sides by (-3)}
s = 35
Substitute s = 35 in equation (II),
l = 45 - s
= 45 - 35
l = 10
[tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]
Help please! For highschool algebra! You will get 20 points and no links please :)
Answer: a. 12x+19
b. 67
Step-by-step explanation:
a. P=a+b+c+d
P=x+7+2x+2+8x+x+10
P=x+2x+8x+x+7+2+10
P=3x+9x+19
P=12x+19
b. P=12(4)+19
P=48+19
P=67
help with this question please! with show work
Is this answer correct?
Answer:
yes this is correct
Step-by-step explanation:
this is correct because angle gqh is adjacent to mqk, meaning they are the same degree which would mean kqg and hqm are adjacent
If 21% of a number is 3, find 7% of that number.
Answer:
7% of the number is 1.
Step-by-step explanation:
21%=3
Divide both sides by 3
7%=1
Answer:
1
Step-by-step explanation:
let x be the number.so.......
if 21%of a number means 21÷100*the number(x)=3
21÷100×X=3 so when we solve this first we have to criss-cross and then 21*X=3*100
then we both divide by 21 in order to get x .so x is going to be 100 divided by 7
then.......
we are asked to get how much percent of 100÷7 is 7% so...let the answer be y
7÷100*X=y
7÷100*100*7 =Y
when calculated the answer will possibly be 1 :)))
Members of a softball team raised $1943.50 to go to a tournament. they rented a bus for $1148.50 and budgeted $53 per player for meals. write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
The number of players the team can bring to the tournament are 15
Firstly we need to form the equation. The components of equation based on given information are as follows -
Total amount raised by softball team = Cost of bus + Cost of meal × number of players
Let the number of players be represented with x.
1943.50 = 1148.50 + 53×x
Rewriting the equation
53x = 1943.50 - 1148.50
Performing subtraction to Right Hand Side of the equation
53x = 795
Shifting 75 to Right Hand Side of the equation
x = 795 ÷ 53
Performing division at Right Hand Side of the equation
x = 15
Hence, 15 players the team can bring to the tournament.
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a consumer affairs investigator records the repair cost for 1010 randomly selected vcrs. a sample mean of $72.82$72.82 and standard deviation of $24.17$24.17 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the vcrs. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
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Consumer affairs investigator records the repair cost for 10 randomly selected VCRs. A sample mean of $72.82 and standard deviation of $24.17 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Construct the 90% confidence interval. Round your answer to two decimal places.
We get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).
We are given that the number of VCRs are 10.
So, we get that:
Sample size = n = 10
Now, we get the degree of freedom as:
d o f = n - 1
d o f = 10 - 1
d o f = 9
For 90% confidence interval , critical value will be:
t (0.10, 9) = 1.833
Lower limit of 90% confidence interval will be:
Lower interval = Mean - t (0.10,9) × s / √n
= 72.82-1.833 × 24.17 /√10
= 58.81
Upper limit of 90% confidence interval will be:
Upper interval = Mean + t (0.10,9) × s /√n
= 72.82 + 1.833 × 24.17/√10
= 86.83
Therefore, we get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).
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Jessiah can run 624 feet in 36 seconds. malik can run 720 feet in 54 seconds. who can run faster? show or explain how you know.
Hello!
Answer:
Jessiah is faster than Malik because 17.33 > 13.33.
Step-by-step explanation:
To solve this exercise, we will calculate the average speed of each of them, using the formula:
[tex]A_{s} =[/tex] Δ[tex]\frac{s}{t}[/tex]
Let's calculate each average velocity by replacing the values:
Jessiah:[tex]A^s^{}=\frac{624}{36} =\frac{312}{18} =\frac{156}{9} =\frac{52}{3}[/tex] ≈ [tex]17.33~feet/second[/tex]Malik:[tex]A^s^{}=\frac{720}{54} =\frac{360}{27} =\frac{120}{9} =\frac{40}{3}[/tex] ≈ [tex]13.33~feet/second[/tex]Hope this helps!
Answered by:
AshTheNeko
5. The box plot represents the distribution of the number of points scored by a cross country team at 12 meets.
Answer:5 teams
Step-by-step explanation:
let v = (2, 3, 1), w = (1, 1, 1), and 3u + 2v 4w = (1, 2, 3). find (a) the vector u (b) the linear combination: 2u 3v + 5w
The vector u is [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex].
The linear combination 2u + 3v + 5w is 19/3 i + 17/3 j + 6k.
According to the given question.
v = (2, 3, 1)
w = (1, 1, 1)
And
3u + 2v + 4w = (1, 2, 3)
From,
v = (2, 3, 1)
⇒ v = 2i + 3j + 1k
w = (1, 1, 1)
⇒ w = i + j + j
a). Let vector u be xi + yj + zk
Here,
3u + 2v + 4w = (1, 2, 3)
⇒ 3u + 2v + 4w = i + 2j + 3k
⇒ 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j +k) = i + 2j + 3k
⇒ 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k = i + 2j + 3k
⇒3xi + 3yj + 3zk + 8i + 10j + 6k = i + 2j + 3k
⇒ 3xi + 3yj + 3zk = i + 2j + 3k - 8i -10j -6k
⇒ 3xi + 3yj + 3zk = -7i -8j -3k
⇒ xi + yj + zk = (1/3)(-7i -8j-3k)
⇒ xi + yj + zk = [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex]
b). The linear combination
2u + 3v + 5w
= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)
= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k
= -14/3 i -16/3j -2k + 11i + 11j + 8k
= 19/3 i + 17/3 j + 6k
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