Write 3log7x-4log7y as a single logarithm.
Answers
Answer:
\(3\log7x - 4\log7y = log(\frac{x^3}{7y^4} )\)
Step-by-step explanation:
The given logarithm can be re-written as:
\(\log(7x)^3 - log(7y)^4\)
For the power property:
\(\log_ba^c = c\log_ba\)
Know for the quotient property you get:
\(log_ba - log_bc = log(\frac{a}{c} )\)
\(\log{\frac{(7x)^3}{(7y)^4} } =\log{\frac{7^3x^3}{7^4y^4} } =\log{\frac{x^3}{7y^4} }\)
so the final answer is \(\log{\frac{x^3}{7y^4} }\)
Related Questions
A. 4 in
B. 5 in
C.60 in
D. 1.7 in
FOR BRAINLIST!!!!
Answers
Answer:
A. 4in
Step-by-step explanation:
Since the triangles are similar, their sides are in ratio. Therefore, we can say that:
KL/JK=BC/AB
x/1.5=16/6
x=(1.5)(16/6)
x=4
Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment
m
(Round to one decimal place as needed)
ample Get more help-
HW Score: 39.53%, 17 of 43 points
O Points: 0 of 6
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 14 subjects had a mean wake time of 105 0 min After treatment, the 14 subjects had a
mean wake time of 782 min and a standard deviation of 24 1 min Assume that the 14 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the
mean wake time for a population with drug treatments What does the result suggest about the mean wake time of 105 0 min before the treatment? Does the drug appear to be effective?
Answers
The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.
Confidence interval is written in the form as;
(Sample mean - margin of error, sample mean + margin of error)
The sample mean represent x , it is the point estimate for the population mean.
Margin of error = z × s/√n
Where s = sample standard deviation = 21.8
n = number of samples = 17
Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
then the degree of freedom, df for the sample.
df = n - 1 = 17 - 1 = 16
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.01/2 = 0.005
Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995
the t distribution table, z = 2.921
Margin of error = 2.921 × 21.8/√17
= 15.44
The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44
The upper limit is 90.3 + 15.44 = 105.74 mins
The lower limit is 90.3 - 15.44 = 74.86 mins
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What’s the square root of √125
Answers
Answer: \(5\sqrt 5\)
Step-by-step explanation:
Sol \(\sqrt 125\) = \(\sqrt{25.5}\)
= \(\sqrt{25}\) x \(\sqrt{5}\)
\(5 \sqrt{5}\)
What is the solution to 3+x=x+3
Answers
Answer:
all real numbers
Step-by-step explanation:
if you subtract x from both sides, you get x=x. This is true for basically any number
908636549723 times 47647647 divided bye 98
Answers
Answer:
4.4177953e17
Step-by-step explanation:
i think that's the answer im not sure i worked it out in my notebook sorry if it's wrong
Evaluate the expression: −(8 − 12) + 60 + (−4)2.
Answers
Answer: 80
Step-by-step explanation:
⇒ −(8 − 12) + 60 + (−4)²
⇒ -(-4) + 60 + 16
⇒ 4 + 60 + 16
⇒ 80
need help i dont understand
Answers
Answer:
Step-by-step explanation:
it would be "c" because the question asks for the number that makes the inequality true
4x≤ x+3
the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example
4 x -7=-28
-28+3=-25
-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5
5 is not greater than 8 so it doesnt work
In a survey of 259 professional athletes, it was found that 110 of them owned a convertible, 91 of
them owned a giant screen TV, and 120 owned a sporting goods store. 15 owned a convertible and a
store, 43 owned a TV and a store, and 44 owned a covertible and a TV. 9 owned all three items.
1. How many athletes did not own any of the three items?
2. How many owned a covertible and a TV, but not a store?
3. How many athletes owned a convertible or a TV?
4. How many athletes owned exactly one type of item in the survey?
5. How many athletes owned at least one type of item in the survey?
6. How many owned a TV or a store, but not a convertible?
Answers
1. Number of athletes did not own any of the three items = 259 - 228
= 31.
2. Number of athletes own a convertible and a TV but not a store = 44 - 9
= 35.
3. Number of athletes own a convertible or a TV = 110 + 91 - 44
= 157.
4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
5. Number of athletes owned at least one type of item = 259 - 31
= 228
6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71
= 118.
The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.
Total number of athletes surveyed = 259
Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228
Number of athletes who did not own any of the three items = 259 - 228 = 31.
The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.
Number of athletes who own a convertible and a TV = 44
Number of athletes who own all three items = 9
Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35
The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.
Number of athletes who own a convertible or a TV = 110 + 91 - 44
= 157.
The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.
Number of athletes own a convertible only = 110 - 15 - 9 = 86
Number of athletes own a TV only = 91 - 44 - 9 = 38
Number of athletes own a store only = 120 - 15 - 43 - 9 = 53
Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
The number of athletes who owned at least one type of item can use the result from part (1).
Number of athletes who owned at least one type of item = 259 - 31
= 228
The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.
Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159
Number of athletes own a TV or a store not a convertible = 13 + 34 +71
= 118.
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The value of x varies directly with y, and when x = 13, y = 12. Write an equation to represent the direct variation.
Answers
The equation of the direct variation is x = (13/12)y, owing to the fact that x varies directly with y.
How to solve proportionality problems?Direct variation equation is a linear equation in two variables expressed
as; a ∝ b
Hence, a = kb.
Where k is the proportionality constant.
Given the data in the question;
x = 13y = 12Equation of the direct variation = ?First, we determine the proportionality constant.
a = kb
x = k(y)
13 = k( 12 )
k = 13/12
Now substitute the value of the proportionality constant into the equation to determine the equation of the direct variation.
x = k(y)
x = (13/12)y
Therefore, the equation of the direct variation is x = (13/12)y, owing to the fact that x varies directly with y.
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Draw and label diagrams that show these two methods for calculating 19 • 15
Answers
The answer for long multiplication is 285. The answer for expanded form of multiplication is 285.
What is multiplication?Multiplication is a mathematical operation that involves combining two or more quantities to find their product. It is usually denoted by the symbol "x" or "•". Multiplication can also be thought of as repeated addition, where the same quantity is added to itself a certain number of times. Multiplication is used in many areas of mathematics and real-world applications, such as calculating the area and perimeter of geometric shapes, scaling quantities, and determining rates and proportions.
Here,
Method 1: Long Multiplication
1 9
x 1 5
-------
2 8 (9 x 5)
1 5 (1 x 5)
-------
2 8 5
Method 2: Expanded Form Multiplication
19 • 15 = (10 + 9) • (10 + 5)
= 10 • 10 + 9 • 10 + 10 • 5 + 9 • 5
= 100 + 90 + 50 + 45
= 285
Diagram:
10 9
x 10 5
------
50 45 (9 x 5)
90 (9 x 10)
------
100 35 (10 x 5, and carry over 3 to next column)
------
150 (total sum of all columns)
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Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.
If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.
Answers
The number 100 would land in column 2
The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?Given that we have the array of numbers
The length of each row in the array is 7
Dividing 100 by 7, we have
100/7 = 14 Remainder 2
This means that
Column = 2
In which row would the number 100 land?In (a), we have
100/7 = 14 Remainder 2
This means that
Row = 14
The location of 100 in rows of 6 numbersHere, we have
The length of each row in the array is 6
Dividing 100 by 6, we have
100/6 = 16 Remainder 3
So, the location of 100 in rows of 6 numbers is row 16 and column 3
Predicting the row and column 100 will landLet the length of each row in the array be n
Dividing 100 by n, we have
100/n = q Remainder r
This means that the location of 100 in rows of n numbers is row q and column r
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Factorise fully 5a + 15ab
Answers
Answer:
Therefore, the fully factorised form is 5a(1 + 3b).
Step-by-step explanation:
5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.
PLEASE ANSWER AS SOON AS POSSIBLE
Answers
Answer:
4 to 1
Step-by-step explanation:
Tablespoon of cocoa to Tablespoon of sugar
8 : 2
\(\frac{8}{2}\) : \(\frac{2}{2}\)
4 to 1
When recipe is doubled: ( 8 x 2) to (2 x 2)
16 : 4
\(\frac{16}{4}\) : \(\frac{4}{4}\)
4 to 1
It can be observed that the ratio remains the same
4. *—3 - 15 – 91 5. ** –23 - 132 + (-2)21 - 5 6. |116 - 81 – 42 7. V42+32-4 ** 1-4-(-3) 9. Evaluate g(4) if g(x) = -x2 - 4x + 9 8. * Evaluate f(-3) if f(x) = x2 – [x] + 5
Answers
4.
\(\begin{gathered} -3-|5-9| \\ -3-|-4| \\ \text{ By the symmetry property of the absolute value:} \\ |a|=|-a| \\ so\colon \\ |-4|=4 \\ -3-4=-7 \end{gathered}\)Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared plus 2 times x minus 3 end quantity and g(x) = log4x, evaluate (g – f )(2).
negative one half
0
one half
1
Answers
f(2) = (2+3)/(2^2+(2*2)-3) = 5/7
g(2) = log4(2)
Therefore, (g-f)(2) = g(2) - f(2) = log4(2) - 5/7. Since log4(2) is approximately 0.5, we can estimate that (g-f)(2) is approximately 0.5 - 5/7 = -1/14.
So the answer is negative one half. I THINKKK
URGENT LOL PLS HELP
Answers
Answer:
\( {3x}^{2} + 24x - 6\)
Step-by-step explanation:
To find the area of a rectangle you have to multiply the length by the width.
In your problem, the length and width are both equations, so you just have to multiply each part of the equation separately.
For example, if you were to put both equations with one over the other, you just have to multiply the aligned numbers.
The length is: x2 + 6x + 3
The width is: 3x2 + 4x - 2
and if you multiply the aligned numbers together, you get
3x2 + 24x - 6. Because:
x2 × 3x2 = 3x2,
6x × 4x = 24x,
and 3 × -2 = -6
Answer:
Blah
Step-by-step explanation:
2x + 5y= 10; (4,9)
Write answer in slope intercept form.
Answers
Answer:
y = 5x - 5/2xy + 79
Step-by-step explanation:
First we need to solve for m which is slope.
Subtract 5y from both sides
2x = 10 - 5y
Then divide each term by 2
2x/2 = 10/2 + -5y/2
Then simplify to the left
x = 10/2 + -5y/2
Then simplify the right side
x = 5 - 5y/2
Next we have to find the value of b using the formula y = mx + b
So
y = (5 - 5y/2) * x + b
y = (5 - 5y/2) * (4) + b
9 = (5 - 5(9)/2) * (4) + b
Rewrite
(5 - 5(9)/2) * 4 + b = 9
Simplify more
Multiply 5 by 9
(5 - 45/2) * 4 + b = 9
Multiply by 2/2 to write 5 as a fraction
5 * 2/2 - 45/2) * 4 + b = 9
Then combine 5 and 2/2
(5 * 2/2 - 45/2) * 4 + b = 9
Combine the numerator over the denom
5 * 2 - 45/2 * 4 + b = 9
Simplify the numerator
-35/2 * 4 + b = 9
Cancel the common factor of 2
-35 * 2 + b = 9
Multiply
-70 + b = 9
Move the terms without b to the right side
b = 9 + 70 > b = 79
Now we substitute all the values into y = mx + b
y = 5x - 5/2xy + 79
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f "(2)
A) f "(x) 0,f , (2)-0
B) f , (x)-9; f , (2) = 9
C)f"(x) = 5; f "(2) = 5
D) f '(x) 5x; f '(2) 10
Answers
The correct question is;
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f '(2)
A) f'(x) = 0; f'(2) = 0
B) f'(x) = 9; f '(2) = 9
C)f'(x) = 5; f'(2) = 5
D) f '(x) = 5x; f '(2) = 10
Answer:
Option C: f'(x) = 5 and f '(2) = 5
Step-by-step explanation:
We want to find the derivative of f(x) = 5x + 9.
Now, the derivative with respect to x will be;
f'(x) = 5
Now,we also want to find out f'(2)
This means we are to put 2 for x in the derivative function.
In the derivative function, we don't have x as we have just 5.
Thus,f'(2) = 5
How do you show your work for this problem?
Answers
Answer:
i cant see it
Step-by-step explanation:
giving 15 points
SCATTER PLOT RELATIONSHIP
Answers
Answer:alla
Step-by-step explanation:
Answer: As the time spent training increases, the time to run 100m decreases.
Step-by-step explanation:
The scatterplot shows a negative correlation. Thus, as x increases, y decreases. Since x is training time and y is 100m time, the second option would be the appropriate response.
What is the surface area of the net? *inches squared*
Answers
9514 1404 393
Answer:
75 in^2
Step-by-step explanation:
The central vertical rectangle (including "ears") has dimensions
3 in wide by (9+2+2) = 13 in tall
Its area is
A = LW = (3 in)(13 in) = 39 in^2
__
The two rectangles either side of that have dimensions 2 in by 9 in. The area of each of them is
A = LW = (2 in)(9 in) = 18 in^2
__
The total net area is the sum of the areas of the parts:
left rectangle + central rectangle + right rectangle
= 18 in^2 + 39 in^2 + 18 in^2 = 75 in^2 . . . . surface area of the net
Simple math question (Pic provided) (Algebra)
Answers
Answer:m<k+m<k=180+167-133=100
Step-by-step explanation:
Miguel is 4 years older than of Harper's age. The sum of their ages is 34 yr. what is Harper's age?
Answers
Answer:
Harper's age =15
Step-by-step explanation:
let Harper's age be x
and Miguel's age be x+4
x+x+4=34
2x+4=34
2x=30
x=15
therefore Harper's age is 15.
use interval notation to express the following: the set of all numbers greater than or equal to 5 and less than or equal to 7
Answers
[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
What is a set?A set is a 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.
Let x belong to the set of real numbers (R)
Now, x≥5 and x≤7.
So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]
Therefore, the notation will be [5, +∞) ∪ (-∞,7].
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This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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Help APSP!!!!!!!!!!!!!
Answers
Answer:
d
Step-by-step explanation:
Answer
its d
Step-by-step explanation:
10. If log8=a and log7=b write log5.6 as an expression in terms of a and b
Answers
Answer:
log 56 = a + b
Step-by-step explanation:
log8 = a and log7 = b (Given)log 56 = log (8*7)-> log 56 = log 8 + log 7-> log 56 = a + bGeraldine is picking a four-digit password by using the digits 0 through 9. She can use each digit only once. How many different passwords are possible? 34 40 5,040 10,000
Answers
Answer:
5040 different combinations
Step-by-step explanation:
0-9 = 10 numbers
1st digit can be 1 0f 10
2nd digit can be 1 of 9
3rd digit can be 1 of 8
4th digit can be 1 of 7
10×9×8×7=5040
Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.
Answers
The correct answer is C. It is the graph of f(x) translated 11 units to the left.
The correct answer is:
C. It is the graph of f(x) translated 11 units to the left.
When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.
In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.
The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.
Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.
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what is 3/8 divided by 3/5
Answers
Answer:
\( \frac{3}{8} \div \frac{3}{5} \)
It equals 0.625