Given log_73≈0.5646 and log_716≈1.4248, evaluate the expressions. Please show work using given values.
Answers
Answer:
(a) [tex]\log_72 \approx 0.3562[/tex]
(b) [tex]\log_7(\frac{147}{16} ) = 2[/tex]
Step-by-step explanation:
For the point a:
For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex]
16 can be re-write as [tex]2^4[/tex]. Then you have:
[tex]\log_72^4[/tex]
Using the power property of the logarithm we have:
[tex]\log_ba^c = c\log_ba[/tex]
[tex]\log_72^4 = 4\log_72[/tex]
And this expression is equal to:
[tex]4\log_72 \approx 1.4248\\\log_72\approx \frac{1.4248}{4} \approx 0.3562\\[/tex]
For the point b:
For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex] and [tex]\log_73 \approx 0.5646[/tex]
The first is use the quotient property in the given log.
[tex]\log_c\frac{a}{b} = \log_ca-\log_cb[/tex]
[tex]\log_7\frac{147}{16} = \log_7147 -\log_716[/tex]
We already know the value of [tex]\log_716[/tex] then we have to calculate the value of [tex]\log_7147[/tex].
So we factorize the number 147 in [tex]3 \cdot 7 \cdot 7[/tex] (for factorize the number start with the smaller prime and check if the remainder is 0, it is then is a primer factor of the number).
Now re-write [tex]\log_7147[/tex] as [tex]\log_73 \cdot 7^2[/tex] and by the product property get:
[tex]\log_bmn = \log_b m +\log_b n\\\log_73 \cdot 49 = \log_7 3 +\log_7 49 = 0.5646 + 2 = 2.5646[/tex]
Know replace each value in the subtraction and get the result:
[tex]\log_7147 -\log_716 = 2.5646 - 0.5646 = 2[/tex]
Related Questions
Help !!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
One must rearrange the function to decreasing value of exponents
f(x) = -7x⁴ + 8x³ - 3x² - 9x + 11
to see that it is a 4th degree polynomial with leading coefficient of -7
The table above shows the number of each type of plant in Robert's garden. What is the ratio of the total number of plants in Robert's garden to the number of tomato plants?
Answers
Answer: C.
Step-by-step explanation:
Total number of plants in Robert's garden = 8 + 4 + 16 + 22
= 50
Number of tomato plants in Robert's garden = 8
Ratio of total number of plants to the number of tomato plants = 50 : 8
Simplify
50 : 8 = 25:4
Cassidy places 40 stamps on each of 8 albums pages how many stamps dose she place
Answers
Answer:
Cassidy places 5 steps on each album page.
Cassidy places 320 stamps in total.
Step-by-step explanation:
40÷8=5 stamps on each album page
40×8=320 stamps in total
p l s… h e l p… m e…
Match the unknown entries in the two matrices with their correct values
Answers
Answers:
v = 54y = 0u = 6w = -48x = -1===================================================
Explanation:
The left hand side is
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}[/tex]
That -6 outside the matrix is multiplied with each item inside the matrix. This is known as scalar matrix multiplication. Effectively, it's very similar to the idea of the distributive property.
So for the first row, we have the three columns of: -6*3 = -18 and -6*(-1) = 6 and -6*3 = -18
The other two rows are handled the same way. This is what should result:
[tex]-6\begin{bmatrix}3 & -1 & 3\\8 & x & -9\\4 & -1 & y\end{bmatrix}= \begin{bmatrix}-18 & 6 & -18\\-48 & -6x & 54\\-24 & 6 & -6y\end{bmatrix}[/tex]
From here, you'll then match up the terms in the given right hand side matrix. The top row has the variable 'u' in the middle, which matches with the '6' in the middle of the top row shown. Therefore, u = 6.
-----------------------------
Now to the second row.
The -48 in the first spot pairs up with the w in the other matrix. So we can see that w = -48. Similarly, we have v = 54.
Also, we have -6x in the middle which matches with the 6 in the same corresponding spot. Solving -6x = 6 leads to x = -1.
-----------------------------
Finally, the third row.
There's only one variable here and that's the variable y in the bottom right corner. It pairs up with 0 in the same corresponding spot for the right hand side matrix. Therefore, y = 0.
Help me answer 5d, thank you!
Answers
Answer:
5. is III. Since there is a vertical asymptote at x= -3 and hole at x=0
If 20% of a number is 28 and 25% of the same number is 35, find 45% of that number.
Answers
explanation: 20% + 25% = 45% and 20%= 28
25%= 35
thus, 28 + 35 = 45% = 63
Simplify this equation
Answers
Answer:
I think the answer might be 12x⁷
What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?
Answers
Answer:
I will cryy because I only want to write 78 why it recorded as 98
please help!
15 - (-20)
Answers
b) Complete the table to show the total amount of calories Mary will burn for
cycling and running for 0, 10, 15, and 30 minutes. Show and explain your work.
Minutes (m)
Total Calories Burned (C)
0
10
Answers
For 0 minutes she can burn 0 calories
For 10 minutes she can burn 20-40 calories
For 15 mins she can burn 40-60 calories
For 30 minutes she can burn 140-295 calories
I hoped this helped!
Have a great day/night! :)
Due Tomorrow: answer question 1 with steps
Answers
Answer:
the 1 st qn that is no2 c is just down right corner am I right
Step-by-step explanation:
plzzz make me ans as the brainliest ans
Jill had some candy to give to her five
children. She first took seven pieces for
herself and then evenly divided the rest
among her children. Each child received
five pieces. With how many pieces did
she start?
Answers
Explanation: If she had 5 children and each child received 5 pieces, you can determine that she gave her children a total of 25 pieces because 5 x 5 = 25. If she took 7 pieces for herself before giving the rest away, you can determine that she had 32 pieces of candy to start with because 25 + 7 = 32.
Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?
Answers
Robert has 4 times as many pennies as he does nickels. If Robert has $1.44 worth of pennies and nickels, how many nickels does he have?
Answers
9514 1404 393
Answer:
16 nickels
Step-by-step explanation:
Robert can group his coins into groups consisting of 1 nickel and 4 pennies. The value of each group is 9¢, so the number of groups Robert can make is ...
$1.44/$0.09 = 16 . . . groups
Since there is 1 nickel in each group, Robert has 16 nickels.
Answer:
16
Step-by-step explanation:
Forty six minus twenty
Answers
Answer:
26 po hahahahahahahahahahaha
do anyone know what’s the answer to this problem ?
Answers
i tried to explain it best i could in the picture
I need help with number 9 please
Answers
Answer:
29.85
Step-by-step explanation:
1 month = 9.95
2 months = 19.9
3 months= 29.85
It shows the progression through three months and how much it was starting off from one month.
Answer: $29.85
per day it charges $9.95
she has the subscription for three months
we will then multiply the amount charged per month
$9.95 x 3 = $29.85
I hope this helps! :)
68% of US adults have very little confidence in newspapers you randomly select 10 US adults find the probability that the number of US adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, (c) less than four.
Answers
Answer:
A) 12.29%
B) 81.33%
C) 1.55%
Step-by-step explanation:
This is a binomial model, and I assume you're meant to use a calculator to solve.
A)
This is what I have in my notes for the binompdf function:
binompdf(n, p, x) - find the probability of exactly x successes in n trials given p probabilityThat is exactly what we want in this case, we're looking for exactly 5 people who meet the conditions (successes) given n trials and p probability.
Using a calculator:
binompdf(10, 0.68, 5) ≈ 0.1229
That means you have about a 12.29% chance to randomly select exactly 5 adults who have little confidence in newspapers.
B)
For this one, use the binomcdf function:
binomcdf(n, p, x) - find the probability of x or fewer successes in n trials given p probabilityIn this case, we're looking for more, not less. However, you can think of the probability of getting more than 6 as just the probability of not getting less than 6.
With a calculator:
binomcdf(10, 0.68, 5) ≈ 0.1867
That means you have about an 18.67% chance to randomly select 5 or less people. We're looking for more though. As said above, the probability of getting 6 or more is just the probability of not getting 5 or less. To find the probability of something not happening, just subtract the probability from 1.
1 - 0.1867 = 0.8133
An 81.33% chance to randomly select at least 6 adults who have little confidence in newspapers.
C)
Same as the above, I don't see a need to explain it all again. Use binomcdf:
binomcdf(10, 0.68, 3) = 0.0155
Notice I used 3 rather than 4. binomcdf calculates x or fewer, or 'rather less than or equal to'. We want just 'less than 4', and that means 'less than or equal to 3'.
That's a 1.55% chance to select less than 4 adults with little confidence in newspapers.
Which statement is true?
Answers
Hope this helped!!
Please help please help please help please help
Answers
Answer:
2 , 3
Step-by-step explanation:
What percent of 80 is 84?
Answers
Answer: 105
Step-by-step explanation: if you are using a calculator, simply enter 84÷80×100 which will give you 105 as the answer.
How do you evaluate (-12)3
Answers
Step-by-step explanation:
-1728 y'all i do by using calculator and it is correct
Answer:
its -1728
Step-by-step explanation:
i worked it out right.
PLEASE HELP ME WILL MARK BRAINLIEST AND PLZ EXPLAIN
Answers
Y= a (x-h)^2 + k
Now we have to identify the vertex which is (-4,-3). Now substitute the vertex for (h,k). So now we have.
Y= a( x-(-4)^2 + (-3)
This gives us
Y = a(x+4)^2 -3
Now we have to pick a point from the graph to substitute for the x and y values. This can be any point expect for the vertex. I have chosen (-3,-1). Now let’s substitute:
-1= a(-3+4)^2-3
Now we have to solve for a:
-1=a(1)^2 -3
-1= a-3
-1+3=a
a= 2
Now that we know the value of a we can write the equation down:
Y= 2(x+4)^2 + 3
Simplify -3(xy + 2y) + 5y - x.
Answers
Answer:
Step-by-step explanation:
-3 (xy+2y)+5y-x
-3xy-6y+5y-x
-3xy-y-x
Look at attached photo. Will give brainiest to correct answer. Trigonometry.
Answers
Answer:
Step-by-step explanation:
Which fractions are equivalent to 1012?
Select each correct answer.
23
56
1224
3036
5060
6084
Answers
Answer:
5/6, 30/36, 50/60
Step-by-step explanation:
10/12 divided by 2= 5/6
10/12•3= 30/36
10/12•5= 50/60
evaluate -x^3 - 3x^2 + 4 when x = -2
Answers
-(-2)^3 = 8
-3(-2^2)= -12
Then add 4
-12 + 4 + 8 = 0
Answer:
32
Step-by-step explanation:
x = -2
-x^3 - 3x^2 + 4
-(-2)^3+6^2+4
8+36+4=48
Hope this helps :)
find the length of fencing required to go all the way around the rectangular field that is 136000mm wide and 425m long
Answers
Can someone tell me what’s going on here
Answers
Answer:
c = 105 degres
Step-by-step explanation:
When two lines cross like that and form an x, the opposite sides are equal (so the angle below the 75 degree one is also 75 degees). Using this, you can figure out the rest.
If both the top an bottom are equal, you know that 150 degres are taken (75+75) and you know that there can only be 360 degres in total here, so you subtract 150 from 360 and get 210. Now you know that the last two sides together are 210, and since they are equal, you divide it by two to get 105 degrees.
Write an equation of a line with an x-coefficient of - 3 and a y-intercept of 7
Answers
Answer:
y = -3x + 7
Step-by-step explanation:
For an equation in the format y = ax + b, a is the coefficient of x, and b is the y intercept.