Answer:
Neither expression (A) nor expression (B) would be positive. A calculator is not required.
Step-by-step explanation:
Assume that [tex]A[/tex] and [tex]B[/tex] are both positive real numbers. Consider the property of logarithms with the same base:
[tex]\ln A + \ln B = \ln(A \cdot B)[/tex].
[tex]\displaystyle \ln A - \ln B = \ln\left(\frac{A}{B}\right)[/tex].
Apply these two properties to combine the logarithms in each expression into a one.
First expression:
[tex]\begin{aligned}&\ln 2+ \ln 3 + \ln 0.161 \\ &= \ln(2 \times 3) + \ln (0.161) \\ &= \ln(2 \times 3 \times 0.161) = \ln(0.966) \end{aligned}[/tex].
Second expression:
[tex]\begin{aligned}&\ln 3+ \ln (1.4) - \ln 16 \\ &= \ln(3 \times 1.4) - \ln (16) \\ &= \ln\left(\frac{3 \times 1.4}{16}\right) = \ln(0.2625) \end{aligned}[/tex].
The logarithm of a real number is positive if and only if that number is greater than one.
Neither [tex]0.966[/tex] nor [tex]0.2625[/tex] is greater than one. Therefore, neither of their respective logarithms would be positive.
105. A circular sector has an 8.26-inch radius and a 12.84-inch arc length. There is another sector that has the same area and the same perimeter. What are its measurements
Answer:
Area of another sector=[tex]53.0292 in^2[/tex]
Perimeter of another sector=29.36 in
Step-by-step explanation:
We are given that
Radius, r=8.26 in
Arc length , l=12.84 in
Area of circular sector=[tex]\frac{arc\;length} {Circumference\;of\;circle}\times \pi r^2[/tex]
Area of circular sector=[tex]\frac{l}{2\pi r}\times \pi r^2=\frac{l}{2}\times r[/tex]
Where Circumference of circle=[tex]2\pi r[/tex]
Substitute the values
Area of circular sector=[tex]\frac{12.84}{2}\times (8.26}[/tex]
Area of circular sector=[tex]53.0292 in^2[/tex]
Area of another sector=[tex]53.0292 in^2[/tex]
Perimeter of circular sector=8.26+8.26+12.84
Perimeter of circular sector=29.36 in
Perimeter of another sector=29.36 in
As the radius of a sector decreases, the arc length increases to have an
equal area with a sector with a radius that is longer.
The measurements of another sector with the same perimeter and area are;
The radius of an alternative sector is 6.42 inchesThe arc length of an alternative sector is 16.52 inchesReasons:
Radius of the sector, r = 8.26 inches
Arc length of the sector = 12.84 inches
Perimeter of sector = 2·r + Arc length
Perimeter of the given sector = 2 × 8.26 inch + 12.84 inch = 29.36 inch
Circumference of the circle = 2 × 8.26 × π = 16.52·π
Area of the given circle, A = π × 8.26² = 68.2276·π
[tex]\displaystyle Area \ of \ sector = \frac{12.84}{16.52 \cdot \pi} \times 68.2276 \cdot \pi = 53.0292[/tex]Area of the sector, A = 53.0292 inch²
Therefore, we have;
2·R + A = 29.36 inches
[tex]\displaystyle \mathbf{\frac{A}{2\cdot \pi \cdot R} \times \pi \cdot R^2} = 53.0292[/tex]
A·R = 53.0292 × 2
[tex]\displaystyle New \ arc \ length, \ A = \mathbf{\frac{53.0292 \times 2}{R}}[/tex]
Which gives;
[tex]\displaystyle 2 \cdot R + \frac{53.0292 \times 2}{R} = 29.36[/tex]
[tex]\displaystyle R + \frac{53.0292 }{R} = 14.68[/tex]
R² + 53.0292 = 14.68·R
R² - 14.68·R + 53.0292 = 0
Factorizing with a graphing calculator, gives;
(R - 6.42)·(R - 8.26) = 0
R = 6.42 or R = 8.26
The measurement of R = 8.26 is for the first sector
Given that the sectors are different, we have;
The radius of the other sector, R = 6.42 inchesThe arc length, A = 29.36 - 2·R
∴ A = 29.36 - 2 × 6.42 = 16.52
The arc length of the other sector, A = 16.52 inchesLearn more about the sector of a circle here:
https://brainly.com/question/2501134
plz hurry for brainlyest also show your work and this is rates and ratios
Answer:
125 because if you divide 150 by 30 to find how much it was multiplied by its 5, so then if you multiphy 25 by 5 you get 125 to be the same as the seconds
Step-by-step explanation:
9. Find the slope represented in the table
below. Show all work.
X
y
7
-30
11
-54
13
-66
20
- 108
Answer:still tryna figure this out
Step-by-step explanation:
which are the correct measures of interior angles of CDE
Answer:
the second one
Step-by-step explanation:
If the coefficient of determination is equal to 1 the the correlation coefficient must be?
Answer:
It must be a strong, positive correlation
Brayden is 2 yards tall. His sister is 61 inches tall. How much taller is Brayden than his sister
Answer:
11 inches
Step-by-step explanation:
2 yards = 72 in
72 in - 61 = 11 in
The distance between two towns is 120 kilometers there are approximately 8 kilometers in 5 miles which measurement is closest to the number of mules between these two towns
Answer:
75 Kilometers
Step-by-step explanation:
We have been given that the distance between two towns is 120 km.
We are also told that there are approximately 8 km in 5 miles. Let us find number of miles per km by dividing 5 by 8.
\text{Number of miles in 1 km}=\frac{5\text{ miles}}{\text{8 Km}}
\text{Number of miles in 1 km}=0.625\frac{\text{ miles}}{\text{ Km}}
Therefore, there are 0.625 miles in 1 km.
To convert our given distance into miles we will multiply our given distance by number of miles in 1 km.
\text{Number of miles in 120 km}=120\text{ km}\times \frac{0.625\text{ miles}}{\text{ km}}
\text{Number of miles in 120 km}=120\times 0.625\text{ miles}
\text{Number of miles in 120 km}=75\text{ miles}
Therefore, the distance between two towns is 75 miles.
Answer:
The answer is 75, I had this question a few days ago and I got it right
Answer:75
The ratio of people who have dogs to people who have cats is 4 to 2. If there are 40 people, how many have cats?
Answer:
13 people
Step-by-step explanation:
let ratio be 4x and 2x
4x+2x=40
6x=40
x=40/6
x=6.66
so,
2x=2×6.66
=13.33
approx 13
again
4x=4×6.66
=26.64
approx 27.
What is 10/3 x 17.04
Answer:
56.8
Step-by-step explanation:
Answer:
56.8
Step-by-step explanation:
10 / 3 = 3.3333333
3.3333333
x 17.040000
------------------
56.8
What are three ratio is equivalent to 11 to 1
Answer:
22 to 2, 33 to 3, 44 to 4
Step-by-step explanation:
do 7 and 8! will give brainliest
Answer:
7. <4 and <6
8. <1 and <7
Step-by-step explanation:
hope this helps :)
Answer:
7. ∠6 ≅ ∠4
8. ∠7 ≅ ∠1
Step-by-step explanation:
In the figure at the top, the alternate exterior angles are the angles that are on opposite sides of the transversal and are on the outside of the parallel lines. Those pairs of angles are congruent because of the alternate exterior angle theorem since the two lines are parallel.
Question: Round to one decimal place.
1.58336707117
solve for x PLEASE ANYONE
71+x+74+39=180
Answer:
x = -4
Step-by-step explanation:
Step 1: Write equation
71 + x + 74 + 39 = 180
Step 2: Solve for x
Combine like terms: x + 184 = 180Subtract 184 on both sides: x = -4Step 3: Check
Plug in x to verify it's a solution.
Substitute: -4 + 184 = 180Evaluate: 180 = 180Please answer this :)
3,510 × 10 to the zero power
Answer:
3
Step-by-step explanation:
Please help me find this angle!!!! I will make you brain list
Answer:
i cant hjelp sorry but can u heart
Step-by-step explanation:
so i can get points
what is the sum of .1458862555.05x74446.555623=
Answer: the correct answer is 10,860.72923508417
Answer:
uhm there is no sum to that. Its called the product. Also .1458862555.05 isn't a number
Step-by-step explanation:
what is 4021 divided by 68
Answer:
4021/68 = 59.13
Step-by-step explanation:
Hope this helps you out!!!
Answer: 59.1323529412
Step-by-step explanation:
Susan found a bag of 20 golf balls at a garage sale, and bought the bag for $2.00. Express the ratio of cost to number of balls in lowest terms. Use the colon to write the ratio.
Answer:
10 cents : 1 ball
Step-by-step explanation:
$2.00 : 20 balls = $1.00 : 10 balls = 100 cents : 10 balls = 10 cents : 1 ball
A customer selects three different toppings for a pizza. If there are 10 different toppings from which to choose, how many different pizzas can be made?
Answer:
30 different combinations
Step-by-step explanation:
10 x 3 = 30
Please turn 64/7 & 70/6 into proper fractions (Simplify the answer)
Answer:
64/7 = 9 ¹/7
70/6 = -35/3
Answer:
64/7 cant be simplified
11 2/3
and also can be 35/3
Step-by-step explanation:
help quickly pls its due soon
Find the reciprocal:
5
6
StartFraction 1 Over 6 EndFraction
StartFraction 1 Over 5 EndFraction
StartFraction 5 Over 6 EndFraction
StartFraction 6 Over 5 EndFraction
Answer:
The answer is 6/5 ^.^
Step-by-step explanation:
I got it right =^.^=
Hope this helps you =^.^=
I need some assistance please and thank you
Answer:
y=-4x-3
Step-by-step explanation:
passes through-2,5
slope -4
PLEASE HELP QUICK WILL GIVE BRAINLIEST
Answer:
+ and -
Step-by-step explanation:
+ positive
- negative
A dolphin travels through the water a speed of 25 kilometers per hour which representation shows the distance a dolphin can travel at this rate
Answer:
50km 2hours
100km 4hours
150km 6hours
200km 8hours
The effects of caffeine on the body have been extensively studied. In one experiment1, researchers examined whether caffeine increases the rate at which people are able to tap their fingers. Twenty students were randomly divided into two groups of
Question attached
Answer and explanation:
Here we would use the two sample t test. In finding the hypotheses for a two sample t test we test the sample mean of one group against the other group to determine if there is a statistical difference or they are equal. We have this to compare the mean finger tapping rate of the two groups being tested in the question. Our null and alternative hypotheses here are:
H0: u1 = u2 null hypothesis
H1: u1 > u2 alternative hypothesis
Where u1 and u2 are the sample means for each group in the caffeine experiment
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3 ?
O y+2=} (x+3)
O y-2 = }(x-3)
y + 3 = {(x + 2)
O y-3= {(x-2)
Answer:
use the point slope formula y-y1 =M(x -x1) the M = slope and P1 = (x1, y1) = the given point (3,2)
Step-by-step explanation:
y-2=(1/3)*(x-3)
Please help with this question I’m confused
Answer:
D) X=4
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
[tex]13x - 5x = 8x[/tex]
[tex]8x = 32[/tex]
[tex]x = 32 \div 8[/tex]
[tex]x = 4[/tex]
How would I solve this system of equations with SUBSTITUTION? Please explain step by step!!BRAINLIEST, THANKS, AND 5-STAR REVIEW TO BEST ANSWER!