What is the value of log0.5^16? a.–4.00 b.–0.25 c.1.51 d.2.41
Answer:
The correct option is a.
Step-by-step explanation:
The given expression is,
[tex]log(0.5)^{16}[/tex]
Use property of logarithm
[tex]loga^b=bloga[/tex]
[tex]log(0.5)^{16}=16\times log(0.5)[/tex]
The value of log(0.5) is -0.30103.
[tex]log(0.5)^{16}=16\times -0.30103[/tex]
[tex]log(0.5)^{16}=-4.81648[/tex]
The value of given expression is -4.81648.
If the final answer appromatted to preceding integer, then the correct option is -4.00.
Find the area under the curve y = 5/x3 from x = 1 to x = t. evaluate the area under the curve for t = 10, t = 100, and t = 1000. t = 10 t = 100 t = 1000 find the total area under this curve for x ≥ 1.
The area under the curve from x = 1 to x = t is [tex]-\frac{5}{2} (\frac{1}{t^2} -1)[/tex].
For, t = 10, 100, and 1000, the areas are 2.475, 2.49975, and 2.4999975 respectively.
The total area is 2.5.
Given that:
[tex]y=\frac{5}{x^3}[/tex]
In order to find the area integrate it with limits from x = 1 to x = t.
[tex]A=\int\limits^t_1 {\frac{5}{x^3} } \, dx[/tex]
This can be written as:
[tex]A=\int\limits^t_1 {5x^{-3} } \, dx[/tex]
[tex]=5[\frac{x^{-2}}{-2} ]_1^t[/tex]
[tex]=-\frac{5}{2} (t^{-2}-1^{-2})[/tex]
So, the area is [tex]A=-\frac{5}{2} (\frac{1}{t^2} -1)[/tex].
When t = 10,
[tex]A=-\frac{5}{2} (\frac{1}{10^2} -1)[/tex]
[tex]=2.475[/tex]
When t = 100,
[tex]A=-\frac{5}{2} (\frac{1}{100^2} -1)[/tex]
[tex]=2.49975[/tex]
When t = 1000,
[tex]A=-\frac{5}{2} (\frac{1}{1000^2} -1)[/tex]
[tex]=-2.4999975[/tex]
To find the total area, the value of t = ∞.
Now, ∞⁻² is always 0, since any negative number to the power of infinity is 0.
So, the area is:
[tex]A=-\frac{5}{2} (0-1)[/tex]
[tex]A=2.5[/tex]
Hence, the total area is 2.5.
Learn more about Area using Integrals here :
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The dimensions of an office conference room are 10 feet by 18 feet. If the conference room blueprint dimensions are 5 centimeters by 9 centimeters, what is the scale of the blueprint?
A. 1 centimeter = 9 feet
B. 1 centimeter = 2 feet
C. 1 centimeter = 5 feet
D. 1 centimeter = 10 feet
solve for y
11x+7y=-35
solve the inequality -×/2 <4
a puppy weighs 9/10 pound. it's mother weighs 8 times as much. how much does the mother weigh?
Experts/ace/geniuses
What is the y-intercept of the line that has a slope of -1/2 and passes through the point (2, 3)?
The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle? 5, 10, or 25?
Jim Abbott purchased a $60,000 recreational vehicle (RV) with a 40 percent markup on selling price. a. What was the amount of the dealer’s markup? Markup amount $ b. What was the dealer’s original cost? Original cost $
Answer:
24,000 dealer paid
mark up : 36,000
Step-by-step explanation:
60,000 * 0.40= 24,000
60,000-24,000= 36000
G let z be a random variable with a standard normal distribution. find the indicated probability. p(z ≤ −0.27)
The probability P(Z <= -0.27) in a standard normal distribution is determined by finding the corresponding right-tail probability of Z = 0.27 and subtracting it from 1, reflecting the distribution's symmetry.
To find the probability P(Z \<= -0.27), we use the properties of the standard normal distribution, which is symmetric about zero. The probability of Z scoring below -0.27 is equal to the probability of Z scoring above 0.27 due to this symmetry. Looking up the corresponding value for Z = 0.27 in a standard normal table, or using a calculator, we would find the right-tail probability. To get our desired left-tail probability for Z = -0.27, we subtract this from 1. For example, if the right-tail probability for Z = 0.27 was 0.3936, then P(Z \<= -0.27) would be 1 - 0.3936 = 0.6064.
Indicate whether each of the following fractions is proper or improper. a. 4⁄16 b. 75⁄70 c. 2⁄15 d. 6⁄6
Find all integer solutions to the pair of congruences (if any) x ≡ 17 (mod 23) 70x ≡ 3 (mod 93).
Which of the following functions is graphed below?
The graph consists of two parts: left part (with sign < or ≤) - parabola and right part (with sign > or ≥) - straight line.
Determine signs:
From the diagram you can see that the right endpoint (4,19) of parabola is not included. This means that x cannot be equal to 4 at this part of graph and the sign should be <.
Also you can see that the left endpoint (4,8) of line is included. This means that x=4 belongs to the right part and the sign should be ≥.
Using previous conclusions, you can state that correct choice is D.
what are the slope and why intercept shown on the graph below
what is -10+2 because this is really confusing to me.
the average adult human has approximately 2.5 x 10 ^ 13 red blood cells + 7 x 10 ^ 9 white blood cells about how many times as great is the number of red blood cells than the number of white blood cells
A jar of crunchy peanut butter contains 1.35 kg of peanut butter. if you use 8.0 % of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container?
2/3 of the product of 3/8 and 16
tossing a number cube numbered from 1 to 6 and getting an odd number that is less than or equal to 3
a coin is tossed twice what is the probability of the coin landing heads up both times
Which of the following describes the roots of the polynomial function f(x)=(x-3)^4(x-6)^2? –3 with multiplicity 2 and 6 with multiplicity 4 –3 with multiplicity 4 and 6 with multiplicity 2 3 with multiplicity 2 and –6 with multiplicity 4 3 with multiplicity 4 and –6 with multiplicity 2
Answer:
3 with multiplicity 4 and -6 with multiplicity 2
mrs. west is 14 years younger than her aunt. if mrs. west’s age in years is as much below 60 as her aunt’s age is over 40, how old is each?
Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.
Let's represent Mrs. West's age as W and her aunt's age as A.
Given that Mrs. West is [tex]14[/tex] years younger than her aunt, we can write the equation:
[tex]W=A-14[/tex]
Also, it's given that Mrs. West's age is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex] . This can be represented as:
[tex]W=60-(A-40)[/tex]
Simplify the equation:
[tex]W=60-A+40\\W=100-A[/tex]
Now, we have two equations for [tex]W[/tex]:
[tex]W=A-14\\W=100-A[/tex]
Since both equations equal [tex]W[/tex], we can set them equal to each other:
[tex]A-14=100-A[/tex]
Now, solve for A:
[tex]A+A=100+14\\2A=114\\A=57[/tex]
Now, plug the value of [tex]A[/tex] into either equation to find [tex]W[/tex]:
[tex]W=57-14\\W=43[/tex]
So, Mrs. West is [tex]43[/tex] years old, and her aunt is [tex]57[/tex] years old.
COMPLETE QUESTION:
Mrs. west is [tex]14[/tex] years younger than her aunt. if mrs. west’s age in years is as much below [tex]60[/tex] as her aunt’s age is over [tex]40[/tex], how old is each?
Alex is decorating a large box with pieces of ribbon. He needs 7 sections of ribbon with a length of (3/4) yard. He is going to cut the 7 pieces from a roll of ribbon that is 30.2 yards long
Experts/ace/geniuses
What is greater than 1 kg
Estimate by division ..70/9.24
Here we have to divide 70 by 9.24.
we can first covert the decimal 9.24 into fraction, shifting the decimal two units to the right and dividing by 100, we have
9.24 = 924/100
Now let us divide 70 by 924/100
in division of fraction we take reciprocal of second fraction and multiply it with first.
reciprocal of 924/100 is 100/924.
multiplying 70* 100/924, we have
[tex] 70 * \frac{100}{924} [/tex]
[tex] = \frac{7000}{924} [/tex]
converting into decimal we have
[tex] \frac{7000}{924} = 7.5757..... [/tex]
if 5 lemons cost £1 and a bag of 4 oranges cost £1.80, how much more does one orange cost than the lemon?
In which graph does y vary directly as x? It’s not C, I got it wrong.
0.698 to the bestest hundreth