simplify log 4 - log 8

Answer:

Step-by-step explanation:

A rational number can be written as a fraction of two integers.

√23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction.

104.42 is rational because it can be expressed as 10442/100 . We can express it as this because

104.42 * 1 = 104.42 * 100/100 = 10442/100, and multiplying something by 1 keeps it the same

√64 is rational because it is equal to 8, and 8/1 is equal to 8

49.396 with the 6 repeating is rational because we can express 49.39 as

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

For example, 0.6 with the 6 repeating can be represented as 6/9. This is because 0.6 * 10 = 6, and we divide that by 9. Similarly, 0.006 with the 6 repeating can be represented by 0.06/9

We add the two fractions together to get

4939/100 + 0.06/9

multiply both fractions by the other's denominator to even them out and make the numerator of the second fraction an integer

(4939*9)/(100*9) + (0.06*100)/(9*100)

= 44451/900 + 6/900

= 44460/900

Assuming that the last number has only the digits given, that is rational because, similarly to 104.42, it can be multiplied by a power of 10 to result in (integer)/(integer), making it rational. If the dots represent infinite digits, then it is not rational because there are infinite digits that are not repeating, and there is no way to know the last digit, so it is impossible to write a fraction from it

the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)

half life = 12.4 hours

initial amount = 746g

time elapsed = 62 hours

Using the half-life formula:

Substitute for the values:

Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)

9514 1404 393

Answer:

  C.  36√3 square units

Step-by-step explanation:

Your knowledge of special triangles tells you that height CD is ...

  CD = 6√3

so the area is ...

  A = 1/2bh

  A = 1/2(12)(6√3) = 36√3 . . . . square units

_____

Additional comment

The 30°-60°-90° right triangle that is half an equilateral triangle has a short side equal to half the length of the long side. The Pythagorean theorem tells you that the middle-length side is √(2²-1²) = √3 times the shortest side. That is, the side length ratios in this "special" triangle are ...

  1 : √3 : 2

This means the length DB is 12/2 = 6, and the length CD is 6√3.

Answer: The first answer choice

AKA: y = -1.74x + 46.6

Step-by-step explanation:

Answer:

Graph C with values below

Step-by-step explanation:
To do this you substitute x with the values of x given to solve for y:
-3:

-2:

0:

2:

Using these values we can fill out the table and see the It must be graph C that is the correct curve.

Answer: It is True

Step-by-step explanation:

The increase in thermal energy allows molecules to decrease their density and escape the liquid state to become gas molecules.

Answer:

0

Step-by-step explanation:

You can’t divided 0 by 0 so it’s 0

Answer:

x=7/5

Step-by-step explanation:

Answer:

100x = 140 or 100x -140 = 0

Step-by-step explanation:

(80 + 20) = 100 - they both have x so they can be added together

you can either subtract 10 from 150 or 150 from ten to get 140 or -140 depending if you want the equation to be on the left side or spilt

Answer:

$1200

Step-by-step explanation:

Let cost of 1 square foot be x

So, Cost of 450 square feet =  450x

We are given that A 450-square-foot apartment in New York City cost $540,000.

So, 450x = 540000

x= \(\frac{540000}{450}\)

x= 1200

Cost of 1 square foot = $1200

Hence the price per square foot is  $1200

We can start by creating a table to organize the information:

                  Likes Chocolate (c) Does Not Like Chocolate (~c) Total

Likes Sprinkles (s) 0.25                                                           0.40

Does Not Like Sprinkles (~s)            0.60

Total 0.70                                               0.30                       1.00        

We are given that 40% of friends like sprinkles, so we can fill in that cell of the table. We are also given that 25% of friends who like chocolate also like sprinkles, so we can fill in the cell for likes chocolate and likes sprinkles as 0.25.

To find the proportion of friends who like sprinkles and chocolate, we need to divide the number of friends who like both by the total number of friends who like sprinkles:

proportion = likes chocolate and sprinkles / likes sprinkles

proportion = 0.25 / 0.40

proportion = 0.625

So, approximately 62.5% of friends who like sprinkles also like chocolate.

Answer:

110

Step-by-step explanation:

a probabability of rolling a 2 on a dice is 1/6, and times that by 660 is 660/6 which equals 110

hope this helps!

please give brainliest. Thanks!

Answer:

110 times

Step-by-step explanation:

The probability (P) of rolling a 2 is

P(2) = \(\frac{1}{6}\)

expected number = \(\frac{1}{6}\) × 660 = 110

the original price was really "x", which oddly enough is the 100%.

Now, we know the prices are reduced by 15%, so 100% - 15% = 85%, so whatever "x" sold for, we know is 85% of "x", and we also know that's $9.60.

\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 9.60& 85 \end{array} \implies \cfrac{x}{9.60}~~=~~\cfrac{100}{85} \\\\\\ \cfrac{ x }{ 9.60 } ~~=~~ \cfrac{ 20 }{ 17 }\implies 17x=192\implies x=\cfrac{192}{17}\implies x\approx 11.29\)

Answer:

$7

multiply .07 times 100

Using the linear approximating polynomial, e^(-0.7) is approximately 1.7, and using the quadratic approximating polynomial, e^(-0.7) is approximately 1.945.

To find the linear approximating polynomial, we need the first-degree Taylor polynomial centered at a = 0. The linear approximating polynomial is given by p_1(x) = f(a) + f'(a)(x - a), where f(x) = e^(-x).

First, we find f(a) and f'(a):

f(a) = f(0) = e^0 = 1

f'(a) = f'(0) = -e^0 = -1

Substituting these values into the linear approximating polynomial, we get:

p_1(x) = 1 - 1(x - 0) = 1 - x

b. To find the quadratic approximating polynomial, we need the second-degree Taylor polynomial centered at a = 0. The quadratic approximating polynomial is given by p_2(x) = f(a) + f'(a)(x - a) + (1/2)f''(a)(x - a)^2.

First, we find f''(a):

f''(a) = f''(0) = -f'(0) = -(-1) = 1

Substituting all the values into the quadratic approximating polynomial, we get:

p_2(x) = 1 - 1(x - 0) + (1/2)(1)(x - 0)^2

= 1 - x + (1/2)x^2

= 1 - x + (1/2)x^2

c. Using the linear approximating polynomial p_1(x) = 1 - x, we can approximate e^(-0.7) by substituting x = -0.7:

p_1(-0.7) = 1 - (-0.7) = 1 + 0.7 = 1.7

Using the quadratic approximating polynomial p_2(x) = 1 - x + (1/2)x^2, we can approximate e^(-0.7) by substituting x = -0.7:

p_2(-0.7) = 1 - (-0.7) + (1/2)(-0.7)^2 = 1 + 0.7 + (1/2)(0.49) = 1 + 0.7 + 0.245 = 1.945

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Answer:

C x=8

Step-by-step explanation:

Chúc bạn ngày mới tốt lành

Answer:

33.3

Step-by-step explanation:

tan A = opp/adj

tan 39° = 27/x

x tan 39° = 27

x = 27/(tan 39°)

x = 33.3

Answer: D

4x^4 + 3x^3 + 2x^2 - 11x -5

Step-by-step explanantion:

Flip and make the 4x-5 in the front and then multiply all terms by 4x and then all terms by -5 and then add both answers together.

A line goes through point (-7,1) and is parallel to -3y+7x=12. Find a equation in point slope form and find equation in slope intercept form. Show your work

step 1

Find the slope of the given line

-3y+7x=12

isolate the variable y

3y=7x-12

y=(7/3)x-4

slope is m=7/3

step 2

Remember that

If two lines are parallell , then their slopes are equal

so

the slope of the parallel line is m=7/3

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=7/3

point (-7,1)

substitute

step 3

Find the equation in slope intercept form

y=mx+b

we have

m=7/3

point (-7,1)

substitute

1=(7/3)(-7)+b

1=-49/3+b

b=52/3

therefore

Problem N 2

A line goes through the point (3,-4) and is perpendicular to 5x+9y=1. Find an equation in point slope form and find equation in slope intercept form

step 1

Find the slope of the given line

5x+9y=1

9y=-5x+1

y=-(5/9)x+1/9

slope is m=-5/9

step 2

slope of the parallel line is m=-5/9

equation in point slope form is

step 3

equation in slope intercept form is

y=mx+b

m=-5/9

point (3.-4)

-4=-(5/9)(3)+b

-4=-(5/3)+b

b=-4+5/3

b=-7/3

therefore

Answer:

200 miles

Step-by-step explanation:

you travel 20 miles for 1 gallon, so 10*20=200miles

Answer:

200

Step-by-step explanation:

if you have to dive its 20 times 10 because 20 miles 10 dollars

Therefore, the volume of the solid generated by revolving the region R about the y-axis is π/3 cubic units.

To find the volume of the solid generated by revolving the region R in the first quadrant, bounded by the curves y = x and y = x², about the y-axis, we can use the disk method.

The region R is defined by 0 ≤ x ≤ 1.

For each value of x in the interval [0, 1], we can consider a vertical strip of thickness Δx. Revolving this strip about the y-axis generates a thin disk with a radius equal to x and a thickness equal to Δx.

The volume of each disk is given by the formula V = π * (radius)² * thickness = π * x² * Δx.

To find the total volume of the solid, we need to sum up the volumes of all the disks. This can be done by taking the limit as Δx approaches zero and summing the infinitesimally small volumes.

Using integration, we can express the volume as:

V = ∫[0,1] π * x² dx

Evaluating this integral, we get:

V = π * [x³/3] [0,1] = π/3

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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This situation should be analyzed using a two-sample independent method. The two-sample independent method is used when comparing two independent groups, in this case, taxi ride times in San Diego and Phoenix. The two-sample paired method is used when comparing the same group under two different conditions, which is not the case here, as the taxi ride times are taken from two separate cities. There is no common characteristic that makes these data paired.

A two-sample independent method is used to compare the means of two independent populations, which is appropriate for this situation. The independent samples t-test is a common statistical test used to compare the means of two independent populations.On the other hand, if the data were obtained from the same set of taxis in both cities or from the same set of riders in both cities, then the situation would be a paired situation, and a two-sample paired method would be more appropriate.Paired data refers to data that is collected from the same sample, subject, or group at different points in time or under different conditions. For example, if the data were obtained from the same set of taxis in both cities, then the data would be paired because each taxi in San Diego would have a corresponding taxi in Phoenix. Similarly, if the data were obtained from the same set of riders in both cities, then the data would be paired because each rider in San Diego would have a corresponding rider in Phoenix.In summary, since the data in this situation were obtained from two different cities, a two-sample independent method is appropriate. If the data were obtained from the same set of taxis or riders in both cities, a two-sample paired method would be appropriate.

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(a) The sampling distribution of x, the sample mean, is approximately normal according to the Central Limit Theorem, with a mean of 85 and a standard deviation of 3. (b) The probability of observing a sample mean greater than 90.1 (P(x > 90.1)) is approximately 0.0446 or 4.46%. (c) The probability of observing a sample mean less than or equal to 78.7 (P(x <= 78.7)) is approximately 0.0154 or 1.54%. (d) The probability of observing a sample mean exactly equal to 82.3 (P(x = 82.3)) is zero, as the probability of obtaining a specific value from a continuous distribution is zero.

(a) The sampling distribution of x, the sample mean, will be approximately normal according to the Central Limit Theorem. The mean of the sampling distribution will be equal to the population mean (mu), which is 85, and the standard deviation of the sampling distribution (standard error) will be equal to the population standard deviation (sigma) divided by the square root of the sample size, which is 21/sqrt(49) = 3.

(b) To find P(x > 90.1), we need to calculate the z-score and then find the corresponding area under the standard normal distribution curve. The z-score is calculated as (90.1 - 85) / 3 = 1.7. Using a standard normal distribution table or a calculator, we can find the area to the right of the z-score of 1.7. This gives us P(x > 90.1) ≈ 0.0446, or approximately 4.46%.

(c) To find P(x <= 78.7), we need to calculate the z-score and find the corresponding area under the standard normal distribution curve. The z-score is calculated as (78.7 - 85) / 3 = -2.17. Using a standard normal distribution table or a calculator, we can find the area to the left of the z-score of -2.17. This gives us P(x <= 78.7) ≈ 0.0154, or approximately 1.54%.

(d) To find P(x = 82.3), we need more information. The probability of obtaining a specific value from a continuous distribution, such as the normal distribution, is zero. Therefore, P(x = 82.3) is equal to zero.

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Answer:

The derivative of infinity is undefined. Infinity is not a number, but rather a concept that represents a quantity that is unbounded or limitless. The derivative of a function at a point is a measure of the rate of change of the function at that point. Since infinity itself does not have a numerical value or a well-defined location, it is not possible to take the derivative of infinity. This means that the concept of the derivative does not apply to infinity and the derivative of infinity is undefined.

The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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