can you please answer this for me

The simplification of the logarithm is determined as [tex]\log_32 - 11[/tex].

To solve the problem, we can first convert all the logarithms into the same base, which will be base 3. Using the logarithmic identity that

[tex]\log_a b = \frac{\log_c b}{\log_c a}[/tex]

where;

we get:

[tex]3\log_9(18) + \log_3\left(\sqrt{\frac{8}{27}}\right) - \log_{\frac{1}{27}}(81) - \log_{\sqrt{3}}(2\sqrt{2}) &\\\\= 3\frac{\log_3(18)}{\log_3(9)} + \frac{1}{2}\log_3\left(\frac{8}{27}\right) - \frac{\log_{3}(81)}{\log_{3}(1/27)} - \frac{\log_{3}(2\sqrt{2})}{\log_{3}(\sqrt{3})}[/tex]

[tex]= 6\frac{\log_3(2)+\log_3(3)}{2\log_3(3)} + \frac{1}{2}\left(\log_3(2^3)-\log_3(3^3)\right) - \frac{\log_{3}(3^4)}{\log_{3}(3^{-3})} - \frac{\log_{3}(2\sqrt{2})}{1/2}\\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) + \frac{3\log_3(2)-9\log_3(3)}{6} - \frac{12}{3} - 2\log_{3}(2\sqrt{2})[/tex]

[tex]= 3\left(\frac{\log_3(2)}{\log_3(3)}+1\right) - \frac{3}{2} + \frac{\log_3(2) }{2} - 4 - \log_3(8) \\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{\log_3(2) }{2} - \log_3(2^3)\\\\= 3\left(\frac{\log_3(2)}{\log_3(3)}\right) - \frac{5}{2} + \frac{1}{2} (\log_3(2) )- \log_38\\\\= 6\left (\frac{\log_3(2)}{\log_3(3)}\right) -5+ \log_3(2) - 2\log_3(8)\\\\= 6\log_32 \ - \ 6\log_33 - 5 + \log_32-2\log_38\\\\= \log_3\left (\frac{2^6\times 2 }{3^6\times 8^2}\right) - 5\\\\[/tex]

[tex]= \log_3\left (\frac{2^7 }{3^6\times 2^6}\right) - 5\\\\= \log_3\left (\frac{2 }{3^6}\right) - 5\\\\= \log_32 - \log_33^6 - 5\\\\= \log_32 - 6 - 5\\\\=\log _32 \ - 11[/tex]

Learn more about simplification of logarithm here: https://brainly.com/question/28041634

#SPJ1

Answer:

The answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Step-by-step explanation:

Allstars mean height:

= (73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15

= 1007 / 15

= 67.6 inches

Super Stars mean height:

= (66 + 68 + 62 + 63 + 47 + 64 + 65 + 50 + 60 + 64 + 65 + 65 + 58 + 60 + 55) / 15

= 912 / 15

= 60.2 inches

We can see that the Allstars team has a higher mean height than the Super Stars team, with an average of 67.6 inches compared to 60.2 inches. Therefore, the Allstars team typically has the tallest players

Thus the answer to your problem is, A. The Allstars, with a mean of about 67.1 inches

Answer:

41 chickens and 9 cows

Step-by-step explanation:

Chickens have 2 legs each.

Cows have 4 legs each.

There are 50 animals total.

There are 118 legs total.

You can set up a system to represent this situation.

Let x represent the number of chickens and y represent the number of cows.

x + y  = 50

2x + 4y = 118

Multiply the first equation by 2 and subract it from the second equation.

    2x + 4y = 118

-    2x + 2y = 100

_____________

2y = 18

y = 9

So there are 9 cows. There are 50 animals total so there must be 41 chickens.

There is a total of 50 chickens and cows.

Chickens have 2 legs each. Cows have 4 legs each.

There are 118 legs in total. We are focusing on how much chickens there are.

CHICKENS=50-COWS.

2CHICKENS+4COWS=118

2(50-COWS)+4COWS=118

100-2COWS+4COWS=118

2COWS=118-100

2COWS=18

C0WS=18/2

COWS=9

CHICKENS+9=50

CHICKENS=50-9

CHICKENS=41

PROOF:

2*41+4*9=118

82+36=118

118=118

This is a bit long and confusing but I hope this helps!

the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

To describe the end behavior of a polynomial function, we need to examine the degree and leading coefficient of the function. In the polynomial function f(x) =[tex]2x^3 + 5x^2 - 2x - 3[/tex], the degree is 3 and the leading coefficient is 2.

The end behavior of the polynomial function f(x) is determined by the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the leading term dominates the behavior of the function. Since the leading coefficient is positive and the degree is odd, the function will increase without bound, or approach positive infinity. In other words, as x becomes very large and positive, the function will also become very large and positive.

As x approaches negative infinity, the leading term also dominates the behavior of the function. However, since the degree is odd, the function will decrease without bound, or approach negative infinity. In other words, as x becomes very large and negative, the function will also become very large and negative.

Therefore, the end behavior of the polynomial function f(x) = [tex]2x^3 + 5x^2 - 2x - 3[/tex] is that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

learn more about polynomial here

https://brainly.com/question/11536910

#SPJ4

Answer:

Step-by-step explanation:

The required larger and smaller number is 7 and 3 respectively.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

Let the larger number be x and smaller number be y,

According to the question,

the sum of the larger and twice the smaller is equal to 13.

x + 2y = 13 - - - -(1)

And, twice their positive difference is equal to eight.

2(x - y) = 8

x - y = 4 - - - -(2)

Subtracting equation 1 by 2

3y = 9

y = 3

Now,

x - y =4

x -3 = 4

x = 7

Thus, the required larger and smaller number is 7 and 3 respectively.

Learn more about models here:

brainly.com/question/22591166

#SPJ2

A parabola is a U-shaped curve that can open upwards or downwards. Its equation is typically in the form y = ax^2 + bx + c, where a, b, and c are constants. The properties of a parabola are determined by these constants.

Description about vertex,max/min,axis of

Description about vertex,max/min,axis ofsymmetry,zero(s),direction of opening,y-intercept of parabola:

Vertex: The vertex is the point where the parabola changes direction. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards. The vertex is located at the point (-b/2a, f(-b/2a)), where f(x) is the

function that defines the parabola.

Max/min: The maximum or minimum value of the parabola is the y-coordinate of the vertex. If the parabola opens downwards, the maximum value occurs at the vertex. If the parabola opens upwards, the minimum value occurs at the vertex.

Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two mirror-image halves. The equation of the axis of symmetry is x = -b/2a.

Zero(s): The zero(s) of the parabola are the x-values where the parabola intersects the x-axis. These are also called roots or solutions of the quadratic equation. If the discriminant (b² - 4ac) is positive, the parabola intersects the x-axis at two points. If the discriminant is zero, the parabola intersects the x-axis at one point (which is also the vertex). If the discriminant is negative, the parabola does not intersect the x-axis and has no real roots.

Direction of Opening: The direction of opening of the parabola is determined by the sign of the coefficient a. If a is positive, the parabola opens upwards, and if a is negative, the parabola opens downwards.

y-intercept: The y-intercept is the point where the parabola intersects the y-axis. It is located at the point (0, c), where c is the constant term in the quadratic equation.

Learn more about Parabola:

https://brainly.com/question/29635857

#SPJ1

Correct question is "For each parabolas, describe the following properties:

Vertex

Max/min

Axis of

Symmetry

Zero(s)

Direction of

Opening

y-intercept."

Answer:

Let x be Taub and y for Chloe

y-x=1. since their ages are consecutive

y-1=x

xy=12.…..... eq 1

(y-1)y=12....... eq 2

y²-y-12=0

y=4 or y=-3

since age can never be a negative, we choose y=4 and substitute in eq 1

4x=12

x=12/4=3

Taub is 3 years old

Answer:

1.28*10^6

Step-by-step explanation:

It is up to you whether you convert 1400000 into scientific notation or convert 1.2*10^5 into decimal notation, subtract, and then convert once more into scientific notation for your final answer.

Either way, it will come out to be 1.28*10^6

Work is below:

1.2*10^5 = 120,000

1400000 - 120000 = 1280000

= 1.28*10^6 (remember it is every number behind the decimal)

Both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

To simplify the expression 2k+2+k+3+2k, we can combine like terms, as follows:

2k + k + 2k + 2 + 3 = 5k + 5

Therefore, the expression 2k+2+k+3+2k is equivalent to 5k+5. We can also write this expression as 5(k+1), since we can factor out the common factor of 5 from both terms:

5(k+1)

Therefore, both Option C. 5k+5 and Option D. 5(k+1) are equivalent expressions to 2k+2+k+3+2k.

Option A, [tex]5k^5[/tex], is not equivalent to the given expression, as it contains an exponent of 5, which is not present in the original expression.

Option B, [tex]5+k^5[/tex], is also not equivalent to the given expression, as it contains a term k^5, which is not present in the original expression.

Option C, 5k+5, is equivalent to the given expression, as shown above.

Option D, 5(k+1), is also equivalent to the given expression, as shown above.

Learn more about factor :

https://brainly.com/question/29128446

#SPJ4

The complete question is :

Select all expressions that are equivalent to 2k+2+k+3+2k.

A. [tex]5k^5[/tex]

B. [tex]5+k^5[/tex]

C. [tex]5k+5[/tex]

D. [tex]5(k+1)[/tex]

The non - markup price of the pair of shoes is $103. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. After division, multiplication, addition, and subtraction in mathematics are the operations quotient, product, sum, and difference.

We are given that the store sells the shoes for $193.21 which includes the 87% markup.

So, using the subtraction operation, we get

⇒ Non - markup price = ($193.21 * 100) ÷ 187

⇒ Non - markup price = $19321 ÷ 187

⇒ Non - markup price = $103.3208

Hence, the non - markup price of the pair of shoes is $103.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ1

Answer:

[tex]x = \frac{5}{p - 1} [/tex]

p ≠ 1

Step-by-step explanation:

20 = 4x (p - 1)

20 = 4xp - 4x

4xp - 4x = 20

(4p - 4)x = 20 / : (4p - 4)

[tex]x = \frac{20}{4p - 4} = \frac{20}{4(p - 1)} = \frac{5}{p - 1} [/tex]

we determine the scope of the definition:

4p - 4 ≠ 0

4p ≠ 4 / : 4

p ≠ 1

The correct numerical expression for "9 times 4 added to the difference of 3 and 2" is:

9 x 4 + (3 − 2)

First, we need to calculate the difference of 3 and 2, which is 1. Then, we add it to the product of 9 and 4, which is 36. So the final expression is:

36 + 1 = 37

Therefore, the correct numerical expression is 9 x 4 + (3 − 2) = 37.

Answer:

1. is the distance from the center of the circle to any point on it's circumference

Answer:

a) The circumference of a circle is the perimeter of the circle. The circumference of the circle is the distance around a circle, that is the arc length of the circle. The circumference of a circle is given by:

Circumference = 2π × radius; but diameter = 2 × radius. Hence:

Circumference = π * diameter.

Given that diameter of the tire = 2.5 ft:

Circumference of the tire = π * diameter = 2.5 * π = 7.85 ft

b) since the circumference of the tire is 7.85 ft, it means that 1 revolution of the tire covers a distance of 7.85 ft.

1 mile = 5280 ft

The number of rotation required to cover 1 mile (5280 ft) is:

number of rotation =

Step-by-step explanation:

Thats the best i can find.

Answer:

Your answer is correct and you showed all the necessary steps to find the circumference and the number of times the tire would have to rotate to travel one mile. Well done!

a. Correct answer is C as sample contains more pink marbles than red marbles, so it's predicted that the bowl has more pink marbles.

b. With 750 marbles in the bowl and proportion of pink marbles being 0.7, there are approximately 525 pink marbles and 225 red marbles, thus you are more likely to pick a pink marble.

a. The correct answer is C. Yes. Because the representative sample contains more pink marbles than red marbles, you can predict that the bowl contains more pink marbles than red marbles.

b. If there are 56 pink marbles and 24 red marbles in a sample of 80 marbles, then the proportion of pink marbles in the sample is 56/80 = 0.7, and the proportion of red marbles in the sample is 24/80 = 0.3. If there are 750 marbles in the bowl, then there are about 0.7750 = 525 pink marbles and 0.3750 = 225 red marbles. So, you are more likely to pick a pink marble.

Learn more about probability here: brainly.com/question/30034780

#SPJ1

Answer:

[tex]90 { \: cm}^{2} [/tex]

Step-by-step explanation:

First, we can find one triangle's area (they are all the same and isosceles):

h = XY = 6 cm, a = BC = 5 cm

[tex]s(triangle) = \frac{1}{2} \times h \times a = \frac{1}{2} \times 6 \times 5 = 15[/tex]

And now, multiply this number by 6 (since there are 6 of these identical triangles):

S(hexagon) = 15 × 6 = 90 cm^2

The number of sacks of trash that Jorge's brother picked up is given as follows:

3.75 sacks.

The number of sacks of trash that Jorge's brother picked up is obtained applying the proportions in the context of the problem.

Jorge picks up 2 1/2 sacks of trash, which is a mixed number, hence the decimal number that represents this amount is given as follows:

2 + 1/2 = 2 + 0.5 = 2.5 sacks.

His brother picks up 1 1/2 times as much as Jorge, which is 1 + 1/2 = 1.5 times the amount picked by Jorge, hence the number of sacks of trash that Jorge's brother picked up is obtained as follows:

2.5 x 1.5 = 3.75 sacks.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The exponential function in the graph can be written as:

h(x) = 3*2^x

We can see that h(x) is an exponential function, so we can write this in a general form as:

h(x) = a*b^x

Where a is the initial value and b is the base of the exponential.

First, we can see that it passes through the ponit (0, 3), replacing these values we will get:

3 = a*b^0

3 = a

So the equation is:

h(x) = 3*b^x

We also can see that it passes through (1, 6), replacing these values we will geT:

6 = 3*b^1

6 = 3*b

6/3 = b

2 =b

The exponential function is:

h(x) =3*2^x

Learn more about exponential functions at:

https://brainly.com/question/2456547

#SPJ1

Answer:

3/4.

Step-by-step explanation:

y = x^1/2

dy/dx = 1/2 x^-1/2

dy/dt = dy/dx * dx/dt

        =  1/2 x^-1/2 * 3

         = 3/2 x^-1/2

When x = 4:

dy/dt = 3/2 * 4 ^-1/2

         = 3/2* 1/ √4

         = 3/2 * 1/2

         = 3/4.

The sample mean for the given data set is 3.044 miles.

Let's use the given data to calculate the sample mean. We have the distances in miles that 10 visitors live from the library: 0.5, 0.8, 0.8, 1.5, 1.8, 3.5, 4.8, 6.2, and 8.3.

To find the sample mean, we first add up all the distances:

0.5 + 0.8 + 0.8 + 1.5 + 1.8 + 3.5 + 4.8 + 6.2 + 8.3 = 27.4

Next, we divide the sum by the total number of distances, which is 9 (since we have data for 10 visitors):

27.4 / 9 = 3.044 (rounded to three decimal places)

This means that, on average, the visitors to the library live about 3.044 miles away from the library.

To know more about mean here

https://brainly.com/question/30891252

#SPJ4

Answer:

  25 cm

Step-by-step explanation:

You want to know the length of the hypotenuse in a right triangle with legs 15 cm and 20 cm.

The given leg lengths have the ratio ...

  15 : 20 = 3 : 4 . . . . . . . scale factor of 5

This means they are part of a 3 : 4 : 5 right triangle.

The length "t cm" is 5·5 cm = 25 cm.

The value of t is 25.

__

Additional comment

In case you've never heard of a {3, 4, 5} right triangle, you can figure the missing hypotenuse from the Pythagorean theorem:

  c² = a² +b²

  t² = 15² +20² = 225 +400 = 625

  t = √625 = 25

The {3, 4, 5} Pythagorean triple is used repeatedly in algebra, geometry, and trig problems, along with some others: {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. These can appear as multiples of the basic triple, as here, where the multiple is 5 × {3, 4, 5} = {15, 20, 25}.

The probability that a basketball player makes all four of his free throws when the probability of making one is 80% is 0.4096.

This is calculated using the binomial probability formula, which states that the probability of k successes in n trials is given by the following:

P(k successes in n trials) = [tex](n!/(k!(n-k)!))\timespk(1-p)(n-k)[/tex]

In this case, the probability of making a single free throw is 80% (0.8),

so we can plug this into the formula.

We know that the player is taking 4 free throws, so k is 4 and n is also 4.

Plugging these values into the formula, we get:

P(4 successes in 4 trials) = [tex](4!/(4!(4-4)!))\times 0.84(1-0.8)(4-4) = 0.4096[/tex]

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

Answer:-72x

Step-by-step explanation:

Answer:

2.64

Step-by-step explanation:

b*h=5.28

5.28/2=2.64

Answer:

360∘

The sum of the exterior angles of a polygon is always 360∘ . Therefore, the sum of the exterior angles of a 25-gon is 360∘ .

Answer:

Step-by-step explanation:

The probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601 (rounded to four decimal places).

The probability of an event is defined as the number of ways the event can occur divided by the total number of possible outcomes. To solve the given problem, we will use the binomial distribution formula.

The formula for the probability of less than 4 successes in n trials, given the probability of success p, is:P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)Where X is a binomial random variable with n = 50 trials and p = 0.03 probability of success, i.e., taking general education courses on a pass/fail basis.

Now, let's calculate each term:

P(X = 0) = C(50, 0) (0.03)⁰ (0.97)⁵⁰P(X = 0) = 1 × 1 × 0.97⁵⁰ ≈ 0.3669P(X = 1) = C(50, 1) (0.03)¹ (0.97)⁴⁹P(X = 1) = 50 × 0.03 × 0.97⁴⁹ ≈ 0.3937P(X = 2) = C(50, 2) (0.03)² (0.97)⁴⁸P(X = 2) = 1225 × 0.0009 × 0.97⁴⁸ ≈ 0.1872P(X = 3) = C(50, 3) (0.03)³ (0.97)⁴⁷P(X = 3) = 19600 × 0.000027 × 0.97⁴⁷ ≈ 0.0123P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)P(X < 4) = 0.3669 + 0.3937 + 0.1872 + 0.0123P(X < 4) ≈ 0.9601

Hence, the probability that less than four students out of fifty students registered for a general education course will pass/fail the course is 0.9601.

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

The probability that p falls between 0 and 0.06 is 0.00000205.

How to calculate the probability

Based on the information, to calculate the probability that p falls between 0 and 0.06, we need to first calculate the standard error (SE) of the sample proportion, which can be calculated as:

SE = ✓[ p * (1-p) / N ]

where p is the sample proportion and N is the sample size.

In this case, we have:

p = 25/85 = 0.2941

N = 85

SE = ✓[ 0.2941 * (1-0.2941) / 85 ] = 0.0545

Next, we need to calculate the z-score corresponding to the upper limit of the interval (0.06). This can be calculated as:

z = (0.06 - p) / SE = (0.06 - 0.2941) / 0.0545 = -4.4702

Using the dCMP normal distribution tool, we can find the probability that a standard normal random variable falls below this z-score as:

P(z < -4.4702) = 0.00000205

Learn more about probability on;

https://brainly.com/question/24756209

#SPJ1