Which exponential equation is equivalent to the logarithmic equation below?
log 300 = a
A. 3000 = 10
B. a10 = 300
C. 100 = 300
D. 30010 = a

I hope the answer is helpful

To calculate[tex]2^2873686243768478237864767208[/tex] mod 101 using Fermat's little theorem, we can simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.

Fermat's little theorem states that if p is a prime number and a is any integer not divisible by p, then a^(p-1) ≡ 1 (mod p). In this case, p = 101, and we need to find[tex]2^2873686243768478237864767208[/tex]mod 101.

First, we simplify the exponent by taking it modulo 100, since 100 is the Euler's totient function value of 101. The exponent 2873686243768478237864767208 is congruent to 8 modulo 100. So, we need to calculate 2^8 mod 101. Applying Fermat's little theorem, we know that 2^(101-1) ≡ 1 (mod 101), since 101 is prime. Therefore, 2^100 ≡ 1 (mod 101).

We can express [tex]2^8[/tex] in terms of 2^100 as [tex](2^100)^0.08[/tex]. Simplifying this, we get [tex](2^100)^0.08 ≡ 1^0.08[/tex]≡ 1 (mod 101).

Thus, we conclude that[tex]2^8[/tex] ≡ 1 (mod 101), and therefore 2^2873686243768478237864767208 ≡ [tex]2^8[/tex] (mod 101).

Finally, evaluating [tex]2^8[/tex] mod 101, we find that [tex]2^8[/tex] ≡ 57 (mod 101).

Therefore,[tex]2^2873686243768478237864767208[/tex] mod 101 is equal to 57.

Learn more about congruent here:

https://brainly.com/question/30596171

#SPJ11

Answer:

5 batches

Step-by-step explanation:

1/6 oatmeal  can make 1 batch, so 5/6 makes 5 batches

The correct statement is : M spans P2.

The set M = {[tex]x+1, x^2-2, 3x[/tex]} consists of three polynomials in the variable x.

To determine whether M spans P3 or P2, we need to consider the highest degree of the polynomials in M.

The highest degree of the polynomials in M is 2 (from [tex]x^2-2[/tex]), which means that M can span at most the space of polynomials of degree 2 or less, i.e., P2.

To check whether M spans P2 or not, we need to see if any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M.

We can write any polynomial of degree 2 or less as [tex]ax^2 + bx + c[/tex], where a, b, and c are constants.

To express this polynomial as a linear combination of the polynomials in M, we need to solve the system of equations:

[tex]a(x^2-2) + b(x+1) + c(3x) = ax^2 + bx + c[/tex]

This can be written as:

[tex]ax^2 + (-2a+b+3c)x + (b+c) = ax^2 + bx + c[/tex]

Equating the coefficients of [tex]x^2, x,[/tex] and the constant term, we get:

[tex]a = a,\\-2a+b+3c = b,\\b+c = c.[/tex]

The first equation is always true, and the other two equations simplify to:

[tex]-2a+3c = 0,\\b = 0.[/tex]

Solving for a, b, and c, we get:

[tex]a = 3c/2,\\b = 0,\\c = c.[/tex]

Therefore, any polynomial of degree 2 or less can be expressed as a linear combination of the polynomials in M. This means that M spans P2.

However, M cannot span P3, because P3 includes polynomials of degree 3, which cannot be expressed as a linear combination of the polynomials in M (since the highest degree polynomial in M is [tex]x^2[/tex]).

Therefore, the correct statement is: M spans P2.

Learn more about Polynomial span : https://brainly.com/question/31857690

#SPJ11

Answer:

12.6

Step-by-step explanation:

divide the length value by 3

Given that a hockey tournament consists of 16 teams. In the first round, every team is randomly assigned to one of 8 games (2 teams per game). We are supposed to find the probability that all three Alberta teams are randomly assigned to different games. Let A be the event of assigning all three Alberta teams to different games.

Then the number of ways to select 3 teams from 16 teams is $\ dbinom {16}{3}$, the number of ways to assign 3 teams to different games is $8\times7\times6$, and the number of ways to assign the remaining 13 teams to games is $(13!) / (2^6\times6!)$.The probability of event A is given by;$$

P(A) = \frac{\text{number of ways to assign 3 teams from Alberta to different games}}{\text{number of ways to assign all teams to games}} = \frac{8\times7\times6 \times (13!) / (2^6\times6!)}{\dbinom{16}{3} \times (14!) / (2^7\times7!)}
$$Simplifying the above expression,$$
P(A) = \frac{8\times7\times6 \times 13! \times 2}{\dbinom{16}{3} \times 14!} = \frac{8\times7\times6 \times 2}{\dbinom {16}{3}} = \frac{336}{560} = \frac{3}{5}

Therefore, the probability that all three Alberta teams are randomly assigned to different games is $\frac{3}{5}$.

Know more about probability:

https://brainly.com/question/31828911

#SPJ11

Answer:

3/10 inches apart

Step-by-step explanation:

total miles based on 2" equals 33 miles can be found by solving this proportion:

2/33 = 6/x

2x = 198

x = 99

99 miles divided by 11 rest stops means each stop is 9 miles apart

now use new ratio of 1" equals 30 miles

1/30 = x/9

30x = 9

x = 9/30 or 3/10 inches

Answer:

(x - 3)^2 + (y - 6)^2 = 17

Step-by-step explanation:

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

(x - 3)^2 + (y - 6)^2 = 17

(a) If there are 4 candidate,  the smallest number of votes that a plurality candidate could have is 33.

(b) If there are 8 candidate,  the smallest number of votes that a plurality candidate could have is 17.

The smallest number of votes that a plurality candidate could have is calculated as follows;

(a) If there are 4 candidate, the number of votes for each candidate;

= 129 / 4

= 32.25

The least number of votes for the plurality candidate = 33

(b) If there are 8 candidate, the number of votes for each candidate;

= 129 / 8

= 16.125

The least number of votes for the plurality candidate = 17

Learn more about smallest number in division here: https://brainly.com/question/29898343

#SPJ4

Answer:

Tens digit, x = 3

Unit digit, y = 8

Number = 38

Step-by-step explanation:

Let the 2 digit number = xy

y = x + 5 - - - (1)

10x + y = 4(x + y) - 6

10x + x + 5 = 4(x + x + 5) - 6

11x + 5 = 4(2x + 5) - 6

11x + 5 = 8x + 20 - 6

11x + 5 = 8x + 14

11x - 8x = 14 - 5

3x = 9

x = 9/3

x = 3

From (1)

y = x + 5

y = 3 + 5

y = 8

Answer:

50

Step-by-step explanation:

this can be solved by ratio   15/x = 30/100.  Cross multiply and solve for x.  The answer is 50.

Answer:

9/2 = 4 1/2

Step-by-step explanation:

Answer:

131.95yd squared

Step-by-step explanation:

A=2πrh+ 2 r(2)=2*π*3*4+2*π*3(2)~131.94689yd(2)

Answer:

angle 1 = 124

angle 2 = 56

angle 3 = 124

angle 4 = 56

Step-by-step explanation:

This problem is a bit like a puzzle. To make notation easier I'm going to do this:

angle 1 = a

angle 2 = b

angle 3 = c

angle 4 = d

Now, let's start with what we know from the image.

All angles added together form a circle or 360 degrees

a + b + c + d = 360

In the same regard a + d = 180, and b + c = 180

Also,

a = c

and

b = d

It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.

d = 1/4(a) + 25

If we look at all the equations we have, we can see that two of the equations have two of the same variables:

a + d = 180

and

d = 1/4(a) + 25

Using substitution we can take the second equation substitute it for d in the first equation giving us:

a + (1/4(a) + 25) = 180

Now we just solve for a

[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]

Therefore a, or angle 1, is 124

Since a = c, then c, or angle 3, is also 124

Since a + d = 180 and a = 124 then

d = 180 -124

d = 56

So, d, or angle 4, is 56

And because b = d then b, or angle 2, is also 56

a = 124

b = 56

c = 124

d = 56

For extra measure, we can check our work by using the first equation

a + b + c + d = 360

124 + 56 + 124 + 56 = 360

Answer:

60 mins

Step-by-step explanation:

15+45=60

The time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

As it is given that Mark can make 9 pancakes in 15 minutes, therefore, the number of pancakes that Mark can make in one minute,

[tex]\text{Number of Pancake in one minute} = \dfrac{9}{15}[/tex]

Now, for Charlotte, it is given that he makes 42 pancakes in 45 minutes, therefore, the number of pancakes that Charlotte can make in one minute,

[tex]\text{Number of Pancake in one minute} = \dfrac{42}{45} = \dfrac{12}{15}[/tex]

Further, the total pancakes that can be made in one minute,

[tex]\text{Total Number of Pancake in one minute} = \dfrac{9}{15} +\dfrac{12}{15} = \dfrac{21}{15}[/tex]

As they both need to make 138 pancakes together, therefore, the time they need is,

[tex]\rm Time\ Needed = \dfrac{\text{Total number of pancakes}}{\text{Total number of pancakes in one minute}}[/tex]

[tex]\rm Time\ Needed = \dfrac{138}{\frac{21}{15}} = \dfrac{138\times 15}{21} = 227.142[/tex]

Hence, the time needed to make 138 pancakes if both Mark and Charlotte work together is 227.142 minutes.

Learn more about Fraction:

https://brainly.com/question/1301963

Answer:

38

Step-by-step explanation:

(10*2)+(9*2)

I think that the answer would be two triangles.

Answer:

B = 48.7°

C = 61.3°

b = 12

Step-by-step explanation:

Given:

A = 70°

a = 15

c = 14

Required:

B, C, and b

Solution:

✔️Using the law of sines, let's find C:

Sin C/c = Sin A/a

Plug in the values

Sin C/14 = Sin 70/15

Cross multiply

Sin C × 15 = Sin 70 × 14

Divide both sides by 15

Sin C = (Sin 70 × 14)/15

Sin C = 0.8770

C = Sin^{-1}(0.8770)

C = 61.282566° = 61.3° (nearest tenth)

✔️Find B:

B = 180 - (70 + 61.3) (sum of triangle)

B = 48.7°

✔️Find b using the law of sines:

b/sinB = a/sinA

Plug in the values

b/sin 48.7 = 15/sin 70

Cross multiply

b*sin 70 = 15*sin 48.7

Divide both sides by sin 48.7

b = (15*sin 48.7)/sin 70

b = 11.9921789

b = 12.0 (nearest tenth)

Answer:

1/2 x 1/2 = 1/4

Step-by-step explanation:

P(H,H) = 1/2 x 1/2 = 1/4

P(T,T) = 1/2 x 1/2 = 1/4

P(H,T) = 1/2 x 1/2 = 1/4

P(T,H) = 1/2 x 1/2 = 1/4

To have a horizontal asymptote at y = 3 and vertical asymptotes at x = 4 and x = -3, the rational function should have the following form:

f(x) = (a polynomial in x) / ((x - 4)(x + 3))

The polynomial in the numerator can have any degree, but it must be of lower degree than the denominator.

Therefore, among the given rational functions, the one that satisfies these conditions would be the one in the form:

f(x) = (a polynomial) / ((x - 4)(x + 3))

Please provide the specific options you have, and I can help you determine which of those options matches this form.

Learn more about rational function here:

https://brainly.com/question/27914791

#SPJ11

Ok. So 14% of 18.00 can be figured out without a calculator. 18.00 / 10 = 1.80 = 10%.

(18.00 / 100) x 4 = 0.72

1.80 + 0.72 = $2.52 is the tip.

$18 + $2.52 = $20.52

⭐ Answered by Foxzy0⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Answer:The diagram that models the ratio in the story is:

Mermaid book: Princess book = 3:2

To find out how many times Nolan has read the mermaid book, we can set up the following proportion:

3/2 = x/20

Cross-multiplying, we get:

2x = 3 * 20

2x = 60

Dividing both sides by 2, we find:

x = 60/2

x = 30

Therefore, Nolan has read the mermaid book 30 times this month.

Answer:

50 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

a = 48

b = 14

c = ?

Step 2: Solve for c

Answer:

Where is the question so that I can help you with it

Answer:

5.318 * 10 to power of 8

Step-by-step explanation:

Answer:

5.318 × [tex]10^{8}[/tex]

Step-by-step explanation:

The expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3.

To find the expected value of a random variable, you multiply each possible value by its corresponding probability and sum them up. In this case, we have a combination of probabilities and numerical values. Let's calculate the expected value:

Multiply each numerical value by its corresponding probability:

(0.35 * 8) + (0.3 * 9) + (0.05 * 10) + (0.1 * 11) + (0.05 * 11) + (0.15 * 11)

Perform the calculations:

2.8 + 2.7 + 0.5 + 1.1 + 0.55 + 1.65

Sum up the results:

8.3

Therefore, the expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3. The expected value provides a measure of central tendency for the random variable.

Learn more about Central Tendency:

https://brainly.com/question/28180169

#SPJ4

Answer:

x=-2

Step-by-step explanation:

Answer:

Yay fun day :DDDDDD

Step-by-step explanation:

The spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

(a) To change from rectangular coordinates to spherical coordinates, we use the following formulas:

rho = √(x² + y² + z²)

theta = atan2(y, x)

phi = acos(z / rho)

Given the rectangular coordinates (5, 5√3, 10√3), we can substitute the values into the formulas to find the corresponding spherical coordinates:

rho = √((5)² + (5√3)² + (10√3)²)

= √(25 + 75 + 300)

= √(400)

= 20

theta = atan2(5√3, 5)

= atan(√3)

≈ 1.0472 radians

phi = acos((10√3) / 20)

= acos(√3 / 2)

= π/6 radians

Therefore, the spherical coordinates for the point (5, 5√3, 10√3) are (20, 1.0472, π/6).

(b) Given the rectangular coordinates (0, -3, -3), we can apply the formulas for spherical coordinates:

rho = √((0)² + (-3)² + (-3)²)

= √(0 + 9 + 9)

= √(18)

= 3√2

theta = atan2(-3, 0)

= -π/2 radians

phi = acos((-3) / (3√2))

= acos(-1/√2)

= π/4 radians

Hence, the spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

To know more about coordinates follow the link:

https://brainly.com/question/29189189

#SPJ4