Given log base 2 =1/6, what is log base 4

f(x) is a linear function, so both the domain and the range are the set of real numbers.

Answer:

Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.

Answer:

A is correct yes

Step-by-step explanation:

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Answer:

66

Step-by-step explanation:

The sequence you provided seems to be arithmetic as it increases as 4 each term. Assuming 1 is the first term the equation would be [tex]a_{n}=1 + 4(n-1)[/tex]. You could just take the first 6 terms and add them together since you already have 4 values calculated and you could calculate the other 2 by adding 4. This would give you

(1 + 5 + 9 + 13 + 17 + 21) = 66

But there's an easier way to do it. You could use the formula [tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]. You can calculate [tex]S_6[/tex] by plugging in those values. You would need to calculate [tex]a_6[/tex] before hand, but you can calculate that using the formula I defined above. Which in general is [tex]a_n = a_1 + d(n-1)[/tex] where d is like the slope, or how much it changes each term. So if you calculate [tex]a_6[/tex] you'll get [tex]1+4(6-1) = 1+4(5) = 21[/tex]. Now plug this into the series formula above and you get [tex]S_6 = \frac{6(1+21)}{2}=\frac{6(22)}{2}=\frac{132}{2}=66[/tex] which is exactly what you get if you add the first 6 terms as shown above when you do it manually.

[tex]\text{First let's find two more terms, because we have only six. We can do that by}\\\text{adding 4:: 13+4=17; 17+4=21}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now we just add the terms: 1+5+9+13+17+21}[/tex]

[tex]\rule{300}{1.7}\\\text{66}[/tex]

Answer:

The answer will be A. 6 or fewer.

The probability that during a given 10 minutes the number of smokers passing will be 6 or fewer.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Example

Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The following terms in probability help in a better understanding of the concepts of probability.

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

There are 5 smokers who passes by in every 10 minutes.

So, the probability that during a given 10 minutes the number of smokers passing will be approx 5 or less.

i.e., 6 or fewer.

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The monthly payment for purchasing the home will be $457.85.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]

In order to purchase a home, a family borrows $110,000 at 2.9% for 30 years.

We have

P = $110,000

r = 0.029 / 12 = 0.0024

n = 30 × 12 = 360

Then the monthly payment will be

[tex]\rm MP = 110,000\times \dfrac{0.0024(1+0.0024)^{360}}{(1+0.0024)^{360} - 1}\\\\[/tex]

On further solving, we have

MP = 110000 × 0.0024 × 1.723

MP = $ 457.85

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The length and width of the rectangle are equal to: 7 ft and 5 ft, respectively

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2L+2W.

For this question, the length is 2ft longer than the width - L=2+W. Thus,

24=2*(2+W)+2W

24=4+2W+2W

24-4=4W

20=4W

W=5 ft

If W=5, L will be 2+5=7 ft.

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The expression for the total revenue from x thousand sales is 155,000x - 100x².

The value of x is 775 cents and the maximum revenue is $60,062,500.

First, come up with an expression for total revenue from x thousand sales:

= (155  - x /10 ) × x × 1,000 units

= 155,000x - 100x²

The value of x would then be:

Derive the function from the total revenue function to give:

0 = 155,000 - 200x

x = 775 cents

The maximum revenue is therefore:

= 155,000(775) - 100(775)²

= $60,062,500

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Answer:

[tex] \frac{289}{111} [/tex]

Step-by-step explanation:

[tex]2 + \frac{603}{1000 - 1} = 2 \frac{603}{999} = 2 \frac{67}{111} = \frac{289}{111} [/tex]

Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]

Step-by-step explanation:

This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.

To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.

The income of the man in discuss as in the task content is; rs 10,200.

Since, it follows that 100 paisas make one rupee. This insinuates that the income tax rate which corresponds to 5 paisa per rupee is; 5%.

Hence, the amount earned by the man in discuss can be evaluated as follows;

(5/100) × Income = 510

Hence, Income = 510/0.05 = rs 10,200.

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Answer:

√96

Step-by-step explanation:

halve the diameter to set up the pythagorean theorem

2²+b²=10²

4+b²=100

-4 on each side

b²=96

square root each side

b=√96

it could the be further simplified to 4√6

Answer:

1. 30 ft

2. sqrt(2164) yd

3: 12 cm

Step-by-step explanation:

For all three questions I'll be using the Pythagorean Theorem which states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the base and height

Question 1:

40^2 + d^2 = 50^2

1600 + d^2 = 2500

d^2 = 900

d = 30

Question 2:

42^2 + 20^2 = c^2

2,164 = c^2

c = sqrt(2164)

Question 3:

5^2 + a^2 = 13^2

25 + a^2 = 169

a^2 = 144

a = 12

It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.

This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]

Answer:

0.04

Step-by-step explanation:

0.03508772

Answer:

3x-4=5

Step-by-step explanation:

it is correct

Answer:

1/4 + x = (-5)/4

x = -5/4 - 1/4

x = (-5)-1 /4

x = (-6)/4

Answer:

Range =  4365-4635

Step-by-step explanation:

4500 * 3/100 = 135

4500 + 135  = 4635

4500 - 135  = 4365

Range =  4365-4635

The actual range of resistance is from 4365 ohms to 4635 ohms.

To express the tolerance in ohms, we need to calculate 3% of the rated resistance, which is 4500 ohms.

Tolerance in ohms = 3% of 4500 ohms

Tolerance in ohms = 0.03 * 4500

Tolerance in ohms = 135 ohms

The actual range of resistance can be found by adding and subtracting the tolerance from the rated resistance:

Lower limit = Rated resistance - Tolerance

Lower limit = 4500 ohms - 135 ohms

Lower limit = 4365 ohms

Upper limit = Rated resistance + Tolerance

Upper limit = 4500 ohms + 135 ohms

Upper limit = 4635 ohms

So, the actual range of resistance is from 4365 ohms to 4635 ohms.

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C) The probability that you pick at least one purple marble is 98%.

The question is incomplete, since the number of marbles of each color in the bag is missing: 3 blue, 5 green, and 2 purple marbles.

Now, to answer the questions, the following calculations must be done:

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Answer:C) The probability that you pick at least one purple marble is 98%.

Step-by-step explanation:

Answer:

1,260

Step-by-step explanation:

[tex]\implies C(9,4)*C(5,3)*C(2,2)[/tex]

[tex]\implies 9!/4!(9-4)!*5!/3!(5-3)!*2!/2!(2-2)![/tex]

[tex]\implies 9!/4!5!*5/3!2! *2!0![/tex]

[tex]\implies (9 * 8 * 7 * 6 / 4 * 3 * 2 * 1) * (5 * 4 / 2 * 1) * 1[/tex]

[tex]\implies 1260[/tex]

Therefore, 1,260 committees can be formed.

Answer:

X=5

Step-by-step explanation:

f(1)= -1^2+4(1)+12=15

f(2)= -2^2+4(2)+12=16

f(3)= -3^2+4(3)+12=15

f(4)= -4^2+4(4)+12=12

f(5)= -5^2+4(5)+12=7

g(1)=1+2=3

g(2)=2+2=4

g(3)=3+2=5

g(4)=4+2=6

g(5)=5+2=7

so g(5)=f(5)= X=5

Answer:

Step-by-step explanation:

You're suppose to plug in the values 1, 2, 3, 4, 5, and 6 into f(x) and g(x) to find where they're equal to find the solution to f(x) = g(x) (when the column values are equal).

So for example

f(1) = -(1)^2 + 4(1) + 12

f(1) = -1 + 4 + 12

f(1) = 15

g(1) = 1 + 2

g(1) = 3

put these two values in the table for f(1) and g(1)

f(2) = -(2)^2 + 4(2) + 12

f(2) = -4 + 8 + 12

f(2) = 16

g(2) = 2 + 2

g(2) = 4

f(3) = -(3)^2 + 4(3) + 12

f(3) = -9 + 12 + 12

f(3) = 15

g(3) = 3 + 2

g(3) = 5

f(4) = -(4)^2 + 4(4) + 12

f(4) = -16 + 16 + 12

f(4) = 12

g(4) = 4 + 2

g(4) = 6

f(5) = -(5)^2 + 4(5) + 12

f(5) = -25 + 20 + 12

f(5) = 7

g(5) = 5 + 2

g(5) = 7

f(5) = g(5) so the solution is when x=5

f(6) = -(6)^2 + 4(6) + 12

f(6) = -36 + 24 + 12

f(6) = 0

g(6) = 6 + 2

g(6) = 8

Answer: Wasp has greater kinetic energy of 0.002 Joules

Given for bee:

Given for wasp:

Formula:

Kinetic energy of bee:

Kinetic energy of wasp:

From this, it is determined wasp has greater kinetic energy.

We can see that, when the input is 5, the output is 24.

Here we have the equation:

[tex]y = x^2 - 1[/tex]

Where y is the output and x is the input.

We want to evaluate it with the input as 5, so we need to replace the variable x by the number 5, we will get:

[tex]y = 5^2 - 1 = 24[/tex]

Then we can see that, when the input is 5, the output is 24.

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Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.

So, the number of possible arrangements is

(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800

Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

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The equation of the line is x = -9 , Option  is the correct answer

The equation of a line is given by y = mx+c

where m is the slope and c is the intercept

It is given that

A line passes through (-9,-6) and has an undefined slope.

undefined slope means it is a vertical line at -9

Therefore the equation of the line is x = -9 , Option  is the correct answer

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I don't even know Brian tanks

Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.

Probability helps us to know the chances of an event occurring.

P =  [tex]\dfrac{Desired \ outcomes}{Posiible \ outcomes}[/tex]

The probabilities of different color cards being pulled are 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black Therefore, the probability of pulling  a green or red card is,

Probability = 1/20 + 1/25

                 = (5 + 4) /100

                 = 9 / 100

Hence, the probability of pulling a green or red card is  9 / 100.

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