Just Logarithms! 80 points!

1. Evaluate: log216
Select the appropriate response
A) 0
B) -1
C) 7

2. Express as a simple logarithm 2loge2+3logen.
Select the appropriate response:

A) Ln 2n2
B) ln 4n3
C) 4Ln 2n2

3. Solve log3 (27)
Select the appropriate response
A) 1
B) 2
C) 3
D) 8

4. Solve log2 (64)
Select the appropriate response:
A) 6
B) 5
C) 4
D) 13

5. Solve: log5 (625)
Select the appropriate response
A) 4
B) 6
C) 9
D) 2

6. Evaluate: log216
Select the appropriate response
A) 5
B) 8
C) 4

7. Solve log3 (81)

Select the appropriate response
A) 8
B) 6
C) 4
D) 72

8. Solve log4 (1)
Select the appropriate response
A) 0
B) 3
C) 1
D) 5

Also I don’t know why there is one two times with different answers

Answer:

7.065 m ^ 2

8.935 m ^ 2

Step-by-step explanation:

The first thing is to calculate the surface of each one, that is, the area

For the room that is square, each side measures 4m, therefore:

As = 4 * 4 = 16 m ^ 2

The area of the carpet is that of a circle, that its area is the number pi times the radius squared, we know that the radius is half the diameter, therefore r = 3/2 = 1.5 m

replacing in the area formula

Ac = pi * r ^ 2 = 3.14 * 1.5 ^ 2

Ac = 7.065 m ^ 2

In other words, the area covered by the carpet is 7,065 m ^ 2 and the area not covered would be the subtraction between the area of the room minus the area of the carpet, that is:

16 m ^ 2 - 7.065 m ^ 2 = 8.935 m ^ 2

8.935 m ^ 2 would be the area that the carpet does not subside.

Answer:

0x^2 + 2x -3 = 0

a = 0

b = 2

c = -3

Step-by-step explanation:

3 = 2x

0 = 2x - 3 (move three to other side)

0x^2 + 2x -3 = 0  (Finish off the equation by adding zeros in the empty spots to make the eeqution ax^2 + bx + c = 0)

a = 0

b = 2

c = -3

Answer:

2x + 3(8 - 3x) = 3

x = 3

y = -1

Step-by-step explanation:

2x + 3y = 3

y = 8 – 3x

2x + 3(8 - 3x) = 3

2x + 24 - 9x = 3

7x = 21

x = 3

y = 8 - 3(3)

y = -1

Answer:

✔ 2x + 3(8 – 3x) = 3

What is the value of x?

✔ 3

What is the value of y?

✔ –1

mark me brainiest plz thank you

Step-by-step explanation:

Answer:

The speed of light through the medium is 2.1 * 10^8 m/s

Step-by-step explanation:

In this question, we are asked to calculate the speed of light beam as it travels through a medium given the refractive index of the medium.

Mathematically;

n = c/v

where n is the refractive index, v is the speed of light through the medium and c is the speed of light in a vacuum.

From the question, we can identify that the refractive index is 1.46 and the speed of light through vacuum is 3 * 10^8 m/s

Rearranging the equation; we have;

v = c/n

v = (3 * 10^8)/1.46

v = 2.1 * 10^8 m/s

Answer:

Chord

Step-by-step explanation:

It's a chord because if you Google the examples of all the lines, Chord looks the most like Line LB

Answer:

This would most probably result in biased sample since only a specific part of the community is being surveyed that does not represent all of the community.

Step-by-step explanation:

A survey is being conducted to determine how a city's residents feel about building a new youth center.

They are considering to survey 50 random children at a local elementary school.

This would most probably result in biased sample since only a specific part of the community is being surveyed that does not represent all of the community.

Moreover, it is likely that the students of elementary school might not even have any interest in youth center so results would be biased.

Therefore, it is suggested to include a variety of samples that is surveying different age groups that covers all of the community.

Answer:

1. The survey is only considering elementary school students, but not children in middle school or high school.

2. The survey is also not considering any adult at all. Most likely they represent the majority of the local residents.

3. Finally, it's important to understand in advance what would be the main differences with the current youth center and include those specific questions in the survey. It's important to determine if the new youth center will fill the gap.

Step-by-step explanation:

Answer: 65

Step-by-step explanation:

participants obeyed because the learners' protests were not convincing. The new teachers complied fully, to the last switch, 65 percent of the time.

Answer:

1. 60,000 is __10_ times greater than 6,000.

2. 60,000 is __100__ times greater than 600.

3. 60,000 is _1000__ times greater than 60.

4. 2.0 is _10___ times greater than 0.2.

5. 2.0 is __100__ times greater than 0.02.

6. 2.0 is _1000___ times greater than 0.002.

Step-by-step explanation:

I mean, you can divide any number by the other number to get the answer

for example 60000/6000 = 10, or you can just count the difference in decimal points for example 60000 has 1 more 0 than 6000 so you know its 10x greater

Answer:

The mean and median will change.

Step-by-step explanation:

Mean takes the sum of all the numbers and divide by the amount of numbers there are. This would add 1 to the denominator, which would decrease the total mean score, as the numerator does not change.

The Median will also change. The median is found by finding the middle number of the set. Adding 0 to the set would result in a different number being chose for the median.

~

Answer:

The distance between the two airplanes (to the nearest mile) is 1058 miles.

Step-by-step explanation:

Use Law of cosines  

d = √(800^2 + 1200^2 - 2·800·1200·COS(60°)) = 1058 miles

Answer:

1058

Step-by-step explanation:

Plato

Answer:

n=4

Step-by-step explanation:

3n+6 = 54-9n

3n+9n = 54 - 6

12n = 48

n=4

Answer:

4

Step-by-step explanation:

3n+6=54-9n

3n+9n=54-6

12n=48

n=48/12

n=4

Answer:

a) 1/48 or 2.0833%

b) 46/48 or 95.8333%

no it would not be unusual

c) I'm not sure sorry

Answer:

Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler, considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”

Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.

Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.

Answer:

dividing and multiplying decimals

Step-by-step explanation:

Answer:

  yes

Step-by-step explanation:

We can estimate* that the total price including tax of the game will be less than ...

  $43.31 +10% of 43.31 = $43.31 +4.33 = $47.61

Todd easily has enough to pay for the game, including tax.

_____

You can work this more exactly a couple of ways.

  1. Price + tax = 1.085×$43.31 = $46.99 . . . less than Todd's budget

  2. Most Todd can afford: $55.50/1.085 = $51.15 . . . more than the game price

_____

* For estimating purposes, we like to use numbers that are easy to compute with. 10% is one such number, as it only requires moving the decimal point.

The frequency of the note a perfect fifth below C4, which is F3, is calculated by multiplying the frequency of C4 (261.63 Hz) by 2/3, resulting in 174.42 Hz.

The frequency of the musical note C4 is about 261.63 Hz. A perfect fifth below a note is 7 half-steps below on the chromatic scale, which corresponds to a frequency ratio of approximately 2/3. Therefore, to find the frequency of the note that is a perfect fifth below C4, we multiply the frequency of C4 by 2/3.

Calculating this, 261.63 Hz × (2/3) = 174.42 Hz which is the note F3. Hence, the frequency of the note a perfect fifth below C4 is 174.42 Hz.

Answer:

a) $4635

b) $1545

c) $29.7 per week

Step-by-step explanation:

Hermosa Menendez is employed by Chemical Industries. She has a family membership in the group preferred provider organization (PPO). The annual premium is $6,180. Her employer pays 75 percent of the premium.

a) How much does the employer pay annually

b) How much does she pay annually

c) How much is deducted each week as her weekly cost

a)

Given that:

The annual premium = $6180

Employers percent = 75% = 0.75

The money the employer pays annually = Annual premium × Employers percent = $6180 × 0.75 = $4635

b)

Since the employers percent = 0.75, her percent = 1 - 0.75 = 0.25

The money that she would pay annually = Annual premium × her percent = $6180 × 0.25 = $1545

c)

There are 52 weeks in a year.

The money she would pay weekly = money that she would pay annually / 52 weeks = $1545 / 52 weeks = $29.7 per week

Answer:

A. $ 4,635

B. $ 1,545

C. $ 29.72 (Rounding to the next cent)

Correct statement and questions:

Hermosa Menendez is employed by Chemical Industries. She has a family membership in the group preferred provider organization (PPO). The annual premium is $6,180. Her employer pays 75 percent of the premium.

a) How much does the employer pay annually

b) How much does she pay annually

c) How much is deducted each week as her weekly cost

Source:

Previous question that can be found at brainly

Step-by-step explanation:

A. The employer will pay annually the 75% of the annual premium:

6,180 * 0.75 = $ 4,635

B. Hermosa will pay annually the difference:

6,180 - 4,635 = $ 1,545

C. Hermosa will pay weekly:

1,545/52 = $ 29.72 (Rounding to the next cent)

The value of A is [tex]\left( \dfrac{6}{17}\right)^{9}[/tex].

Given that,

Equation; [tex]\rm \left(\dfrac{6}{17}\right)}^{9x}[/tex]

We have to find,

The value of A when the function is written as [tex]\rm A^x[/tex]?

According to the question,

To determine the value [tex]A^x[/tex] by applying the exponent property in the equation following all the steps given below.

By using the exponent property rewrite the equation,

[tex]\rm \left ( a )\right ^{mn} = ( a^m )\right^{n}[/tex]

Applying the property in the equation,

[tex]\rm \left(\dfrac{6}{17}\right)}^{9x}= \left( \left(\dfrac{6}{17}\right)^{9}\right) \right)^{x}[/tex]

By comparing the equation with [tex](A)^{x}[/tex],

[tex]\rm A ^{x}= \left( \left(\dfrac{6}{17}\right)^{9}\right) \right)^{x}\\\\A = \left( \dfrac{6}{17}\right)^{9}[/tex]

Hence, The required value of A is [tex]\left( \dfrac{6}{17}\right)^{9}[/tex].

For more details click the link given below.

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The value of [tex]\( A \)[/tex] when rewriting [tex]\( \left( \frac{6}{17} \right)^{9x} \) as \( A^x \) is \( \left( \frac{6}{17} \right)^9 \)[/tex]. The correct answer is option B) [tex]\( A = \left( \frac{6}{17} \right)^9 \)[/tex] .

Step 1

Let's break down the calculation step by step to rewrite [tex]\( \left( \frac{6}{17} \right)^{9x} \) as \( A^x \)[/tex].

Given:

[tex]\[ \left( \frac{6}{17} \right)^{9x} \][/tex]

To express this in the form [tex]\( A^x \)[/tex], we observe that [tex]\( \left( \frac{6}{17} \right)^{9x} \)[/tex] can be rewritten using exponent rules:

[tex]\[ \left( \frac{6}{17} \right)^{9x} = \left( \left( \frac{6}{17} \right)^9 \right)^x \][/tex]

Now, calculate [tex]\( \left( \frac{6}{17} \right)^9 \)[/tex] :

[tex]\[ \left( \frac{6}{17} \right)^9 = \frac{6^9}{17^9} \][/tex]

Step 2

Calculate [tex]\( 6^9 \)[/tex] and [tex]\( 17^9 \)[/tex]:

[tex]\[ 6^9 = 10077696 \][/tex]

[tex]\[ 17^9 = 1667988092 \][/tex]

So,

[tex]\[ \left( \frac{6}{17} \right)^9 = \frac{10077696}{1667988092} \][/tex]

Therefore, [tex]\( A \)[/tex] in [tex]\( A^x \)[/tex] is:

[tex]\[ A = \left( \frac{6}{17} \right)^9 \][/tex]

Thus, the correct answer is:

B) [tex]\( A = \left( \frac{6}{17} \right)^9 \)[/tex].

Complete question : What is the value of A when we rewrite [tex]\( \left( \frac{6}{17} \right)^{9x} \) as \( A^x \)[/tex]?

A) [tex]\( A = \frac{54}{17} \)[/tex]

B) [tex]\( A = \left( \frac{6}{17} \right)^9 \)[/tex]  

C) [tex]\( A = \left( \frac{17}{6} \right)^9 \)[/tex]

D) [tex]\( A = -\frac{1}{9} \)[/tex]

Answer:

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:

[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]

And the margin of error is given by:

[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:

[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]

And the margin of error is given by:

[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]

Answer:

110/7 yards

Step-by-step explanation:

Given:-

- The radius of circular patio, r = 5 yards

Find:-

What is the circumference of circular patio

Solution:-

- The circumference "C" of a circle is given as:

            [tex]C =2 *\pi*r\\\\\pi = \frac{22}{7} \\\\ C = 2*\frac{22}{7}*5\\\\C = \frac{110}{7} yards[/tex]

- The circumference of the circular patio is 110 / 7 yards.            

Answer:

The volume of shipping container is 2880 cubic inches.

Step-by-step explanation:

We are given the following in the question:

Dimensions of tissue box =

4 inches by 6 inches by 3 inches

Volume of tissue box =

[tex]V = l \times w\times h\\V = 4\times 6\times 3\\V = 72\text{ cubic inches}[/tex]

Number of tissue box in shipping container, n = 40

Volume of shipping container =

[tex]V = n\times \text{Volume of tissue box}\\V = 40\times 72\\V = 2880\text{ cubic inches}[/tex]

Thus, the volume of shipping container is 2880 cubic inches.

This question is based on volume of cuboid. Therefore, the volume of the shipping container is 2880 cubic inches.

Given:

A shipping container holds 40 tissue boxes the dimensions of a tissue box are 4 inches by 6 inches by 3 inches.

We need to calculating the  volume of the shipping container.

According to this question,

It is given that, dimensions of tissue box =  4 inches by 6 inches by 3 inches

As we know that,

Volume of tissue box = [tex]length \times breadth \times height[/tex]

[tex]= 4 \times 6 \times 3\\= 72 \, inch^3[/tex]

As it is given that, number of tissue box in shipping container, n = 40.

[tex]Volume \,of \,40\, tissue \,box = n \times 72\\\\Volume \,of \,40 \,tissue \,box = 40 \times 72\\\\Volume \,of \,40 \,tissue \,box = 2880 \, inch^3[/tex]

Therefore, the  volume of the shipping container is 2880 cubic inches.

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Answer:

160 pages.

Step-by-step explanation:

That is 125 - 0.20 * 125

= 125 - 25

= 160 pages.

Answer:

The answer is you saved $25.00 and the new total is $100.00

Step-by-step explanation:

so first you set up the equation of is over of = percent over 100

[tex]\frac{a}{125}=\frac{20}{100}\\\\[/tex]

then simplify the [tex]\frac{20}{100}=\frac{1}{5}[/tex]

then you see if 5 can go into 125. It can so you divide 125 by 5=25

so you multiply the [tex]\frac{1}{5}=\frac{25}{125}[/tex]

so now you just [tex]\frac{a}{125}=\frac{25}{125}[/tex]

then you just subtract the 25 because that is how much you are saving and your total will be $100.00

Answer:

30 students

Step-by-step explanation:

18/3 = 6

6 x 2 = 12 boys

12 boys + 18 girls = 30 students

- Hope this helps! Please let me know if you would like a further explanation.

the sum of the angles in a triangle is 180°

=>180-50=130

def: in an isosceles triangle two angles measure the same

case 1: if two angles measure 50°

180-2*50=80

=> angles: 50, 80

case 2: if the other 2 angles measure the same

(180-50)/2=130/2=65

=> angle: 65

For 42 cups of punch 168 cups lemonade is used.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have, For one punch 4 cups of lemonade to 3 cups of sparking juice is used.

Now, for 42 cups the amount of Lemonade needed

= 4 x 42

= 168 cups

and, Amount of Sparking juice needed

= 3 x 42

= 126 cups

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Answer: A. Representative, since blood types are probably not different among students at the cafeteria compared to the U.S. population, B. Not representative, since students in the cafeteria may eat most of their meals at the cafeteria instead of eating fast food

Step-by-step explanation:

I Hope that this helps! :)

a) The variable used gives the appropriate estimate.

b) The variable used does not give the appropriate estimate.

Statistical research is the methodical creation of enhanced or novel statistical techniques based on statistical theory and probability.

A property that can be measured and given varied values is known as a variable. Variables include things like height, age, income, province of birth, school grades, and kind of dwelling. There are two basic types of variables: category and numeric.

Given:

a) Since kids in the cafeteria probably have the same blood types as people in the United States.

So, it can be Representative.

b) As opposed to eating fast food, students may eat the majority of their meals in the cafeteria.

So, this is not representative.

Learn more about Research here:

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Answer:

2%, low probability

Step-by-step explanation:

In this case we have that the avatars are distributed as follows:

5 subjects and 10 versions of the application for each subject, therefore they are a total of:

5 * 10 = 50

In total there are 50 avatars.

To know the probability that I get 1 in specific, in this case that of a lion is:

1/50 = 0.02

The probability is 2%, that is to say a really low probability, that is to say that the most probable thing is that you do not receive it.

Answer:

2%

Step-by-step explanation:

Answer: The displacement is -4 ft.

Step-by-step explanation:

The velocity is:

v(t) = 2t - 5ft/s

If we want to find the displacement between t = 0s and t = 4s, we need to find the difference between the position at t = 0s and at t= 4s

The equation for the position is obtained by integrating over time:

P(t) = (2t^2)/2 - 5*t + c

where c is the initial position, then we have:

P(t) = t^2 - 5t

P(4) - P(0) = 4*4 - 5*4 - 0 = 16 - 20 = -4

The total displacement is -4 feet

Answer:

Displacement, d = - 4ft

Step-by-step explanation:

Given,

The velocity function for a particle v(t) = 2t - 5 ft/sec.

To obtain the displacement for the particle from t = 0 to t = 4 sec

We integrate v(t) with respect to t

: Displacement, d = ∫₀⁴ ( 2t - 5) dt

= t² - 5t |₀⁴ = (4² - 5(4)) - 0² - 5(0)

=16 - 20 = - 4ft

Answer:

The correct answer is 4 window frames.

Step-by-step explanation:

Sue bought 54 feet of lumber for building window frame.

Each window frame requires 13 1/2 feet = [tex]\frac{27}{2}[/tex] feet of lumber.

Therefore the number of window frames Sue can make with 54 feet of lumbers she bought is given by dividing the total amount of lumber she has by the lumber it takes to make a single window frame.

= [tex]\frac{54}{27}[/tex] × 2 = 2 × 2 = 4

Thus Sue can make 4 window pane from 54 feet of lumber, each of 13 and a half feet.

Sue can make 4 window frames with the 54 feet of lumber she purchased, as each frame requires 13.5 feet.

Sue bought 54 feet of lumber to build window frames, with each window frame requiring 13.5 feet of lumber. To determine how many window frames Sue can make, we divide the total amount of lumber by the amount required for one frame.

Here's the calculation:

Start with the total amount of lumber: 54 feet.

Divide this by the amount required for one window frame: 13.5 feet.

Perform the division: 54 / 13.5 = 4.

Sue can make 4 window frames with the lumber she has purchased.

Answer:

  A.  (2, 7), (1, 4)

Step-by-step explanation:

The first equation tells you that y cannot be negative. (Both terms are positive.) So, the only viable answer choice is A.

Answer:

you take all the point from around then multiply and do the same with the base

Step-by-step explanation: