Write each equation in logarithmic form.


5^3 = 125

Answer:

The angular velocity is 6.72 π radians per second

Step-by-step explanation:

The formula of the angular velocity is ω = [tex]\frac{v}{r}[/tex] , where v is the linear velocity and r is the radius of the circle

The unit of the angular velocity is radians per second

∵ The diameter of the tire is 25 inches

∵ The linear velocity is 15 miles per hour

- We must change the mile to inch and the hour to seconds

∵ 1 mile = 63360 inches

∵ 1 hour = 3600 second

∴ 15 miles/hour = 15 ×  [tex]\frac{63360}{3600}[/tex]

∴ 15 miles/hour = 264 inches per second

Now let us find the angular velocity

∵ ω = [tex]\frac{v}{r}[/tex]

∵ v = 264 in./sec.

∵ d = 25 in.

- The radius is one-half the diameter

∴ r = [tex]\frac{1}{2}[/tex] × 25 = 12.5 in.

- Substitute the values of v and r in the formula above to find ω

∴ ω = [tex]\frac{264}{12.5}[/tex]

∴ ω =  21.12 rad./sec.

- Divide it by π to give the answer in terms of π

∴ ω = 6.72 π radians per second

The angular velocity is 6.72 π radians per second

The result is approximately 21.12 or  6.72 π radians per second.

The question asks for the angular velocity of a point on a bicycle tire with a diameter of 25 inches, traveling at 15 miles per hour.

Convert speed to inches per second:
15 miles per hour = 15 × 5280 feet per hour = 15 × 5280 × 12 inches per hour = 950400 inches per hour

Since there are 3600 seconds in an hour:
950400 inches per hour ÷ 3600 seconds per hour ≈ 264.00 inches per second

Convert diameter to radius in inches:
Diameter = 25 inches, so Radius = 25 ÷ 2 = 12.5 inches

Using the formula:
Linear speed (v) = Angular velocity (ω) × Radius (r)

264.00 = ω × 12.5
ω = 264.00 ÷ 12.5 ≈ 21.12 radians per second

Thus, the angular velocity of a point on the bicycle tire is approximately 21.12 or  6.72 π radians per second in terms of π.

Answer:

A part of a whole expressed in hundredths is a percent.

Answer:

A) [tex]log_{5}(12)[/tex]

B) [tex]log_{8}(9)[/tex]

C) [tex]log_{9}(25)[/tex]

Step-by-step explanation:

Hello! I am going to walk you through how some simple rules regarding logs!

For A, we will use the 'AM' rule! When adding logs of the same base (in this case 5), you multiply the two answers (3 and 4)!

3 · 4 = 12, giving us [tex]log_{5}(12)[/tex]!

For B, we will use the 'SD' rule! When subtracting logs of the same base (in this case 8), you divide the two answers (9 and 5)!

9/5 = [tex]\frac{x}{5}[/tex] ; simplify! (9/5) x 5 = 9, giving us [tex]log_{8}(9)[/tex]!

For C, we will use the 'MS' rule! When multiplying a number times a logarithm, you can get the same argument by removing the coefficient (2) and squaring the log's answer (5)!

[tex]5^{2} = 25[/tex], giving us [tex]log_{9}(25)[/tex]!

I hope that this helps!

Answer:

A. x equals 5 plus or minus the square root of thirty-three all over 2

Step-by-step explanation:

Let's move all the terms to one side:

[tex]x^2=5x+2[/tex]

[tex]x^2-5x-2=0[/tex]

Now, we want to use the quadratic formula, which states that for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex], the roots can be found with the equation: [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex].

Here, a = 1, b = -5, and c = -2, so plug these in:

[tex]x=\frac{-(-5)+\sqrt{(-5)^2-4(1)(-2)} }{2(1)}=x=\frac{5+\sqrt{25+8} }{2}=\frac{5+\sqrt{33} }{2}[/tex]

OR

[tex]x=\frac{-(-5)-\sqrt{(-5)^2-4(1)(-2)} }{2(1)}=x=\frac{5-\sqrt{25+8} }{2}=\frac{5-\sqrt{33} }{2}[/tex]

Thus, the answer is A.

Hope this helps!

Answer:

First one:

x = x equals 5 plus or minus the square root of thirty-three all over 2

Step-by-step explanation:

x² = 5x + 2

x² - 5x - 2 = 0

Using quadratic formula:

x = [-(-5) +/- sqrt[(-5)² - 4(1)(-2)]/2(1)

x = [5 +/- sqrt(33)]/2

Answer:

The probability is 0.000000207176

Step-by-step explanation:

In this question, we are asked to calculate the probability that if 6 cards are selected from a deck of cards, we will be having 4 kings and 2 queens.

Before we answer, we should understand that in a deck of cards, there are 4 queens and 4 kings. The probability of selecting a king is the same as the probability of selecting a queen which is 4/52 = 1/13

Okay now we want to find the probability of the six cards being 4 kings and 2 queens. Since the probabilities are equal, we proceed to calculate at the same time.

That would be (1/13)^6 = 0.000000207176

The probability of selecting 4 kings and 2 queens is 0.000000207176

Final answer:

The probability of getting four queens and two kings out of six cards from a standard deck of 52 cards is calculated by dividing the product of the combinations of getting those particular cards by the total number of six-card combinations available from the deck.

Explanation:

To calculate the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards, we can follow these steps:

Identify the total number of ways to choose 6 cards from 52: This can be calculated using combinations, as the order the cards are drawn doesn't matter. The formula for combinations is:

C(n, k) = n! / (k! × (n-k)!)

In this case, n = 52 (total cards) and k = 6 (cards chosen). Therefore, the total number of ways to choose 6 cards is:

C(52, 6) = 52! / (6! × (52-6)!) ≈ 270,735,576

Identify the number of ways to get four queens and two kings: We need to choose 4 queens out of 4 and 2 kings out of 4. Again, using combinations:

C(4, 4) × C(4, 2) = 1 × 6 = 6

There are only 6 ways to get this specific combination (4 queens and 2 kings) within the 6 cards chosen.

Calculate the probability: Finally, divide the number of successful outcomes (6) by the total number of possibilities (270,735,576) to get the probability:

Probability = 6 / 270,735,576 ≈ 0.000002217 ≈ 0.0002%

Therefore, the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards is incredibly low, at approximately 0.0002%.

Answer:

Geometric sequence.

Step-by-step explanation:

This is a Geometric Sequence with common ratio -2:

-2 = 1* -2

4 = -2*-2

-8 = 2 * -2.

the nth term = (-2)^(n-1).

The perimeter of the trapezoid is 26cm. Using the formula, the area is approximately 47.92cm², rounded to two decimal places.

To find the perimeter and area of the given shape, we first need to determine what type of shape it is. From the given measurements (5cm, 6cm, 7cm, and 8cm), it seems like a quadrilateral, specifically a trapezoid, as the lengths are not all equal.

To calculate the perimeter of the trapezoid, we simply add the lengths of all four sides:

Perimeter = 5cm + 6cm + 7cm + 8cm = 26cm

Now, to find the area of the trapezoid, we can use the formula:

Area = (1/2) × (sum of parallel sides) × (height)

First, let's determine the height of the trapezoid. Since it's not given directly, we can use the formula for the height of a trapezoid:

[tex]\[h = \sqrt{a^2 - (\frac{1}{2}(b_1 - b_2))^2}\][/tex]

Where:

- (a) and (b_1, b_2) are the lengths of the trapezoid's legs and bases, respectively.

Let's plug in the values:

[tex]\[h = \sqrt{6^2 - (\frac{1}{2}(8 - 5))^2}\][/tex]

[tex]\[h = \sqrt{36 - (\frac{1}{2}(3))^2}\][/tex]

[tex]\[h = \sqrt{36 - \frac{9}{4}}\][/tex]

[tex]\[h = \sqrt{\frac{135}{4}}\][/tex]

[tex]\[h = \frac{\sqrt{135}}{2}\][/tex]

Now, we can calculate the area using the formula:

[tex]\[Area = \frac{1}{2} \times (5 + 8) \times \frac{\sqrt{135}}{2}\][/tex]

[tex]\[Area = \frac{13}{2} \times \frac{\sqrt{135}}{2}\][/tex]

[tex]\[Area = \frac{13\sqrt{135}}{4}\][/tex]

So, the perimeter of the trapezoid is 26cm and the area is[tex]\(\frac{13\sqrt{135}}{4} cm^2\).[/tex]

Answer:850

Step-by-step explanation:

To find this 2% of x= 17

2/100×x=17

2x/100=17

2x=1700

x=850

Answer: Yolanda spent $6.60 at her favourite restaurant, including the tip.

Step-by-step explanation:

We know that 20% of 5.50 is: 1.10

So, 5.50 + 1.10 = 6.60.

Yolanda spent $6.60 at her favourite restaurant, including the tip.

Answer: 14 grams

Step-by-step explanation:

It took 4 balloons to make a duck that weighs 56 grams to float. With one balloon, the number of grams that will float will be 56 grams divided by 4. This will be:

= 56 grams ÷ 4

= 14 grams

Weight carry by 1 balloon is 14 gram

Weight of duck = 56 grams

Number of balloon need to float duck = 4

Weight carry by 1 balloon

Weight carry by 1 balloon = Weight of duck / Number of balloon need to float duck

Weight carry by 1 balloon = 56 / 4

Weight carry by 1 balloon = 14 gram

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Answer: 194 degrees

Step-by-step explanation:

Answer:

Total assets $274,500

Total liabilities $156,000

Net worth $118,500

Step-by-step explanation:

Vijay's assets consist of a house, stock investment , balance in checking account , a piano as well as car owned

Total assets=$250,000+$3,000+$1,700+$1,800+$18,000=$ 274,500.00  

Vijay's liabilities are obligations owed to others, which include mortgage loan and car loan

total liabilities=$150,000+$6,000=$156,000

net worth=total assets-total liabilities=$274,500-$156,000=$118,500.00  

Answer:

2.) P(Chocolate, sprinkles)

Step-by-step explanation:

A lot of people choose chocolate ice cream over other flavors, and a lot of people also like sprinkles on their ice cream.

Answer:

The GCF is 28

Step-by-step explanation:

Step 1:  Find the factors of both numbers

84 → 1,  2 ,  3 ,  4 ,  6 ,  7 ,  12 ,  14 ,  21 ,  28 ,  42 ,  84

56 → 1 ,  2 ,  4 ,  7 ,  8 ,  14 ,  28 ,  56

The factor that is the biggest common in both is the GCF.  We see that 28 is the biggest factor that matches for both numbers.

Answer:  The GCF is 28

Answer: 4x _ 12

Cheese

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

arrange from the smallest to the largest or largest to the smallest and then carry out binary division

Answer:

All the people who have tried their beverages will be the representing population.

Step-by-step explanation:

If people in the United States like the new logo of a beverage company that the company wants to determine.

Now, we have to choose from the given options that represent the population.

From my point of view, option fourth option gives the correct answer.

Therefore, all the people who have tried their beverages will be the representing population.

Answer:

Every person in the united states

Answer:

$11

Step-by-step explanation:

According to the statement, you have that 6 tickets for the price of each ticket is equal to $174 and from that, you can determine the price of each ticket:

6*P=174

P= price of each ticket

P= 174/6= 29

Now, as it says that one of Henry's friends gives him two $20 bills, that means that he gives him $40 and you have to subtract the price of the ticket from that:

40-29= 11

The answer is that if one of Henry's friends gives him two $20 bills, Henry has to return $11.

Final answer:

The cost of one ticket is $29, and if a friend pays with two $20 bills, totaling $40, Henry should return $11 in change.

Explanation:

Henry buys 6 circus tickets for a total of $174. To determine the cost of each ticket, you divide the total cost by the number of tickets:

$174 ÷ 6 tickets = $29 per ticket.

When one of Henry's friends pays him back with two $20 bills, the friend gives Henry $40 in total. To find out how much change Henry should return, you subtract the cost of one ticket from the amount the friend gave:

$40 - $29 = $11.

Therefore, Henry should give his friend $11 in change.

Answer:

450 $

Step-by-step explanation:

1). Bench = x

   Garden Table = x - 60

2). x + x - 60 = 840

    2x = 900

    x = 450 $ - the cost of the bench.

Hope this Helps)))

The cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A garden table and a bench cost $840 combined.

The garden table costs $60 less than the bench.

Let the cost of the bench is x

Cost of the Garden Table = x - 60

x + x - 60 = 840

2x = 900

x = 450 $ - the cost of the bench.

Thus, the cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.

Learn more about the linear equation here:

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The study investigates the connection between office habits and health outcomes. Key considerations include factors such as stress, job status, personal hygiene, and historical trends in workforce health. The goal is to improve policies to promote healthier workplaces.

The ministry of health study you're referring to is looking into how habits within the office workplace can impact employees' health. Various factors such as stress levels, personal hygiene habits, the status of the job, and societal impacts can influence the health outcomes of individuals in workplaces.

Stress is a critical factor, as studies have suggested those in high stress or low status jobs, such as the mentioned British civil servants, are more prone to health issues like heart disease. This emphasizes the necessity of stress management in the workplace.

Another element of consideration is personal hygiene, which relates to individuals' private habits in maintaining their physical appearance, not strictly health-related. Various habits could reflect differently on personal health outcomes.

Historical context also plays a role in understanding workforce health trends, such as the transformation during and after World War II. Anthropologists worked intensively on public and private health initiatives, focusing on improving health outcomes both in warfare and post-war times, which influenced the health perspectives in today's workplaces.

This is a multidimensional investigation that potentially will reveal valuable insights that could inform policies on how to better protect workers' health and productivity. Overall, a healthy workforce translates to a more robust and vibrant society.

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Answer:

(9,-4)? I'm not sure.

Answer:

178.85

Step-by-step explanation:

Answer:

153 !

Step-by-step explanation:

begin by multiplying 180 by .15 then you should get 27. next, subtract 27 from 180 and you're left with 153.

Final answer:

The point (3,8) does not satisfy either of the two equations y = -5x + 1 and y = 3x - 2, therefore it is not a solution to the system of equations.

Explanation:

To determine whether the point (3,8) is a solution to the system of equations given by y = -5x + 1 and y = 3x - 2, we need to substitute the x and y values of the point into both equations to see if the equations are satisfied.

For the first equation:
y = -5x + 1
8 = -5(3) + 1
8 = -15 + 1
8 ≠ -14

The point (3,8) does not satisfy the first equation because 8 does not equal -14.

For the second equation:
y = 3x - 2
8 = 3(3) - 2
8 = 9 - 2
8 = 7

The point (3,8) does not satisfy the second equation because 8 does not equal 7.

Since the point (3, 8) fails to satisfy both equations, it is not a solution to the system of equations.

Final answer:

The point (3,8) is not a solution to the system of equations y = -5x + 1 and y = 3x - 2, as it does not satisfy either equation when substituting the values of x and y.

Explanation:

The student is asking whether the point (3,8) is a solution to the system of linear equations:

y = -5x + 1

y = 3x - 2
To determine if (3,8) is a solution, we can substitute x with 3 and y with 8 into both equations and see if they hold true.

Substituting into the first equation:
8 = -5(3) + 1
8 = -15 + 1
8 ≠ -14
This does not hold true, so (3,8) is not a solution to the first equation.

Substituting into the second equation:
8 = 3(3) - 2
8 = 9 - 2
8 = 7
This also does not hold true, so (3,8) is not a solution to the second equation either.

Since (3,8) does not satisfy either of the given equations, it is not a solution to the system of equations.

Answer: The percentage of hotels in the city have a nightly cost of more than $200 is 21%

Step-by-step explanation:

Since the nightly cost of hotels in a certain city is normally distributed,

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the nightly cost of hotels.

µ = mean cost

σ = standard deviation

From the information given,

µ = $180.45

σ = $24.02

The probability that a hotel in the city has a nightly cost of more than $200 is expressed as

P(x > 200) = 1 - P(x ≤ 200)

For x = 200,

z = (200 - 180.45)/24.02 = 0.81

Looking at the normal distribution table, the probability corresponding to the z score is 0.79

Therefore,

P(x > 200) = 1 - 0.79 = 0.21

The percentage of hotels in the city have a nightly cost of more than $200 is

0.21 × 100 = 21%

Answer:

62

Step-by-step explanation:

Answer:

62 units

Step-by-step explanation:

this is the answer on edg 2020

Answer:

A = 70 and N=30

Step-by-step explanation:

Total - 100 cards

American League = A

National League = N

A = 2N + 10 and A+N = 100

100-10 = 90

90/3 = 30

A = 2(30) + 10 = 70

A = 70 and N=30

Answer:

After 49 months the total cost of the two systems will be equal.

Step-by-step explanation:

To Find: We need to find the number of months will the total cost of the two systems be equal

Solution:

For Satellite receiver:

Satellite receiver cost = $298.90

Monthly charge = $68.70

Let the Number of months be denoted by 'x'.

Now we can say that;

Total cost using Satellite receiver is equal to sum of Satellite receiver cost and Monthly charge multiplied by number of months.

framing in equation form we get;

Total cost using Satellite receiver = [tex]298.90+68.70x[/tex]

For Using Cable:

Monthly charge = $74.80

So we can say that;

Total cost using cable is equal to Monthly charge multiplied by number of months.

framing in equation form we get;

Total cost using cable = [tex]74.80x[/tex]

Now to find the number of months when both the cost will be the same so we will make both the equation equal we get;

[tex]298.90+68.70x=74.80x[/tex]

Combining the like terms we get;

[tex]74.80x-68.70x=298.90\\\\6.1x=298.90[/tex]

Dividing both side by 6.1 we get;

[tex]\frac{6.1x}{6.1}=\frac{298.90}{6.1}\\\\x=49[/tex]

Hence After 49 months the total cost of the two systems will be equal.

Answer:

12

Step-by-step explanation:

The ratio of cars to trucks to motorcycles is $4:3:2.

If there are $42$ cars and trucks total,

To get how many motorcycles are there

Sum up the ratio of cars and trucks 4:3= 4+3 = 7

Sum up the ratio of cars and trucks and motorcycles

4+3+2 =9

Let the total number of cars and trucks and motorcycles be represented as A

The total number of cars and trucks in the question is 42

(7/9) x A = 42

7A/9 = 42

cross multiply

7A = 42×9 = 378

A= 378/7 = 54

The total number of cars and trucks and motorcycles is 54

To get the number of motorcycles can be calculated through

a. The total number of cars and trucks and motorcycles subtracted by the number of cars and trucks = 54-42=12 or use the ratio which is

2/9 × 54 = 2×6=12

Answer:

23.4 feet

Step-by-step explanation:

Please refer to the attached image for explanations

Using similar triangles and a proportion, the length of the tree's shadow that will allow it to be cut down needs to be 448 inches, or 37.3 feet to the nearest tenth of a foot.

To find the length of the tree's shadow that would allow for the tree to be tall enough (41 feet or more) to be cut down, we need to use similar triangles. The person cutting the tree is 5 feet 3 inches tall, which is 63 inches, and their shadow is 36 inches long. Using this information, we can set up a proportion since the tree and the person form similar triangles with their respective shadows. The proportion is 63 inches / 36 inches = 492 inches (41 feet) / length of tree's shadow. To find the tree's shadow length, we cross multiply and solve for the tree's shadow length as follows:

63 * length of tree's shadow = 36 * 492

Length of tree's shadow = (36 * 492) / 63

Length of tree's shadow = 28224 / 63

Length of tree's shadow = 448 inches

Therefore, the length of the tree's shadow needs to be 448 inches, or to the nearest tenth of a foot, 37.3 feet.

Answer:

The area of the triangular sail is 20 square inches.

Step-by-step explanation:

We are given the following in the question:

Dimensions of triangular sail:

Base, b = 8 inches

Height, h = 5 inches

Area of triangular sail =

= Area of triangle

[tex]=\dfrac{1}{2}\times b\times h[/tex]

Putting values, we get,

[tex]A = \dfrac{1}{2}\times 8\times 5\\\\A = 20\text{ square inches}[/tex]

Thus, the area of the triangular sail is 20 square inches.