There are 225 pieces of cereal and 15 marshmallows in a bowl of cereal. What is the ratio of cereal pieces to marshmallow pieces?​

Check the picture below.

Answer:

-7/4

Step-by-step explanation:

The slope for line A is 4/7 and you find the perpendicular slope by finding the reciprocal so you would get 7/4 then you multiply that by -1. The end result would be -7/4.

Answer:

— 7/4

Step-by-step explanation:

1) Find the slope of line A:

m=∆y/∆x

=(4—0)/(0+7)

= 4/7

2) When a line is perpendicular to another we have: mm' = — 1

(m' stands for slope of second line)

In this case m' is: m' = — 7/4

Based on equations, Angus worked 6 hours on Saturday and 10 hours at his after-school job last week earning a total of $127.80.

The hourly rate at Angus' Saturday job = $8.80

The hourly rate at Angus' after-school job = $7.50

The total earnings last week = $127.80

Let the hours Angus worked at Saturday job = x

Let the hours Angus worked after-school = 4 + x

The total hours worked = x + x + 4

2x + 4

The total earnings last week 127.80 = 8.8x + 7.5x + 4 (7.5)

127.80 = 8.8x + 7.5x + 30

127.8 - 30 = 16.3x

x = 6 hours

x + 4 = 10 hours

2x + 4 = 16 (12 + 4)

Check:

Earnings at Saturday job = $52.80 ($8.80 x 6)

Earnings at after-school job = $75.00 ($7.50 x 10)

Total earnings = $127.80

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Answer:

x = 8

Step-by-step explanation:

Step 1: Write equation

5x - 11 = 3x + 5

Step 2: Solve for x

Subtract 3x on both sides: 2x - 11 = 5

Add 11 to both sides: 2x = 16

Divide both sides by 2: x = 8

Step 3: Check

Plug in x to verify it is a solution.

5(8) - 11 = 3(8) + 5

40 - 11 = 24 + 5

29 = 29

The depth of snow in the yard one hour after the snow depth was 9 inches, obtained using the linear function used for finding the snow depth, D = 1.4·t + 3 is; 10.4

A linear function is a function that produces a straight line graph when plotted.

The function that can be used to calculate the depth of the snow D in inches is; D = 1.4·t + 3

Where;

D = The snow depth in inches

t = The time duration (hours)

The present depth of the snow = 9 inches

The depth of the snow one hour from now can be found as follows;

The function for the depth of the snow; D = 1.4·t + 3 is a linear function

Therefore, the slope, which is the coefficient of the input variable, t, when the coefficient of the output variable, D, is 1

Therefore, the slope = 1.4

The slope is the rate of change of the output variable D when the input variable increases by one unit

The slope therefore, indicates that the depth of the snow in the yard, increases by 1,4 inches per hour

If the depth of the snow is presently 9 inches, the depth of the snow 1 hour later is therefore; D = 9 inches + 1.4 inches = 10.4 inches

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The significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality.

Quote means to cite something as a form of proof. It has several other senses as a verb and a noun. It should be noted that to quote something or someone is to repeat the exact words they said or to recite the exact words written in a book.

Great speakers often quote other inspiring people when making speeches. When you quote, you include the words and ideas of others in your text exactly as they have expressed them.

You signal this inclusion by placing quotation marks (“ ”) around the source author's words and providing an in-text citation after the quotation.

In this case, the significance of the quoted text is to illustrate the less privileged in an overwhelmingly crowded and disordered chronological reality. A quotation is the repetition of a sentence, phrase, or passage from speech or text that someone has said or written.

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The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:SSS

Step-by-step explanation:

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Qualitative with 2 possible outcomes of variable is required to construct a confidence interval for a population proportion.

The goal of qualitative research is to collect and analyze non-numerical (descriptive) data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality. In-depth interviews, focus groups, or observations are frequently used in this kind of study to gather the information that is rich in context and detail.

To investigate complicated phenomena or to learn more about people's viewpoints and experiences on a certain subject, qualitative research is frequently used. It is especially helpful for academics who wish to comprehend the meaning that individuals attribute to their experiences or who want to identify the fundamental causes of people's conduct. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches.

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Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

The solution is, given below.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

We assume that the question is interested in the probability that a randomly chosen class is a Friday class with a lab experiment (2/15). That is somewhat different from the probability that a lab experiment is conducted on a Friday (2/3).

Based on our assumption, we want to create a simulation that includes a 1/5 chance of the day being a Friday, along with a 2/3 chance that the class has a lab experiment on whatever day it is.

That simulation can consist of choosing 1 of 5 differently-colored marbles, and rolling a 6-sided die with 2/3 of the numbers being designated as representing a lab-experiment day. (The marble must be replaced and the marbles stirred for the next trial.) For our purpose, we can designate the yellow marble as "Friday", and numbers greater than 2 as "lab-experiment".

The simulation of 70 different choices of a random class is shown in the attachment.

Comment on the question

IMO, the use of 70 trials is coincidentally the same number as the first 70 days of school. The calendar is deterministic, so there will be exactly 14 Fridays in that period. If, in 70 draws, you get 16 yellow marbles, you cannot say, "the probability of a Friday is 16/70." You need to be very careful to properly state the question you're trying to answer.

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We need to determine the length per year, so take the ratio of 450/9 and simplify it.

r = 450cm/9yr
r = 50cm/1yr
r = 50cm

50cm/100cm = 1/2

So, the coastline recedes 1/2 meters every year.

Answer:0.50 meters

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

pythagorean theorm calculator

enter the values for each leg

Answer:

Let x be the number of children that attended.

Let y be the number of adults that attended.

x+y=2200

1.5x+4y=5050

Solving this system, our answer is:

x=1500

y=700

1500 kids attended and 700 adults attended.

Let me know if this helps!

Data:

When you have two variables directly proportional they follows the next:

If the variables are time (t) and speed (s):

Then, if you have:

t1=3

s1=16.5

t2=7

s2=?

Answer:

9 hours, 20 minutes

Step-by-step explanation:

When two ferries work together, they transport a day's cargo in 7 hours

The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1

The sum of the ratio = 4 (3 + 1)

This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.

Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.

9.33 hours = 9 hours, 20 minutes.

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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Answer:

216

Step-by-step explanation:

Plug in 1 to f(x). 2(1) + 4 = 6

Plug that answer in to h(x).

6^3 = 6*6*6 = 216

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

1 From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

2 The reason for the determination made in the previous step is A. From the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

The diagonals of a parallelogram bisect each other, but this is true for all parallelograms, regardless of whether they are squares, rectangles, or rhombuses.

Therefore, the given information is not sufficient to determine whether the parallelogram is a rhombus, a rectangle, or a square.

In conclusion, from the given information, no determination can be made as to whether the parallelogram is a rhombus, a rectangle, or a square.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answers:

1. -2y^3+9y-3y-16

2. 14x^3-23x^2+19x-24

Hi!

I'm really sorry but I'm not sure how to solve these equations however I have searched online and this is what it has said. I hope it is what you are looking for! I have attached screenshots of the working out above in order of each question. You may want to double check but the first two are for the first question and second two are for the second question.

Answer: 9x+4

Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.

Answer:

9x + 4

Step-by-step explanation:

9x + 2x - 6 - 2x + 10

Rearranging,

=> 9x + 2x - 2x + 10 - 6

=> 9x + 4

Answer:

x = 5

Step-by-step explanation:

First, we move all variables to one side of the equation. (Don't forget to change signs.)    

9x - 8x + x = 7 + 3

Then, we simplify

x + x = 10

2x = 10

10 divided by 2 is equal to 5.

Therefore, x = 5

Hope this helps!

The solution of the given equation  9x-3-8x=7-x for x will be 5.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

9x - 3 - 8x = 7 - x

x - 3 = 7 - x

x + x = 7 + 3

2x = 10

x = 5

Hence "The solution of the given equation  9x-3-8x=7-x for x will be 5.".

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The value of x after solving the equation 2log(x+86)=4 is: -9.83

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

A logarithmic function

⇒ 2log(x+86) = 4

⇒  log(x+86) = 4/2

⇒  log(8x + 86) = 2

Now making both the expressions a power of e  

⇒  e^log(8x + 86)  =  e²

⇒  8x + 86 = e²

⇒  8x  = e² - 86

⇒  x = (e² - 86)/8

the value of e is approximately 2.7

⇒ x = -9.83

Hence, the value of x is -9.83

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The quantity of red blood cell that is in the sample would be = 42 × 10⁵

Blood cells are those vascular cells that makes up the circulating blood of living organism which includes the white blood cells and the red blood cells.

The amount of white blood cells = a

The amount of red blood cells = 6 x 10² (a)

The amount of white blood cells in the sample = 7 × 10³

Therefore the amount of red blood cell in that sample =

6× 10² × 7 × 10³ = 42 × 10⁵

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