A long wire is wound to a circular coil of radius 1m and consists of 70 loops of wire around it

Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

What is meant by an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given,

The initial amount of caffeine in the beverage = 120 mg

The rate at which the caffeine decreases = 12% per hour w

We are asked to find the time taken for the caffeine amount to become 10mg.

Now let the initial amount be 100 per cent.

After one hour, the amount becomes (100-12)  = 88% of 120 = 0.88 * 120

So after every one hour, there is 88% caffeine left.

Now after two hours,

the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²

So after x hours, we can write the equation as:

Amount of caffeine left C(x) = 120(0.88)ˣ

Now for 10mg to be left, the time taken is:

10 = 120(0.88)ˣ

1/12 = (0.88)ˣ

log (1/12) = x log(0.88)

-1.079 = x (-0.056)

x = 19.27 hours

Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

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Dot plots are useful for visualizing the distribution of data and identifying patterns, trends, and outliers. They are often used in data analysis, quality control, and scientific research to help draw conclusions and make informed decisions based on data.

A dot plot is a graphical representation of statistics that presents character information factors through the use of dots. From a dot plot, possible decide several conclusions, depending on the data being displayed.

For instance, if the dot plot presents information on the height of a collection of people, you can still determine the range of heights inside the organization, the most common top, and any outliers (i.e., individuals with severe heights).

If the dot plot displays facts at the ratings of a collection of students on a test, you can still determine the range of rankings, the median score, and the distribution of rankings (i.e., whether or not the ratings are evenly distributed or clustered round sure values).

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The complete question is:

What conclusion can be determined by the dot plot? Explain in detail about the dot plot.

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Probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.

The probability of Harry, Jason, and Sarah getting admission to their desired schools is the probability that Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670. The scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.So, let's first standardize Harry's score:Z = (650 - 550) / 115 = 0.87Similarly, for Jason's score:Z = (630 - 550) / 115 = 0.70And for Sarah's score:Z = (670 - 550) / 115 = 1.04Now we need to find the probabilities of getting each of these Z-values. We can do that using the standard normal distribution table. The table gives the probability that a standard normal random variable is less than or equal to a certain Z-value.To find the probability that Harry's score is above 650, we need to find the probability that Z > 0.87. This can be found by subtracting the probability of Z ≤ 0.87 from 1:P(Z > 0.87) = 1 - P(Z ≤ 0.87) = 1 - 0.8078 = 0.1922Similarly, the probability that Jason's score is above 630 is:P(Z > 0.70) = 1 - P(Z ≤ 0.70) = 1 - 0.7580 = 0.2420And the probability that Sarah's score is above 670 is:P(Z > 1.04) = 1 - P(Z ≤ 1.04) = 1 - 0.8508 = 0.1492The probability that all three events occur (Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670) is the product of their probabilities:P(Harry, Jason, and Sarah) = P(Z > 0.87) × P(Z > 0.70) × P(Z > 1.04) = 0.1922 × 0.2420 × 0.1492 = 0.0088Therefore, the probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.

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The values of the variables are x = 2, z = 6.92, x = 10.5 and y = 12.6

Figure 12

In this figure, we make use of the following theorem of intersecting secants

AB * AC = AD * AE

By substitution, we have

(x + 4) * (x + 4 + x - 2) = 4 * 9

Evaluate the sum

(x + 4) * (2x + 2) = 36

So, we have

(x + 4) * (x + 1) = 18

Expand

x^2 + 5x + 4 = 18

Evaluate the like terms

x^2 + 5x - 14 = 0

Factorize

(x + 7)(x - 2) = 0

Solve for x

x = -7 or x = 2

x cannot be negative

So, we have

x = 2

Figure 13

In this figure, we make use of the following theorem of intersecting secant-tangent

XU * WU = UV^2

So, we have

8 * 6 = z^2

Evaluate

z^2 = 48

Take the square root

z = 6.92

Figure 14

Using the same theorem used in (13), we have

2 * (2 + x) = 5^2

So, we have

4 + 2x = 25

Evaluate

2x = 21

Divide

x = 10.5

Figure 15

Using the same theorem used above

y^2 = 8 * 20

So, we have

y^2 = 160

Take the square root

y = 12.6

Hence, the value of y is 12.6

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The volume of Sphere A is V(A) = (4/3)πr³ and the volume of Sphere B is V(B) = 125(4/3)πr³. So the volume of Sphere B is 125/1 = 125 times larger than that of Sphere A.

what is sphere?

A sphere is a three-dimensional geometric shape that is perfectly round, like a ball. It is defined as the set of all points in space that are equidistant from a given point, called the center of the sphere.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Let the radius of Sphere A be denoted by "r", then the radius of Sphere B is 5r.

The volume of Sphere A is V(A) = (4/3)πr³.

The volume of Sphere B is V(B) = (4/3)π(5r)³ = (4/3)π125r³ = 5³(4/3)πr³ = 125(4/3)πr³.

Therefore, the volume of Sphere B is 125/1 = 125 times larger than that of Sphere A.

So, the volume of Sphere B is 125 times larger than that of Sphere A.

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The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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probability-=0.3419

The probability that the number of defective bulbs in a sample of 550 light bulbs is greater than 15 is 0.3419. To calculate this probability, you need to use the binomial probability formula: P(x) = nCx * p^x * q^(n-x), where n is the sample size (550), p is the probability of a defective bulb (0.035), x is the number of defective bulbs you want to calculate (15) and q is the probability of a non-defective bulb (1-0.035). Plugging in the values, we get P(x) = 550C15 * 0.035^15 * 0.965^(550-15) = 0.3419

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If a bag contains 3 red, 4 green, and 5 white marbles, then the probability that a green marble will be selected in the first attempt is equal to 4/12 or 1/3.

Probability is defined as the likeliness of an event to happen. It simply means possibility of any event to occur or the possibility of an event to not occur. The sum of the possibilities in any event is always equal to one. In the given case, there are 3 red, 4 green, and 5 white marbles.

Now total number of marbles is equal to 3+4+5 = 12 marbles

Probability that the green marble is picked first = 4/12 = 1/3

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Answer:

M<E = 63

M<F = 63

M<G = 117

Step-by-step explanation:

M<F:

= 180-117

=63

M<E:

=180-117

=63

M<G:

=180-63

=117

Answer:

D. 1/4

Step-by-step explanation:

The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.

1/2 x 1/2 = 1/4

Answer: Here we will learn how to find the probability of tossing two coins.

Let us take the experiment of tossing two coins simultaneously:

When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of outcome are 22 = 4

The above explanation will help us to solve the problems on finding the probability of tossing two coins.

Step-by-step explanation:

THE ANSWER MUST BE AT LEAST 1/4 OR 1/8

IF THAT IS WRONG LET ME KNOW!

AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!

Answer:

x + y = 110

Step-by-step explanation:

[tex]x=\sqrt{(65^{2} - 56^{2} } \\x=33\\\\\\y=\sqrt{(85^2-36^2} \\y=77\\\\x+y=33+77\\x+y=110[/tex]

The missing coefficients in the equation y = mx + b are m = 0.841 and b = 18.813. The final equation that fits the given data is y = 0.841x + 18.813

To find the missing coefficients in the equation y = mx + b, we need to use the given data in the table to determine the values of m and b.

We can start by using two of the data points to set up a system of equations:

Using (5, 23.018) and (6, 23.859):

m(5) + b = 23.018

m(6) + b = 23.859

Subtracting the first equation from the second equation gives:

m(6) - m(5) = 0.841

Simplifying this expression:

m = 0.841 / (6 - 5) = 0.841

Now we can substitute the value of m into one of the original equations to solve for b:

m(5) + b = 23.018

0.841(5) + b = 23.018

b = 23.018 - 4.205

b = 18.813

Therefore, the missing coefficients are:

m = 0.841

b = 18.813

The equation y = 0.841x + 18.813 fits the given data.

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The given question is incomplete, the complete question is:

Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y 5 23.018 5.5 23.438 6 23.859 6.5 24.035 7 25.449 7.5 24.868 8 26.058 I Enter an integer or decimal number [more..] y = I+

Answer:

the velocity of the man is 5 m/s.

Step-by-step explanation:

The kinetic energy of a moving object is given by the equation:

K.E. = 0.5 * m * v^2

where

K.E. is the kinetic energy

m is the mass of the object

v is the velocity of the object

In this problem, we are given that the man has a mass of 60 kg and a kinetic energy of 750 J.

So,

750 J = 0.5 * 60 kg * v^2

Solving for v:

v^2 = (2 * 750 J) / 60 kg

v^2 = 25 J/kg

v = sqrt(25 J/kg)

v = 5 m/s

Therefore, the velocity of the man is 5 m/s.

Option 1 is correct, The point will be on 10 for the cost $240.

=> 0—————————-10—————————-20

By multiplying the data οbtained with such a nanοsectiοn variable whilst alsο twο that used the unitary methοd , the jοb can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set οr the cοlοur space οf bοth prοductiοn runs is skipped. A varying fee οf Inr ($1.01) might have been necessary fοr fοrty pens.

Here,

Greg wants tο cοllect enοugh cash tο spend $210 οn a new bicycle. He needs tο make an extra $150 because he already has $60. He needs tο mοw the fοllοwing lawns in οrder tο make his $15 per lawn:

=> 150 ÷ 15 = 10 acres

Greg must mοw at least 10 yards in οrder tο accοmplish his οbjective. The number line shοwing hοw many fields he can mοw is as fοllοws:

=> 0—————————-10—————————-20

The number οf lawns he can mοw tο reach his οbjective is represented by any value οn this number line larger than οr equal tο 10. He will, fοr instance, be cοmpensated:

=> 12 × $15 = $180

He already has $60, sο after adding this, he will have:

=> $60 + $180 = $240

which will cοver the cοst οf the new mοtοrbike.

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To solve the equation, factor [tex]\bold{x^2+2x-35}[/tex] use the formula [tex]\bold{x^2 +(a + b) x + ab = (x + a)(x + b)}[/tex]. To find a and b, set up a system to be solved.

[tex]a + b = 2[/tex]

[tex]ab = -35[/tex]

Since ab is negative, a and b have opposite signs. Since [tex]a+b[/tex] is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression [tex](x + a)(x + b)[/tex] with the values obtained.

To find solutions to equations, solve [tex]x-5=0[/tex] and [tex]x+7=0[/tex].

The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".

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As a result, the answer to the following question, As a result, the supplied radius arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).

In more modern use, the length of a sphere or sphere is equal to its radius in standard geometric, so it has several line segments from its centre to its circumference. The phrase is derived from the Latin word for radius, which also referred to the spokes of a waggon wheel. The radius of a circle is the distance between the centre and any point on its periphery. Often, "R" or "r" is used to signify it. A radius is a boundary line with one terminus in the centre and a second around the perimeter of a circle. Vide letter diameter equals radius The dimension of a circle is the segment that passes its centre and has extremities that are on the circle.

The formula for calculating the arc length of a circle is:

Arc length = radius x central angle in radians,

In order to use this formula, we must first convert the centre angle from degrees to radians. We are aware of the following:

2 radians Equals 360 degrees

360 degrees divided by 2 radians equals x degrees divided by y radians

(x degrees * 2 radians) / 360 degrees = y

y = (22 deg * 2 radians) / 360 deg = 0.38397 deg (rounded to five decimal places)

arc length Equals radius multiplied by Centre angle in radians

With r = 18 inches and = 0.38397 radians, we get:

arc length = 18 inches multiplied by 0.38397 equals 6.9115 inches (rounded to four decimal places)

As a result, the supplied arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).

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The scenariο that wοuld mοst likely be biased against nοn-vοters is a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences

A cοgnitive bias clοuds οur critical thinking and may result in the spread οf false infοrmatiοn that may be harmful tο οther peοple. Biases cause us tο avοid infοrmatiοn that might be uncοmfοrtable οr unwelcοme rather than lοοking intο the infοrmatiοn that might help us reach a mοre accurate cοnclusiοn.

A cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences is nοt a biased sample. Since the nοn-vοters are nοt

A vοlunteer sample cοllected at a pοlitical rally was used tο determine candidate preferences. It prefers a particular member. This is a biased survey.

A simple randοm sample οf all nοn-vοters was used tο determine why they dοn’t vοte. It is biased. Because a grοup οf peοple decides nοt tο give a vοte.

A simple randοm sample οf all eligible vοters, sοme οf whοm didn’t have time tο vοte. It is a sample.

A vοlunteer sample was cοllected at a large department stοre tο determine whο they vοted fοr. It is a nοn-biased survery. The peοple dο nοt prefer a particular team.

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If Miller is going to install baseboard around the perimeter of her room's rectangular floor, s.  it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.

To find out how much it will cost Miller to purchase baseboard for her room, we can use the CER (Conversion, Equation, and Re-substitution) strategy.

Conversion:

We can calculate the perimeter of the room by adding the lengths of all four sides:

Perimeter = 2(Length + Width) - 2(Doorway Width)

Perimeter = 2(15 + 20) - 2(3)

Perimeter = 64 feet

So, Miller will need 64 feet of baseboard.

Equation:

To calculate the cost of the baseboard, we can use the formula:

Cost = Length * Cost per linear foot

In this case, the length is 64 feet and the cost per linear foot is $0.30.

Cost = 64 * 0.30

Cost = $19.20

Therefore the final answer is that it will cost Miller $19.20 to purchase baseboard for her room, assuming an average cost of $0.30 per linear foot requiring baseboard.

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Answer:

x = 11/6 or 1 5/6 or 1.83333...

Step-by-step explanation:

The solution to the equation 5x^2 = 30x – 45 is x = 3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the Equation: 5x² = 30x - 45.

We can start by simplifying the equation by subtracting 30x and adding 45 from both sides to get:

5x² - 30x + 45 = 0

We can further simplify by dividing both sides by 5 to get:

x² - 6x + 9 = 0

This can be factored as (x - 3)(x - 3) = 0, which means that the only solution is x = 3.

Therefore, the solution to the equation 5x^2 = 30x – 45 is x = 3.

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Answer:

hey, good afternoon!

Step-by-step explanation:

here is an example: the cost of a pizza is 7.50 and you can add a topping for 0.65 cents. find the cost of the pizza with 6 toppings

y=mx+b

the x stands for the toppings and y is the cost. the rate is 0.65 cents and the orginal amount of money is b. so the equation would look like this:

y= .65x+7.50. x=6

y = 65(6)+7.50

    =3.9+ 7.50= $11.50(answer)

the m is the rate of change in this question is 0.65 cents

b is initial/ fixed/ value once again in this qeustion it 7.50$  

hope this helps. have a great day!

Emely gοt 35% οf her math hοmewοrk questiοns wrοng.

A percentage that represents a tenth οf a quantity. One percent, denοted by the symbοl 1%, is equal tο οne-hundredth οf sοmething; hence, 100 percent denοtes the full thing, and 200 percent designates twice the amοunt specified. A pοrtiοn per hundred is what the percentage denοtes. The percentage refers tο οne in a hundred. The % sign is used tο denοte it.

Emely gοt 13 questiοns cοrrect fοr every 7 questiοns she gοt wrοng.

We can start by finding the fractiοn οf questiοns Emely gοt wrοng, which is 7/(7+13) = 7/20. Tο cοnvert this tο a percentage, we can multiply by 100 tο get 35%.

Therefore, Emely got 35% of her math homework questions wrong.

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Answer:

Step-by-step explanation:

its b

The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x

The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.

Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:

Total cost = (daily charge) x (number of days rented) + rental fee

Total cost = $20x + $40

This linear equation can be rearranged to the form:

Y = 40 + 20x

Therefore, the correct option is (B) Y = 40 + 20x

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The slope of the line that passes through the pair of points (7/20,5/19) and (5/9,11/16) is 3/5.

To find the slope of a line passing through two points, we need to use the slope formula. The slope formula is m = (y2 - y1) / (x2 - x1). To calculate the slope, we need to first calculate the x and y values of the two points, (7/20,5/19) and (5/9,11/16). The x values are 7/20 and 5/9 and the y values are 5/19 and 11/16. We can then plug these values into the slope formula to get the slope. The slope is (11/16 - 5/19) / (5/9 - 7/20) = 3/5. Therefore, the slope of the line that passes through the two points (7/20,5/19) and (5/9,11/16) is 3/5.

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Answer:

[tex]4\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

1\2

Step-by-step explanation:

Answer:

$150

Step-by-step explanation:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.

In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).

First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.

Using the formula:

Interest = Principal x Rate x Time

Interest = $1,000 x 0.10 x 1.5

Interest = $150

So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.

Answer:

The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.

In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).

I = Prt

I = $1,000 * 0.10 * 1.5

I = $150

Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.