A set of data items is normally distributed with a mean of 500 and a standard deviation of 30. Find the data item in this distribution that corresponds to we givenz-score
z= -7
The data item that corresponds to z= -7 is (Type an integer or a decimal.)

Answers

Answer 1

The data item in this distribution corresponding to a z-score of -7 will be 290.

What is Z-score?

The standard score in statistics is the number of standard deviations that a raw score's value is above or below the mean value of what is being observed or measured. Raw scores that are higher than the mean have positive standard scores, whereas those that are lower than the mean have negative standard scores. The Z-score measures how much a particular value deviates from the standard deviation. The Z-score, also known as the standard score, is the number of standard deviations above or below the mean for a given data point. The standard deviation reflects the level of variability within a particular data collection.

Here,

z=(X-μ)/σ

-7=(X-500)/30

-210=X-500

X=290

The data item in this distribution that corresponds to we given z-score

z equals to -7 will be 290.

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Related Questions

if a point is characterized as having both a nonzero x and y coordinate and oppositely signed coordinates, then the point must be in which of the labeled quadrants in the standard xy coordinate plane?

Answers

The labeled quadrants in the standard xy coordinate plane is Quadrant II

What is Quadrants?

The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.

Concept:

The x and y coordinates are both positive in quadrant I. In quadrant II, the x and y coordinates are oppositely positive. The x and y coordinates are both negative in quadrant III. The x-coordinate is positive and the y-coordinate is negative in quadrant IV.

The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).

The point is in the first quadrant if both x and y are positive. If both x and y are negative, the point will be in the second quadrant. In the third quadrant if both x and y are negatives, the point is located.

The labeled quadrants in the standard xy coordinate plane is Quadrant II

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Zehra owns a bakery and is getting ready for the Thanksgiving rush. She needs to stock up on pumpkin pie filler to be able to meet demand, so she begins buying a constant number of cans of pumpkin pie filler per week. After 5 weeks, she has 29 cans. After 9 weeks, she has 57 cans. How many cans is she buying per week?

Answers

Based on the rate of change, Zehra is buying 7 cans per week.

What is the rate of change?

The rate of change gives the ratio between the change in one quantity to the change in another quantity.

Linear relationships have a constant rate of change and the rate of change is usually represented as the slope or gradient.

For instance, the number of cans changed from 29 to 57, a difference of 28, as the number of weeks changed from 5 to 9, a difference of 4.

The rate of change can be expressed as 28/4 or 7.

The number of cans after 5 weeks = 29

The number of cans after 9 weeks = 57

The change in weeks = 4 (9 - 5)

The change in the number of cans = 28 (57 - 29)

The rate of change = 7 (28/4)

Thus, we can conclude that Zehra buys 7 cans weekly.

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Frank gets a Lamborghini for Christmas from Bill Nye for $225,000. Frank crashes the Lamborghini and survives. But his car is damaged. His repairs will cost 55% of the original price, but 30% of the price is covered by insurance. How much money does Frank owe?

Answers

Answer: Frank has to pay 56,250 dollars

Step-by-step explanation:  If Frank's repair costs 55% of the original price, that means he'll have to pay 123,750 dollars because 55% of 225,000 is 123,750. But he doesn't have to pay that amount because the car insurance is paying 30% of 225,000 which is 67,500 dollars. So the car insurance is paying 67,500 dollars out of the 123,750 dollars in damage. So you'll have the subtract 123,750 by 67,500 which is 56,250 dollars.

A line passes through the point (6,-1) and is perpendicular to the line with the equation -2x + 3y = -6.

Answers

Answer: A

Step-by-step explanation:

Before we find the equation of the perpendicular line, we have to find the slope of the original line.

The slope-intercept form of the equation is y=mx+b, so let's change that.

[tex]-2x+3y=-6[/tex]            [add both sides by 2x]

[tex]3y=2x-6[/tex]                  [divide both sides by 3]

[tex]y=\frac{2}{3} x-2[/tex]

This gives slope as [tex]\frac{2}{3}[/tex].

There are 2 things for us to do to find the slope of a perpendicular line.

1. reciprocal

2. change sign

Let's apply those rules.

1. [tex]\frac{3}{2}[/tex]

2. [tex]-\frac{3}{2}[/tex]

Now, we can find the perpendicular lines by plugging in our new point.

[tex]y=-\frac{3}{2} x+b[/tex]          [plug in x and y]

[tex]-1=-\frac{3}{2}(6)+b[/tex]     [multiply]

[tex]-1=-9+b[/tex]          [add both sides by 9]

[tex]b=8[/tex]

Now we can plug in for our slope-intercept equation.

[tex]y=-\frac{3}{2} x+8[/tex]

Since answers are in standard form, we have to manipulate it.

[tex]y=-\frac{3}{2} x+8[/tex]        [add both sides by [tex]\frac{3}{2} x[/tex]]

[tex]\frac{3}{2}x+y=8[/tex]            [multiply both sides by 2]

[tex]3x+2y=16[/tex]

Therefore, our final answer is A.

1. Which of the following is equivalent to 5a³ + 4a³??
O (5+4) a³+3
O (5+4) a³
(5.4) a³+3
O (5.4) a³
ہے

Answers

The equivalent to 5a³ + 4a³ is (5+4) a³, according to the question.

What do you mean by Equivalent ?

Equivalent refers to the mathematical notion that distinct terms and expressions having a similar value are treated equally.

According to the given question,

We have the given options are:

O (5+4) a³+3

O (5+4) a³

O (5.4) a³+3

O (5.4) a³

Now, we will find the equivalent,

5a³ + 4a³

Then, we will taking common factor from the given equation:

5a³ + 4a³

= a³(5+4)

So that is same as (5+4)a³.

Therefore, the equivalent to 5a³ + 4a³ is (5+4) a³.

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What does y equal, in this picture with 30 60 90 triangles?

Answers

The value of y= 5.49≈ 5.5cm

What is 30-60-90 traingle?

The 30-60-90 triangle is cut straight through the middle along its altitude, like one half of an equilateral triangle. Its name is derived from its three angles of 30 degrees, 60 degrees, and 90 degrees. Any triangle with angles of 30-60-90 will look like this: The hypotenuse is always twice as long as the shortest leg, and the length of the long leg can be calculated by multiplying the short leg by the square root of three. The shortest leg is across from the 30-degree angle.

By 30-60-90 triangle rule,

Side across 60° angle = x

Hypotenuse side = 2x= 15

Side across 30° angle = x√3

By solving,

2x= 15

x= 7.5cm

So side across 60° angle= 7.5 cm

Side across 30° angle = 7.5×√3

                                     = 7.5× 1.732= 12.99≈ 13cm

As the figure given us square so,

13= 7.5+y

y= 13-7.5

y= 5.5 cm

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If you roll a fair die, what is the probability you will roll a 5 or a number less than 3?

Answers

Answer:

1/2

Step-by-step explanation:

Since 5 is one of the six possible numbers available, rolling a 5 is a 1/6 probability.

Since rolling a number less than 3 means rolling a 1 or 2, rolling a 1 or 2 is a 2/6 probability.

Add those probabilities up since you can get either of those outcomes and you get 1/6+2/6=3/6

3/6=1/2

a restaurant is introducing a new gluten-free recipe for the topping in its baked zucchini recipe. the chef will continue to use this topping if less than 8% of her customers complain about the new taste. using a random sample of customers, she conducts a hypothesis test with h0: the complaint rate is 8%, and ha: the complaint rate is less than 8%. what is a type i error and its consequence in this context?

Answers

By hypothesis testing, The chef believes the complaint rate is less than 8%, when in fact it is not less than 8%. The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

What does testing your hypotheses mean?

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample.

               First, a hazy assumption about the parameter or distribution is made.

What is hypothesis testing, and how can it be used?

A statistician will test a hypothesis about a population parameter in a process known as hypothesis testing. The type of data used in the study and its purpose will determine the methodology the analyst uses.

                     The plausibility of a hypothesis is evaluated using sample data in a process known as hypothesis testing.

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If 1.5 liters of washing up liquid is 2.70$ find the cost of 1 liter

Answers

The cost of one liter of washing up liquid would be = $1.8

What is liters?

Liters is a variable that is can be used to denote the measurement of a liquid.

The quantity of the washing up liquid that was given= 1.5 liters.

The cost of 1.5 liters of washing up liquid =$2.70

If 1.5 L = 2.70

1 L = X

Make X the subject of formula;

X = 1× 2.70/1.5

X = $1.8

Therefore, the cost of one liter of washing up liquid would be = $1.8

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an irs auditor randomly selects 3 tax returns from59returns of which7contain errors. what is the probabilitythat she selects none of those containing errors?

Answers

Therefore , the probability that she selects none of those containing errors is 0.6798.

What does probability really mean?

Calculating how likely or "possible" it is for an event to occur is the subject of probability. Words like "definitely," "impossible," or "likely" may be used to communicate the likelihood that a particular event will occur. Mathematics always expresses probabilities as fractions, decimals, or percentages, with values ranging from 0 to 1.

Here,

Number of ways of selecting 3 returns out of 59 is C(59,3).

Out of 59 returns, 59-7 = 52 returns has no error so number of ways of selecting 3 returns out fo 52 is C(52,3).

The probability that she selects none of those containing errors is

P( No errors )=[tex]\frac{C(52,3)}{C(59,3)}[/tex]=0.6798

Therefore , the probability that she selects none of those containing errors is 0.6798.

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If a plane can travel 480 miles per hour with the wind and 380 miles per hours against the wind, find the speed of the wind and the speed of the plane in still air

Answers

Answer:

Step-by-step explanation:

I am not super sure about this one

the speed of the wind would be 50 mph and the speed of the plane in still air would be 430 mph

Ryanne is 14. Her brother's age is three more than half her age. How old is her brother?
OA 7
OB. 8.5
OC. 10
OD. 31
Question

Answers

Answer:

10 years old

Step-by-step explanation:

fast as you can. point slope form. algebra 1)

Answers

Answer: Y=mx+b

Step-by-step explanation:

Graph Y= -1/4 x + 6.

Answers

The x-intercept and y-intercept of the line will be at (24, 0) and (0, 6). And the line is drawn below.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The linear equation is given below.

y = -(1/4)x + 6

Convert the equation into intercept form, then we have

y = -(1/4)x + 6

4y = - x + 24

x + 4y = 24

x / 24 + y / 6 = 1

The x-catch and y-capture of the line will be at (24, 0) and (0, 6) and the line is drawn underneath.

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Inequality
x + y > 11
.05x + .10y < .95

Answers

the inequality model will be x+2y<19

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

x + y > 11

.05x + .10y < .95

by multiplying 20 in inequality we get x+2y<19

Hence, the inequality model will be x+2y<19

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Michael is building a skateboard
ramp. The ramp needs to include a
right angle to be safe. If the side
lengths are 10 feet, 2.5 feet, and 10.5
feet, will the ramp be safe? Prove
your answer with an inequality.

Answers

In order for a ramp to be safe, the longest side length must be less than or equal to the sum of the other two side lengths. In this case, the longest side length is 10 feet, and the sum of the other two side lengths is 10.5 feet + 2.5 feet = 13 feet. Therefore, the ramp will not be safe because 10 > 13.

To prove this using an inequality, we can represent the side lengths using the variables x, y, and z, where x is the longest side length, y is one of the shorter side lengths, and z is the other shorter side length. We can then write the inequality as follows:

x ≤ y + z

In this case, we have:

x = 10 feet
y = 2.5 feet
z = 10.5 feet

Substituting these values into the inequality, we get:

10 ≤ 2.5 + 10.5

which simplifies to:

10 ≤ 13

Since 10 is not less than or equal to 13, the inequality is not true, and the ramp will not be safe.

Given that the side lengths of the ramp are 10 feet, 2.5 feet, and 10.5 feet.

We know that for making a right angle A Pythagoras triplet must follow

So, a² + b² = c²

Where a, b, c are the lengths of the triangle and a, b <=c

So, on applying the above formula

We have,

2.5² + 10² = 10.5²

6.25 + 100 = 110.25

But 106.25 is not equal to 110.25

So all these sides are not good for making the ramp safe.

There are three types of the triangle based on angle -

1. Acute angled triangle

2. Right-angled triangle

3. Obtuse angled triangle

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the table shows the number of stickers three friends have, Hannah has fewer stickers than Marco but more stickers than Addison. how many stickers could Hannah have?

Answers

Easy 551 or c is your answer :) good luck

2. The basic advertising package has a value of $1,000
and the premium package has a value of $2,500. The
goal of the agency is to sell more than $60,000 worth
of small-business advertising packages.
If you know that exactly 10 premium packages were
sold, what can you say about the number of basic
packages the agency needs to sell to meet its goal?

Answers

1000b + 2500p = 60,000

1000b + 2500(10) = 60,000

1000b + 25000 = 60,000

1000b = 35,000

b = 35

they need to sell 35 basic packages to reach their goal of 60,000 dollars

Please help! Division of Polynomials, Find the quotient and remainder.

Answers

First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

A) Q''(−5, 6), R''(−2, 1), S''(1, 5)

B) Q''(7, 11), R''(10, 16), S''(13, 12)

C) Q''(−5, 2), R''(−2, 7), S''(1, 3)

D) Q''(13, 2), R''(10, 7), S''(7, 3)​

Answers

The correct answer is C.

(URGENT!!) In the diagram, △FEL∼△JOS. Which ratios are equivalent to tanF? Select all that apply.

Responses
EF/EL
EL/EF
EL/FL
FL/EF
OJ/OS
OJ/JS
OS/OJ
OS/SJ

Answers

The equivalent ratios to tan F = EL/ EF = OS/OJ

Similar triangles:

Similar triangles are those with the same shape but different sizes. Similar triangles include all equilateral triangles and squares with any side length.

All related pairs of angles will be equal and corresponding sides of similar triangles will have the same ratio. The symbol '∼' is used to represent the similarity.

Given that

△FEL∼△JOS

That means △FEL and △JOS are similar triangles

As we know tan θ = Opposite side / Adjacent side

From the triangle △FEL,

=> tan F = EL/EF      

By the given information,

The similar triangle's corresponding sides will have the same ratio  

=> EL/ EF = OS/OJ

Therefore

The equivalent ratios to tan F = EL/ EF = OS/OJ

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Juan borrowed $2000 for 1 year and
paid 15% interest. How much
interest did he pay in a year?

Answers

Answer:At the rate of 15% the amount of interest on $2000

Step-by-step explanation:

simple amount= Principle(1+rt)

where r= rate of inetrest

t= time

principal is initial amount

therefore, amount=2000(1+15*1)

Amount = $2,300.00

Interest = Amount - Principal = $300.00

Answer:

Step-by-step explanation:

Interest = Principle * Rate * Time /100

Principle =  $2000

Rate = 15 %

Time =  1 year

I = 2000 * 15 * 1/100

I = 300

Juan has to pay $300 in a year

Identify the rate of decay r (as a percent) of the exponential function f(x) = 0.3(0.82)^x

a. r = 30%
b. r = 18%
c. r = 70%
d. r = 82%

Answers

Answer:

b. r = 18%

Step-by-step explanation:

0.3(0.82)^x:

0.3(0.82)^x:

The 0.82 is getting affected since it is raised to the power of x

Hence, for every iteration of x, the object is becoming 82% of itself.

100%-82%=18%

r = 18% ==> b

Option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

What is a function?

A relation is a function if it has only One y-value for each x-value.

The exponential function f(x) = 0.3(0.82)^x can be written in the form f(x) = a(b)ˣ, where a = 0.3 and b = 0.82.

In an exponential function of the form f(x) = a(b)ˣ

the base b represents the rate of change.

If b is between 0 and 1, then the function represents exponential decay. The rate of decay r can be found using the formula:

r = (1 - b) x 100%

In this case, b = 0.82, so the rate of decay is:

r = (1 - 0.82) x 100%

= 0.18 x 100%

= 18%

Hence, option B is correct, 18% is the  rate of decay of the exponential function f(x) = 0.3(0.82)ˣ

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Enter the measurement of the vehicle part.

Answers

Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

How can we use the formula M= 58h + 135 to determine the mile marker that Sam passed at hour 6

Answers

Sam passed the marker of 483 miles, in 6 hours.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given as M = 58h + 135. shows how many miles the same has traveled for h hours,
To evaluate the mile marker that sam passed at 6 hours, substitute the value with h in a given expression.
M = 58×6 +135

Simplifying the above expression gives the mile marker
M = 483 miles

Thus, the required miles are 483.

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y= 1/2x + 1
y=-x + 7

Answers

Answer: point form: (4,3) equation form: x=4 y=3

Step-by-step explanation:

Answer: point form: (4,3) equation form: x=4y=3

Miguel’s Skate Shop is having a sale on skateboards. The original price for its Extreme Skateboard is $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard?

Answers

The required percent decrease in the price of the skateboard is 40%.

What is the percentage?

A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Here, we have

Original price = $84.50

sale price = $50.70

Percent decrease = 84.50-50.70/84.50 × 100 = 40%

Hence, the required percent decrease in the price of the skateboard is 40%.

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If f(x) = 3x-1 and g(x) = x^2+2, what is (f ° g)(x)?

Answers

Answer:

(f ○ g)(x) = 3x² + 5

Step-by-step explanation:

substitute x = g(x) into f(x) , that is

(f ○ g)(x)

= f(g(x))

= f(x² + 2)

= 3(x² + 2) - 1

= 3x² + 6 - 1

= 3x² + 5

what is the z-score of a value 20 from a binomial distribution with 50 trials and probability 0.76 of success? round your answer to three decimal places. incorrect answer:

Answers

z-score of a value is  -5.96

What is z-score in binomial distribution?

The Z score represents the number of standard deviations above or below the mean. The Z score of the mean is 0 by definition.

What is Probability?

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

Given,

A random variable, let's call it X, has parameters that fit the Binomial distribution: n (number of trials) = 50 and p (success probability) 0.76.

We must ascertain the z-score (Z) of the value 20 =  that this random variable X has chosen.

Now, for a random variable, say X, its z-score (Z) is defined as ,

Z = (X - mean of X)/ Standard deviation of X

A binomial random variable with the parameters once more n and p, its mean is given as np and its standard deviation is given as [tex]\sqrt{n*p*(1-p)}[/tex]

The standard deviation of X is provided as [tex]\sqrt{50*0.76*0.24}[/tex] = [tex]\sqrt{9.12}[/tex] = 3.0199933  while the mean of X is given as 50*0.76 = 38.

Therefore, the required z-score (Z) for X = 20, is given as,

Z = 20-38/3.0199933

Z= -5.9602781238

Z= -5.96 that is the necessary z-score.

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Write and equation of the line in slope-intercept form. (0,-2) (1,3)

Answers

Answer:

y=5x−2

I hope this helps!

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B. it is effective because she uses reasoning to draw a specific conclusion from general observations.C. it is not effective because she leaves important questions unanswered.D. it is not effective because she uses a false analogy to describe the connection between clothes and work two stores sell identical sandwich rolls in different size packages, store A sells a six pack for $5.28 store B sells a four pack for $3.40, which store offers the better per-roll price A random sample of 100 people was taken. eighty-five of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 80%. the test statistic is? early inspections can . question 42 options: increase any further costs being spent on units that are already spoiled prevent any further conversion costs being wasted on units that are already good prevent any further costs being wasted on units that are already spoiled increase conversion costs on units that are already spoiled elizabeth blackwell group of answer choices was england's first female member of parliament. became the first formally educated female doctor in america. was england's first great feminist leader. became renowned as a painter specializing in realist art. was one of england's first female publishers and book-dealers. a prekindergarten teacher wants to plan instructional activities to help students understand the concept of rhyme. which of the following should the teacher plan first? Which two countries are economically interdependent? Butchart Gardens is a very large garden in Victoria, British Columbia, renowned for its beautiful plants. It is so large that it could hold many times more visitors than currently visit it. The garden charges an admission fee of approximately $30. At this price, 1,000 people visit the garden each day.Are visits to Butchart Gardens excludable or nonexcludable? Are they rival in consumption or nonrival? What type of good is it?What do you think would happen to the number of visitors if the admission fee were reduced to $15? In your opinion, what is the socially optimal admission fee? Justify your answer.Defend your views by citing information from the book, the Web and/or your own experiences. First, post your response on the discussion board, and then read and reply to the posts of at least two other students, citing those views with which you agree or disagree as well as your reasons for agreeing or disagreeing Two frequency generators are creating sounds of frequencies 460 and 471 Hz simultaneously. Randomized Variables f1 = 460 Hz f2 = 471 Hz Part (a) What average frequency will you hear in Hz? On a team,8 girls and 5 boys devoted a total of 87 points. The difference between the number of points scored by the 8 girls and the number of points scored by the 5 boys is 57. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and boy The owner of Paradise Pets works hard to keep her store clean. It takes her 15 minutes toclean 2 hamster cages.Complete the table.Minutes15Cages cleaned 2 4Graph the data from the table.Cages cleaned201816141210830 55908 10 2. nutritional assessment should be done a. annually. b. on sick pets. c. if a pet is overweight. d. at every visit on every pet. Victor put a match on a balance and found that its mass was 6.0 grams. Then he lit the match and put it out after a few seconds.He put the partially burned match on the balance again. This time, its mass was 4.5 grams.Which of the following best explains what happened as the match burned? A. Some of the matter changed from solid to gas and went into the air. B. The matter moved to a different part of the match. C. Some of the mass was destroyed by the fire. D. The mass of the match combined with the mass of the fire.