Suppose the amount of a radioactive element remaining in a sample of 100
milligrams after x years can be described by A(x) = 1002-0.01121x. How much is remaining after
172 years? Round the answer to the nearest hundredth of a milligram.
687.66 mg
0.15 mg
14.54 mg
192.81 mg

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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1 st picture,

Other names of <1 are - <F, <YFP, <PFY

2 nd picture,

Acute

3 rd picture,

Point E

Answer:

1. ∠F, ∠YFP, ∠PFY

2. Acute

3. Point E

Step-by-step explanation:

Answer:

x is 5 and y is 6

Step-by-step explanation

we find 2/3 factors that equal 10. 2 and 3. the only other number that can be added that equals 10 is 5. i apply the same logic to y

Answer:

Y -- 6

X -- 5

Step-by-step explanation:

we first find y by finding the side that is the longest that is parallel to y (16) we also find that two sets of fives are also parallel to y and 16 as seen in the first screenshot. Then to find the missing value we will subtract the 5 two times from 16 to find y. 16 - 5  = 11 - 5 = 6.

we do the same thing to find x, (10 - 2 = 8) (8 - 3 = 5) X = 5

Answer:

21

Step-by-step explanation:

15 + (3)2

15 + 6

21

Answer:

24

Step-by-step explanation:

15+x2

= 15 + (3x3)

= 15 + 9

= 24

Step-by-step explanation:

yes, the 2 events are entirely independent

neither one influences the other.

Answer:yes

Step-by-step explanation:

Answer:

addittional property

Step-by-step explanation:

The volume comparison of the given data is written below:

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.

Given, The height of the cone and cylinder is twice the radius, while the radius of a sphere is the same.

The volume of the cone =   πr²h

Since, h = 2r

The volume of the cone =   πr² * 2r = 2/3 πr³

The volume of the Cylinder = πr²h

Since, h = 2r

The volume of the Cylinder = πr² * 2r = 2πr³

The volume of the sphere = 4 πr³

Thus, the volume of 3 cones = 2πr³

that is also equal to The volume of one Cylinder.

Thus, the volume of 2 cones = 4/3πr³

that is also equal to The 1/3 volume of the Cylinder.

Thus, the volume of 1 sphere = 4πr³

that is also equal to The volume of 2 cylinders.

Thus, the volume of 1 cone = 2/3πr³

that is also equal to The 1/6 volume of the cone.

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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The algebraic expression for \(8\) more than \(5\) times a number will be \((8+5x)\) and the verbal expression for \(4(n + 6)\) will be four times the sum of a number and six.

Expressions is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

\(8\) more than \(5\) times a number

Now,

Let a number \(=x\)

So,

According to the question,

We get, \((8+5x)\)

So, this is the algebraic expression .

We have,

\(4(n + 6)\)

So,

According to the question,

\(4(n + 6)\) will be written as four times the sum of a number and six.

So, this is the verbal expression .

Hence, we can say that the algebraic expression for \(8\) more than \(5\) times a number will be \((8+5x)\) and the verbal expression for \(4(n + 6)\) will be four times the sum of a number and six.

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Answer:

9 x + 42.

Step-by-step explanation:

Answer:

72x+178" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.017px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">72x+17872x+178

Answer:

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

Step by Step:

Keep this in mind >>

Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.

All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.

Answer:

the woman has to live 1 mile from work to minimize the expenses

Step-by-step explanation:

Given the data in the question;

the distance within 9 miles ⇒ 0 < x > 9

Total costs Q = cx + 4c/( x + 1)

costs should be minimum  ⇒ dQ/dx = 0

⇒ d/dx [ cx + 4c/( x + 1) ] = 0

⇒ ( x + 1)² = 4

take square root of both side

√[ ( x + 1)² ] = √4

x + 1 = 2

x = 2 - 1

x = 1

Therefore, the woman has to live 1 mile from work to minimize the expenses

Answer:

a) 120

b) 10

c) 1/12

Step-by-step explanation:

The number of ways that a sample of r can be selected from a population of n is:

nCr = n! / (r! (n−r)!)

a) 3 people selected from a group of 10

₁₀C₃ = 120

b) 3 women selected from a group of 5

₅C₃ = 10

c) Of the 120 committees that can be chose, 10 are all women.  So the probability is 10/120 = 1/12.

Answer:

yes

Step-by-step explanation:

Answer:

The formation of ∆ is possible .

Step-by-step explanation:

Three sides of triangle are given which are 10 , 7 & 15. And we need to determine whetherwecanmake a triangle with these three sides or not . So we know that ,

" Sum of any two sides of a triangle is Greater

than the third side "

Let ,

Here we will see by three cases. And the formation of triangle will be possible if and only of all the three cases are possible.

So , let's check ,

Case 1:-

→ a + b > c

→ 10 + 7 > 15

→ 17 > 15

Case 2:-

→ b + c > a

→ 7 + 15 > 10

→ 22 > 10

Case 3 :-

→ a + c > b

→ 10 + 15 > 7

→ 25 > 7

Since all the three cases are true Hence formation of ∆ is possible.

A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer:

???

Step-by-step explanation:

We answered 72 questions correctly.

Here, we are given that our raw score was 70.

Also, total answered questions = 80

Let total number of correct answers = x

Thus, the total number of incorrect answers will be = (80 - x)

Points for 1 correct answer = 1

Thus, marks from correct answers = 1x

Points deducted for 1 incorrect answer = 1/4

Thus, marks deducted because of incorrect answers = (80-x)/4

Now, we can form the following equation-

x - (80-x)/4 = 70

{4x - 80 + x}/ 4 = 70

{4x - 80 + x} = 70 * 4

5x - 80 = 280

5x = 360

x = 360/5

x = 72

Thus, we answered 72 questions correctly.

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Your question was incomplete. Check for full content below-

On a college entrance exam, you answered 80 of 85 questions. Each correct answer adds 1 point to your raw score, each unanswered question adds nothing, and each incorrect answer subtracts 1/4 point. Your raw score was 70. How many questions did you answer correctly?

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

Answer:

(-3, -1)

(11, -169)

(-17, -105)

(3, -25)

(-1, -1)

Step-by-step explanation:

-x² - 4x - 4

x = -3

-9 + 12 - 4 = -1

x = 11

-121 - 44 - 4 = - 169

x = -17

-169 + 68 - 4 = -105

x = 3

-9 - 12 - 4 = -25

x = -1

-1 + 4 - 4 = -1

Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

Accοrding tο the prοvided statement, there will be 21 favοrable results.

A cοmpοsite number is a pοsitive integer that can be fοrmed by multiplying twο smaller pοsitive integers. Equivalently, it is a pοsitive integer that has at least οne divisοr οther than 1 and itself.

A prime integer οnly has twο factοrs: οne and itself. A cοmpοund integer is made up οf at least three cοmpοnents, and οccasiοnally much mοre.

A prime number (οr a prime) is a natural number greater than 1 that is nοt a prοduct οf twο smaller natural numbers. A natural number greater than 1 that is nοt prime is called a cοmpοsite number. Fοr example, 5 is prime because the οnly ways οf writing it as a prοduct, 1 × 5 οr 5 × 1, invοlve 5 itself. Hοwever, 4 is cοmpοsite because it is a prοduct (2 × 2) in which bοth numbers are smaller than 4.

Primes are central in number theοry because οf the fundamental theοrem οf arithmetic: every natural number greater than 1 is either a prime itself οr can be factοrized as a prοduct οf primes that is unique up tο their οrder.

4, 6, 8, 9, 10, 12 - these are the cοmpοsite numbers pοssible as sum.

Favοurable number οf οutcοmes = 21 ans.

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Please find full question attached Answer:

Barbara is not more well off as the typical individual has a higher well being score

Explanation:

please find explanation attached

Answer:

38.25, 39 if you need to round up

Step-by-step explanation:

8 fluid ounces for each customer times 153 customer = 1224 ounces, divide that by 32 to equal your quarts

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .

We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is  \($149,000\)  and \($151,000\):

0.6826 x 100% = 68.26%

Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\)  for this model of new homes.

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