A U.S. dime has a diameter of about 18 millimeters. What is the area of one side of a dime to the nearest square millimeter? Use 3.14 as an approximation for pi. The area of one side of a U.S. dime is approximately _____ square millimeters.

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

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Answer:

1.5 kg

Step-by-step explanation:

Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:

9/6 · 1 kg = 1.5 kg

Answer:

a) 0.65 mpg

b) Between 24.99 mpg and 28.01 mpg.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]

a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?

s = 0.65 mpg

b. Within what interval would you expect the sample mean to fall, with 98 percent probability?

From the: 50 - (98/2) = 1st percentile

To the: 50 + (98/2) = 99th percentile

1st percentile:

X when Z has a pvalue of 0.01. So X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = -2.327*0.65[/tex]

[tex]X = 24.99[/tex]

99th percentile:

X when Z has a pvalue of 0.99. So X when Z = 2.327.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = 2.327*0.65[/tex]

[tex]X = 28.01[/tex]

Between 24.99 mpg and 28.01 mpg.

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

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Step-by-step explanation:

40children - 23 (with A, O) = 17left

26 letter in alphabet- ( A, O) = 24 letter left

24 letters left - 14 (not used for 1st letters) = 10

10 letters left to use/ 17 children left

10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get

There are six surnames that start with each letter other than A and O when more than one surname does.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.

Since, 14, of the letters of the alphabet do not appear as the first letter of a surname

14 of the letters of the alphabet do not appear as the first letter of the surname

∴ the no. of letters that appeared = 26-14 = 12 alphabets

15 surnames begin with 10 letters beside O and A

∴ 6 surnames begin with a letter

Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.

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Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{s}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]X = 17.79, \mu = 17, s = 0.08[/tex]

How many standard deviations is the sample mean from the mean of the distribution of sample?

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{17.79 - 17}{0.08}[/tex]

[tex]Z = 9.875[/tex]

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Answer:

There are 172 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

   9/25            1

     50             18

     100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 172

Thus, there are 172 butterflies  in the conservatory.

Answer:

There are 162 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

  9/25            1

    50             18

    100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 162

Thus, there are 162 butterflies  in the conservatory.

Answer:

1/2

Step-by-step explanation:

The numbers 3 or odd are 1, 3, 5, and 7.

4 numbers out of 8.

4/8 = 1/2

P(3 or odd) = 1/2

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

=m+m-4-5

=2m-9

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

take the like terms

= 2m-4-5

= 2m-9

Sorry if that didn't help

Answer:

Piecewise function;

y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Step-by-step explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

 Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

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

                                        = 2

 Therefore, equation of this segment will be in the form of y = mx + b,

 ⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

 y = 4  where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

 Let the equation of the line is,

 y = mx + b

 Where m = slope of the line

 b = y-intercept

 Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                           = [tex]\frac{2}{2}[/tex]

                           = 1

 Equation of this line will be,

 y = 1(x) + b

 y = x + b

 Since, this line passes through (5, 6),

 6 = 5 + b

 b = 6 - 5 = 1

 Therefore, equation of this line will be,

 y = x + 1 where x > 5

 Graphed piecewise function is,

 y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Answer:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

Answer:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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Answer:

The probability is 40%

Step-by-step explanation:

a) There are ten pieces of paper with ten numbers

Probability of selecting four pieces of paper = 4/10 or 40%

Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%

Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.

b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes.   In other words, it is a measure of the likelihood of an event (or measure of chance).

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

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Answer:

A.

Step-by-step explanation:

Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.

Answer:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

I suppose the curve is [tex]r(\theta)=e^\theta[/tex].

Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.

[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

We have

[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]

[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]

[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]

[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]

[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]

(where [tex]n[/tex] is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]

[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

Step-by-step explanation: 4

Answer:

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The equation of the translation image of the function is  y - 4 = f(x + 3).

which is the correct answer would be an option (D).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

To determine the graph of y (x) is translated as 3 units right and 4 units down.

The x-coordinate will increase by 3 if we move it to the right.

If we shift it downward, it will become negative and read as y - 4.

So y - 4 = f(x + 3)

Therefore, the equation of the translation image of the function is  y - 4 = f(x + 3).

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Answer:

Step-by-step explanation:

t=V100-50/4

t=V50/4=1.76≈1.8 s

when h=0

t=V100/4=10/4=2.5 s

Answer:  a) (5√2)/4 ≈ 1.77 seconds

               b) 5/2 = 2.5 seconds

Step-by-step explanation:

[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]

Answer:

1st 2nd 4th 5th

Answer:

Step-by-step explanation:

The perimeter of the triangle △SMP is the sum of al the sides of the triangle.

Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.

Given LM=9, NR=16 and SR=8

NR = NP+PR

Since NP = PR

NR = NP+NP

NR =2NP

NP = NR/2 = 16/2

NP = 8

From △LSM,  NP = PR = MS = 8

Also since LM = MN, MN = 9

From △SRP, SR = RP = PS =  9

Also SR = MP = 8

From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||

perimeter of △SMP = 8+8+9

perimeter of △SMP = 25

Answer:

12.5%

Step-by-step explanation:

There is only one number 5 from a total of 8 parts.

1 out of 8.

1/8 = 0.125

P(5) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Spinner divided in parts = 8

Number 5 = 1

P(5) = 12.5%

Answer:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Step-by-step explanation:

Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:

[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]

Solving the linear system:

[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]

The price of each item is:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Answer:

233

Step-by-step explanation:

Answer:

B. 533in²

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = lw

A = (29)13

A = 377

Step 2: Find the leg of the triangle

13 + 11 = 24

Step 3: Find the area of the triangle

A = 1/2bh

A = 1/2(24)(13)

A = 12(13)

A = 156

Step 3: Add the areas of the 2 figures together

377 + 156 = 533

Answer:

2/3

Step-by-step explanation:

divide by a fraction = multiply by reciprocal

1/4 * 8/3

2/3

Answer:

⅔

Step-by-step explanation:

= ¼ ÷ ⅜

= ¼ × ⁸/3

= ⅔

Have a great day !

Answer:

22.2

Step-by-step explanation:

The missing side is x

x = 22.21≈ 22.2