Find the mass of each object. (Round answers to two decimal places.) (a) A thin copper wire 1.25 feet long (starting at x = 0) with density function given by p(x) = 4x² + 2x lb/ft. Ib m = ...
(b) A frisbee with radius 6 inches with density functuin given by p(x) = √3x kg/in
m = ...

Answer:

1 Hour =

0.00011407946 Years

(rounded to 8 digits)

Step-by-step explanation:

Answer:

67 years = 587322 hours

67 years = 3.524e+7 minutes

67 years = 2.114e+9 seconds

Step-by-step explanation:

24 hours in a day, 365 days in a year

(about 16 leap years)

You can also find specifics on G00g1e.

I hope this helps!
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Have a great day!

the function is x^2-9, so all you have to do is replace x with a number. for example, 2.

so 2^2-9 is -5. the plot would be 2, -5. basically, plug in a number to be the x coord, and whatever number you get will be your y coord.

after you graph a few plots (doing the same thing above), draw a line through all of them.

if the line goes up towards the right top corner, it's increasing. if it goes down the right bottom corner, it's decreasing.

False: The decrease in sample size will increase the margin of error and decrease the confidence interval.

Interval is a set of values that are located between two specific points on a line. It can be used to measure the amount of time between two events, the difference between two numbers, or the distance between two points. Intervals can also be used in data analysis to identify patterns or trends. In mathematics, intervals are often represented as a pair of numbers, such as (1, 5).


The decrease in sample size will decrease the margin of error and increase the confidence interval. This is because when the sample size is decreased, the margin of error is increased and the confidence interval is decreased since the precision of the estimate is lower. This means that the range of the confidence interval is wider and the estimates are less precise.

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Answer:

38.5 for mowing

29.6 for babysitting

Step-by-step explanation:

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

$ 25.26

Step-by-step explanation:

x = premium membership - diffrence between premium membership and standard membership

x = 41.25 - 15.99

x = 25.26

The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ lim θ → 0 ( sin θ / θ ) = 1

Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.

⇒ lim θ → 0 ( sin θ / θ ) = 1

Take LHS;

⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )

⇒ lim θ → 0 ( cos θ / 1 )

⇒ ( cos 0 )

⇒ 1

⇒ RHS

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L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

Given data:

X: height of seaweed.

       X~N (μ;σ²)

       μ= 10 cm

       σ= 2 cm

We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

              P(X ≤ x) = 0.30

              P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

        Z = (X - μ)/σ

translates the Z value to the corresponding X value.

           P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                  z= -0.52

Now you have to clear the value of X:

        Z= (X - μ)/σ

        X= (Z * σ) + μ

       X = (-0.52 * 2) + 10

         = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

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Answer:

Consisting of billions of galaxies

Step-by-step explanation:

Answer:

X = 9
Landyn is 9 and his brother is 14

Step-by-step explanation:

X + Y = 23
Y = X + 5
X + X + 5 = 23
2x + 5 + 23

     - 5   - 5  

2x / 2 = 18 / 2

Simplified = 9 / 1
Y = 9 + 5
Y = 14

Answer:

\(\boxed{\boxed{\sf 1 }}\)

Step-by-step explanation:

\(\sf 9p^2 \:if\: \:p=\cfrac{1}{3}\)

__________

\(\sf 9\left(\cfrac{1}{3}\right)^2\)

\(\sf {Calculate\: 1 \:to \:the \:power\: of \:1=1}\)

\(\longmapsto \sf 9\times \left(\cfrac{1}{3}\right)^2\)

\(\sf Now, \: calculate \: \frac{1}{3} \: to\: the\: power\: of \:2 \:which\: will\: give\: you\: \frac{1}{9}\)

\(\longmapsto \sf 9\times \left(\cfrac{1}{9}\right)\)

\(\sf Multiply\: 9\: and\: \frac{1}{9} =1\)

\(\longmapsto 1\)

___________________________

Answer:

1. 8-8-18 =

   0-18 =

     -18

To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Answer:

what happened

Step-by-step explanation:

The smallest recorded data point for the pesticide DDT in mg, based on the given stem-and-leaf plot, is 0 (Option A).


In the stem-and-leaf plot, each stem represents a tens digit, and the leaves represent the ones digit of the recorded measurements of the pesticide DDT. The smallest data point can be determined by examining the lowest value in the plot. In this case, the stem “1” has a leaf of “0,” indicating a value of 10.

However, since the leaf unit is 1.0, we need to multiply the stem value by the leaf unit to obtain the actual measurement. Multiplying 10 (stem) by 1.0 (leaf unit) gives us 10.0 mg. Among the options provided, the closest value to 10.0 mg is 0. Therefore, the smallest recorded data point for the pesticide DDT is 0 mg.

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Answer:

\(SA = 2.94 \, \textrm{units}^2\)

Step-by-step explanation:

The surface area of a regular 3D figure can be represented as:

\(SA = A_{\textrm{\,1 side}} \cdot (\# \textrm{ of sides})\).

Therefore, the surface area of a cube is:

\(SA = s^2 \cdot 6\)

where \(s\) is the length of a side.

To solve this problem, simply input the given side length into the above formula:

\(SA = 0.7^2 \cdot 6\)

and simplify.

\(SA = 0.49 \cdot 6\)

\(SA = 2.94 \, \textrm{units}^2\)

Answer:

$3

Step-by-step explanation:

$9.25/2.8

= $3.3035714285

= $3 (rounded to the nearest whole number)

Hope this helped!

We can conclude that T(n) = O(n²) for the recurrence relation T(n) = T(n-1) + n. We can conclude that T(n) = O(2ⁿ) is a valid upper bound for the recurrence relation T(n) = 2T(n-1) + 1.

1. To show that the solution of T(n) = T(n-1) + n is O(n²), we can use the substitution method. Let's assume that T(n) = O(n²). This means there exists a constant c and a positive integer k such that T(n) ≤ cn² for all n ≥ k.

Using the substitution method:

T(n) = T(n-1) + n

≤ c(n-1)² + n (by the assumption T(n-1) ≤ c(n-1)²)

= cn² - 2cn + c + n

≤ cn² - cn + n (for large values of n)

Now, we need to find values of c and k such that cn² - cn + n ≤ cn² for all n ≥ k. Choosing c = 2 and k = 1, we have:

2n² - n + n ≤ 2n² for all n ≥ 1

Therefore, we can conclude that T(n) = O(n²) for the recurrence relation T(n) = T(n-1) + n.

2. For the recurrence relation T(n) = 2T(n-1) + 1, let's use a recursion tree to determine an asymptotic upper bound. Starting with T(0) as the root, each node has two child nodes corresponding to T(n-1). Each node also has a constant cost of 1.

The height of the recursion tree is n, and at each level, the cost doubles. Therefore, the total cost of all levels in the tree is 2⁰ + 2¹ + 2 + ... + 2⁽ⁿ⁻¹⁾ = 2ⁿ - 1.

Hence, the asymptotic upper bound for T(n) is O(2ⁿ), as the cost increases exponentially with respect to n. Using the substitution method to verify this answer, let's assume T(n) = O(2ⁿ). This means there exists a constant c and a positive integer k such that T(n) ≤ c * 2ⁿ for all n ≥ k.

Using the substitution method:

T(n) = 2T(n-1) + 1

≤ 2(c * 2⁽ⁿ⁻¹⁾) + 1 (by the assumption T(n-1) ≤ c * 2⁽ⁿ⁻¹⁾)

= 2cn + 1

≤ c * 2ⁿ for large values of n

Thus, we can conclude that T(n) = O(2ⁿ) is a valid upper bound for the recurrence relation T(n) = 2T(n-1) + 1.

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Answer:

It's the third one, I hope so. y<1/2x

Step-by-step explanation:

I hope this helps. :)

Answer:

there are 20 students in mr.clarks fourth grade class there are 5 times as as many students in the entire fourth grade class as there are in mr.clacks. which equation can be used to determine the number of students,n, in the entire fourth grade?

n= 20(5)

100 kids in the fourth grade

or

there are 140 kids in the 4 th grade

Step-by-step explanation:

the equation is n=20(5)

because 20(5) is the same as 20×5 so that 8s the equation

Answer:

WL = 12

Step-by-step explanation:

The slope is given by

m = (y2-y1)/(x2-x1)

7 = (-5 -2)/(WL - 13)

Multiply each side by (WL - 13)

7 (WL - 13) = -5-2

7 (WL - 13) = -7

Divide each side by 7

(WL - 13) = -1

Add 13 to each side

WL - 13+13 = -1 +13

WL = 12

Answer:

x = -7.25

Step-by-step explanation:

multiply -4 by 2x + 5 = -8x - 20

-8x -20 -3 = 35

-8x - 23 = 35

-8x = 35 + 23

-8x = 58

x = 58 / -8

x = -7.25

To approximate the probability of having between 50 and 60 bad days in a year, we can use the Poisson distribution as an approximation.

Let's define the random variable X as the number of bad days in a year. Since the waiting time for the first customer follows an exponential distribution with a rate parameter of 1/10 (mean of 10 minutes), we can consider each day as a Bernoulli trial with a success (bad day) probability of P(X = 1) = P(waiting time > 20 minutes).

The probability of a bad day can be calculated using the exponential distribution as :\(P(X = 1) = ∫[20, ∞] (1/10)e^(-t/10) dt\)

To approximate the number of bad days in a year, we can assume that the number of bad days follows a Poisson distribution with parameter λ = 365 * P(X = 1). The mean and variance of the Poisson distribution are both equal to λ.

Using this approximation, we can calculate the probability of having between 50 and 60 bad days in a year by summing the probabilities of X taking values from 50 to 60 using the Poisson distribution with parameter λ.

This approximation is valid because the Poisson distribution is often used to model rare events with a low probability of occurrence, and in this case,  the assumption of independence between the waiting times for different days allows us to use the Poisson distribution.

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Simplify:

Answer: -2a

Therefore, based on the given information, the estimated age of the tomb is approximately 3,970 years.

To estimate the age of the tomb based on the radioactive carbon-14 (C-14) content in the cypress beam, we can use the decay equation:

A = A₀ * e*(kt)

Where:

A = Final amount of radioactive substance (55% of the original C-14 content)

A₀ = Initial amount of radioactive substance (100% of the original C-14 content)

k = Decay constant (ln(2) / half-life of C-14)

t = Time (age of the tomb)

Given that the half-life of C-14 is approximately 5600 years, we can calculate the decay constant:

k = ln(2) / 5600 years

Now we can plug in the values:

0.55A₀ = A₀ * e*((ln(2) / 5600 years) * t)

Dividing both sides by A₀:

0.55 = e*((ln(2) / 5600 years) * t)

Taking the natural logarithm of both sides:

ln(0.55) = (ln(2) / 5600 years) * t

Now we can solve for t, the age of the tomb:

t = (ln(0.55) * 5600 years) / ln(2)

Evaluating the expression:

t ≈ 3,970 years

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The number of bottles collected by the high school is 1922 bottles since the total collected bottles is 3627.

The total number of bottles collected by both elementary and high schools is 3627 bottles, which means that the number of bottles collected by the high school can be determined as the total bottles minus the ones collected by the elementary school:

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Answer:

A) (2,5)

B) (4,4)

C) (3,2)

D) (3,-1)

E) (1,-3)

F) (-1,-3)

G) (-3,-1)

H) (-3,2)

I) (-4,4)

J) (-2,5)

K) (-1,4)

L (1,4)