Ms. Taylor has a box on her desk for paper clips with a total volume of 120 cubic cm. The
paper clip box has a length of 6 cm and a width of 4 cm. What is the height of the box?

The exact length of the curve defined by the parametric equations x = 7t^2 and y = 36t^3, where 0 ≤ t ≤ 1, is approximately 128.47 units.

To find the exact length of the curve defined by the parametric equations x = 7t^2 and y = 36t^3, where 0 ≤ t ≤ 1, we can use the arc length formula for parametric curves:

L = ∫ [a, b] √(dx/dt)^2 + (dy/dt)^2 dt

In this case, a = 0 and b = 1.

Let's calculate the derivatives dx/dt and dy/dt:

dx/dt = d/dt (7t^2) = 14t

dy/dt = d/dt (36t^3) = 108t^2

Now, we can substitute these derivatives into the arc length formula:

L = ∫ [0, 1] √(14t)^2 + (108t^2)^2 dt

L = ∫ [0, 1] √(196t^2 + 11664t^4) dt

To solve this integral, we can simplify the expression inside the square root:

L = ∫ [0, 1] √(4t^2(49 + 2916t^2)) dt

L = ∫ [0, 1] 2t√(49 + 2916t^2) dt

Next, we can make a substitution to simplify the integrand further. Let u = 49 + 2916t^2, then du = 5832t dt.

When t = 0, u = 49, and when t = 1, u = 49 + 2916 = 2965.

Now, the integral becomes:

L = ∫ [49, 2965] (1/2916)√u du

L = (1/2916) ∫ [49, 2965] √u du

To solve this integral, we can apply the power rule:

L = (1/2916) * (2/3) * u^(3/2) | [49, 2965]

L = (2/3)*(1/2916) * (2965^(3/2) - 49^(3/2))

Finally, we can calculate the exact length of the curve:

L = (2/3)*(1/2916) * (2965^(3/2) - 49^(3/2)) ≈ 128.47

To learn more about  parametric equations go to:

https://brainly.com/question/30748687

#SPJ11

The correct options regarding the fractions are given as follows:

13) The non-equivalent fraction is 3 and 3/4.

14) The product of the two fractions is given by: 2 and 2/3.

15) The fraction is closest to the number 14.

16) The number of eights needed is:

Fractions are called equivalent if the division of the numerator by the denominator is the same.

Hence, for item 13, we have that:

3 and 3/4 = 3 + 0.75 = 3.75, which is different of 4.25, hence it is the non-equivalent fraction.

To multiply two fractions, we multiply the numerators and the denominators, hence:

12/20 x 15/6 = 12 x 20/(15 x 6) = 2 x 4/3 = 8/3.

8/3 as mixed number is 2 and 2/3, as the division of 8 by 3 has quotient 2 and remainder 2.

A fraction is converted to decimal dividing the numerator by the denominator, hence:

96/7 = 13.7, hence closest to 14.

2 and 3/4 inches is equivalent to 2.75 inches, hence the number of eights needed is:

2.75/(1/8) = 2.75 x 8 = 22.

More can be learned about fractions at https://brainly.com/question/1622425

#SPJ1

Answer:

31

Step-by-step explanation:

thx for the points

Mean (Average) 31

Median 32

Range 27

Mode All values appeared just once.

Geometric Mean 29.741208270684

Largest 43

Smallest 16

Sum 310

Count 10

Sorted Data Set: 16, 21, 23, 30, 31, 33, 35, 37, 41, 43

Answer:

x = 80, y = 100

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7 , then

sum = 180° × 5 = 900°

Sum the interior angles and equate to 900

y + 135 + 140 + 150 + 120 + 135 + 120 = 900, that is

y + 800 = 900 ( subtract 800 from both sides )

y = 100

x and y are adjacent angles and are supplementary, that is sum to 180°

x + y = 180

x + 100 = 180 ( subtract 100 from both sides )

x = 80

Thus x = 80 and y = 100

Answer: D. as a total number of family member increases the amount of money that the family spends on food increases

Step-by-step explanation:

i.e. independent variable acts like a cause to effect the dependent variable.

This can be seen only in Option D. as it is very obvious that increase in family member will increase the cost of food.

Hence, there is direct effect of number of people on food's cost.

Rest of options represents correlation but not causation .

Hence, the correction option is D.

Answer:

c

Step-by-step explanation:

Answer:

X = 2

Step-by-step explanation:

2 x 2 x 2 = 8

Hope this helps. Pls give brainliest.

Answer:

2 :)

Step-by-step explanation:

For both scenarios, a sample is selected without replacement from a batch of items. In the first scenario, the batch contains 3 defective items ('d') and 10 good items ('g'). The ordered sample space consists of all possible ordered pairs of items: {dd, dg, gd, gg}. In the second scenario, the batch contains the items {a, b, c, d}. The ordered sample space also consists of all possible ordered pairs of items: {aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}.

In the first scenario, the ordered sample space is derived by considering all possible combinations of the two items selected from the batch. Since the selection is done without replacement, the first item can be either defective ('d') or good ('g'). For each case, the second item can also be defective or good, depending on what was chosen as the first item. Therefore, the ordered sample space consists of four possibilities: dd, dg, gd, and gg.

In the second scenario, the batch consists of four distinct items: a, b, c, and d. Again, the ordered sample space is obtained by considering all possible combinations of the two items selected without replacement. Since there are four items, there are 16 possible combinations. Each combination is represented by an ordered pair of the selected items, such as aa, ab, ac, and so on.

To know more about ordered sample space, click here: brainly.com/question/29189463

#SPJ11

Answer:

r = 3

Step-by-step explanation:

(r + 1)(r + 9) = 16r ← expand left side using FOIL

r² + 9r + r + 9 = 16r

r² + 10r + 9 = 16r ( subtract 16r from both sides )

r² - 6r + 9 = 0

(r - 3)² = 0 , then

r - 3 = 0 ( add 3 to both sides )

r = 3

Average speed  is: \(\frac{D}{\frac{D/2}{94.} +\frac{D/2}{72} }\), the average speed is: \(\frac{D}{\frac{D/2}{94.} +\frac{D/2}{72} }\), the average speed for the entire trip is:\(\frac{2D}{\frac{D/2}{94.} +\frac{D/2}{72} }\) and the for the entire trip is also zero.

To calculate the average speed, we can use the formula:

\(Average \:Speed = \frac{Total \:Distance} {Total \:Time}\)

(a) From San Antonio to Houston:

Let's assume the total distance from San Antonio to Houston is D.

On the way to Houston, you drive half the distance at \(72 km/h\) and the other half at \(94 km/h.\) So, the time taken for the first half is \(\frac{D/2}{72.}\), and the time taken for the second half is\(\frac{D/2}{94.}\)

The total time : \(\frac{D/2}{72} +\frac{D/2}{94.}\)

The average speed is: \(\frac{D}{\frac{D/2}{94.} +\frac{D/2}{72} }\)

(b) From Houston back to San Antonio:

The same logic applies here. The total distance from Houston back to San Antonio is also D.

On the way back, you drive half the distance at 72 km/h and the other half at 94 km/h. So, the time taken for the first half is \(\frac{D/2}{72}\), and the time taken for the second half is \(\frac{D/2}{94}\).

The total time taken is : \(\frac{D/2}{72} +\frac{D/2}{94.}\).

The average speed is: \(\frac{D}{\frac{D/2}{94.} +\frac{D/2}{72} }\)

(c) For the entire trip:

The total distance for the entire round trip is 2D (going from San Antonio to Houston and then back).

The total time taken for the entire trip is the sum of the time taken from San Antonio to Houston and from Houston back to San Antonio.

The average speed is:\(\frac{2D}{\frac{D/2}{94.} +\frac{D/2}{72} }\).

(d) Average velocity takes into account both speed and direction. Since you return to the starting point, your displacement is zero. Therefore, the average velocity is 0.

Please note that the calculations above assume constant speeds and do not account for factors such as traffic, stops, or variations in the actual distances traveled. They provide an approximation based on the given information.

Learn more about average here:

https://brainly.com/question/33780781

#SPJ11

The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.

Let's consider the following interpretation:

Domain of discourse: {1, 2}

A(x): x is even

B(x): x is odd

Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).

However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).

In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.

Learn more about domain here:

https://brainly.com/question/28135761

#SPJ11

Step-by-step explanation:

The given quadratic equation is in standard form.

The correlation coefficient with the correct association is listed as:

-0.86  = 1

-0.66 = 1

-0.01 = 2

0.52 = 3

0.93 = 1

Correlation is a statistical measure that describes the extent to which two variables are linearly related to each other.

A negative correlation is when two variables move opposite each other i.e. when one variable increases, the other decreases

For  absolute values of the correlation coefficient:

0-0.19 => very weak

0.2-0.39 => weak

0.40-0.59 => moderate

0.6-0.79 => strong

0.8-1 => very strong

Thus, the matching is listed below:

-0.86  = strong

-0.66 = strong

-0.01 = weak

0.52 = moderate

0.93 = strong

Learn more about correlation coefficent on:

brainly.com/question/4219149

#SPJ1

To complete the square for the expression x² + 11x, we need to find a term that, when added to the expression, creates a perfect square trinomial.

To complete the square, we take half of the coefficient of the x-term, square it, and add it to both sides of the equation. In this case, the coefficient of x is 11, so half of it is 11/2, and when squared, it becomes 121/4. Adding 121/4 to both sides of the equation, we have x² + 11x + 121/4 = x² + 11x + 121/4. Now, the left side of the equation can be factored as a perfect square trinomial, which is (x + 11/2)².

Therefore, the complete square form of x² + 11x is (x + 11/2)².To complete the square for a quadratic expression in the form x² + bx, we take half of the coefficient of the x-term, square it, and add it to both sides of the equation. The result is a perfect square trinomial. In the given expression x² + 11x, the coefficient of x is 11. Half of 11 is 11/2, and when squared, it becomes 121/4.

By adding 121/4 to both sides of the equation, we create a perfect square trinomial on the left side. The expression x² + 11x + 121/4 can be factored as (x + 11/2)². Therefore, the complete square form of x² + 11x is (x + 11/2)².

Learn more about square here: brainly.com/question/13747846

#SPJ11

Answer:

I believe "U" is the symbol for your answer hope this helps!

Step-by-step explanation:

Answer:

5.12

Step-by-step explanation:

It's 3.59*0.7÷1 so 5.12

Step-by-step explanation:

1) B

2) A

3) C

4) C

yeahhh that's about right

Answer:

1) B

2) B

3) C

4) D

5) A (I think )

Step-by-step explanation:

Answers:

The diagrams for each are shown below (attached image).

==========================================================

Work Shown:

Problem 1

\(a^2 + b^2 = c^2\\\\3^2 + b^2 = 12^2\\\\9 + b^2 = 144\\\\b^2 = 144 - 9\\\\b^2 = 135\\\\b = \sqrt{135}\\\\b = \sqrt{9*15}\\\\b = \sqrt{9}*\sqrt{15}\\\\b = 3\sqrt{15}\\\\\)

--------------------------------------

Problem 2

\(a^2 + b^2 = c^2\\\\90^2 + 120^2 = c^2\\\\8100 + 14400 = c^2\\\\22500 = c^2\\\\c^2 = 22500\\\\c = \sqrt{22500}\\\\c = 150\\\\\)

--------------------------------------

Problem 3

\(a^2 + b^2 = c^2\\\\a^2 + 12^2 = 15^2\\\\a^2 + 144 = 225\\\\a^2 = 225 - 144\\\\a^2 = 81\\\\a = \sqrt{81}\\\\a = 9\\\\\)

--------------------------------------

Problem 4

\(a^2 + b^2 = c^2\\\\10^2 + 15^2 = c^2\\\\100 + 225 = c^2\\\\325 = c^2\\\\c^2 = 325\\\\c = \sqrt{325}\\\\c = \sqrt{25*13}\\\\c = \sqrt{25}*\sqrt{13}\\\\c = 5\sqrt{13}\\\\\)

--------------------------------------

Side notes:

The probability function of ΣYi (i=1 to n) is the Poisson distribution with mean Σλi (i=1 to n).

The conditional probability function of Y1, given that ΣYi=m (i=1 to n), follows a binomial distribution with parameters m and p = λ1 / Σλi (i=1 to n).


1. Since Y1, Y2,...,Yn are independent Poisson random variables, their sum (ΣYi) also follows a Poisson distribution.

2. To find the mean of this distribution, simply sum the means of the individual random variables: Σλi (i=1 to n).

3. For the conditional probability function of Y1, given that ΣYi=m (i=1 to n), consider the sum as a whole with m total events.

4. The probability of Y1 having a specific number of events is determined by the ratio of λ1 to the total mean: p = λ1 / Σλi (i=1 to n).

5. Since we're interested in the distribution of the number of events in Y1 out of m total events, this follows a binomial distribution with parameters m and p.

To know more about binomial distribution click on below link:

https://brainly.com/question/29163389#

#SPJ11

Answer:

Option D is the correct answer.

Step-by-step explanation:

I just know.

Answer:

Step-by-step explanation:

yes

The integral ∫-4 to 4 ; (3−|x|)dx can be interpreted as the area of two triangles with base 4 and height 3 each. Thus, the total area under the curve is equal to the sum of the areas of the two triangles, which is 12.

To interpret the integral of areas, we can split it into two parts, one where x is positive and one where x is negative.

For x between 0 and 4, the integrand is given by (3 - x), which represents a line with a slope of -1 that passes through the point (3, 0) and intersects the x-axis at (0, 3). Therefore, the integral of (3 - x) dx from x = 0 to x = 4 represents the area of a triangle with base 4 and height 3, which is (1/2)(4)(3) = 6.

For x between -4 and 0, the integrand is given by (3 + x), which represents a line with a slope of 1 that passes through the point (-3, 0) and intersects the x-axis at (0, 3). Therefore, the integral of (3 + x) dx from x = -4 to x = 0 represents the area of another triangle with base 4 and height 3, which is also equal to 6.

Therefore, the total area under the curve given by the integral from x = -4 to x = 4 of (3 - |x|) dx is equal to the sum of the areas of the two triangles, which is 6 + 6 = 12.

To know more about integral of areas:

https://brainly.com/question/11630709

#SPJ4

Answer:

sdf67566655 so x is 129

Step-by-step explanation:

ytr654564676

Answer:32

Step-by-step explanation:

32 + 5 is funny

Answer:

p²q + 3pq³

Step-by-step explanation:

(p + 3q²) pq ← multiply each term in the parenthesis by pq

= p²q + 3pq³

Answer:

18/25

Step-by-step explanation:

Therefore, the total cost of the pens that were returned is 200 Dhs.

To find the total cost of the pens that were returned, we need to multiply the number of defective pens by the cost of each pen.

The stationary store ordered 500 pens, and out of those, 40 pens were defective. Therefore, the number of pens that were returned is 40.

Now, we can calculate the total cost of the returned pens. The cost of each pen is Dhs. 5. Thus, we multiply the cost per pen by the number of pens returned:

Total cost = Cost per pen × Number of pens returned

= 5 Dhs. × 40 pens

= 200 Dhs.

For such more question on multiply

https://brainly.com/question/29793687

#SPJ8

Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

To determine the amount of taxable income for Aaron Rentz in 2020, we need to consider his wages, interest income, and any deductions or credits he may be eligible for.

From the given information, Aaron has $900 of wages and $1,400 of interest income.

In 2020, the standard deduction for a single individual was $12,400. Since Aaron is a qualifying child of his parents, he may not be able to claim his own personal exemption.

To calculate Aaron's taxable income, we subtract the standard deduction from his total income:

Taxable Income = Total Income - Standard Deduction

Taxable Income = $900 + $1,400 - $12,400

Taxable Income = $2,300 - $12,400

Taxable Income = -$10,100

Since Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

To know more about income visit:

brainly.com/question/14732695

#SPJ4

Answer:

O A. Principal

Step-by-step explanation:

happy to help ya :)

Given:

The piecewise rectangular figure.

To find:

The area of the piecewise rectangular figure.

Solution:

Draw a line and divide the given figure in two parts (a) and (b) as shown in the below figure.

Figure (a) is a rectangle of length 5 yd and width 3 yd. So, the area of the rectangle is:

\(Area=length\times width\)

\(A_a=5\times 3\)

\(A_a=15\)

Figure (b) is a square of edge 2 yd. So, the area of the square is:

\(Area=(edge)^2\)

\(A_b=(2)^2\)

\(A_b=4\)

The area of the given figure is:

\(A=A_a+A_b\)

\(A=15+4\)

\(A=19\)

Therefore, the area of the given figure is 19 square yd.