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1024/3 units³ is the required volume of the given solid using the triple integral theorem.

As the name implies, triple integrals are 3 sequential integrations, used to determine a volume or to integrate into a 4th dimension, over 3 other independent dimensions.

∭Ef(x,y,z)dV=∬D[∫u2(x,y)u1(x,y)f(x,y,z)dz]dA.

So, we must use the triple integral formula in rectangular coordinates to get the volume of the solid (v):

[tex]V=\iiint d y d x d z[/tex] ...(1)

The solid is restricted by the following intervals:

[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]

Then, this triple integral is now characterized as:

[tex]V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z[/tex]

Now we continue to integrate again to get the volume:

[tex]\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}[/tex]

Therefore, 1024/3 units³ is the required volume of the given solid using the triple integral theorem.

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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.

The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.

Considering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).

We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:

(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]

open brackets and simplify;

(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)

add and subtract like terms;

(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)

(a + b)² - (b + c)² = (a + 2b + c)(a - c)

In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.

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Answer: D

Step-by-step explanation:

-2 is not a repeating decimal.

It is not a fraction

And it is a rational number

Any value x not explicitly associated with a positive probability is taken as P(X=x) = 0. The function pX(x)= P(X=x) for any x in the range of X is given as a probability. It is often called the probability mass function of a discrete random variable X.

Binomial Distribution:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own It has a Boolean result: success (for probability p) or failure (for probability q = 1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

The binomial distribution is commonly used to model the number of successes in a sample of size n drawn from a population of size N with replacement. If sampling is performed without replacement, the resulting distribution is hypergeometric rather than binomial because the plots are not independent. However, for N much larger than n, the binomial distribution remains a good approximation and is widely used.

In the binomial distribution, the trials to be investigated must have the same probability of success. For example, if you toss a coin, the probability of flipping the coin is 1/2. 0.5 for each trial because there are only two possibilities.

Binomial Random Variable:

This is a special kind of discrete random variable. A binomial random variable counts the number of times a particular event occurs over a fixed number of trials or trials.

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The common ratio of the geometric sequence will be negative 2.

Given that:

Geometric sequence: 17, -34, -68, .....

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The common ratio of the geometric sequence is calculated as,

r = (-34) / (17)

r = - 2

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The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)

The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.

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Step-by-step explanation:

Since a perimeter is a total distance around the figure.

And a square is a quadrilateral(with four sides) which are equal.To find the length of each side,divide the perimeter by 4.

hope it helps you.

Answer:

Area of square = 225 cm²

Step-by-step explanation:

Perimeter of square formula,

→ P = 4 × side

→ P = 4a

Now the side of square will be,

→ P = 4a

→ 4a = 60

→ a = 60/4

→ [ a = 15 cm ]

Then the area of square will be,

→ (a)²

→ (15)²

→ 225 cm²

Hence, area of square is 225 cm².

The value of composite function g(f(-2) is when f(x) = x^2+9 and g(x) = x-9 is 4

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

We are given two functions  f(x) = x^2+9 and g(x) = x-9

and we are asked to find g(f(-2))

this term means we first substitute f(x) in the place of x in function g

We get

g(f(x))= f(x) - 9

Now substitute the value of f(x) in the above function

g(f(x))= x^2+9 -9

g(f(x))= x^2

g(f(-2))= (-2)^2

g(f(-2))= 4

Hence the value of the function if 4

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Answer:

The lowest common denominator is 12

Step-by-step explanation:

Finding the lowest common denominator

Multiples of 6: 6,12,18,24

Multiples of 4: 4,8,12,16,20

The lowest common multiple is 12

The lowest common denominator is 12

The probability that all 3 will be vowels will be .01 to the nearest hundredth

Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.

There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.

First of all, we need to know the number of vowels in the 26 letters.

There are 5 vowels among the 26 letters,

probability (3 vowels of 3)

= (5/26)*(5/26)(5/26)    multiplication of probability of each letters

=0.1923*0.1923*0.1923

≈0.0071

≈0.71%

or .01 to the nearest hundredth

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The value of a for which v is a linear combination is given as follows:

a = -8.

v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.

From the vectors, the system is defined as follows:

From the first equation, the value of x is obtained as follows:

-x = -1

x = 1.

From the second equation, the value of y is obtained as follows:

2x - y = 4

2 - y = 4

y = 2 - 4

y = -2.

From the third equation, the value of z is obtained as follows:

5x + 4y - 3z = -6.

5 - 8 - 3z = -6

3z = 3

z = 1.

Then the value of a needed for the linear combination is of:

a = -x + 3y - z

a = -1 - 6 - 1

a = -8.

The problem is given by the image shown at the end of the answer.

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After 13 years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old iddm women, if the incidence rate remains constant over time.

In this question we have been given the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

We need to find the number of years after which we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time.

Let n be the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females.

The probability of becoming blind over n years is 0.10

Given that the annual incidence rate of blindness per year was 0.74% IDDM females.

This means the rate r = 0.0074

For n years the annual incidence rate of blindness  0.0074n

We need to find the value of n,

0.0074n = 0.10

n = 13.51

n ≈ 13 years

Therefore, the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females = 13

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The complete question is:

A study [12] of incidence rates of blindness among insulin-dependent diabetics reported that the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.

After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time?

Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both

Step-by-step explanation:

problem a                                                    problem b

(6²-4)/2                        or                              6²-4/2

     |                                                                      |

[tex]6^2=36\\[/tex]                                                            [tex]6^2=36[/tex]

36-4=32                                                         36-4/2

32/2=16                                                          36-2=34

   16                                                                    34

After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.

We must apply the sine rule and the cosine rule to the non-right-angled triangles.

So, we have the function:

tan (15π - 2t)

Now, evaluate as follows:

(15π - 2t)

Rewrite using trigonometric identities:

- sin(2t)/cos(2t)

Rewrite using trigonometric identities:

- tan(2t)

Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

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When the temperature increased by 19.8 degrees fahrenheit , the temperature in degrees Celsius got increased by 11 degree

The equation C that gives the temperature in degree Celsius is

C = [tex]\frac{5}{9}(x - 32)[/tex]

Where x denotes the degree Fahrenheit

According to the question,

Temperature has increased by 19.8 degree Fahrenheit

So, let the new temperature be " x' "

x' = x + 19.8

Therefore, For calculating temperature in degree Celsius

=> C' = 5/9 (x' - 32)

Substituting the value of x'

=> C' = 5/9 (x + 19.8 - 32)

=> C' = 5/9 ( x - 32) + 5×19.8/9

=> C' = C + 99/9

=> C' = C + 11

Hence , The temperature increased by 11 degree Celsius

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The solution for x in the pentagon is 90

From the question, we have the following parameters that can be used in our computation:

Shape = pentagon

This means that

n = 5

The sum of the internal angles is calculated as

Angles = 180(n - 2)

Substitute the known values in the above equation, so, we have the following representation

Angles = 180(5 - 2)

So, we have

Angles = 540

This means that

x + 90 + 90 + 135 + 135 = 540

So, we have

x + 450 = 540

Evaluate

x = 90

Hence, the value of x is 90

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The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

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Answer:

nah

Step-by-step explanation:

Answer: 69/20

Step-by-step explanation:

5 1/5 = 26/5

1 3/4 = 7/4

26/5 - 7/4

= 104/20 - 35/20

= 69/20

The dimensions of the rectangular box is 2.

The base will be 4×4 and the height will be 2 (all numbers in feet)

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is

base+height×perimeter

=b2+4bh=48

From which we can determine:

h=48−b24b

The Volume of the box:

V(b)=b2h=b2⋅(48−b24b)

=12b−3b34

b=±4

Plugging this back into the formula

h=48−b24b

we get

h=2

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Answer:

7/8

Step-by-step explanation:

2/3 * 1 5/16 =

2/3 * (1 + 5/16)=

2/3 * (16/16 + 5/16)=  -> common denominator numbers are easy to simplify

2/3 * (16+5)/16 =

2/3 * 21/16=

(2*21)/(3*16)=

42/48=

21/24=7/8

Answer: 5,400

Step-by-step explanation:

In a triangle, the sum of angles is is 180. In a quadrilateral, the sum of angles is 360. In a pentagon, the sum of angles is 540. We can see that as the every time the number of sides increases by 1, the interior angle sum increases by 180.

Let's subtract the given amount of sides by the amount of sides in a triangle to see how many sides it has increased by.

32 - 3 = 29.

Now we multiply the increase in sides by 180 to get how much the interior angle sum has increased.

29 * 180 = 5220.

Finally add back the sum of angles in a triangle.

5220 + 180 = 5,400.

Answer:

5,400

Step-by-step explanation:

5220 + 180 = 5,400

Answer: 312=(2)(2)(2)(3)(13)

Step-by-step explanation:

312  |  2

156  |  2

78   |  2

39   |  3

13    | 13

Hence, 312=(2)(2)(2)(3)(13)

The value of the test statistic for the test is 1.52

From the question, we have the following parameters that can be used in our computation:

H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9

The above parameters mean that

The value of the test statistic for the test is calculated as

[tex]t = \frac{x - \mu_0}{s/\sqrt n}[/tex]

Substitute the known values in the above equation

[tex]t = \frac{4.2 - 3.8}{1.9/\sqrt {52}}[/tex]

Evaluate the equation

t = 1.52

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Answer:

bro fr has the nicest notes not just for the points but like actually

Answer:

y = -x - 1 ;  y = 11x - 25

Step-by-step explanation:

y = x² + x

y-(-3) = m(x-2)

y = x²+x

y + 3 = mx - 2m

y = x² + x

y = mx - 2m - 3

x² + x = mx - 2m - 3

x² + x - mx + 2m + 3 = 0

x² + (1-m)x + 2m + 3 = 0

discriminant = m² + 1 - 2m -4 (2m + 3)

m² + 1 - 2m - 8m  - 12

m² - 10m - 11

the line is tangent so the discriminant must be equal to 0

m² - 10m - 11 = 0
(m-11)(m+1) = 0

m = 11

m = -1

y + 3 = -(x-2)

y+ 3 = -x + 2

y = -x + 2 - 3

y = -x - 1

y + 3 = 11(x-2)

y + 3 = 11x - 22

y = 11x -22 - 3

y = 11x - 25

To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.

Given,

A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.

We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

Here,

To obtain the sample size,

n = z² pq / ME²

Where,

P is the proportion of voters

M. E is the margin of error.

q is the proportion of non-voters

z is the corresponding z score

The z score for the 95% confidence interval is 1.96.

n = 1.96² pq / 0.05²

n = 1536.64 pq

If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.

n = 1536.64 pq = 61.42

≈ 62 voters

Therefore,

62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

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Answer:

12

Step-by-step explanation:

2 is 40 percent of 5

12 is 40 percent of 30

Answer:

15 people would be running out of 30

Step-by-step explanation:

30/2

The answer for this Simplifiction 4x3−12x24x2 7x−22x2−6x5x2 11x 2 using  BODMASS rule is -19316

=4*3-12*24*27*-22*2-6*5*211*2

=-19316

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