Write the equation 3x+2y- 5 = 0 in normal form. Then, find the length of the normal and the angle it makes with the


positive x axis.
​

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

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The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer:

Probability = 0.894

Expected value = 5.2

Standard deviation = 1.349

Step-by-step explanation:

Given that

p = 0.65

n = 8

q = 1 - p

= 1 - 0.65

= 0.35

\(P(x) = ^n(c_x)\times P^x\times q^{n-x}\)

For P(3)

\(= ^8c_3\times 0.65^3\times 0.35^5\)

Which gives result

= 0.0808

For P(2)

\(= ^8c_2\times 0.65^2\times 0.35^6\)

Which gives result

= 0.0217

For P(1)

\(= ^8c_1\times 0.65^1\times 0.35^7\)

which gives result

= 0.0033

For P(0)

\(= 0.35^8\)

= 0.0002

Now probability is at least getting admitted of 4 students

= 1 - {P(3) + P(2) + P(1) + P(0)}

= 1 - (0.0808 + 0.0217 + + 0.0033 + 0.0002)

= 1 - 0.106

= 0.894

Expected value = \(n\times p\)

\(= 8\times 0.65\)

= 5.2

Standard deviation

\(= \sqrt{n\times p\times q} \\\\\ = \sqrt{8\times 0.65\times 0.35}\)

= 1.349

Answer:

her call lasted 18 minutes

Answer:

The answer is 18 minutes

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

(4, -2 1/2)

Step-by-step explanation:

The 4 is positive because it goes to the right on the x axis, and the 2 1/2 is negative because it goes down on the y axis.

Answer:

(4, -2 1/2)

Step-by-step explanation:

i did edge test

Answer:

2534

Step-by-step explanation:

2x^3+5x^2+3x+4

x=10, so:

2(10)^3+5(10)^2+3(10)+4

2000+500+30+4

Answer: 2534

Answer:

4.16%/ year

Step-by-step explanation:

(3)(-4)(2)

= -24

Negative sign will be there since if we multiply a negative integer with a positive integer, it will be negative only.

So, the answer is -24.

Please mark me Brainliest.

Answer:

\( - 24\)

Step-by-step explanation:

\((3)( - 4)(2) \\ =3 \times (- 4) \times 2 \\ = - 12 \times 2 \\ = - 24\)

Answer:

270 people

Step-by-step explanation:

Because she wants to 90% confident, the number of people she should sample is 90% * 300.

90% * 300 = 0.90 * 300 = 270

Answer:

Step-by-step explanation:

real number can be irrational or integer.

otherwise there is no number which can be irrational,integer and real (all together)

Answer: The answer is B) there is no such number.

Step-by-step explanation:

So we have to find which number is irrational, and integer, and a real number. Let's examine the problem closely:

- irrational means not rational and cannot be represented by a simple fraction (like pi )

- an integer means a number that can be written without a fractional component ( -1, 2, 0, -10000 )

- and a real number means that it is not imaginary ( like 2i, \(\sqrt{-1}\) )

And our choices here are:

-  -4/2

-  there is no such number

Let's take a look at -4/2. This number is a fraction, but it can be simplified down to -2/1, which is an integer. -2 is a real number, not an imaginary number. But, -2 is not irrational, because as it just was shown here, it CAN be represented by a fraction. So, since only two out of the three criteria are true, then we have to consider choice B.

Answer: There is an association because the distribution of correct guesses is the same among the mint groups.

Step-by-step explanation:

We would have to see the graph but I know it's either B or C because the other answer choices don't make sense. I chose B because it seems like the most logical choice of the two.

the polynomial must be even, so we chose x²

it has at least 2 terms, then we add 1 to the previous item, we get: x² + 1

to get outputs larger and larger in the negative direction, we have to multiply the previous item by -1 to get: -x² - 1

This function has a graph like the next one:

Then, -x² - 1 satisfies all the features needed

Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer:

Step-by-step explanation:

Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.

Answer:

Step-by-step explanation:

For this kind of problem, all you need to know is one formula:

The Distance Formula

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

in this case,

\(x_2=1\), \(x_1=0\), \(y_2=-3\), \(y_1=-10\)

\(D = \sqrt{(1-0)^2+(-3--10)^2}\)

\(D = \sqrt{1^2+7^2}\\D = \sqrt{1+49}\)

\(D = \sqrt{50}\\D = \sqrt{25*2} D = 5\sqrt{2}\)

The ordered pair (3, - 2) is not a solution to the equation 2x - y = 4

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, an equation 2x - y = 4 now if  (3, - 2) is an ordered pair then putting the numerical value of x must satisfy the y value.

when x = 3,

2(3) - y = 4.

6 - y = 4.

- y = 4 - 6.

- y = - 2.

y = 2.

So,  (3, - 2) is not a solution to an equation 2x - y = 4.

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Answer:

Chloe is making a mural. She spends 6 hours designing it.

She paints it during 3 sessions. Each session is the same

number of hours long. In all, Chole spends 24 hours making

the mural.

Step-by-step explanation:

Answer:

Each painting session is 6 hours long

Step-by-step explanation:

You can represent the situation with an equation.

3h+6=24

3h+6/3=24/3

h+2=8

h+2-2=8-2

h=6

Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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Answer:

The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.

Step-by-step explanation:

Answer:

17.021 CM

Step-by-step explanation:

7.74 +9.281 = 17.021

Answer:

17.021 CM

Step-by-step explanation:

Answer:

Definitely rational because 576 and 684 are both natural numbers

Step-by-step explanation:

Answer:

$71.50

Step-by-step explanation:

13hper hour and 5 hours is $65

and half an hour would be $6.50

and adding those together js $71.50

Answer: 2/7

Step-by-step explanation:

You take the top numbers and multiply them and then take the bottom numbers and multiply them and then you simplify.

1/3 × 6/7 = 6/21 = 2/7

To multiply fractions we'll multiply numerator with the numerator and denominator with the denominator and simplify (1/3 × 6/7) = 6/21 = 2/7.

Fractions are written in p/q form,where q ≠ 0 as it would become undefined.Fractions are of two types one is proper fraction and another one is improper fraction.

A fraction is is the form of numerator divided by the denominator.

To multiply two or more fraction we simply have to multiply numerator with the numerator and denominator with the deominator to combine them into one fraction and then we simplify the combined fraction until both the numerator and the denominator has HCF of 1.

Given (1/3 × 6/7) which is,

= 6/21.

= 2/7.

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Answer:

3

Step-by-step explanation: because 15 divided by 5 equals 3

A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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Answer:

Graph C

Step-by-step explanation:

Point T is located on Graph C at T(1, 7). To help, (x, y) = count over however many spaces horizontally, then count however many spaces vertically.

It will always be this way.

The following options are provided for which the matched pair t-test is NOT appropriate: Option (D): Calculations of the combined annual income of 100 married couples chosen at random.

This test is used whenever we need to compare the means of two sets of paired data.

For instance, if you trained several people, the pair would consist of the untrained person and the trained version of the same person.

Similarly to this, if we want to compare the means of two randomly chosen groups from a single linked unit, we can apply this test.

The first four alternatives in the list were valid pairs because they were chosen at random or under the same conditions.

In the final option, the couples were paired in biased ways because they were not normally in conditions that other spouses would be in (for example, imagine a first spouses pair is present).

After a lengthy, difficult process, the pairing was completed. Another intricate procedure was utilized to match up other spouse pairs, and so on.

Hence, the pairing is not done under the same circumstances (the complex processes tell that there is rarely any chance for the conditions to be the same)

The option for which the matched pair t-test is NOT suitable is provided by: Option D: Calculations of the combined annual income of 100 randomly chosen married couples.

Therefore, te following options is provided for which the matched pair t-test is NOT appropriate: Option (D): Calculations of the combined annual income of 100 married couples chosen at random.

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Complete question:

A matched-pairs t-test is NOT an appropriate way to analyze data consisting of which of the following? Measurements of annual income taken both before and after a two-year training course for a random sample of 100 people who took the course

A . Measurements of annual income for each twin for 100 randomly selected pairs of twins

B. Measurements of annual income for both individuals in pairs formed by matching 100 people from State A and 100 people from State B based on level of education

C. Measurements of annual income for both individuals in pairs formed by assigning 100 people to pairs at random

D. Measurements of annual income recorded for both spouses of 100 randomly selected married couples