Rewrite the expression with rational as a radical expression

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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The answer choice which represents a function among the given answer choices is; Choice B.

According to the given task content; the table which represents a function among the given answer choice is to be identified.

Recall that a function can be defined as a relation in which case; each input value is assigned not more than one value.

By observation, only the answer choice B has a combination of input and output values in which case; each input value is assigned only one output value.

Hence, since a function is a relation which is characterized by assigning only one output value to each input value; the correct answer choice is; Choice B.

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Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

vhhg

Step-by-step explanation:

rrgggggggjjhjjhgghghhh

The auditory canal would resonate at approximately 7154.17 Hz and 14304.35 Hz for the first two harmonics. The corresponding sound wavelengths would be approximately 0.048 m and 0.024 m for the fundamental frequency and second harmonic, respectively.

To determine the resonant frequencies of the auditory canal in its first two harmonics, we can use the formula for the resonant frequencies of a closed-end cylindrical tube:

f = (n * c) / (2L)

Where:

f = resonant frequency

n = harmonic number (1 for the fundamental frequency, 2 for the second harmonic, and so on)

c = speed of sound in air (approximately 343 m/s at room temperature)

L = length of the auditory canal (2.4 cm = 0.024 m)

A. Resonant frequencies in the first two harmonics:

For the fundamental frequency (n = 1):

f₁ = (1 * 343) / (2 * 0.024) ≈ 7154.17 Hz

For the second harmonic (n = 2):

f₂ = (2 * 343) / (2 * 0.024) ≈ 14304.35 Hz

B. Corresponding sound wavelengths in part A:

The wavelength of a sound wave can be determined using the formula:

λ = c / f

For the fundamental frequency (n = 1):

λ₁ = 343 / 7154.17 ≈ 0.048 m (or 4.8 cm)

For the second harmonic (n = 2):

λ₂ = 343 / 14304.35 ≈ 0.024 m (or 2.4 cm)

Therefore, the auditory canal would resonate at approximately 7154.17 Hz and 14304.35 Hz for the first two harmonics. The corresponding sound wavelengths would be approximately 0.048 m and 0.024 m for the fundamental frequency and second harmonic, respectively.

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Answer:

30 strawberry sundaes.

Step-by-step explanation:

We know there is a total of 70 sundaes.

3 sundaes will be strawberry.

4 sundaes will be choclate.

When you add 3 and 4 together, you get 7. This is your total ratio.

So 3/7 of the sundaes are strawberry.

And 4/7 of sundaes are choclate.

We know there is a total of 70 sundaes.

The total ratio we figured out is 7.

If the total sundaes is 70, and the total ration is 7. Then the total sundaes is 10 times bigger than the ratio.

This means we need to multiply the 3 strawberry sundaes and 4 choclate sundaes by 10.

3*10=30

4*10=40

So there are 30 strawberry sundaes and 40 choclate sundaes.

We need to find the strawberry sundae amount, so the answer is 30.

Hope this helps!

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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Answer:

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Given equation,

→ 3x - 12 = 15

Now the value of x will be,

→ 3x - 12 = 15

→ 3x = 15 + 12

→ x = 27/3

→ [ x = 9 ]

Hence, the value of x is 9.

Answer: wowwww LOL

Step-by-step explanation:

Thanks Mr Shady, the f r e e p o. i n t s are now mine.

Answer:

Hey mate, here's ur answer:

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

-2x^5. 4x^2

=(−2)*x5*4*x2

=−8*x7

=−8x7

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

Hope it helps

#stayhomestaysafemate

:D

Step-by-step explanation:

Rearrange the equation so "y" is on the left and everything else on the right. or below the line for a "less than" (y< or y≤).

Answer:

23:18 23 to 18 23/18

Step-by-step explanation:

So really there is no step by step process. You just need to know the ways to write ratios!

Hope this helps!!

The total area of the first floor of the tiny house is 121 square feet

The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:

Total area = Area of kitchen + Area of bathroom

The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:

Area of kitchen = 11 x 7 = 77 square feet

Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:

Area of bathroom = 11 x 4 = 44 square feet

Substituting these expressions into the equation for the total area, we get:

Total area = Area of kitchen + Area of bathroom

= 77 + 44

= 121 square feet

Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.

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Answer:

\(<F+<K+<H+<G=360\)°

\(90\)°\(+3x+90+2x=360\)°

⇒\(5x+80=360\\\)

⇒\(5x=360-+80\)

⇒\(5x=-+80\)

⇒\(x=\frac{-+80}{5}\)

⇒x=36°

3x=3×36=108°

2x=2×36=72°

FG≈HG=17

hope it helps...

have a great day!!

Step-by-step explanation:

1st - false

2nd - true

3rd - false

Answer:

it is true, true, false. your welcome

Answer:

Answer should be 24.......

Answer:

12

Step-by-step explanation:

Substitute 5 for x in 4(2x - 7):

4(2[5] - 7), or

4(10 - 7), or

4(3) = 12

The triangle is solved to ;

A = 28. 8°, a = 26, c = 52. 8

Using the sine rule, we have that;

sin B/b = sin C/c

Where;

Then, we have;

sin 49.2/40.9 = sin 102/c

cross multiply the values, we have;

c = 40. 006/0. 75

c = 52. 8

For A, we have;

A = 180 - 151.12

A = 28. 8 degrees

To determine a, we have;

sin 49.2/40. 9 = sin 28.8/a

a = 19. 703/0.75

a = 26

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First part (to find mMON) is correct.

To find mPON, we can't assume the angle has been divided into two equal parts; so we need to apply the same procedure as on finding MON:

tan⁻¹(2/6) = 18.26°

Answer:

correct answer : 3 questions

Step-by-step explanation:

alexa completed = 20% of 30 = 6 questions

Brent completed = 30% of 30 = 9 questions

so Brent completed 3 questions more than Alexa ...

plz mark my answer as brainlist plzzzz vote me

Answer:

5/5

Step-by-step explanation:

Assuming that when you say 1 as a whole number, the value 1 would be 5/5 when the denominator is five.

Answer:

z = 10

Step-by-step explanation:

Lets explain this to you,

Step one: Solve with the parenthesis first (2 times z is 2z and 2 times -8.5 is

-17)

Step two: Subtract 2z from both sides (0.3z - 2z = - 1.7) (2z - 2z = 0)

Step three: Divide negative 1.7 on both sides (-1.7 = -17)

Step four: Simplify - 1.7 / 17 which will finally be 10

There is an easier way but im also in class so I'll do it later!!!!

The given statement is false.

You can compare two marginal distributions to see if the corresponding two variables are related - False.

Comparing marginal distributions can only disclose information about the distribution of each variable individually, not whether the variables are connected or not.

To see if two variables are connected, we must look at their joint distribution or conditional distribution. To examine the degree and direction of a link between two variables, statistical approaches such as correlation analysis or regression analysis can be utilised.

As a result, comparing marginal distributions is insufficient to tell whether two variables are connected or not.

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The total volume of the sculpture is 87.625 cubic units. The total volume of the solid sculpture can be calculated by adding the volume of the larger cube and the smaller cube, then subtracting the overlapping volume.

The larger cube has dimensions of 4 × 4 × 4, so its volume is 4³ = 64 cubic units. The smaller cube has dimensions of 3 × 3 × 3, so its volume is 3³ = 27 cubic units.

The smaller cube is attached to the larger cube such that one of its vertices touches the edges of the larger cube, which means that 1/8 of the smaller cube is inside the larger cube. To find the overlapping volume, we need to calculate 1/8 of the volume of the smaller cube: (1/8) × 27 = 3.375 cubic units.

Now we subtract the overlapping volume from the sum of the volumes of both cubes to find the total volume of the sculpture:

64 (larger cube) + 27 (smaller cube) - 3.375 (overlapping volume) = 87.625 cubic units.

So, the total volume of the sculpture is 87.625 cubic units.

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The distance of the jot air balloon to ground is 21.62 ft.

Here, we have,

In triangle ACB:

tan36° = x/y

x  = y tan36°

In triangle ADB:

tan25° = x/y + 12

x  = y+12 * tan25°

Therefore equating both equations gives:

y tan36°  =  y+12 * tan25°

y tan36°  =  y tan25° + 12tan25°

so, we get,

y = 21.50 ft

Therefore x = 21.50*tan(36) = 15.62 ft

The distance of the jot air balloon to ground = 15.62 + 6 = 21.62 ft

Hence, The distance of the jot air balloon to ground is 21.62 ft.

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The correct statement about their work is: Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.

Adler started with the equation (13/8) = k(1/2) and subtracted 1/2 from both sides to get (13/8) - (1/2) = k(1/2) - (1/2). Then simplifying, Adler obtained (9/8) = k.

Erika started with the equation (13/8) = k(1/2) and multiplied both sides by -1/2 to get (13/8)(-1/2) = k(1/2)(-1/2). Simplifying, Erika obtained (9/8) = k.

Both Adler and Erika arrived at the correct value of k = 9/8, despite using slightly different approaches. The inverse of addition (subtracting 1/2) and the opposite of one-half (multiplying by -1/2) were correctly applied in their respective calculations.

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The value of x in the triangle UVW is 45°.

A polygon which has three sides and three vertices is called as triangle.

The sum of all the angles of the triangle is 180°.

Given:

The measures of the angle of the triangle UVW are 24°, 30° and (3x - 9)°.

The sum of all the angles of the triangle is 180°.

24° + 30° + (3x - 9)° = 180°.

3x - 9 = 180 - 54

3x = 135

x = 45.

Therefore, the value of x is 45°.

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The volume of the given solid over the indicated region of integration, f(x,y) = 2x + 2y - 5 and R = {(x,y): -4 ≤ x ≤ 1, 3 ≤ y ≤ 6}, is 63 units³.

To find the volume, we will integrate the function f(x,y) over the region R. Follow these steps:

1. Set up the double integral: ∬R (2x + 2y - 5) dA

2. Set up the limits of integration: ∫(from -4 to 1) ∫(from 3 to 6) (2x + 2y - 5) dy dx
3. Integrate with respect to y: ∫(from -4 to 1) [(2xy + 2y²/2 - 5y)] (evaluated from 3 to 6) dx
4. Simplify and evaluate: ∫(from -4 to 1) [6x + 18 - 5(6-3)] dx
5. Integrate with respect to x: [3x² + 18x - 15x] (evaluated from -4 to 1)
6. Simplify and evaluate: (3 + 18 - 15) - (-12 + 72 + 60)
7. Calculate the final result: 6 - (-30) = 36

The volume of the region is 63 units³.

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Answer:

Answer:

Permutation:

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Formula:

\(nPr=\frac{n!}{(n-r)!}\)

Example:

Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.

Combination:

In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.

Formula:

\(nCr=\frac{n!}{r!(n-r)!}\)

Example:

Combination: Picking a team of 3 people from a group of 10.

C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Formula:

Conditional Probability P(A | B) = P(A∩B) / P(B)

Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)

Example:

Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.

~permutation~

Permutation is a term that in mathematics refers to several different meanings in different areas.

Permutation can be permutation with repetition and permutation without repetition.

nPr=

(n−r)!

n!

~Permutation without repetition~

Permutation means to combine the default elements in all possible ways so that each group contains all the default elements.

The number of permutations of a set of n different elements is equal Pn=n×(n-1)×...×2×1=n!

~Permutation with repetition~

If between n given elements there are k1 equals of one kind, k2 equals of another kind,..., ky equals of rth kind, we speak of permutations with repetition.

~combinations without repetition~

In many counting problems, the order of the selected elements is not important.

Each choice of r different elements of an n-member set determines one of its subsets that has r elements, we call it a combination of r-th class without repetition of n elements.

nCr=

r!(n−r)!

n!

~combinations with repetition~

Repetition combinations are combinations in which elements can be repeated.

~Variations without repetition~

A variation of the r-th class in an n-membered set is each ordered r-torque of different elements.

(We can determine this number using the principle of consecutive counting).

~Variations with repetition~

If the elements in ordered r-tuples can be repeated we are talking about variations with repetition.

(We can determine this number using the principle of consecutive counting).

Answer: X=3

Step-by-step explanation:

This triangle has a centroid which means the line is 2/3 and 1/3.

3x+1= 2(2x-1)

3x+1= 4x-2

x=3

Answer:

Option E

Step-by-step explanation:

The two points are (1,6) and (-3,-6) . We can find the Equation of the line using two point form , as ,

\(\implies y - y_1 =\dfrac{y_2-y_1}{x_2-x_1}(x - x_1) \\\\\implies y - 6 = \dfrac{-6-6}{-3-1}(x-1) \\\\\implies y-6 = \dfrac{-12}{-4}(x-1) \\\\\implies \boxed{\boxed{y -6 = 3(x-1)}} \)

On looking at options we see that option E is correct .