The perimeter of a triangle is 84cm and it's area is 336cm². If one of it's sides is 30cm, find the length of other two sides. ​

According to the combination method, the number of elements in the sample space for this experiment is 3060

Combination method:

Basically, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter

Given,

A person eating at a cafeteria must choose 4 of the 18 vegetables on offer.

Here we have to calculate the number of elements in the sample space for this experiment.

While we looking into the given question, we have identified the following things,

They are

Total number of available vegetables = 18

Number of choices we have made = 4

Therefore, here the value of n = 18 and the value of x = 4,

Therefore, according to the ncx formula, it can be written as,

=> ¹⁸n₄ = 18! / 4! (18 - 4)!

=> ¹⁸n₄ = 18! / 4! (14)!

=> ¹⁸n₄ = 3060.

Therefore, there are 3060 number of elements in the sample space for this experiment.

To know more about Combination method here.

https://brainly.com/question/28571537

#SPJ4

Step-by-step explanation:

\(\sqrt{93}\approx 9.64365\)

The total area of the regions between the curves is 8 + 5π square units

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

y = 5sin(x) and y = 5 - sin(x)

The curves intersect at

x = 0 and x = π

So, the area of the regions between the curves is

Area = ∫5sin(x) - 5 - sin(x)

This gives

Area = ∫4sin(x) - 5

Integrate

Area =  -4cos(x) - 5x

Recall that x = 0 and x = π

So, we have

Area =  -4cos(0) - 5(0) + 4cos(π) - 5π

Area =  -4 - 4 - 5π

Evaluate

Area =  -8 - 5π

Take the absolute value

Area =  8 + 5π

Hence, the total area of the regions between the curves is 8 + 5π square units

Read more about area at

brainly.com/question/15122151

#SPJ4

Answer:

10 sandwiches

Step-by-step explanation:

I included the work below in the photo. Hope this helps! :)

Answer:

Step-by-step explanation:

Sum of all angles of a triangle = 180

∠M + ∠N + ∠P = 180

∠M + 119 + 31 = 180

∠M + 150        = 180

             ∠M = 180 - 150

∠M = 30°

Use Sine Rule:

\(\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}\\\\\\\dfrac{10}{Sin \ 30}=\dfrac{n}{Sin \ 119}\\\\\\\dfrac{10}{\dfrac{1}{2}}=\dfrac{n}{ 0.8746}\\\\\\10*2= \dfrac{n}{0.87}\\\\20*0.87=n\\\\\)

n = 17.4

\(\dfrac{p}{Sin \ P}=\dfrac{m}{Sin \ M}\\\\\\\dfrac{p}{Sin \ 31}=\dfrac{10}{Sin \ 30}\\\\\\\dfrac{p}{0.5150}=\dfrac{10}{\dfrac{1}{2}}\\\\\dfrac{p}{0.52}=10*2\\\\\dfrac{p}{0.52}=20\\\\\\p=20*0.52\\\\p =10.4\)

p = 10.4

Answer: x = 136.4 minutes

Step-by-step explanation:

x = (100/22)(30) minutes = 136.4 minutes

Answer:

The new graph has a steeper slope and a y-intercept of 8.

Step-by-step explanation:

From Analytical Geometry, we define a straight line by following first order polynomial (linear function):

\(y = m\cdot x + b\) (1)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(b\) - y-Intercept.

\(m\) - Slope.

And the slope represents the change in dependent variable (\(\Delta y\)) divided by the change in independent variable (\(\Delta x\)). That is:

\(m = \frac{\Delta y}{\Delta x}\)

If \(m_{1} > 0\) and \(m_{2} > m_{1}\), then the new line is steeper with respect to the original line.

Let \(y = 5\cdot x\), its slope and y-intercept are 5 and 0, respectively. If slope is changed into 9 and y-intercept becomes 8, then the new graph has a steeper slope and a y-intercept of 8.

We are given a two-way probability table

Part a)

If one of the vehicles is selected at random, determine the probability that the vehicle is a car.

From the table, we see that the total number of cars are 1441

Also, the total number of vehicles is 2420

Then the probability of selecting a car is

Therefore, the probability that the vehicle was a car is found to be 0.5955

Part b)

If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.

This is a conditional probability problem.

The conditional probability is given by

From the table, we see that,

So, the probability is

Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727

The probability that the randomly chosen vehicle is a car is  59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is  61.94%.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

The probability that the randomly chosen vehicle is a car is the total no of cars divided by the total no. of vehicles which is,

= 1441/2420.

= (1441/2420)×100%.

= 59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is the total no. of cars that used the toll pass divided by the no. of vehicles that used the toll pass which is,

= (537/867)×100%.

= 61.94%.

learn more about conditional probability here :

https://brainly.com/question/11899923

#SPJ2

Given statement solution is :- The value of m is -98/9.

The correct answer is A. -98/9.

To determine the value of m in the given system of equations, we need to find the condition under which the system has no solutions.

The system of equations can be written in matrix form as:

css

Copy code

[  9  -7 ]   [ x ]   [ 11 ]

[ 14   m ] * [ y ] = [  6 ]

For this system to have no solutions, the coefficient matrix [ 9 -7 ; 14 m ] must be singular, which means its determinant must be zero.

Determinant of the coefficient matrix:

det([ 9 -7 ; 14 m ]) = (9 * m) - (-7 * 14) = 9m + 98

Setting the determinant equal to zero, we have:

9m + 98 = 0

Solving for m:

9m = -98

m = -98/9

Therefore, the value of m is -98/9.

So, the correct answer is A. -98/9.

For such more questions on Find value m for no solutions.

https://brainly.com/question/13725258

#SPJ8

Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

Option (a) False:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

Option (b) False:

It is true that AB invertible implies \($(A B)^{\top}$\) is invertible but this does not imply B is invertible (not a valid statement).

Option (c) False:

A B is invertible does not mean \($A=B^{-1}$\). Since \($A=B^{-1}$\) implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

Option (d) True:

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

For more questions on matrices

https://brainly.com/question/13424110

#SPJ4

Answer:

soooo u do dis and dat and OPE lookit the time

Dum Step-by-step explanation:

looks like its time to act dum ayy friend me. im givin out free points every weekday. if its friday, i do it every hour, called free point friday. check me out.

Answer:

one-solution

Step-by-step explanation:

I took the test.

The square root of x² - 8x + 16, where -4 ≤ x < 4, can be simplified to |x - 4|.

1. Start with the expression x² - 8x + 16.

2. Factor the expression inside the square root: (x - 4)².

3. Since we are given the condition -4 ≤ x < 4, we know that x - 4 will always be non-negative.

4. Take the square root of (x - 4)², resulting in |x - 4|.

5. Therefore, the simplified expression is |x - 4|.

Note: The absolute value ensures that the output is always positive, regardless of the value of x within the given range.

For more such questions on square root , click on:

https://brainly.com/question/428672

#SPJ8

Answer:

I think the answer will be - 159

Because the number with similar sign are always added

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

Answer:6 and 9

Step-by-step explanation:

6*9= 54

6+9=15

Answer:

  6, 9

Step-by-step explanation:

You want the numbers that have a product of 54 and a sum of 15.

The prime factors of 54 are ...

  54 = 2 · 3³

Adding 1 to the exponents, we have (1, 3) +(1, 1) = (2, 4). The product of these increased exponents is 2·4 = 8, which means there are 8 divisors of 54, including 1 and 54.

We can write the factor pairs as ...

  54 = 1·54 = 2·27 = 3·18 = 6·9

The sums of these divisor pairs are 55, 29, 21, 15

The two numbers you seek are 6 and 9.

__

Additional comment

The reason for figuring the number of divisors is so we can check to make sure we have found factor pairs for all of them. The 8 divisors give us 8/4 = 4 factor pairs. We have found it is usually easier to find the desired sum once we have the list of factor pairs for a number.

The smallest sum of two factors will be 2√54 ≈ 14.7. This tells you that the sum of 15 will involve factors that are close to √54 ≈ 7.4. You find the factors of interest when you consider divisors that are near 7: 6 and 9.

You may have noticed it is very helpful to have a great command of your multiplication facts when working problems of this sort.

A graph can provide a quick solution, too.

#95141404393

For f(1), the given polynomial function f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 is zero.

Given,

The polynomial function;

f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120

We have to all the zeros .

Here,

We can use Rational zero theorem;

That is,

f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120

Find p/q

Where, p is 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 and q is 16

So,

p/q = (±16, ±72, ±137, ±43, ±244, ±120) / ±16

= ±1, ±4.6875. ±8.5625, ±2.6875, ±15.25, ±7.5

Now,

f(1) = 1 × 1⁵ - 4.6875 × 1⁴ + 8.5625 × 1³ + 2.6875 × 1² - 15.25 × 1 + 7.5

f(1) = 1 - 4.6875 + 8.5625 + 2.6875 - 15.25 + 7.5

f(1) = 0

That is,

For f(1), the given polynomial function f(x) = 16x⁵ - 72x⁴ + 137x³ + 43x² - 244x + 120 is zero.

Learn more about polynomial function here;

https://brainly.com/question/7215379

#SPJ1

If the mean number of people who attended three basketball games was 8,242, that means the sum of the number of people who attended all three games is equal to 8,242 multiplied by the number of games, which is 3.

What does math mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Total attendance = mean attendance * number of games

Total attendance = 8,242 * 3

Total attendance = 24,726

So the total attendance at the three games is 24,726 people.

Learn more about mean

https://brainly.com/question/1136789

#SPJ1

Answer:

Step-by-step explanation:

(-7 + 7i) - (-7 -3i) + (-7 - 8i) = -7 + 7i -7*(-1) -3i*(-i) - 7 - 8i

                  = -7 + 7i + 7 + 3i - 7 - 8i

                   = -7+ 7 - 7 + 7i +3i - 8i

Combine like terms

                  =  - 7 + 2i

The equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5 is y = - 1 / 3 x - 5 / 3

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

The equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5

Therefore, the slope of the line is - 1 / 3.

Parallel lines have the same slopes.

Therefore, let's find the y-intercept using (-2, -1)

y = - 1 / 3 x + b

-1  = - 1 / 3 (-2) + b

b = -1 - 2 / 3

b =  -3 - 2/ 3

b = - 5 / 3

Therefore, the equation is y = - 1 / 3 x - 5 / 3

learn more on equation of a line here: https://brainly.com/question/27947321

#SPJ1

Find H

\(\\ \rm\rightarrowtail H^2=36^2+15^2\)

\(\\ \rm\rightarrowtail H^2=39^2\)

\(\\ \rm\rightarrowtail H=39\)

Now

\(\\ \rm\rightarrowtail sinR=\dfrac{P}{H}=\dfrac{15}{39}=\dfrac{5}{13}\)

\(\\ \rm\rightarrowtail cosR=\dfrac{B}{H}=\dfrac{36}{39}=\dfrac{12}{13}\)

\(\\ \rm\rightarrowtail tanR=\dfrac{P}{B}=\dfrac{5}{12}\)

\(\\ \rm\rightarrowtail sinT=\dfrac{36}{39}=\dfrac{12}{13}\)

\(\\ \rm\rightarrowtail cosT=\dfrac{5}{13}\)

\(\\ \rm\rightarrowtail tanT=\dfrac{12}{5}\)

Using geometry or symmetry we get, the value of the double integral is 36π.

To evaluate the given double integral using geometry and symmetry, first observe that the region D is a semicircle with radius 6 centered at the origin (since y = sqrt(36 - x^2) is the equation of the upper half of the circle x^2 + y^2 = 36).

Now, let's set up the double integral in polar coordinates.

Let x = r * cos(θ) and y = r * sin(θ). Then, dA = r dr dθ, and the bounds for r and θ are 0 ≤ r ≤ 6 and 0 ≤ θ ≤ π, respectively. The double integral now becomes:

∬(7x+2) dA = ∬(7r*cos(θ) + 2)r dr dθ

Now, integrate with respect to r:

∫[0,π]∫[0,6] (7r^2*cos(θ) + 2r) dr dθ

= ∫[0,π] [(7/3)r^3*cos(θ) + r^2] (from r=0 to r=6) dθ

= ∫[0,π] (504*cos(θ) + 36) dθ

Now, integrate with respect to θ:

= [(504 * sin(θ) + 36θ) (from θ=0 to θ=π)]

= 504 * (sin(π) - sin(0)) + 36 * (π - 0)

= 36 * π

Learn more about symmetry , here: brainly.com/question/1597409

#SPJ11

Answer:

C)  ∠7 and ∠9

Step-by-step explanation:

Complementary angles are two angles whose measures sum to 90°.

Note that the two angles do not have to be adjacent to one another.

As lines a and b are parallel, and ∠2 and ∠4 are denoted as right angles, the sum of ∠6 and ∠7, and the sum of ∠9 and ∠10, are both 90° since angles on a straight line sum to 180°.

As ∠6 ≅ ∠7 and ∠9 ≅ ∠10 then angles ∠6, ∠7, ∠9 and ∠10 must each be 45°. Therefore, any two of these four angles are complementary.

Therefore, the pair of angles that are complementary from the given answer options is ∠7 and ∠9.

The inverse of a number is it's reciprocal. Divide 1 by the number to obtain its reciprocal.

For example, the reciprocal of 5 is 1/5, and the reciprocal of 0.5 is 2. The reciprocal of a number x is denoted by 1/x or x^(-1).

For example, to find the reciprocal of 8, you would divide 1 by 8, like this:

1/8 = 0.125

To find the reciprocal of a fraction, you can also turn the fraction upside down to get its reciprocal. For instance, 4/3 is 3/4's inverse.

To find the inverse of a matrix, you can use the following formula:

A^(-1) = (1/det(A)) * adj(A)

where A is the matrix, det(A) is the determinant of the matrix, and adj(A) is the adjugate of the matrix. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.

For example, consider the matrix A:

[a b]

[c d]

The determinant of A is:

det(A) equals (a * d) - (b * c).

The cofactor matrix of A is:

[d -b]

[-c a]

The adjugate of A is the transpose of the cofactor matrix, so it is:

[d -c]

[-b a]

The inverse of A is then:

A^(-1) = (1/det(A)) * adj(A)

= (1/((a * d) - (b * c))) * [d -c]

[−b a]

To learn more about the inverse, refer;-

https://brainly.com/question/13715269

#SPJ4

The equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\) is \(36x + 36y + 36z = 432\).

To find the equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\), we can use the point-normal form of the equation of a plane.

Step 1: Find two vectors in the plane.

Let's find two vectors by taking the differences between the given points:

Vector v₁ = \((6, 0, 6) - (0, 6, 6) = (6, -6, 0)\)

Vector v₂ = \((6, 6, 0) - (0, 6, 6) = (6, 0, -6)\)

Step 2: Find the normal vector.

The normal vector is perpendicular to both v₁ and v₂. We can find it by taking their cross product:

Normal vector n = v₁ \(\times\) v₂ = \((6, -6, 0) \times (6, 0, -6) = (36, 36, 36)\)

Step 3: Write the equation of the plane.

Using the point-normal form, we can choose any point on the plane (let's use the first given point, \((0, 6, 6)\)), and write the equation as:

n · (x, y, z) = n · (0, 6, 6)

Step 4: Simplify the equation.

Substituting the values of n and the chosen point, we have:

(36, 36, 36) · (x, y, z) = (36, 36, 36) · (0, 6, 6)

Simplifying further:

\(36x + 36y + 36z = 0 + 216 + 216\\36x + 36y + 36z = 432\)

Therefore, the equation of the plane passing through the given points is:

\(36x + 36y + 36z = 432\)

For more questions on equation of the plane:

https://brainly.com/question/30655803

#SPJ8

Hope this helps you

Answer:

the third one/second one

Step-by-step explanation:

Answer:

D: -5.3333333...​

Step-by-step explanation:

Which number is rational?

All given options are non-terminating, but the last one has repeating decimal

It can be represented as fraction:

Answer:

Yeah its D i just checked

Step-by-step explanation:

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

To read more about population, visit:

https://brainly.com/question/30396931

#SPJ11

The rapidly increase of radius of spill is

when the area is 8 is 0.9 miles/hr.

let the radius and area of oil spill be r and A .

we have given that,

Area increases at a constant rate of 6 miles²/hr i.e., dA/dt = 9

we have to find out the rapid change in radius of circle i.e., dr/dt = ?

Area of circle (A) = π r²

Takeing the derivative with respect to time

dA/dt = 2 π r × (dr/dt)

Substitute values and solve for dr/dt:

When A = 8 -> 8 = π r²-> r = sqrt(8/π)

putting all values in equation (1) we get,

9= 2 π sqrt(18/π) × (dr/dt)

dr/dt = 9/2(π× sqrt(8/π)) miles/hr

=> dr/dt = 9/10.023 = 0.89

Hence , 0.9miles / hr is rate of change of radius of oil spill when area is 8.

To learn more about Rate of change of radius , refer:

https://brainly.com/question/19672359

#SPJ4

Answer:

Its 4.

Step-by-step explanation:

So the if its 4 superscript 5, the big number is 4 and its the base, the small number is the exponent.

hope it helps! And Goodluck on your test luv ☺