I need help with this! ASAP

Answer:  \(\frac{n!}{(n-r)!}\)

The exclamation marks indicate factorial.

For instance, 4! = 4*3*2*1 = 24. You start with the given number and multiply your way down to 1.

For more information, check out the nPr permutation formula.

The five-number summary is:

Minimum: 5

Q1: 60.5

Median (Q2): 72

Q3: 84

Maximum: 99

The middle number or central value within a set of data is known as the median. The number that falls in the middle of the range is also the median.

To find the five-number summary, we need to arrange the given test scores in ascending order:

5, 31, 41, 45, 48, 52, 55, 56, 58, 63,

65, 67, 67, 69, 70, 70, 74, 75, 78, 79,

79, 80, 81, 83, 85, 87, 90, 92, 95, 99.

The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

1. Minimum: The smallest value in the data set is 5.

2. Q1: The first quartile is the median of the lower half of the data set. The lower half of the data set is:

5, 31, 41, 45, 48, 52, 55, 56, 58, 63,

65, 67, 67, 69.

The median of this lower half is (58 + 63) / 2 = 60.5. Therefore, Q1 = 60.5.

3. Q2 (Median): The median is the middle value in the data set. Since there are 30 data points, the median is the average of the 15th and 16th values:

Q2 = (70 + 74) / 2 = 72.

4. Q3: The third quartile is the median of the upper half of the data set. The upper half of the data set is:

75, 78, 79, 79, 80, 81, 83, 85, 87, 90,

92, 95, 99.

The median of this upper half is (83 + 85) / 2 = 84. Therefore, Q3 = 84.

5. Maximum: The largest value in the data set is 99.

The five-number summary is:

Minimum: 5

Q1: 60.5

Median (Q2): 72

Q3: 84

Maximum: 99

Learn more about median on:

https://brainly.com/question/14532771

#SPJ4

Answer:

6/12 ≈ 1/2

Step-by-step explanation:

Q) 2/3 × 3/4 = ?

→ a = 2/3 × 3/4

→ a = (2 × 3)/(3 × 4)

→ a = 6/12

→ [ a = 1/2 ]

1/2

Multiply the numerators and the denominators of both fractions,

2  *  3

_____    

3  *  4

= 6/12

Simplify.

1/2

Answer:

100 percent written as a decimal would just be 1

Step-by-step explanation:

For example, 50% is 0.50 in decimal form that would make 100% well, 1.0

Hope this helps and have a great day!

You got this :)

Answer:

Mrs. Taylor bought 200 oranges ;) .

Answer:

200

Step-by-step explanation:

If 30% of the oranges were bad, then that means 0.3 * total number of oranges, were bad. so if 0.3 * total = 60, then 60/0.3 = total number of oranges.

By the concept of unitary method, she will take 20 hours to complete a video as definition of unitary method says "The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value".

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method refers to the process of determining the value of a single unit from the values of several other units and using that value to determine the value of the necessary number of units.

Here,

As she takes 4 hours to edit a 3 minute video,

by unitary method,

so she take 4/3 hour to edit a 1 minute video.

To edit a 15 minute video,

she will take 15*4/3 hours.

=20 hours

As stated in the definition of the unitary method, "the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value," it will take her 20 hours to complete a video using this method.

To know more about unitary method,

https://brainly.com/question/23423168?referrer=searchResults

#SPJ1

The value of x regarding the given situation is 0.25.

Give that the spinner has sections labelled 1, 2, 3, 4 and 5.

In probability theory, the sum of all probabilities within a particular sample space should always be equal to 1.

This principle is known as the axiom of probability or the normalization condition.

The probability of an event represents the likelihood of that event occurring. When considering all possible events within a sample space, the sum of their probabilities must be 1.

This signifies that one of the possible outcomes within the sample space is certain to occur.

Here,

The probability of each number is given but probability of number 1 is not given,

So,

The probability of number 1 = 1 - (0.15 + 0.05 + 0.2 + 0.35) = 1 - 0.75 = 0.25

Hence the value of x regarding the given situation is 0.25.

Learn more about probability click;

https://brainly.com/question/32117953

#SPJ1

Answer:

  B(-π/3, 1/2), D(7π/6, -√3/2), E(11π/12, -1/2)

Step-by-step explanation:

You want the coordinates of various points marked on the graph of the sine and cosine functions.

The horizontal divisions on the graph are multiples of π/6. That is, there are 6 divisions between 0 and π. This means the x coordinates of interest are ...

  B = -π/3

  D = 7π/6

  E = 11π/6

Points B and D lie on the red curve, which the graph tells you is a plot of cos(x). Then the coordinates are ...

  B = (-π/3, cos(-π/3)) = (-π/3, 1/2)

  D = (7π/6, cos(7π/6) = (7π/6, -√3/2)

Point E lies on the blue curve, which is a plot of sin(x). Its coordinates are ...

  E = (11π/6, sin(11π/6)) = (11π/6, -1/2)

__

Additional comment

The attachment shows the coordinates of points on the unit circle as (cos(θ), sin(θ)). On the given graph, θ is on the horizontal axis (x), and sine and cosine are on the vertical axis. To make use of the attachment, you find the angle, then look for the (cos, sin) coordinates at that angle.

Negative angles are clockwise from θ=0. To find the corresponding angle on the attachment, add 2π to any negative angle.

Answer:

Answer:

please join my meeting

We are given a matrix A and a scalar λ and asked to show that λ is an eigenvalue of the matrix and determine a basis for its eigenspace.

To determine if λ is an eigenvalue of matrix A, we need to check if there exists a non-zero vector v such that Av = λv. In other words, if multiplying matrix A by vector v results in a scaled version of v. Given the matrix A = [6, 9; -10, 63] and scalar λ = 5, we can find the eigenvectors by solving the equation (A - λI)v = 0, where I is the identity matrix. Substituting the values, we have: [6-5, 9; -10, 63-5]v = 0. Simplifying the equation, we get: [1, 9; -10, 58]v = 0. Solving the system of linear equations, we can find the eigenvectors v corresponding to the eigenvalue λ = 5.

To know more about eigenvectors here: brainly.com/question/31043286

#SPJ11

Answer:

\(-7^\circ C\)

Step-by-step explanation:

Let

x -----> the height in meters

y ----> the temperature in Celsius degree

we know that

The linear equation in slope intercept form is equal to

\(y+mx+b\)

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit rate is equal to

\(m=-\dfrac{1}{100} \dfrac{^\circ C}{m}\) ---> is negative because is a decreasing function

The y-intercept or initial value is equal to

\(b=4^\circ C\) ----> value of y when the value of x is equal to zero (sea level)

substitute

\(y=-\dfrac{1}{100} x+4\)

For x=1,100 m

substitute in the linear equation and solve for y

\(y=-\dfrac{1}{100} (1,100)+4\)

\(x=-7^\circ C\)

Answer:

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Step-by-step explanation:

Geometric Sequences

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

\(\displaystyle r=\frac{-28}{112}=-\frac{1}{4}\)

Testing with the third term:

\(\displaystyle -28*-\frac{1}{4}=7\)

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

\(a_n=a_1*r^{n-1}\)

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer: LX - 13z - 2

Step-by-step explanation:

(3z + 4z)= 7z

LX - 7z - (6z - 2)

LX + -7z + -6z + -2

LX + -13z + -2

= LX - 13z - 2

To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

Know more about inequality here:

https://brainly.com/question/25275758

#SPJ11

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Step-by-step explanation:

\( \underline{ \text{Let \: the \: required \: number \: be \: x}} : \)

\( \text{According \: to \: question \: (ATQ)} : \)

⟼ \( \tt{ \frac{1}{3} \times x = 7}\)

⟼ \( \tt{ \frac{1 \times x}{3} = 7}\)

⟼ \( \tt{ \frac{x}{3} = 7}\)

Apply cross product property :

⟼ \( \boxed{ \sf{x = 27}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \underline{ \tt{x = 27}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

74 and 32

Step-by-step explanation:

Because the sides AC and BC are equal, their opposite angles will be equal. Therefore angle B will also be 74 degrees.

To find angle C, we subtract 74 and 74 from 180 because a triangle's angle measures should add up to 180 degrees.

180 - 74 - 74 = 32

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$700\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &16 \end{cases}\)

\(A = 700\left(1+\frac{0.105}{12}\right)^{12\cdot 16} \implies A = 700( 1.00875)^{192}\implies A \approx 3728.54\)

Answer:

\( \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C\)

Step-by-step explanation:

we would like to integrate the following integration:

\( \displaystyle \int \frac{ \sin(x + a) }{ \sin(x) } dx\)

we can rewrite the denominator by using algebraic identity given by:

\( \displaystyle \rm\sin( \alpha \pm \beta ) = \sin( \alpha ) \cos( \beta ) \pm \cos( \alpha ) \sin( \beta ) \)

thus substitute:

\( \displaystyle \int \frac{ \sin(x ) \cos(a) + \cos(x) \sin(a) } { \sin(x) } dx\)

we should rewrite integrand as sum therefore we can use sum integration formula

\( \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } + \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx\)

use sum integration formula:

\( \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx\)

reduce fraction:

\( \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx\)

rewrite:

\( \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) } { \sin(x) } \cdot \sin( a) dx\)

use trigonometric indentity:

\( \displaystyle \rm\int \cos(a) dx + \int \cot(x) \cdot \sin( a) dx\)

use constant integration formula

\( \displaystyle \rm\int \cos(a) dx + \sin(a) \int \cot(x) dx\)

use integration rules:

\( \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right)\)

and finally we of course have to add constant of integration

\( \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C\)

And we are done!

\(\text{Note:I used integration by substitution to figure out }\\\displaystyle \int \cot(x)dx \:\text{part}\)

Answer:

300

Step-by-step explanation:

1W+4W=375

5W=375

W=75

75*4

The change in air pressure when the pure tone is produced is mathematically given as

p(1/2000) =0 mP

This pressure is referred to as the atmospheric pressure, air pressure, or simply pressure. It is the force that is exerted on a surface by the air that is above it due to the gravitational pull that gravity has on the surface. A barometer is an instrument most often used to measure the pressure of the atmosphere. When the pressure in the atmosphere changes, a column of mercury contained inside a glass tube in a barometer will either rise or sink.

Generally, the equation for is pressure  mathematically given as

\(p(t) =2sin (4000\pi t)\)

Therefore

p(1/2000) =2sin (4000\pi *1/2000)

p(1/2000) = 2sin (2\pi)

p(1/2000) = 2*0

p(1/2000) =0 mP

In conclusion, the pressure

p(1/2000) =0 mP

Read more about air pressure

https://brainly.com/question/15189000

#SPJ1

Triangle AED and triangle BEC have equal areas. The length of AE can be represented as 14 - x (since AC = 14). AE is equal to 10.

To find the length of AE, we can use the fact that triangle AED and triangle BEC have equal areas. Since the areas of two triangles with the same height are proportional to their base lengths, we can set up the following proportion:

Area of triangle AED / Area of triangle BEC = AE / EC

Let's denote EC as x (the length of EC). Then, the length of AE can be represented as 14 - x (since AC = 14).

Now, let's look at the given information about the lengths of the sides of the quadrilateral:

AB = 9

CD = 12

AC = 14

We can use the given information to find the lengths of the other sides of the quadrilateral:

BC = AC - AB = 14 - 9 = 5

AD = AC - CD = 14 - 12 = 2

Next, we can calculate the areas of triangle AED and triangle BEC using the lengths of their sides:

Area of triangle AED = (1/2) * AD * AE

Area of triangle BEC = (1/2) * BC * EC

Since the areas of the two triangles are equal, we can set up the following equation:

(1/2) * AD * AE = (1/2) * BC * EC

Plugging in the values we know:

(1/2) * 2 * (14 - x) = (1/2) * 5 * x

Simplifying the equation:

14 - x = (5/2) * x

Multiplying both sides by 2 to clear the fraction:

28 - 2x = 5x

Adding 2x to both sides:

28 = 7x

Dividing both sides by 7:

x = 4

Therefore, the length of EC is 4.

Since AE = AC - EC, we can calculate AE:

AE = 14 - EC = 14 - 4 = 10

So, AE is equal to 10.

To learn more about triangles visit:

brainly.com/question/11070154

#SPJ11

The complete question is:<Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC = 14 and triangle AED and triangle BEC have equal areas. What is AE?>

The closest answer to initial value of the account is $538,021.66

It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,

Amount withdrawn every quarter, P = $4567

Rate of interest, r  =  = 0.002525

Time period, n = 35 × 4 = 140

Now, as we know the formula for annuity as,

\(PV = PMT[(1 - (1 / ( 1 + r)^n)) / n]\)

where P = installments, PV = present value, r = rate of interest and n = time period.

This gives,\(PV = PMT[(1 - (1 / ( 1 + r)^n)) / n]= 4567[1 - (1 / 1.00253^40)) / 0.00253]\)

= 4567[(1 - 0.70254) / 0.00253]

= 4567[117.80636]

= $538,021.66

So, the closest answer to initial value of the account is $538,021.66

Learn more about banking at:

brainly.com/question/29616806

#SPJ1

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To know more about continuity visit:

brainly.com/question/21447009

#SPJ1

Answer:

Step-by-step explanation:

We first need to come up with a system of equations that models this situation. Let's call apple pies "a" and lemon pies "L". Then we look to each individual involved in selling these pies and come up with an equation for each. Scott sold 3 apple and 12 lemon pies. The combination of this number of these 2 types of pies grossed him $141. In equation form, the combination of this number of these 2 types of pies is an addition thing. Namely,

3a + 12L = 141

For Paul, his combination was 2 apple and 5 lemon for a total of $64. His equation is

2a + 5L = 64

We need to solve this system either by substitution or elimination/addition to come up with the cost of both types of pies. I chose elimination/addition because I think in this case it is easier, and easier is good.

Setting up for elimination/addition:

3a + 12L = 141

2a  + 5L = 64

Let's first eliminate the a terms. That means that the coefficient on each a has to be the same but with different signs. The LCM of both 3 and 2 is 6, so we will multiply the top equation by 2 and the bottom equation by -3 (we could also have chosen to eliminate the L's first; we also could have chosen to eliminate the a's first but made the 2 negative instead of the 3. As long as you do the math correctly, you'll get the same answer regardless of how you choose to do it). Multiplying the first equation by 2 and the second by -3 gives us a new system:

6a + 24L = 282

-6a - 15L = -192

The reason this is called the elimination or addition method is because the goal is to eliminate, but you do that by adding the columns together. As you can see, 6a - 6a eliminates the a terms, right? What you're left with then is

9L = 90 and

L = 10

Now that we know the cost of a lemon pie, we can back sub in to solve for the cost of an apple pie. It doesn't matter which equation you back sub into, as long as it has both an L and an a in it.  I'll choose the first equation we wrote when we took on this nightmare:

3a + 12L = 141.  Subbing in 10 for L gives us

3a + 12(10) = 141 and

3a + 120 = 141 and

3a = 21 so

a = 7

That means that lemon pies cost 10 each and apple pies cost 7 dollars each.

The order would be DE < FD < EF. To order the sides of triangle ΔDEF from shortest to longest, you need to compare the lengths of the sides.

1. Determine the lengths of sides DE, EF, and FD.
2. Compare the lengths to find the shortest side.
3. Identify the next shortest side.
4. The remaining side will be the longest.

Once you have the side lengths, simply arrange them in ascending order (from shortest to longest) to answer your question. For example, if DE is 3 units, EF is 5 units, and FD is 4 units, the order would be DE < FD < EF.
learn more about triangles here: brainly.com/question/1163433

#SPJ11