to find the average of a set of numbers, add up all the items and divide by?

Complete sentence is,

The square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16

We have to given that;

Taking the square root of a number technically results in two solutions.

Here, The number is,

⇒ 16

Take square root as;

⇒ √16

⇒ ± 4

Since, 4² = 16

And, (- 4)² = 16

Thus, We get;

the square root of 16 is 4 or - 4 because 4² = 16 and (- 4)² = 16.

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The percentage of the data values are between 110 and 170 = 37.5%

We know that in the box plot, the first quartile is nothing but 25% from smallest to largest of data values.

The second quartile is nothing but between 25.1% and 50% (i.e., till median)

The third quartile: 51% to 75% (above the median)

And the fourth quartile: 25% of largest numbers.

In the attached box plot, we can observe that between two numbers on the number line there are 5 equal parts.

So, each unit length measures 10 units.

Also, the median of the data = 110

We need to find the percentage of the data values are between 110 and 170.

i.e., the percentage of the data values are in the third quartile.

The range of this box plot is: 190 - 30 = 160

The data values are between 110 and 170 = 60

Using percentage formula,

P = (60/160) × 100

P = 37.5%

This is the required percentage.

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Find the complete question below.

Answer:

1. C

2. B

3. A

4. D

is the correct answer

Answer:

1. 1/3 --> all sides in an equilateral triangle are equal, so the constant of proportionality would be 1/3

2. 10/4*9 = 22.5

3. 8/2 = 4

4. c/g = m

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The amount of investment in 8% and 7% of the profit will be $14,000 and $6,000, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Sophie put a portion of her $20,000 in bonds that created an 8% gain and the rest in bonds that created a 7% gain. In the event that the benefit on the 8% bonds was 700$ more than the benefit on the 7% bonds.

Let 'x' be the amount of investment in 8% profit. Then the amount of investment in 7% profit is ($20,000 - x). Then the equation is given as,

0.08x - 0.07(20,000 - x) = 700

0.08x + 0.07x - 1,400 = 700

0.15x = 2,100

x = $14,000

Then the amount of investment in 7% profit will be given as,

($20,000 - x) = $20,000 - $14,000

($20,000 - x) = $6,000

The amount of money in 8% and 7% of the benefit will be $14,000 and $6,000, separately.

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Answer: Graph the value of b first on the Y - axis

The slope - intercept form of equation is

y = mx + b

where m = slope , and b = intercept

You graph the value of b on the Y - axis

Answer:

UNDEFINED

Step-by-step explanation:

Can't further simplify the function

The equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

To rewrite the expression \(x^2 + 5x + 6\) in the form \(x^2 + rx + sx + 6\), we need to find values for r and s such that the coefficients of the x terms match.

Given expression: \(x^2 + 5x + 6\)

To factorize this expression, we need to find two numbers that multiply to give 6 and add up to 5. The numbers that satisfy these conditions are 2 and 3.

Now, let's rewrite the expression using these values:

\(x^2 + 2x + 3x + 6\)

By grouping the terms, we can rewrite it as:

\((x^2 + 2x) + (3x + 6)\)

Factoring out the common terms in each group:

x(x + 2) + 3(x + 2)

Now, notice that (x + 2) appears as a common factor in both terms. We can further simplify the expression:

(x + 2)(x + 3)

Thus, the equivalent expression in the form \(x^2 + rx + sx + 6\) is:

\(x^2 + 2x + 3x + 6\), which can be further factored as (x + 2)(x + 3).

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Hey there!

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

= 10 * 10 + (3 + 5)^2 - 5

= 100 + (8)^2 - 5

= 100 + (8 * 8) - 5

= 100 + 64 - 5

= 164 - 5

= 159

Therefore, your answer is: 159

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

10² + (3 + 5)² - 5 = 159

Step-by-step explanation:

Given expression,

→ 10² + (3 + 5)² - 5

Evaluating the expression,

→ 10² + (3 + 5)² - 5

→ 10² + 8² - 5

→ 100 + 64 - 5

→ 100 + 59

→ 159

Hence, the answer is 159.

Answer: 0.4 >-8 /9(8+7)

Sorry if it isn't correct!!

Work Shown:

Range = Max - Min

Range = Oldest - Youngest

Range = 35 - 6

Range = 29

The range of 29 is the gap between the youngest person and the oldest.

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.

In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:

(t, h) = (0 s, 5 ft)

Second, the final height of the ball is equal to:

h = 5 ft

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Hi Bixby can you help me with this Mr. CV is making an area to display 9 pictures for for each pair of different functions there are 2 Irish he can we how many different areas can Mr. Semi make is in the number of a rice old number odd or even

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Given statement solution is :-  For the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.

Regular Pay:

Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:

Regular Pay = Regular Hours x Hourly Rate

Regular Pay = 40 hours x $11.90/hour

Regular Pay = $476

Overtime Pay:

Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.

Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)

Overtime Pay = 13 hours x ($11.90/hour x 1.5)

Overtime Pay = 13 hours x $17.85/hour

Overtime Pay = $231.45

Gross Pay:

Gross Pay is the sum of Regular Pay and Overtime Pay.

Gross Pay = Regular Pay + Overtime Pay

Gross Pay = $476 + $231.45

Gross Pay = $707.45

Therefore, for the third week of April, Patricia's:

Regular pay amount is $476.

Overtime pay is $231.45.

Gross pay is $707.45.

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Answer:

Step-by-step explanation:

5-9.5= whats the awser to make the eqation true

5 - 9.5 = -4.5

Answer:

its -4.5 so I hope this helps you out

The hypotenuse of a right triangle will be $561$.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Lengths of legs of a right triangle are given that are $264$ and $495$.

According to The Pythagorean Theorem,

\(hypotenuse^{2} = lenght^{2} + lenght^{2}\\hypotenuse^{2} = 264^{2} + 495^{2}\\\\hypotenuse^{2} = 69,696 + 245,025\\ hypotenuse^{2} = 314,721\\hypotenuse = 561\)

The hypotenuse of a right triangle will be $561$.

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Answer:

To join (something) to something else so as to increase the size, number, or amount.

Step-by-step explanation:

Dictionary

Answer:

its when you put together (two or more numbers or amounts) to calculate their total value.

Step-by-step explanation:

1+1=2

To express √35 in surd form, we need to simplify the square root as much as possible.

First, we can factor 35 into its prime factors:

35 = 5 × 7

Then, we can write √35 as:

√35 = √(5 × 7)

Using the property of square roots that √(ab) = √a × √b, we can simplify this expression as:

√35 = √5 × √7

So, the surd form of √35 is √5 × √7.

Answer:

C

Step-by-step explanation:

Translate up & left then reflect over y axis.

Answer:

C

Step-by-step explanation:

First you have to translate up and then left, then reflect over the y axis.

Answer:

24/91

Step-by-step explanation:

We can see that the square on the right has a side length of 24 and the square on the left has a side length of 91.

The scale factor = square on right/square on left = 24/91

Answer:

r=144

Step-by-step explanation:

Cross multiply:

12 * 60 = r * 5

Simplifying

12 * 60 = r * 5

Multiply 12 * 60

720 = r * 5

Reorder the terms for easier multiplication:

720 = 5r

Solving

720 = 5r

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-5r' to each side of the equation.

720 + -5r = 5r + -5r

Combine like terms: 5r + -5r = 0

720 + -5r = 0

Add '-720' to each side of the equation.

720 + -720 + -5r = 0 + -720

Combine like terms: 720 + -720 = 0

0 + -5r = 0 + -720

-5r = 0 + -720

Combine like terms: 0 + -720 = -720

-5r = -720

Divide each side by '-5'.

r = 144

Simplifying

r = 144

Answer:

r=144

Step-by-step explanation:

We need to find r. To do that me must make the top numbers the same.

We'll multiply

\( \frac{12}{r} \times \frac{5}{5 } = \frac{60}{5r} \)

\( \frac{5}{60} \times \frac{12}{12} = \frac{60}{720} \)

Since the top numbers are equal that means the bottoms are too.

So we can create the equation:

\(5r = 720\)

Divide each side by 5

r=144

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

Answer:

(1).........option d

(2).....y=8/3

Answer:

A is the answer in no1

xy+y=x+2z

3y=8

y=8/3

Answer:

\(f(x) = 3 {x}^{9 } + 7x ^{5} + 32x ^{2} + 7\)

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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The equation of the relationship is f(200) = 0.75 * 200

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

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

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

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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