Is it possible to get some help with a surds question? Thank you!

Using their concepts concept, we have that:

a) The mean of the data-set is of 81.6.

b) The median of the data-set is of 80.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem, there are 2 + 8 + 6 + 3 + 9 = 28 observations, hence the mean is:

M = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9)/28 = 81.6.

The median of a data-set is the 50th percentile, the value that separates the median in two halfs.

This data-set has an even number of elements, hence the median is the mean of the 14th and 15th elements, as 28/2 = 14. Both elements are 80, hence the median is of 80.

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The required system of equations that can be used to determine the total number of ounces in the jug of water (x), and the total number of ounces in the bottles of juice (y) is

[tex]x - y = 192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

To write an equation,

It is given that,

The difference between the jug of water and the bottle of juice that Kira is drinking is 192 ounces

Kira has consumed a total of 42 ounces, which is 3/32 of the bottle of juice and 9/64 of the jug of water.

Consider,

The total number of ounces in the jug of water = x

The total number of ounces in the bottle of juice = y

Applying these variables in the above sentences,

[tex]x-y=192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

Therefore, these two equations are used to determine the total number of ounces in the jug of water and the bottle of juice.

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The value is J = 1.71*10^-6 kmol/m^2.s

According to the given conditions we get,

The length the tube l= 0.20m

The diameter of the tube d= 0.01m

The total pressure inside the tube P= 101.32kPa

The partial pressure of CO2 at the first end is

P1= 456mm Hg = 60794.832 Pa

The partial pressure of CO2 at the other end is

P2= 76mm Hg = 10132.472 Pa

The temperature is T = 298 K

The diffusion coefficient D= 1.67* 10^-5 m^2/s

Generally the molar flux of CO2 is mathematically represented as

J= D{p1-p2} / R.T

Here R is the gas constant with value R= 8.314 j/kmol

So we get J= 1.71 * 10^-3 mol/m^2.sec

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Using it's concepts, the mean and the standard deviation of the data-set are given as follows:

B. mean: 17; standard deviation: 7.53.

The mean for this problem is:

M = (22 + 21 + 20 + 4 + 19 + 6 + 24 + 11 + 26)/9 = 17

The standard deviation is:

[tex]S = \sqrt{\frac{(22-17)^2+(21-17)^2+(20-17)^2+(4-17)^2+(19-17)^2+(6-17)^2+(24-17)^2+(11-17)^2+(26-17)^2}{9}} = 7.53[/tex]

Hence option B is correct.

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Answer:

Step-by-step explanation:

B is the answer

Answer:

see explanation

Step-by-step explanation:

to find the zeros let f(x) = 0

1

f(x) = 0 , that is

x(x + 10) = 0

equate each factor to zero and solve for x

x = 0

x + 10 = 0 ⇒ x = - 10

2

f(x) = 0 , that is

x(x - 3) - 4(x - 3) = 0 ← factor out (x - 3) from each term on the left side

(x - 3)(x - 4) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

Answer:

1) x₁ = 0, x₂ = -10

2) x₁ = 3, x₂ = 4

Step-by-step explanation:

Given functions:

[tex]1)\ f(x)=x(x+10)[/tex]

[tex]2)\ f(x)=x(x-3)-4(x-3)[/tex]

.................................................................................................................................................

Zero Product Property: If m • n = 0, then m = 0 or n = 0.

Distributive Property: a(b + c) = ab + ac.

Standard Form of a Quadratic: ax² + bx + c = 0.

.................................................................................................................................................

The Zero Product Property

1) f(x) = x(x + 10)

Step 1: Set the function to zero.

[tex]\implies 0=x(x+10)[/tex]

Step 2: Apply the Zero Product Property.

[tex]\boxed{x_1=0}[/tex]

[tex]x+10=0\implies \boxed{x_2=-10}[/tex]

The solutions to this quadratic are: [tex]x_1=0,\ x_2=-10[/tex].

.................................................................................................................................................

The Zero Product Property

2. f(x) = x(x - 3) - 4(x - 3)

Step 1: Set the function to zero.

[tex]\implies 0 = x(x - 3) - 4(x - 3)[/tex]

Step 2: Factor out [tex]x- 3[/tex].

[tex]\implies 0 = (x - 3)(x - 4)[/tex]

Step 3: Apply the Zero Product Property.

[tex]x-3=0\implies \boxed{x_1=3}[/tex]

[tex]x-4=0 \implies \boxed{x_2=4}[/tex]

The solutions to this quadratic are: [tex]x_1=3,\ x_2=4[/tex].

.................................................................................................................................................

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Answer:

  g(x) = -√(-x +9)

Step-by-step explanation:

The relevant transformations are ...

Applying the transformations in the specified order, we have ...

  f(x) = √x

  f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left

  -f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis

  -f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis

The shifted, reflected function is ...

  g(x) =  -√(-x +9)

__

Additional comment

The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.

Using an exponential function, it is found that:

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

The parameters for this problem are given as follows:

a = 2, b = 2.

Hence the number of bacteria after x hours is given by:

[tex]y = 2(2)^x[/tex]

After 6 hours, the amount is:

[tex]y = 2(2)^6 = 2^7 = 128[/tex]

After 24 hours, the amount is:

[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]

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1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)

2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)

3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)

4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)

Answer:

12.2 cm

Step-by-step explanation:

we are going to use the formula (below).

Our a and b are going to be our two legs: 10cm and 7cm

[tex]C^{2} =10^{2} +7^{2} \\C^{2}=100+49\\C^{2}=149\\C=\sqrt{149} \\C=12.2cm[/tex]

The corresponding range of the domain is (11, -4, -29)

The function is given as:

5x + y = 1

Make y the subject

y = 1 - 5x

The domain is given as:

(-2,1,6)

Substitute these values in y = 1 - 5x

y = 1 - 5(-2) = 11

y = 1 - 5(1) = -4

y = 1 - 5(6) = -29

Hence, the corresponding range of the domain is (11, -4, -29)

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The diagram where angles 1 and 2 form a linear pair is D. A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

It should be noted that a linear pair simply means angles that are formed when two lines intersect each other at a single point.

In this case, when a horizontal line has 1 line extending from it. Angles 1 and 2 are formed. This depicts a linear pair

In conclusion, the correct option is D.

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Based on the given task content; the five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29

Odd integers preceding -31

= -1, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, -25, -27, -29

Therefore, Five consecutive odd integers preceding -31 are: -21, -23, -25, -27, -29

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For the division of the given polynomials, quotient =  4y and remainder =1

Algebraic expressions called polynomials include constants and indeterminates.

A specific kind of expression is a polynomial. A mathematical statement without the equals symbol (=) is called an expression.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.

A polynomial is written in its standard form when its descending power of the variable is used.

[tex]\frac{8y^{2}-4y+1 }{2y-1}[/tex]

Quotient = 4y

Remainder = 1

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The sine and cosine rule is typically used to find the measure of angles in trigonometry.

It should be noted that the sine rule is used when we are given:

The cosine rule is used when we are given:

The advantage is that it can help us understand the connections between the sides and their angles.

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Answer:

the principal amount is 10000 is the rate of interest is 10 and the number of years is 10 you can calculate the simple interest a is equal to 10000 1 + 0 is equal to 1.6 is equal to 16000 interest is equal to a - b is equal to 6000 - 1000

Answer:

$1,760

Step-by-step explanation:

So I'm assuming the interest is simple interest rate which means that the interest applied each year is 12% of the original amount.

So this means that we can find the interest rate from one year by finding 12% of 800, and to do this we convert 12% to a decimal by dividing by 100 to get 0.12 and then use this decimal value to multiply by 800 to get: 0.12 * 800 = 96.

This means annually $96 will be charged in interest. To find how much interest there is after 100 years, simply multiply by 10, to get $96 * 10 = $960.

This is only the interest rate, it's like a fee, you still have to pay back the original amount, so all together you pay: $ borrowed + interest

So we add the interest rate 960 to the amount borrowed 800 to get: 960 + 800 = 1,760

The reference angle after rotating the unit circle anti-clockwise is;  π/3 Radians

To draw the angle θ = -120° in the unit circle, we will move clockwise 90°, and thereafter another angle of 30°.

This tells us that we pass the fourth quadrant and stop in the third quadrant.

The reference angle of an angle theta in the third quadrant, is; θ + 180°.

Thus, the reference angle of -120° is; -120° + 180° = 60°.

Converting 60° to radians gives; (60/360) * 2π Radians = π/3 Radians

Thus, the Reference angle is π/3 Radians

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Answer:

y-intercept = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the coefficient is the slope  (slope = -2/9x)

the constant is the y-intercept   (y-intercept=1/3)

this is true for all functions like this

Answer:

The y-intercept is

c) 1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

the third one is correct

[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]

Answer:

[tex] \large{ \boxed{\tt{2 {x}^{3}y + 7 {y}^{2} x - 3 {x}^{2} - 12y}}}[/tex]

- All you gotta do is writing the polynomial in the descending order of the power of the variable.

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Another name for AXW is <X

The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point

Hence, another name for XW is WX

A ray with an endpoint X is a ray that ends at point X

An example of such ray is XY

The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point

Hence, another name for WX is XW

The name AXW represents an angle

An angle can be named after its middle point

Hence, another name for AXW is <X

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Answer:

Step-by-step explanation:

7+6-8x5=

7+6-40=

13-40=

-37

if the x is multiplying

Answer:

ray

Step-by-step explanation:

Rays only have one endpoint, so it continues infinitely in one direction. Segments have TWO endpoints.

Answer:

15.78°

Step-by-step explanation:

Let the angle be x.

From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)

Therefore, The trigonometric ratio is the tangent ratio.

tan x = O/A

tan x =13/46

x = 15.78°

The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°

The distance of the flagpole from the building = 55ft

The building has the height of = 45ft

The flagpole has the height of = 25ft

The angle can be calculated using the formula;

Tan θ = opposite/adjacent

Where opposite= 45ft

adjacent = 55ft

Tan θ = 45/55 = 0.82

θ = Tan–¹0.82

θ = 39°

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The linear function that shows that the number of cars seen each week by the mechanic is:

f(x) = -5x + 200.

A linear function is modeled by:

y = mx + b

In which:

During the first week analyzed, the amount of cars was of 200, hence the y-intercept is of 200. In 5 weeks, the amount decayed by 25, hence the slope is given by:

m = -25/5 = -5.

Thus the linear function that shows that the number of cars seen each week by the mechanic is:

f(x) = -5x + 200.

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Answer:

f(x) = −5x + 250

Step-by-step explanation:

First, we must find the slope. We can take 2 points. (10, 100) and (15,175)

Using y2-y1/x2-x1=m, we find that the slope =-5. to find the y-intercept, we have to find that y= when x=0. Since 10 weeks passed since the begining, we can inverse the slope to find 5(cars)x10(weeks)=50.

so, 200(week10)+50(week 1)=250

f(x)=-5x+250.

Answer:

16x-2

Step-by-step explanation:

Perimeter is 2w+2l

so we plug it in

2(3x+1) + 2(5x-2)

now we distribute

6x+2 + 10x -4

now we add like terms

6x+10x+2-4

16x-2