The jackets price was 76€ It was sold on sale with 15% discount. Count the discount and discounted price

The possible number of ways of selection by using combination formula is 3060.

What is combination?

A grouping of items where the order in which they were chosen is irrelevant is known as combination.

Given that the number of people in the group is 18. Only 4 people will be member of the council.

The formula of combination is \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\) , where r number of objects are selected from n objects.

In the given question the value of n is 18 and the value of r is 2.

Substitute the value of n and r in \(^{n}C_{r}=\frac{n!}{r!(n-r)!}\).

\(^{18}C_{4}=\frac{18!}{4!(18-4)!}\)

Solve the above expression:

18^C_4 = 18x17x16x15x14/4x14

18^C_4 = 18x17x16x15/4x3x2x1

3060 18^C_4 = 3060

The number of ways such selection is 3060.

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Note that this prompt is designed to test ones knowledge on cosigners and loans. See the correct responses below.

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If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be: D. .95.

A confidence interval is also referred to as level of confidence and it can be defined as a range of estimated values that defines the probability that a population parameter would fall or lie within it.

For instance, the confidence interval at 95% is given by p - E < p < p + E

Since the confidence interval for the mean of a population is at 95%, the confidence coefficient would be calculated by simply dividing the confidence interval by 100:

Confidence coefficient = 95/100

Confidence coefficient = 0.95

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Justin borrow $6,000 from a credit union for 2 years.

What is Principal amount?

The amount of money initially borrowed from the lender, and as the loan is repaid, it can also refer to the amount of money still owed, is called Principal amount.

Given that;

Simple interest = $840

Time = 2 years

Annual rate = 7%

Now, The formula for calculate the principal amount is,

Simple interest = Principal amount × Rate × time / 100

Principal amount = Simple interest × 100 / Rate × time

Hence,

Principal amount = 840 × 100 / 7 × 2

Principal amount = 84,000 / 14

Principal amount = $6000

So, Justin borrow $6,000 from a credit union for 2 years.

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Answer:

y = - 8x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 8 and (0, 3) → c = 3

y = - 8x + 3 ← equation of line

Answer:

52

Step-by-step explanation:

3^3 is 27

5^2 is 25

Add them it is 52

Answer:

X = 25

Step-by-step explanation:

We can calculate the value of x using Euclidean theorem

15^2 = 9 × x

225 = 9x divide both sides by 9

25 = x

2-1. a) The shear stress τ is constant across the flow. b) The velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases. c)v_max = (P₁ - P₂) / (4μL) * \(R^{2}\) and v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr 2-2.a) The shear stress is constant for parallel plates. b) The velocity profile shows that the velocity is maximum at the centerline and decreases parabolically .c)v_max = (P₁ - P₂) / (2μh) and v_avg = (1 / (2h)) * ∫[-h to h] v dr.

2-1. Flow in an annular region between concentric cylinders:

(a) Shear stress profile:

In an incompressible fluid flow between concentric cylinders, the shear stress τ varies with radial distance r. The shear stress profile can be obtained using the Navier-Stokes equation:

τ = μ(dv/dr)

where τ is the shear stress, μ is the dynamic viscosity, v is the velocity of the fluid, and r is the radial distance.

Since the flow is at steady state, the velocity profile is independent of time. Therefore, dv/dr = 0, and the shear stress τ is constant across the flow.

(b) Velocity profile:

To determine the velocity profile in the annular region, we can use the Hagen-Poiseuille equation for flow between concentric cylinders:

v = (P₁ - P₂) / (4μL) * (\(R^{2} -r^{2}\))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the outer and inner cylinders respectively, μ is the dynamic viscosity, L is the length of the cylinders, R is the outer radius, and r is the radial distance.

The velocity profile shows that the velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases, reaching zero at the outer cylinder (r = R).

(c) Maximum and average velocities:

The maximum velocity occurs at the center (r = 0) and is given by:

v_max = (P₁ - P₂) / (4μL) * \(R^{2}\)

The average velocity can be obtained by integrating the velocity profile and dividing by the cross-sectional area:

v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr

where a is the inner radius of the annular region.

2-2. The flow between parallel plates:

(a) Shear stress profile:

For flow between very wide or broad parallel plates, the shear stress profile can be obtained using the Navier-Stokes equation as mentioned in problem 2-1. The shear stress τ is constant across the flow.

(b) Velocity profile:

The velocity profile for flow between parallel plates can be obtained using the Hagen-Poiseuille equation, modified for this geometry:

v = (P₁ - P₂) / (2μh) * (1 - (\(r^{2} /h^{2}\)))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the top and bottom plates respectively, μ is the dynamic viscosity, h is the distance between the plates, and r is the radial distance from the centerline.

The velocity profile shows that the velocity is maximum at the centerline (r = 0) and decreases parabolically as the radial distance increases, reaching zero at the plates (r = ±h).

(c) Maximum and average velocities:

The maximum velocity occurs at the centerline (r = 0) and is given by:

v_max = (P₁ - P₂) / (2μh)

The average velocity can be obtained by integrating the velocity profile and dividing by the distance between the plates:

v_avg = (1 / (2h)) * ∫[-h to h] v dr

These formulas can be used to calculate the shear stress profile, velocity profile, and maximum/average velocities for the given geometries.

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Hello!

Let's subtract!

⇒ 6x² - 2x + 6 - (6x² - 7x - 2)

⇒ 6x² - 2x + 6 - 6x² + 7x + 2

⇒ 5x + 8

∴ The difference will be equal to 5x + 8.

Answer:

Your answer is 5x+8

Step-by-step explanation:

= 6x^2-2x+6 - (6x^2-7x-2)

= 6x^2-2x+6 - 6x^2+7x+2

= 6x^2- 6x^2-2x+7x+6+2

=5x+8

Hope its helpful!

For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et. The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

c = -1: y = e-t

c = 0: y = 0

c = 1: y = et

For c = -1, we have f(t,y) = -y = -1. Rearranging this equation yields y = -1, which simplifies to y = e-t.

For c = 0, we have f(t,y) = -y = 0. Rearranging this equation yields y = 0.

For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et.

The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

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Answer:

Point-Slope: y+1=-5/7(x-5)

Slope Intercept: y=-5/7x+ 2 4/7

Standard: -5x+7y=18

Step-by-step explanation:

Slope: -5/7

Point slope is when the equation is in y-y1=m(x-x1) form.

I used the point (5,-1) but it really doesn't matter which one

Substitute it into (x1,y1)

y--1=-5/7(x-5)

y+1=-5/7(x-5) **2 minus signs is equal to 1 plus sign**

Slope-intercept is when the equation is in y=mx+b form.

y=-5/7x+b

To solve for b, plug in one of the points (again, I choose to use (5,-1)

(-1)=-5/7(5)+b

-1=-25/7+b is equal to asking -1=-3 4/7+b

b=2 4/7

Standard form is when it is in Ax+By=C

We'll covert from slope intercept to standard: y=-5/7+ 2 4/7

y=-5/7x+ 2 4/7 is the same as y=(-5/7x+ 18/7)

7y=5x+18 **Multiply both sides by 7, the common denominators**

-5x+7y=18 **Subtract 5x from both sides**

Sorry it took it while to get everything down but I hope this helps~

Answer:

A. 2.2

Step-by-step explanation:

The average rate of change between 2 x values is the total change of the y values (output values) divided by the change in the x values.Slope is special situation of that.

point 1 (x₁,y₁) → ( 2,7.5)

point 2 (x₂,y₂) → ( 18,42.5)

slope = 42.5 -7.5/18-2 =35 / 16 = 2.1875 ≈ 2.2

Answer:

Wrong order!

Step-by-step explanation:

There's a reason why coordinates are called an "ordered pair", and for every point (a, b) a is the x coordinate and b is the y coordinate. The calculations are correct, the way reporting them are not: the point should be (3.0) and (0,2) - in fact, all points on the x axis are of the form (p, 0) and all points on the y axis of the form (0,q)

Answer:

the midpoint of the point A and B is P( 5,-3)

Step-by-step explanation:

A(8,-7)= ( x1,y1)

B(2,1)= (x2,y2)

P(x,y)= ?

now,

P( x,y) = ( x1+x2/2 , y1+y2/2)

= ( 8+2/2 ,-7+1/2)

=( 10/2 ,-6/2)

=(5 ,-3)

The three numbers that are chosen by Levi are 5, 9 and 10.

It should be noted that the factors of 20 are 1, 2, 4, 5, 10 and 20.

Possible sum of factors of 20 are: 3, 5, 6, 7, 9, 11, 12, 14, 15, 21, 22, and 24.

Difference between 24 and a possible sum of factors of 24 are:

(21, 19, 18, 17, 15, 13, 12, 10, 9, 3, 2 , 0.)

The square numbers less than 24 are ( 1, 4, 9, 16).

Therefore the square number is 9.

And sum of the factors of 20 is 24 -9 = 15.

Therefore, the factors of 20 are = 5 and 10

Thus the given numbers are 5, 9 and 10.

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➢ Calculating for diameter :-

➢ Calculating Diameter :-

__________________________________

This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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The number of miles rode by Abby each day is m.

The number of miles rode by Abby in one week (7days) is 7m.

The inequality can be determined as,

Thus, 7m>70 is the required inequality.

Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

Answer:

Step-by-step explanation:

The FR of the hydraulic jack is 1.94, the VR is 1.95, and the Efficiency is 90%.

To find the FR, VR, and Efficiency of the hydraulic jack, we can use the following formulas:

FR = (F2 / F1)

VR = (D1 / D2)

Efficiency = (F2 x D2) / (F1 x D1)

where F1 is the input force, D1 is the input distance, F2 is the output force, and D2 is the output distance.

Given:

F1 = 6800N

D1 = 0.76m

F2 = ?

D2 = 0.39m

m = 1162kg

To find F2, we can use the formula for work:

Work input = Work output

F1 x D1 = F2 x D2

(6800N) x (0.76m) = F2 x (0.39m)

F2 = (6800N x 0.76m) / 0.39m

F2 = 13,216.41N

To find VR, we can use the formula:

VR = (D1 / D2) = (0.76m / 0.39m) = 1.95

To find Efficiency, we can use the formula:

Efficiency = (F2 x D2) / (F1 x D1)

Efficiency = (13,216.41N x 0.39m) / (6800N x 0.76m)

Efficiency = 0.90 or 90%

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Answer:

soln,

here,1st and 2nd case for a

1st case

so,a=3/2g.

2nd case

a=2/3g.

3rd and 4th case for X

3rdcase

(U+4)/2=X

X=(U+4)/2.

4th case

X=(U+4)/2.

Answer:

To find the diameter of the largest circular sheep pen that can be built with 100 feet of fencing, we need to use the formula for the circumference of a circle.The circumference of a circle is given by the formula: C = πd, where C is the circumference and d is the diameter.Since we have 100 feet of fencing available, the circumference of the pen will be equal to 100 feet.100 = πdTo solve for the diameter (d), we divide both sides of the equation by π:100/π = dApproximating π to 3.14, we can calculate the diameter:d ≈ 100/3.14d ≈ 31.847Therefore, the diameter of the largest pen you can build with 100 feet of fencing is approximately 31.847 feet.

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

Let us set boys as x. Girls would then be x+18

Girls and Boys together would be x + x+ 18

Therefore,

x+x+18=164

2x+18=164

2x=146

x=73

Since girls are x + 18, they would be 73 + 18, or 91.

I hope this helps! :)

Answer:

There were 91 girls.

Step-by-step explanation:

164 students - 18 students = 146 students

146 students divided by 2 genders = 73 students

73 students + 18 girls = 91

Answer:

I solved it for u!

Hope ot helps!!!

Answer: x = 5, y = 2

Step-by-step explanation

x = 0, x = 5

5 - 0 = 5

y = 1, y = 3

3 - 1 = 2

Answer:

B. Rectangle T, Rectangle P, Rectangle S.

Step-by-step explanation:

To determine which list shows the correct order of the length of the diagonals of the rectangles from shortest to longest, let all the lengths be in decimal form:

Rectangle P = 6.7 cm

Rectangle S = \( \frac{34}{5} cm \) = 6.8 cm

Rectangle T = \( \sqrt{36.5} cm \) ≈ 6.04

Thus:

6.04 cm < 6.7 cm < 6.8 cm

Therefore, from the shortest to the longest, we have:

Rectangle T < Rectangle P < Rectangle S.

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As a professional tutor, I will explain how to calculate the perimeter of a badge in the shape of a quarter circle with a 9 cm base and 9 cm height.

Let's break the badge down into its three segments: the two straight sides (the base and height) and the curved outer edge.

1. Straight sides: The base and height are both 9 cm, so this part is straightforward. The combined length of the base and height is 9 cm + 9 cm = 18 cm.

2. Curved outer edge: To calculate the curved outer edge, we need to understand that it is one-fourth of the circumference of the entire circle from which it is cut. The formula for the circumference C of a circle with radius r is C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14. Since the base and height are both 9 cm, it's clear that the radius of the circle is 9 cm. Thus, the circumference of the full circle is C = 2π(9 cm) ≈ 56.55 cm. Since we only have a quarter of the circle, the curved outer edge is 1/4 of this, which is about 56.55 cm / 4 ≈ 14.14 cm.

3. Perimeter: Finally, add up the lengths of the three segments: 18 cm (straight sides) + 14.14 cm (curved outer edge) ≈ 32.14 cm.

So, the perimeter of the badge in the shape of a quarter circle with a 9 cm base and 9 cm height is approximately 32.14 cm (rounded to two decimal places).