Does 5, square root of 50, 5 make a right triangle?

Does square root of 2, square root of 3, 4 make a right triangle?

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

im pretty sure its 30

Step-by-step explanation:

Name all angles when there are two parallel lines cut by a transversal?

Alternate interior angles

Corresponding angles

Vertically opposite

From figure 1,

Since the angles marked with colour fulfil the vertically opposite angles properties ,so

(2x+35)° = (8x-49)°

⇒(2x-8x)=(-49-35)°

⇒-6x=-84

⇒x = 14°

Hence , x = 14°

From figure 2,

Since the angles marked are corresponding angles,therefore on equating both angles we get

(10x-18)°=(15x-48)°

⇒(10x-15x)=(-48+18)°

⇒-5x = -30°

⇒ x = 6°

From figure 3,

Since the given two angles are alternate interior angles ,so

(7x+5)°=(12x-75)°

⇒(7x-12x)=(-75-5)°

⇒-5x=-80°

⇒x = 16°

From figure 4 ,

Since the two angles lies in a straight line ,so sum is 180°

(27x-21)°+(10x-16)°=180°

⇒37x -37° = 0

⇒ x = 1°

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The minimum number of masthead lights for the given vessel is 2.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
A towing vessel 35 meters in length, with a tow 100 meters astern,

Masthead lights = total length of the tow / total length of the vessel
                        = 100 / 35 = 2.85

So, the Number of Masthead lights for the given vessel is 2 ≤ x ≤ 3.
And a minimum number of masthead lights is 2.

Thus, the minimum number of masthead lights for the given vessel is 2.

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To complete this graph identify the variables and label the axis, then draw a dot to represent each set of data, and finally draw a line.

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There are 30 of 1/10's in the number 3

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

How many 1/10's are in 3?​

The above statement is a quotient expression that has the following features

Dividend = 3

Divisor = 1/10

So, we have

Quotient = Dividend /Divisor

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

Quotient = 3/(1/10)

Evaluate

Quotient = 30

Hence, there are 30 1/10's

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The cartesian equation for x = t² and y = 2 + 3t is x = (1/9)y² - (4/9)y + (4/9).

Where the value of A, B, and C are 1/9, - 4/9, and 4/9.

The parameter t that we have

The cartesian equation x = (1/9)y² - (4/9)y + (4/9)

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The surface area A(S) is 64√2 - 128/3

What is a parametric equation?

A parametric equation is a mathematical representation of a curve or surface in terms of one or more parameters. Instead of defining the curve or surface directly in terms of x and y (or x, y, and z for three-dimensional surfaces), parametric equations express the coordinates as functions of one or more parameters.

What is surface area?

Surface area is a measure of the total area that covers the outer part of a three-dimensional object or surface. It represents the sum of all the areas of the individual faces or surfaces that make up the object.

To find the area of the surface given by the parametric equations, we first need to calculate the cross product of the partial derivatives of the vector function r(u, v). Then we will integrate the magnitude of the cross product over the parameter domain D.

Let's calculate the partial derivatives of r(u, v) with respect to u and v:

∂r/∂u = <2u, v, 0>

∂r/∂v = <0, u, v>

Now, let's calculate the cross product of these partial derivatives:

ru × rv = <2u, v, 0> × <0, u, v>

= <v(v), 0, -2u(u)>

The magnitude of ru × rv is |ru × rv| = √(v² + 4u²).

To find the surface area, we need to integrate |ru × rv| over the parameter domain D, which is given as 0 ≤ u ≤ 2 and 0 ≤ v ≤ 4.

A(S) = ∫∫D |ru × rv| dA

= ∫[0,4]∫[0,2] √(v² + 4u²) dudv

Integrating this expression will give us the surface area A(S).

A(S) = ∫[0,4]∫[0,2] √(v² + 4u²) dudv

We can start by integrating with respect to u:

∫[0,2] √(v² + 4u²) du

To integrate this expression, we can make a substitution by letting w = v² + 4u². Then dw/du = 8u, which implies du = (1/8u)dw.

When u = 0, w = v² + 4(0)² = v², and when u = 2, w = v² + 4(2)² = v² + 16.

The integral becomes:

∫[v², v²+16] √w (1/8u) dw

Since u = (w - v²) / (4u), we can rewrite the integral as:

(1/8) ∫[v², v²+16] √w / u dw

Now we can integrate with respect to w:

(1/8) ∫[v², v²+16] √w / ((w - v²) / (4u)) dw

(1/8) ∫[v², v²+16] (4u/ (w - v²)) √w dw

Let's simplify further:

(1/2) ∫[v², v²+16] (u/ (w - v²)) √w dw

We can now evaluate this integral with respect to w. The limits of integration are v² and v² + 16.

(1/2) ∫[v², v²+16] (u/ (w - v²)) √w dw

(1/2) u ∫[v², v²+16] (1/ √w) dw

Integrating (1/ √w) with respect to w gives 2√w.

(1/2) u [2√w] evaluated from v² to v²+16

(1/2) u [2√(v²+16) - 2√v²]

Now, let's evaluate the outer integral with respect to v:

∫[0,4] (1/2) u [2√(v²+16) - 2√v²] dv

To evaluate this integral, we substitute u = 2u:

∫[0,4] (1/2) 2u [2√(v²+16) - 2√v²] dv

∫[0,4] u [2√(v²+16) - 2√v²] dv

Now we can integrate with respect to v:

u ∫[0,4] [2√(v²+16) - 2√v²] dv

To evaluate this integral, we can apply the power rule for integration and simplify:

u [v√(v²+16) - (4/3)v\(^{3/2}\)] evaluated from 0 to 4

Now we substitute the limits of integration:

u [(4√(4²+16) - (4/3)4\(^{3/2}\)]

Simplifying further:

u [(4√(16+16) - (4/3)4\(^{3/2}\)]

u [(4√32 - (4/3)4\(^{3/2}\)]

We can simplify the expression inside the square root:

4√32 = 4√(16 * 2) = 4√16 * √2 = 4 * 4√2 = 16√2

The expression becomes:

u [(16√2 - (4/3)4\(^{3/2}\)]

Simplifying the second term:

(4/3)4\(^{3/2}\) = (4/3) * 4 * √4 = (4/3) * 4 * 2 = 32/3

The expression becomes:

u [(16√2 - 32/3)]

Now, let's substitute the limits of integration:

u [(16√2 - 32/3)] evaluated from 0 to 4

Plugging in the upper limit:

4 [(16√2 - 32/3)] = 4 * (16√2 - 32/3) = 64√2 - 128/3

Finally, let's subtract the value at the lower limit:

0 [(16√2 - 32/3)] = 0

Therefore, the surface area A(S) is:

A(S) = 64√2 - 128/3

Note: The units of area will depend on the units of the original parametric equations (x, y, z).

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The standard deviation of a numerical data set measures the variability of the data. It is a widely used measure in statistics that helps to determine how spread out the values are within a given data set.

By calculating the standard deviation, we can better understand the range and distribution of values in the data set, as well as identify potential outliers. This measure is particularly important in fields such as finance, science, and engineering, where understanding the variability in data can be crucial for making informed decisions and predictions. So, the most appropriate term that makes the statement true is D: variability.

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Answer:

the first, second, and fifth

Step-by-step explanation:

hope this helps :-)

Answer:

3. 1067

4. 11875

5. 1638

6. 19317

7. 3432

8. 42022642

9. 318384

The multiplicative rate of change of the function f(x) = 10(0.5)^x is 0.5, indicating that the function decreases by multiplying by 0.5 with each increase in x.

The function f(x) = 10(0.5)^x represents an exponential decay function. The base of the exponent is 0.5, indicating that the function decreases by multiplying by 0.5 with each increase in x. In other words, the function value decreases to half its previous value for every increase of 1 in x.

When we examine the given ordered pairs, we can see this pattern. As x increases from 0 to 1, the function value decreases from 10 to 5, representing a multiplicative decrease of 0.5. Similarly, as x increases from 1 to 2, the function value decreases from 5 to 2.5, again demonstrating a multiplicative decrease of 0.5.

Therefore, the multiplicative rate of change of the function is 0.5.

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The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

A random sample is drawn from a population with mean μ=73 and standard deviation σ=6.1. To determine if the sampling distribution of the sample mean with n=18 and n=46 is normally distributed, we need to calculate the standard error for each sample size.

For n=18:
The standard error (SE) is calculated using the formula:

     SE = σ / √n
SE = 6.1 / √18

          ≈ 1.441 (rounded to 3 decimal places)

For n=46:
SE = 6.1 / √46 ≈ 0.901 (rounded to 3 decimal places)

To determine if the sampling distribution of the sample mean is normally distributed, we need to consider the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n > 30), the sampling distribution of the sample mean tends to be approximately normally distributed, regardless of the shape of the population distribution.

Since both n=18 and n=46 are larger than 30, we can conclude that the sampling distribution of the sample mean with these sample sizes is approximately normally distributed.

Therefore, the sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

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we have the equation

Solve for x

Applying log on both sides

Given information: Expected sales revenue = $57756Target labour cost percentage = 18%To find: How much money can you spend on labour that day? Solution: Let's assume the amount that can be spent on labour is x. According to the question, Target labour cost percentage is 18%.

Therefore, the amount that will be spent on labour cost = 18% of expected sales revenue. So, we can write it as:

x = 18% of expected sales revenue orx

= (18/100) × 57756Simplify it

,x = 10396.08 (rounded to two decimal places)Thus, the amount that can be spent on labour that day is $10,396.08.

Shawna and Beatrice, by virtue of their status as the offerees, had the option of accepting or rejecting the offer. The acceptance must meet the requirements of a valid contract.

The acceptance must be communicated clearly and immediately. In addition, the acceptance must conform to the offer's terms. In Hyde v Wrench (1840), the court held that an acceptance must be unconditional and absolute and that if the acceptance is not in line with the terms of the offer, it is a counteroffer that terminates the original offer. Since Shawna and Beatrice had not yet responded to the offer, there was no acceptance of the contract. Therefore, there was no legal agreement between the parties as a contract must have both an offer and an acceptance in order to be considered valid.

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Answer:

117 cookies

Step-by-step explanation:

52 ÷ 4 = 13

1 scoop of flour = 13 cookies

13 × 9 = 117

9 scoops of flour = 117 cookies

Answer:

117 cookies

Step-by-step explanation:

Using a ratio

52 cookies      x cookies

--------------   = --------------

4 scoops            9 scoops

Using cross products

52*9 = 4x

Divide each side by 4

52*9/4 =x

117 cookies

Given, the function is f(x,y,z)=5+yxz+g(x,z)Here, we need to find the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) . The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

Using the formula of the directional derivative, the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is given by

(f(x,y,z)) = grad(f(x,y,z)).v

where grad(f(x,y,z)) is the gradient of the function f(x,y,z) and v is the direction vector.

∴ grad(f(x,y,z)) = (fx, fy, fz)

                       = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Hence, fx = ∂f/∂x = 0 + yzg′(x,z)fy

                = ∂f/∂y

                = xz and

fz = ∂f/∂z = yx + g′(x,z)

We need to evaluate the gradient at the point (3,0,3), then

we have:fx(3,0,3) = yzg′(3,3)fy(3,0,3)

                             = 3(0) = 0fz(3,0,3)

                             = 0 + g′(3,3)

                             = g′(3,3)

Therefore, grad(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))Dv(f(x,y,z))(3,0,3)

                                                 = grad(f(x,y,z))(3,0,3)⋅v

where, v = (0,4,0)Thus, Dv(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))⋅(0,4,0)   = 0

The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

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Answer:

Number of 1/8 cups of sugar needed = 2

Number of 1/8 cups of whole wheat flour needed = 6

Number of 1/8 cups of all purpose flour needed = 4

Step-by-step explanation:

Recipes Kelly needs:

Sugar = 1/4 cups

Whole wheat flour = 3/4 cups

All purpose flour = 1/2 cups

She could only find her ⅛ cup measuring cup.

How many ⅛ cups will she need for each ingredient?

Number of 1/8 cups of sugar needed = cups of Sugar needed / 1/8 cups

= 1/4 ÷ 1/8

= 1/4 × 8/1

= 8/4

= 2

Number of 1/8 cups of sugar needed = 2

Number of 1/8 cups of whole wheat flour needed = cups of whole wheat flour needed / 1/8 cups

= 3/4 ÷ 1/8

= 3/4 × 8/1

= 24/4

= 6

Number of 1/8 cups of whole wheat flour needed = 6

Number of 1/8 cups of all purpose flour needed = cups of all purpose flour needed ÷ 1/8 cups

= 1/2 ÷ 1/8

= 1/2 × 8/1

= 8/2

= 4

Number of 1/8 cups of all purpose flour needed = 4

a. The new revenue can be estimated as R(20,11) = 150 - 24 = $126.

b. The food truck would need to sell 20 + 8 = 28 tacos to compensate for the decrease in burrito sales and keep the revenue at $150.

a. To estimate the food truck's revenue when 4 fewer burritos are sold, we can use the given information. We know that Rb(20,15) = 6, which means that the revenue changes by $6 for every additional burrito sold. If 4 fewer burritos are sold, the change in revenue would be 4 * (-6) = -$24.
b. To maintain a revenue of $150 despite selling 4 fewer burritos, we need to find out how many more tacos must be sold. We know that Rt(20,15) = 3, meaning the revenue changes by $3 for every additional taco sold. Since the loss in revenue due to selling 4 fewer burritos is $24, we need to sell enough tacos to make up for this loss. So, 24/3 = 8 more tacos need to be sold.

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In total 10% of the animals at the zoo are monkeys.To solve the problem, you have to divide the number of monkeys by the total number of animals and then multiply by 100 to convert it into a percentage.

The number of monkeys at the zoo is 20 and the total number of animals is 200. Therefore,20 out of 200 animals are monkeys.

Then, we use the formula for percentage:Percent (%) = (Part / Whole) × 100

Substitute the values.

Percent (%) = (20 / 200) × 100

Simplify.

Percent (%) = 10%

Therefore, 10% of the animals at the zoo are monkeys.

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Answer:

63,360 people

Step-by-step explanation:

the area of space =

5280 × 20 = 105,600 sq. ft

15 people occupied 25 sq ft

so, the sum of people will aoccupy the space =

105,600/25 × 15 = 63,360 people

Answer:

63,360 people

Step-by-step explanation:

5280ft × 20ft = 105600 ft²

If 15 people occupied a 25 ft² space, to find how many people occupied 105600 ft² space, divide 105600 by 25 then multiply by 15:

\(\begin{aligned}\implies \sf \dfrac{105600}{25} \times 15 & = \sf 4224 \times 15\\ &= \sf63360 \end{aligned}\)

The salary of the annual management trainee is equal to $15000

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The ratio of middle-management salaries to management trainee salaries by 7:5 and salary of middle management salaries as $21000

Thus if 7 parts of 12 is equivalent to 21000

Then 1 part of 12 is equivalent to $3000

Therefore the salary of the management trainees is

$3000×5=$15000

Hence, The salary of the annual management trainee is equal to $15000

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Answer:

64 inches tall

Step-by-step explanation:

We know in 1 foot, there are 12 inches.

We can convert 5 1/3 feet to 16/3 feet.

To do this you convert 5 feet to 15/3 feet and add it to 1/3 feet.

So we now have 16/3 feet and we will multiply by 12  to find the number of inches she is.

16/3 * 12 = 64 inches tall

Answer: 18

Step-by-step explanation:

12 divided by 2 = 6

6 x 3 = 18

Answer:

the answer is 18

Step-by-step explanation:

this is because 12 divided by 2 = 6

6 x 3 = 18

Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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Answer:

B........... length = 5

Answer:

this answer is length= 20 in

Answer:

\(\frac{41}{99}\)

Step-by-step explanation:

We require 2 equations with the repeating digits placed after the decimal point.

let x = 0.4141.. → (1) Multiply both sides by 100

100x = 41.4141.. → (2)

Subtract (1) from (2) thus eliminating the repeating digits

99x = 41 ( divide both sides by 99 )

x = \(\frac{41}{99}\)

That is 0.4141.... = \(\frac{41}{99}\)

Answer:

Step-by-step explanation: I don’t know