Match the expressions to their limit values.

Answer:

Each square on the travel chessboard is 0.75 inches by 0.75 inches

Step-by-step explanation:

A scale factor of 1/3 when dilating means that we divide 2.25 by 3. That equals 0.75 :)

For given triangle, x is 4√5 using Pythagorean theorem.

What is Pythagorean Theorem?

Pythagoras Theorem (also known as Pythagorean Theorem) is a mathematical concept that explains the relationship between the sides of a right-angled triangle. The sides of a right triangle are also referred to as Pythagorean triples. This theorem's formula and proof are discussed with examples here.

The Pythagorean theorem is used to calculate the length of an unknown side and the angle of a triangle. We can deduce the base, perpendicular, and hypotenuse formulae from this theorem.

The Pythagoras Theorem formula is presented in the definition as:

Perpendicular² + Base² = Hypotenuse²

c² = a² + b²

Now,

Given that perpendicular =19

Hypotenuse=21

then Base²=21²-19²  using Pythagoras theorem

Base=√441-361

=√80

=4√5

Hence,

          x is 4√5

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Answer:

y = -3/4x + 6.75

Step-by-step explanation:

Slope intercept form is y = mx + b, where m is the slope and b is the y intercept.

Plug in the given point and slope into the equation, then solve for b:

y = mx + b

3 = -3/4(5) + b

3 = -3.75 + b

6.75 = b

Then, plug in the slope and y intercept into the equation:

y = -3/4x + 6.75 is the equation of the line in slope intercept form

Step-by-step explanation:

U for "Union" (or "United").

what do you mean by ' ? complement ?

A u B u C = U (all letters from a to h are in it)

(A u B u C)c = {} (empty set, which is the complement of the full set).

The total number of syringes that the ICU had is given as follows:

175.

The total number of syringes that the ICU had is obtained applying the proportions in the context of the problem.

20% of the total supply x is equivalent to 35 syringes, hence the equation is given as follows:

0.2x = 35

Solving the equation, the total number of syringes that the ICU had is given as follows:

x = 35/0.2

x = 175 syringes.

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Answer:

See below!

Step-by-step explanation:

254, 202, 284, 269, 151, 258, 202

Mean of the data:

\(\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}\)

Median of data:

Arrange the data in increasing order.

151, 202, 202, 254, 258, 269, 284

The middle value = 254

So,

Mode in data:

The mode, here, is 202. (occurring 2 times.)

So,

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

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

prime: 17 47 67

Composite: 25 48 99 161 171

25: 1,5,25

48: 1,2,4,6,8,12,24,48

99: 1, 3, 9, 11, 33, 99

161: 1, 7, 23, 16

171: 1,3,9,19,57,171,

And can i please get brainliest and have a good day

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    8*x^2-(8)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 23x2 -  8  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  8x2 - 8  =   8 • (x2 - 1)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  x2 - 1  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  x2  is the square of  x1  

Factorization is :       (x + 1)  •  (x - 1)  

Equation at the end of step

3

:

 8 • (x + 1) • (x - 1)  = 0  

STEP

4

:

Theory - Roots of a product

4.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Equations which are never true:

4.2      Solve :    8   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.3      Solve  :    x+1 = 0  

Subtract  1  from both sides of the equation :  

                     x = -1

Solving a Single Variable Equation:

4.4      Solve  :    x-1 = 0  

Add  1  to both sides of the equation :  

                     x = 1

Two solutions were found :

x = 1

x = -1

Combining like terms yields 7x⁵ - x³ - x² + 4x.

Answer:

number is 2

Step-by-step explanation:

let the number be n then 8 times the number is 8n, subtract 1 from this and

8n - 1 = 15 ( add 1 to both sides )

8n = 16 ( divide both sides by 8 )

n = 2

that is the number is 2

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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a)  There are 3003 different ways the committee members can be selected.

b) The probability that no Democrats are appointed to the committee is 0.073, or about 7.3%.

a. To calculate the number of different ways the committee members can be selected, we use the combination formula:

The number of combinations = n! / (r! * (n - r)!)

Where n is the total number of choices (in this case, 15 representatives), and r is the number of items being chosen (in this case, 5 committee members). Plugging in the values, we get:

The number of combinations = 15! / (5! * (15 - 5)!) = 3003

Thus, there are 3003 different ways the committee members can be selected.

b. To calculate the probability that no Democrats are appointed to the committee, we can use the binomial probability formula:

P(x) = (n! / (x! * (n - x)!) * p^x * (1 - p)^(n-x))

Where n is the total number of trials (in this case, the number of committee members), x is the number of successes (in this case, 0 Democrats), p is the probability of success (in this case, the probability of selecting a Republican), and 1 - p is the probability of failure (in this case, the probability of selecting a Democrat). Plugging in the values, we get:

P(0) = (5! / (0! * (5 - 0)!) * (8/15)^0 * (7/15)^5) = 0.073

Thus, the probability that no Democrats are appointed to the committee is 0.073, or about 7.3%.

If this were to occur, it would suggest that the assumption that the appointments were made at random is questionable. This is because the probability of selecting 5 Republicans in a row without selecting any Democrats is relatively low, which suggests that there may be some bias in the selection process.

c. To calculate the probability that the majority of the committee members are Republican, we can use the binomial probability formula again. There are two ways that the majority of the committee members can be Republican: either 3 Republicans and 2 Democrats, or 4 Republicans and 1 Democrat. The probability of each of these outcomes can be calculated using the formula above.

For 3 Republicans and 2 Democrats:

P(3) = (5! / (3! * (5 - 3)!) * (8/15)^3 * (7/15)^2) = 0.307

For 4 Republicans and 1 Democrat:

P(4) = (5! / (4! * (5 - 4)!) * (8/15)^4 * (7/15)^1) = 0.169

Adding these probabilities together, we get a total probability of 0.476, or about 47.6%.

If this were to occur, it would not necessarily be a reason to doubt that the governor made the selections randomly. While the probability of selecting a majority of Republican committee members is relatively high, it is still within the range of what we would expect to see if the selections were made at random. It is possible, but not necessarily likely, that the governor could have made the selections randomly and still ended up with a majority of Republican committee members.

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Answer:

30

Step-by-step explanation:

If we have 4 integers that have an average of 9, then all the numbers will add up to \(9\cdot4=36\).

If we want the greatest number possible, the other 3 need to be the lowest possible.

Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.

\(1 + 2 + 3 = 6\)

\(36 - 6 = 30\)

So 30 is the greatest value of one of the integers.

Hope this helped!

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

3r + 2b = 600 ---(1)

r + b = 225 ---(2)

We can solve this system of equations using substitution or elimination method.

Using substitution method, we can solve equation (2) for "r" in terms of "b":

r = 225 - b

Substituting this expression for "r" into equation (1), we get:

3(225 - b) + 2b = 600

Simplifying and solving for "b", we get:

675 - 3b + 2b = 600

-b = -75

b = $75

Therefore, the cost of one bag is $75.

Step-by-step explanation:

use brain

Answer: (A) x⁰ = 30⁰

Ok done. Thank to me :>

Answer:

The result is 29/12 = 2 5/12 ≅ 2.4166667 = twenty-nine twelfths (

Step-by-step explanation:

Answer:

4 9/20

Step-by-step explanation:

Answer:

its 6.

hope it helps.. its 6.

The completed entries is added as an attachment

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

3,723 ÷ 51

Express 3,723 as 2295 + 1428

So, we have the following representation

3,723 ÷ 51 = (2295 + 1428) ÷ 51

Expand the expression

So, we have the following representation

3,723 ÷ 51 = 2295 ÷ 51 + 1428 ÷ 51

Evaluate the quotients

3,723 ÷ 51 = 45 + 28

Next, we complete the blanks (see attachment) for the completed entries

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f(x+1)

Answer:

= -12x+10

Step-by-step explanation:

Answer:

Its -12

Step-by-step explanation:

its -12 because 8/2-4x8= -20 and 2+6 is 8 then you add -20 by 8 then you have an Answer of -12

The solutions to the equation sin(θ) = √2/2 over the interval [0, 2π) are θ = π/4 and θ = 3π/4.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

We know that sin(θ) = √2/2 is one of the standard angles in trigonometry, and it corresponds to an angle of 45 degrees or π/4 radians.

To solve the equation sin(θ) = √2/2 over the interval [0, 2π), we need to find all values of θ that satisfy the equation within this interval.

Since sin(θ) is positive in the first and second quadrants of the unit circle, we know that the solutions lie in those quadrants.

The first solution is θ = π/4, which corresponds to the angle of 45 degrees or π/4 radians in the first quadrant.

The second solution is θ = 3π/4, which corresponds to the angle of 135 degrees or 3π/4 radians in the second quadrant.

Therefore, the solutions to the equation sin(θ) = √2/2 over the interval [0, 2π) are θ = π/4 and θ = 3π/4.

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The transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.

On the graph, the shape A is the same size as the shape B but with different angles of transformation.

For shape A,

The width at x-axis = -4,-2

length at y-axis = 1,4

For shape B;

The width at x-axis = 2,4

length at y-axis = 0,3

Therefore, transformation that took place from shape A to shape B is that there was a 180° turn around at point 0,2 on the graph.

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Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

Answer:

10/11

Step-by-step explanation:

Answer:

\(x = \frac{5}{3} \)

Answer:

Car leasing

Step-by-step explanation:

Im not exactly sure but this may be helpful

Car ownership is literally being the owner of the car and paying it full. Car financing is the one ive not heard of before. Car maintenance is literally caring and looking after the car. I know leasing is like giving out so im hoping its like that

Car leasing describes an alternative to car buying where monthly payments

are paid for a specific period of time, after which the vehicle is returned to the dealership or bought

Car leasing is a financial transaction in which a person pays a monthly fee in exchange for the use of a car for a predetermined period of time.

At the end of the lease term, the car is returned to the dealership or bought by the lessee.

So, Car leasing describes an alternative to car buying where monthly payments are paid for a specific period of time

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The dimensions of the cylinder that maximizes its volume are radius = 16.29 cm and height = 32.57 cm

The total surface area of a cylinder is given by A = 2πr² + 2πrh where

Since the total surface area of the cylinder A = 5000 cm². So,

A = 2πr² + 2πrh

5000 = 2πr² + 2πrh

Making h subject of the formula, we have

h = 2500/πr - r

Since the volume of the cylinder V = πr²h where

Substituting h into V, we have

V = πr²h

V = πr²(2500/πr - r)

V = 2500r - πr³

Since we want to maximize V, we differentiate with respect to r and equate to zero.

So, dV/dr = d(2500r - πr³)/dr

dV/dr = 2500 - 3πr²

Equating dV/dr to zero, we have

dV/dr = 0

2500 - 3πr² = 0

2500 = 3πr²

Dividing both sides by 3π, we have

r² = 2500/3π

Taking square root of both sides, we have

r = √(2500/3π)

r = 50/√(3π) cm

r = 50/√(9.4247) cm

r = 50/3.07

r = 16.29 cm

We need to determine if this value of r gives a maximum for V. So, we differentiate dV/dr.

So, d(dV/dr)/dr = d²V/dr²

d²V/dr² = d(2500 - 3πr²)/dr

d²V/dr² = 0 - 6πr

d²V/dr² = - 6πr

Substituting the value of r into the equation, we have

d²V/dr² = - 6πr

d²V/dr² = - 6π(50/√(3π))

d²V/dr² = - 6π(50/√(3π))

Since d²V/dr² = - 6π(50/√(3π)) < 0. V is maximum at r = 50/√(3π) cm

Substituting the value of r into h, we have

h = 2500/πr - r

h = 2500/π(16.29) - 16.29

h = 2500/51.17 - 16.29

h = 48.86 - 16.29

h = 32.57 cm

So, the dimensions of the cylinder that maximizes its volume are radius = 16.29 cm and height = 32.57 cm

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