The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 54 centimeters. Find the length and width of the rectangle.

Answer:

calculate the difference ere

(3-22)+5

remove unnecessary parentheses

-19+5

calculate the sum

= -14

The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Given,

Mean = 4 minutes

= 1/4

= 0.25

The probability that someone will be attended to in less than three minutes on any given day is:

P( X ≤3)

= 1- e⁻⁰²⁵⁽³⁾

= 0.5267

The probability is:

P( X ≥ 4)

= P( X = 4) +P( X = 5 ) + ( X = 6)

= 0.2594 + 0.1159 + 0.216

= 0.3969

The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

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In the given rectangle, the values of f and g are the same that is 2√6cm.

So, the values of f and g are:

Now, calculate the sides as follows:

Formula: A = s²

So, each side of APQD measures  2√6cm.

Then,

Therefore, in the given rectangle, the values of f and g are the same that is 2√6cm.

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Answer:

[tex]\lim_{x \to -\infty} f(x) = \infty[/tex] and [tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hope this helps!

Step-by-step explanation:

Answer:

  105 N

Step-by-step explanation:

You want the force exerted on an area 2 m by 1.25 m by a pressure of 42 N/m².

The area is ...

  A = LW

  A = (2 m)(1.25 m) = 2.50 m²

The force is the product of the pressure and the area:

  F = PA

  F = (42 N/m²)(2.5 m²) = 105 N

The box exerts a force of 105 N on the table.

Answer: 13

Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.

Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.

The ceiling of the ballroom is rectangular in structure.

The dimensions of the rectangle are 12 by 5 meters.

So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.

We will use Pythagoras theorem to calculate the length of the diagonal.

12² +5 ² = D²

or, D² = 144 + 25

or, D =√169

or, D = 13

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.

Hence Tony will need 13 meters of garland.

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The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.

Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.

C1 = 20 + 2m

C2 = 15 + 4m

We need the charge for both companies to be equal.

C1 = C2

20 + 2m = 15 + 4m

Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.

2m = 5

m = 2.5

Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.

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Total cost includes initial charge for printer set up and material cost.

Average cost per T-shirt is

Average cost to print 25 T-shirts

Average cost to print 100 T-shirts

The average cost 4.25 + 35/x depends on the number of T-shirts printed.

The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.

Answer:

[tex]9b + 10u > 1400[/tex]

Answer:

Adult is 10$ and Child is 7$.

Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.

Hope this helps!

Step-by-step explanation:

2x + 4y = 48

5x + 2y = 64

2x + 4y = 48

10x + 4y = 128

( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )

8x = 80

x = 10

2 ( 10 ) + 4y = 48

20 + 4y = 48

4y = 48 - 20

4y = 28

y = 7

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

A discount store sells 5.5 - ounce jars of fish in bundles of 5. A bundle of 5 jars costs $10.45. Then the unit rate is given as,

⇒ ($10.45 x 5) / (5.5 x 5 x 5)

⇒ $0.38 per ounce

The store likewise sells 4.5-ounce jars of similar fish in bundles of 8. A bundle of 8 jars costs $12.96. Then the unit rate is given as,

⇒ ($12.96 x 8) / (4.5 x 8 x 8)

⇒ $0.36 per ounce

The store sells 3.5 - ounce jars in bundles of 4 jars for $4.76. Then the unit rate is given as,

⇒ ($4.76) / (3.5 x 4)

⇒ $0.34 per ounce

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

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The equation of line t in slope intercept form is 5y - 3x = -1

The equation of line s is y=3/5x + 2/5

This is in the slope intercept form

y = mx + c

where m represents the slope of the line

The slope of the line  y=3/5x + 2/5 is 3/5

The slope of two parallel line is same

The slope of line t is 3/5, it passes through the points (2, 1)

The equation of the line is

y - y₁ = m(x - x₁)

y - 1 = 3/5 (x - 2)

5y - 5 = 3x - 6

5y - 3x = -6 + 5

5y = 3x  -1

y = 3/5 x - 1/5

Therefore, the equation of line t in slope intercept form is 5y - 3x = -1

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The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .

A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.

Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.

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The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH

Answer:

A town's population grows at a rate of 5.3% every year.

The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.

How to find the length of a line segment?

A line segment is defined as a line bounded by two  points on a line.

The line segment from negative 5 comma 5 to 3 comma negative 1

is found by using the formula

square root of (x2-x1)² +(y2-y1)²

[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]

[tex]\sqrt{8^{2}+6^{2} }[/tex]

[tex]\sqrt{100}[/tex]

=10 units

therefore the length of the line segment is 10 units

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Greek mathematicians, who were first influenced by the Egyptians, would go on to produce innovations like Pythagoras' theory of right-angled triangles and, by concentrating on the abstract, bring accuracy and clarity to venerable mathematical conundrums.

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The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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An inequality correctly compares One-half, Three-fourths, and Two-thirds is: One-half < Two-thirds < Three-fourths.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values (numbers) and variables in an algebraic equation, especially based on any of the following inequality symbols:

Translating the numbers in word to numerical values, we have:

One-half = 1/2 or 0.5

Three-fourths = 3/4 or 0.75

Two-thirds = 2/3 or 0.67

Next, we would compare the above numerical values by using the less than (<) inequality symbol as follows:

0.5 < 0.67 < 0.75

One-half < Two-thirds < Three-fourths.

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Answer:

x= -7

Step-by-step explanation:

here you go.....

please mark brainliest

the given expressions solved by using factorization.

What is factorization of the expression ?

  To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.

Here

4) [tex]x^4-36[/tex]

=> [tex](x^2)^2 -6^2[/tex]

=> [tex](x^2-6)(x^2+6)[/tex]

5)64[tex]c^3+1[/tex]

=> [tex](4c)^3+1^3[/tex]

=> (4c+1)([tex](16c^2+4c+1)[/tex]

6)[tex]k^3-27[/tex]

=> [tex]k^3-3^3[/tex]

=>(k-3)([tex]k^2+3k+9[/tex])

7)[tex]54x^3+250y^3[/tex]

=> 2([tex]27x^3+125y^3[/tex])

=> 2([tex](3x)^3+(5y)^3[/tex])

=> 2 ( 3x+5y)([tex]9x^2+15xy+25y^2[/tex])

8)[tex]3m^4-48n^2[/tex]

=> 3([tex](m^2)^2-(4n)^2[/tex])

=> 3[tex](m^2-4n)(m^2+4n)[/tex]

9)[tex]a^7b^2-ab^2[/tex]

=> [tex]ab^2(a^6-1)\\[/tex]

=>[tex]ab^2(a^3-1)(a^3+1)[/tex]

=> [tex]ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)[/tex]

10)[tex]x^3y^2-343y^5[/tex]

=> [tex]y^2(x^3-(7y)^3)[/tex]

=>[tex]y^2(x-7y)(x^2-7xy+49y^2)[/tex]

11)[tex]9y^7-144y[/tex]

[tex]= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)[/tex]

Hence we can solve by using factorization formula.

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It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

Given that;

Finding the hourly cost of stamping parts for each machine is one way to approach this issue.

In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).

If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.

By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;

250t + 500t = 1000

750t = 1000

t = 1000/750

t = 1.333

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

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The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x  dollars.

The original value of the gift card was $30.

Coffee costs $2 per cup.

Let 'x' be the number of cup of coffee purchased by Aaliyah.

Total cost be 'A' be paid by her.

Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;

A = 30 - 2x  dollars.

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If we graph the angel's ppc then the slope of angel's ppc will be -1.

Given, Tim and Angel are working on promoting an event for a club they are in on campus.

In one afternoon, Tim can make 4 flyers or 5 posters, and Angel can make 3 flyers or 6 posters.

we have to find the slope of the angel's ppc if we graph the angel's ppc.

As, the graph of the angel's ppc will pass through the point (3 , 6).

so, the slope = (6 - 5)/(3 - 4)

slope = 1/-1

slope = -1

Hence, if we graph the angel's ppc then the slope of angel's ppc will be -1.

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Answer:

$32.50

Step-by-step explanation:

10% of 35$ is $3.50 if ur decreasing $35 by 10% it will be $3.50-$35=$32.50

The speed of the tip of her shadow would be 5.714 ft/sec.  ft/sec.

let H, be the height of the pole = 20 ft.

h, be the height of the woman = 6 ft.

x, be the length of the woman's shadow,

and s, be the distance from the pole to the woman = 15

by using the equation of similar triangles,

[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)

differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]

[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]

[tex]14\frac{dx}{dt} = 24[/tex],

[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.

the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.

thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.

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