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.

The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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Answer:

Step-by-step explanation:

The total quantity of diesel fuel is 15.75 gallons.

The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.

1 quart = 0.25 gallon

For first container, 3 quarts = 0.25 × 3

3 quarts = 0.75 gallon

For second container, 2 quarts = 0.25 × 2

2 quarts = 0.5 gallon

For third container, it has 0.25 gallon

1 pint = 0.125 gallon

For first and third container, it has 0.125 gallon

So, amount of diesel fuel in first container = 3 + 0.75 + 0.125

Amount of diesel fuel in first container = 3.875 gallons

Amount of diesel in second container = 5 + 0.5

Amount of diesel in second container = 5.5 gallons

Amount of diesel in third container = 6 + 0.25 + 0.125

Amount of diesel in third container = 6.375 gallons

So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375

The total quantity of diesel fuel = 15.75 gallons

Hence, the total quantity is 15.75 gallons.

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Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

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The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.

First, we will calculate the speed of the penguin. The speed is represented by the variable "s".

s = 1,760/8

s = 220 feet per minute

The location of the penguin after 2 minutes is calculated below.

d = 2×s

d = 2×220

d = 440

Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.

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The following are the equations which matches the given word problems:

a. Skate rental charges an additional $3 :

y = x+3

b. Jeff is 3 years less than Tony's age:

y=x-3

c. Marie buys balloons for a party that are $3.00 each:

y = 3x

Given, we have the word problems:

a. Skate rental charges an additional $3 :

here, based on the fixed charge, additional charge is taken as $3.

let the total charge be represented as y and

x represent the fixed charge,

hence the equation we get is:

y = x+3

b. Jeff is 3 years less than Tony's age.

let y represent the age of Jeff

and x represent the age of Tony.

hence we frame the equation as:

y = x - 3

c. Marie buys balloons for a party that are $3.00 each:

let the cost of the balloon be represented as y

and x represent the number of balloons Marie wants to buy for $3 each.

hence the equation we frame is:

y = 3x

Hence we get the required equations.

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The slope is m = 5.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

We have to find the slope of the points given.

First to find the change between each y - value.

16 - 11 = 5

21 - 16 = 5

26 - 21 = 5

31 - 26 = 5

So the change between each y - value is 5.

Now, to find the slope of the points.

Since,

Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]

Hence, the slope of the given points is 5.

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Answer:

The answer is 5

Step-by-step explanation:

Though there is also a bottom number, just put a 1 in the bottom number

Answer:

it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps

Step-by-step explanation:

After simplification, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.

In the given question we have to solve the given expression.

The given expression is (-7 + i)(-3 + 6i).

Using the distributive property to solve the given expression.

a(b+c)=ab+ac

Now simplifying the expression.

(-7 + i)(-3 + 6i) = -7(-3 + 6i) + i(-3 + 6i)

(-7 + i)(-3 + 6i) = (-7)*(-3) + (-7)*(6i) + (-3)i + (6i)i

(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6i^2

As we know that i^2 = -1. So

(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6(-1)

(-7 + i)(-3 + 6i) = 21 - 42i - 3i - 6

Simplifying

(-7 + i)(-3 + 6i) = 15 - 45i

Hence, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.

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Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.

Given equation,

[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]

For values (-∞,-7)

equation stands true

For values (-7,5)

equation stands false

For values (5,12)

equation stands true

For values (12,∞)

equation stands false

Hence, x ∈ (-∞,-7)∪(5,12).

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The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The system of equation are

-3x + y = 3

-x + 2y = -4

Here we have to use the substitution method

-3x + y = 3

y = 3 + 3x

Substitute the value of y in the second equation

-x + 2(3 + 3x) = -4

-x + 6 + 6x = -4

-x + 6x = -4-6

5x = -10

x = -10/5

x = -2

Substitute the value of x in the first equation

-3x + y = 3

-3(-2) + y = 3

6 + y = 3

y = 3 - 6

y = -3

Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

The complete question is:

Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?

a) On a coordinate plane, 2 lines intersect at (3, 0).

b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).

c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).

d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).

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Answer:

B

Step-by-step explanation:

both point intersect at ( -2, -3)

The domain is { x ∈ R | x ≠ -2 }.

The range is { y ∈ R | x ≠ -8 }.

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

Find domain:

Set the denominator equal to zero and solve for x.

x+2=0

x=-2

This means, domain is set of all real numbers except x=2.

Set builder notation: { x ∈ R | x ≠ -2 }. R= real numbers

Find range:

Replace f(x) by y in the given equation and solve for x.

[tex]y=\frac{x^2-4x-12}{x+2}[/tex]

Write the factors of the numerator

[tex]y=\frac{(x+2)(x-6)}{x+2}[/tex]

common terms x+2 cancel out

y=x-6

x=y+6

substitute x=-2

-2=y+6

y= -8

This means range is the set of all real numbers except y= -8.

Set builder notation: { y ∈ R | y ≠ -8 }. R= real numbers

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Answer:

2/5

Step-by-step explanation:

flip 5/6 to become 6/5 then cross reduce then cross multiply

The point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

What is equation of line ?

  A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Here the given point ,

=> [tex](x_1,y_1)=(5,1)[/tex]

Slope m = [tex]\frac{1}{5}[/tex]

Here using equation formula

=> [tex]y-y_1 = m ( x- x_1)[/tex]

=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

Hence the point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

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The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.

In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.

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May, 4,000

The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.

The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

A quadratic equation simply refers to the equation which is in an algebraic equation that is of the second degree.

It should be noted that a quadratic equation is in the form of ax² + bx + c = 0.

In this situation, a and b are the coefficients while c is the constant in the equation.

Therefore, based in the information given, the correct options are A, D, abd E.

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Answer:

The equations that are quadratic in form include:

A. x⁴ – 6x²– 27 = 0

D. 6x⁴ = -x² + 5

E. 8x⁴ + 2x² – 4x = 0

Step-by-step explanation:

For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

As given in the question,

Given equation is equal to :

9 ( x - 4) - 5x = _ x - 30

Simplify Left hand side of the given equation we get,

9 ( x - 4) -5x

= 9x - 36 - 5x

Collect the like terms we have,

9x - 5x - 36

= 4x - 36

Now compare left hand side and right hand side to get no solution of the equation,

4x -36 = _x -30

Blank should be filled by 4

Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

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The function of the graph is f(x) = |x - 3| + 5

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

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the minimum point on the graph is located at the point (3, 5)

This means that

Vertex = (3, 5) i.e.  (h, k) = (3, 5)

Recall that the general form of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

On the graph, we have

(x, f(x)) = (2, 6)

So, we have

6 = a|2 - 3| + 5

This gives

a = 1

So, we have

f(x) = 1 * |x - 3| + 5

Evaluate

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².

b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².

Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:

df / dx = (df / du) · (du / dx)

a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:

F'(x) = [2 · g(x) + 6] · g'(x)

F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²

b) Now we proceed to expand the polynomial in its standard form:

F'(x) = [(2 / 3) · x³ + 7] · x²

F'(x) = (2 / 3) · x⁵ + 7 · x²

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Answer: 55.56%

Step-by-step explanation:

To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.

Answer:

Step-by-step explanation:

You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.

Let x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:

  x +y = 36 . . . . . total number of vases

  3x +4y = 125 . . . total number of flowers

Substituting for x, we have ...

  x = 36 -y

  3(36 -y) +4y = 125

  108 +y = 125

  y = 13

  x = 36 -13 = 23

There are 23 vases of daisies and 13 vases of lilacs.

The required value of "b" is 7, where the equation is y = -3x + 7.

As per the given table, we take the two points (9, 1) and (3,7).

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -3, y₁ = 16

x₂ = 1, y₂ = 4

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute the values in the above equation,

y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))

y - 16 = (-12/4)(x+3)

y - 16 = -3(x+3)

y - 16 = -3x - 9

y = -3x - 9 + 16

y = -3x + 7  ....(i)

Compare the given equation y = mx + b with the above equation, and we get

b = 7

Therefore, the required value of "b" is 7.

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With the help of binomial distribution we can conclude our answer.

acc to our question-

The confidence interval can be found out using,

Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).

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Answer: y = -.06x + 0.2

Step-by-step explanation: Find the slope by plugging in the given values to the slope formula to find that the slope is -0.6. Next, determine the y-intercept is b=y1−m⋅x1: b = 2 - (-0.6) ⋅ (-3) = 0.2 Finally, the equation of the line can be written in standard form y= -0.6x + 0.2.

Answer: Ethiopia has a population growth rate above 2.5% and a life expectancy of 61 years old

By studying the change of the y-intercept, we can see that the shift is of one unit upwards.

We know that the original y-intercept of the line is y = -1, then the line is of the form:

y = a*x - 1

Where a is the slope.

Now we apply a vertical shift of N units, this is written as:

y = a*x - 1 + N

And we know that the new y-intercept is 0, so:

y = a*0 - 1 + N = 0

y = -1 + N = 0

-1 + N = 0

N = 1

The shift is of 1 unit up.

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The remaining credit after 81 minutes of calls is $17.04.

Given that, the remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Let x be the number of minutes and y be the number of dollars.

According to question, the ordered pair is

(44, 22.96) and (68, 19.12)

The point slope form is (y-y1)=m(x-x1)

Slope = (y2-y1)/(x2-x1)

= (19.12-22.96)/(68-44)

= -3.84/24

m= -0.16

Put m= -0.16 and (x1, y1)=(44, 22.96), we get

(y-22.96)=-0.16(x-44)

When x=81

y-22.96=-0.16(81-44)

⇒ y-22.96=-0.16×37

⇒ y-22.96=-0.16×37

⇒ y-22.96=-5.92

⇒ y=-5.92+22.96

⇒ y=17.04

Therefore, the remaining credit after 81 minutes of calls is $17.04.

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Answer:

y=6x+2

Step-by-step explanation:

y=mx+c

8=6(1)+c

8=6+c

c=2

y=6x+2

The values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.

According to the question,

We have the following information:

We have a ratio table where two rows from the beginning are given.

In these rows, we have 1:5 and 6:30.

Now, we can easily find that the number in the second column is found by multiplying 5 into the number in the first column.

Now, for the third row, we have the number in the second column,50:

x*5 = 50

x = 50/5

x = 10

Third row: 10 to 50

Fourth row:

Number in the first column = 11

11*5 = 55

11:55

Fifth row:

Number in the first column = 18

18*5 = 90

18:90

Hence, the values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.

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