A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x

B.45(x-3)=60x

C.60(x-3)=45x

D.60(x+3)=45x

There are 264 anagrams of the word CADERNO that have vowels before consonants.

We have,

To count the number of anagrams of the word CADERNO that have vowels before consonants, we can use the following steps:

Count the number of vowels in the word.

In this case, there are three vowels: A, E, and O.

Count the number of consonants in the word.

In this case, there are four consonants: C, D, R, and N.

Determine the possible arrangements of vowels and consonants that satisfy the condition of having vowels before consonants.

Since there are three vowels and four consonants, there are two possible arrangements that satisfy this condition:

a) Vowel - Consonant - Vowel - Consonant - Vowel - Consonant - Consonant

b) Vowel - Consonant - Vowel - Consonant - Consonant - Vowel - Consonant

Calculate the number of ways to arrange the vowels and consonants in each of the possible arrangements determined in step 3.

We can use permutations to calculate this.

For arrangement a):

There are 3 ways to choose the first vowel (A, E, or O)

There are 4 ways to choose the first consonant (C, D, R, or N)

There are 2 ways to choose the second vowel (whichever is left out of the two remaining vowels)

There are 3 ways to choose the second consonant (whichever is left out of the three remaining consonants)

There is 1 way to choose the third vowel (the remaining vowel)

There is 1 way to choose the fourth consonant (the remaining consonant)

There is 1 way to choose the fifth consonant (the remaining consonant)

The total number of arrangements for this case is: 3 x 4 x 2 x 3 x 1 x 1 x 1 = 72

For arrangement b):

There are 3 ways to choose the first vowel

There are 4 ways to choose the first consonant

There are 2 ways to choose the second vowel

There are 2 ways to choose the second consonant (whichever is left out of the two remaining consonants)

There are 2 ways to choose the third consonant (whichever is left out of the two remaining consonants)

There is 1 way to choose the third vowel

There is 1 way to choose the fourth consonant

The total number of arrangements for this case is: 3 x 4 x 2 x 2 x 2 x 1 x 1 = 192

Add up the total number of arrangements for both cases to get the final answer:

72 + 192 = 264

Therefore,

There are 264 anagrams of the word CADERNO that have vowels before consonants.

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The numeric value of f(x) at x = π/5 is given as follows:

f(π/5) = - 2π/5 - 2

We are given the second derivative of the function, as follows:

f''(x) = -25sin(5x).

As we have the second derivative of the function, the function itself is obtaining integrating the second derivative twice.

Using integral by substitution, the first derivative is given as follows:

f'(x) = 5cos(5x) + K1

In which K1 is the constant.

When x = 0, f'(0) = 3, hence the value of K1 is obtained as follows:

3 = 5 + K1

K1 = -2.

Hence:

f'(x) = 5cos(5x) - 2.

Integrating again, the function is given as follows:

f(x) = 5sin(5x) - 2x + K2.

When x = 0, y = -2, hence the constant K2 is obtained as follows:

K2 = -2.

Thus the function is:

f(x) = 5sin(5x) - 2x - 2.

The numeric value of the function at x = π/5 is obtained as follows:

f(π/5) = 5sin(5(π/5)) - 2(π/5) - 2.

f(π/5) = 5sin(π) - 2π/5 - 2

f(π/5) = - 2π/5 - 2 -> as sin(π) = 0.

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Answer:

Step-by-step explanation:

27 times 3

= 81

Answer: 81

Step-by-step explanation: 27x3 ok what 3^to the 4th power so it would be 3x3x3x3

      9x9=81 is the same as saying 27x3

9 divided by 11.91 rounded to the nearest hundredth is: 0.76

To show that two numbers are divided, we can add a division sign '÷' between them. So, for example, if we have to show 36 divided by 6, we can write it as 36 ÷ 6. We can also show it in a fraction form as 36/6.

We want to find 9 divided by 11.91 . Thus, this can be expressed as:

9/11.91

where:

9 is the dividend

11.91 is the divisor

Using calculator, we have:

9/11.91 = 0.76

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The function is invertible and the inverse of the function is y = -3 + √[ (x + 4)/-2]

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

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

Swap the variables x and y

So, we have

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

Add 4 to both sides

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

Divide both sides by -2

(y + 3)^2 = (x + 4)/-2

Take the square root and subtract 3 from both sides

y = -3 + √[ (x + 4)/-2]

This represents the inverse of the function

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The circumference of the circle is 50.272in and the area is 3.142 x 8² = 200.96in².

The formula for circumference of a circle is given as:

  C = 2[tex]\pi[/tex]r

where r is the radius

and [tex]\pi[/tex] is 3.142

Area of a circle is given as:

   A = [tex]\pi r^{2}[/tex]

From the diagram,

diameter (d) given is 16in i.e:

d = 16in

but

r = d/2 = 16/2 = 8in

Now solve the C and A using the formula above:

C = 2 x 3.142 x 8 = 50.272in (approx.)

A = 3.142 x 8² = 200.96in² (approx.)

Briefly, a circle is a two-dimensional geometric shape consisting of all points in a plane that are a fixed distance, called the radius, from a given point called the center.

The distance around the circle, also known as its perimeter, is called the circumference.

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The equivalent area of the parallelogram is 44.4m^2

The formula for finding the area of a parallelogram is expressed as:

Area = base * height

Given the following parameters

Base = 12m

Height = 3.7m

Substitute the given parameters into the formula to have:

Area = 12m * 3.7m

Area of the parallelogram = 44.4m^2

Hence the area of the parallelogram given is 44.4m^2

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A better prediction in the scatter plot when for x when y = 7 would be

A scatter plot, аlso known as a scatter diagram or scatter grаph, is a grаphical representаtion оf dаtа thаt displays thе relаtionship between twо variables.

It is used to investigate thе сorrelation or relаtionship between twо quantitativе variables, tyрically rеprеsеntеd on thе x-axis and y-aхis оf a Сartesian cооrdinate system.

In the coordinate Cartesian system shown, for y = 7 the value closest is 11.  x = 52 is far away and will correspond to higher vales of y.

The relationship is a positive association

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Answer:

y = 3/2x + 3

Step-by-step explanation:

The slope-intercept form is y = mx + b

2y − 3x = 6

2y = 3x + 6

y = 3/2x + 3

So, the answer is y = 3/2x + 3

B) gas mileage decreases with increase of car weight.

The point of tangency and the equation of the tangent line are (x, y) = (- 5, 0) and x = - 5, respectively. (Correct choice: D)

A figure representing a circle and a tangent line, from which we need to determine the point of tangency and the equation of the tangent line. The point of tangency is a point where the tangent line and the circle meet each other.

Thus, by direct inspection, we have the following results:

Point of tangency

(x, y) = (- 5, 0)

Tangent line

x = - 5

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Work Shown:

r = 2 = radius

h = 3 = height

SA = surface area of the cylinder

SA = 2*pi*r^2 + 2*pi*r*h

SA = 2*pi*2^2 + 2*pi*2*3

SA = 8pi + 12pi

SA = 20pi   ....... exact surface area

SA = 20*3.1415926535898

SA = 62.831853071796

SA = 62.832 ....... approximate surface area

The value of x in the triangular pyramid is 8 units.

The volume of the pyramid is given as 240 units cube. Therefore, let's find the value of x in the pyramid.

volume of the pyramid = 1 / 3 ×base area × height

Therefore,

base area = 1 / 2 bh

base area = 1 / 2 × 12 × x

base area = 6x

Therefore,

volume of the pyramid =  1 / 3 × 6x × 15

240 = 30x

divide both sides by 30

x = 240 / 30

x = 8 units

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The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

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The steps to graph the absolute value functions are given below.

We have,

Absolute value functions of form f(x) = |ax + b| have a characteristic shape, which depends on the values of a and b.

Here are some general guidelines for graphing these functions:

Find the y-intercept:

To find the y-intercept of the graph, set x=0 and solve for y.

This gives f(0) = |b|, so the y-intercept is at the point (0,|b|).

Find the x-intercept(s):

To find the x-intercepts of the graph, set y = 0 and solve for x.

If b > 0, there are two x-intercepts: x = -b/a and x = b/a.

If b = 0, there is one x-intercept at x=0.

If b < 0, there are no x-intercepts.

Determine the direction of the graph:

If a > 0, the graph opens upwards, like a "V".

If a < 0, the graph opens downwards, like an upside-down "V".

Determine the vertex:

The vertex is the point where the graph changes direction.

If a > 0, the vertex is at (-b/a, 0).

If a < 0, the vertex is at (b/a, 0).

Sketch the graph:

Use the information above to sketch the graph of the absolute value function.

Plot the y-intercept, the x-intercept(s), and the vertex, and then draw a smooth curve connecting these points.

Thus,

The graph of the absolute value functions is given above.

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Answer:

x ≈ 11.3

Step-by-step explanation:

using the cosine ratio in the right triangle

cos61° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{DE}{DF}[/tex] = [tex]\frac{5.5}{x}[/tex] ( multiply both sides by x )

x × cos61° = 5.5 ( divide both sides by cos61° )

x = [tex]\frac{5.5}{cos61}[/tex] ≈ 11.3 ( to the nearest tenth )

The fraction of the cookies that are peanut butter cookies is 1/5

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

Total = 10

Peanut butter = 2

using the above as a guide, we have the following:

Fraction = Peanut butter /Total

So, we have

Fraction = 2/10

Evaluate

Fraction = 1/5

Hence, the fraction is 1/5

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Answer:

[tex]B. y=-1/4x+6.[/tex]

Step-by-step explanation:

The line perpendicular to the line y = 4x + 5 would need a slope of -1/4.

The slope of any perpendicular line multiplied by the original line must equal -1. Therefore, only answer B works.

Answer:

B

Step-by-step explanation:

The given line is a slope -intercept form

  y = mx + b     m is the slope

   for this line slope = 4

PERPENDICULAR slope is  - 1/m  = = -  1/4   <====you just have to LEARN this!

Answer B has slope = - 1/4

The x and y int for the equation are x = undefined and y-int = 1

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

y = 4^x

Set the variable x to 0 to calculate the y-intercept

So, we have

y-int = 4^0

y-int = 1

Set the variable y to 0 to calculate the x-intercept

So, we have

4^x = 0

So, we have

x = ln(0)/ln(4)

Evaluate

x = undefined

Hence, the x-intercept is undefined

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Answer:5.6

Step-by-step explanation:

28 divided by 5 is 5.6

Answer: $33.6

Step-by-step explanation: 28(.20) will give us our $5.6 discount. now add that on top of 28.

Answer:

James Abbott McNeill Whistler's Nocturne in Black and Gold: The Falling Rocket (c. 1875) is an example of "art-for-art's sake" of the Aestheticism movement.

Any quarter with sales level less than or equal to 7.908 million dollars would be considered a "failure" by this company.

To determine this sales level, we need to find the 20th percentile of the normal distribution with mean 9 million dollars and standard deviation 1.3 million dollars.

By using a standard normal distribution table we can find that the z-score corresponding to the 20th percentile is approximately -0.84.

The sales level that is the cutoff between quarters that are considered "failures" will be:

-0.84 = (x - 9)/1.3

- 0.84 * 1.3 = x - 9

- 1.092 = x - 9

x = 9 - 1.092

x = 7.908

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The area of the triangle is; 33 in².

The area of the rectangle is; 190 in².

The total area as required is; 223 in².

By observation; the triangle is such that its base is 6 in and it's height is; (20 - 9) = 11 in.

Therefore, the area of the triangle given by; (1/2)×b×h is; (1/2) × 6 × 11 = 33 in².

The area of the rectangle of length 20 in and width 9.5 in is; 20 × 9.5 = 190 in².

Ultimately, the total area of the composite shape is; 33 + 190 = 220 in².

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The bearing of the airport from the plane is 245°

The bearing of a point from a location is given by the angle in degrees of rotation from the Northern direction of the location to the direction of the location of the point

The given bearing of the plane from the airport = 65°

Therefore, the direction of the plane from the Northern direction of the airport = 65°

From the Northern direction of the plane, the bearing of the airport = 245°

Hence, the bearing of the airport from the plane is 245°

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The total change in All - Plus stock, given the change in one day and the dip the next day, would be - $ 3.125.

In the one day shown on the table, the price of All - Plus stock dropped by $ 2.50 dollars. The very next day, the price of the stock still dropped but this time by 1 / 4 of the fall in the first day so the fall was ;

= 1 / 4 x 2. 50

= $ 0. 625

This means that the total change in price can be found to be :

= Change in price first day + change next day

= 0. 625 + 2. 5

= $ 3. 125

This means prices of All - Plus stock changed by - $ 3.125.

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If a load of 10 tons was distributed equally among 6 trucks, each truck would carry 1.6667 tons.

In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.

In order to determine the unit rate, we would use the following mathematical equation (formula);

Unit rate = Number of ounces/Number of trucks

Unit rate = 10/6

Unit rate = 1.6667 tons.

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Complete Question:

A load of 10 tons was distributed equally among 6 trucks, how many does each truck carry?

Answer:

x=9 y=-2

Step-by-step explanation:

Substitute -2 for y in x+2y=5

x+2y=5

x+(2)(-2)=5

x-4=5(add 4 to both sides)

x=9

y=-2 as stated before

x=9 y=-2

The degree of the polynomial function f(x) = -2x + 2x3 is 3

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

f(x) = -2x + 2x3

The degree of a polynomial function is the higtest power in the polynomial

In f(x) = -2x + 2x3, the highest power is 3

Hence, the degree is 3

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Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))