A trail mix is made by adding cashews that sell for $2.75 per pound to chocolate candies that sell for $1 per pound. How many of each should be used to get 50 pounds of trail mix that sells for $2 per pound?
Complete the statements.

The 50 pounds of trail mix includes [DROP DOWN 1] pounds of cashews and [DROP DOWN 2] pounds of chocolate candies.

The image after a 270 rotation is (4, -3)

If the point of rotation is not the origin, the steps are as follows:

1. Subtract the point of rotation off each vertex point of

the shape

2. Rotate as you would around the origin

3. Add the point of rotation back to each vertex point of

the shape

Given: R(1, 2) after a 270 rotation about (0, - 2)

step1: (1-0, 2-(-2)) = (1, 4)

step 2: For rotation about the origin through 270°, the image is (y, -x). Thus, (1, 4) => (4, -1)

step 3: (4, -1) => (4+0, -1+(-2) ) = (4, -3)

Therefore, the image of R(1, 2) after a 270 rotation about (0, - 2) is (4, -3)

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Answer:

(simplify 26³)

26³ = 17,576

= 17,576 + 5 = 3³+57

(simplify 3³)

3³ = 27

= 17,581 = 27+57

= 17,581 ≠ 84

After using conversion of measurements , the answer is

60 km = 37.28 miles and 600km = 372.83 miles.

What is conversion of measurements?

  By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet. We must convert between different units in order to have accuracy and prevent measurement confusion.

Here the given we need to convert them km into miles.

To convert km to miles we need to divide the value by 1.609 .

=> 60 km

=> 60/1.609

=> 37.28 miles.

Now ,

=> 600 km

=> 600/1.609

=> 372.83 miles.

Therefore after conversion of measurement answer is

60 km = 37.28 miles and 600km = 372.83 miles.

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Answer:

x = 12 m

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here A = 44 , then

x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )

x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )

11x = 132 ( divide both sides by 11 )

x = 12 m

Answer:

I'm assuming it's just a conversion of mm into cm?? in that case it will be 2.4 cm

Answer:

x ≥ 4

Step-by-step explanation:

-4 ( 8 - 3x ) ≥ 6x - 8

First, solve the brackets.

- 32 + 12x ≥ 6x - 8

Subtract 6x from both sides.

- 32 + 12x - 6x ≥ - 8

- 32 + 6x ≥ - 8

Add 32 to both sides.

6x ≥ - 8 + 32

6x ≥ 24

Divide 6 by both sides.

x ≥ 4

Answer:

The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.

The number written on the right of each category is its frequency

Step-by-step explanation:

Answer:

1350 ml

Step-by-step explanation:

(1800 : 4) * 3

450 * 3

1350 ml

Answer:

$13,720.00

Step-by-step explanation:

Calculate simple interest using the equation A = P(1 + rt)

A = $41,720.00

Interest = total repayment - original cost

$41,720.00 - 28,000 = $13,720.00

The differentiation of the given function is [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex].

In the given question we have to differentiate the given function with respect to x.

The given function is f(x)= [tex]tan(x^4)\cdot(3x^3+2)[/tex].

We have to differentiate the given function so we differentiate using the Product Rule.

The Product Rule of Differentiation is

d/dx[h(x)g(x)]=h(x) d/dx g(x)+g(x) d/dx h(x)

In the given function the value of

h(x) = [tex]tan(x^4)[/tex] and g(x) = [tex](3x^3+2)[/tex]

So;

f'(x)= [tex]tan(x^4)[/tex]d/dx [tex](3x^3+2)[/tex] + [tex](3x^3+2)[/tex] d/dx [tex]tan(x^4)[/tex]............(1)

We firstly find the value of d/dx [tex](3x^3+2)[/tex] and d/dx [tex]tan(x^4)[/tex].

We firstly find the value of d/dx [tex](3x^3+2)[/tex]

As we know that d/dx of x^n =nx^(n-1) and d/dx a=0

So;

d/dx [tex](3x^3+2)[/tex]= 3 d/dx [tex]x^3[/tex]+d/dx 2

d/dx [tex](3x^3+2)[/tex]=3(3[tex]x^2[/tex])+0

d/dx [tex](3x^3+2)[/tex]=9[tex]x^2[/tex]

Now finding the value of d/dx tan([tex]x^4[/tex])

d/dx [tex]tan(x^4)[/tex] = d/dx [tex]tan(x^4)[/tex] d/dx [tex]x^4[/tex]

d/dx [tex]tan(x^4)[/tex]= [tex]sec^2(x^4)\cdot(4x^3)[/tex]

d/dx [tex]tan(x^4)[/tex]= [tex]4x^3sec^2(x^4)[/tex]

Now putting the values of differentiation in equation 1

f'(x)= [tex]tan(x^4)\cdot9x^2[/tex] + [tex](3x^3+2)\cdot4x^3sec^2(x^4)[/tex]

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]3x^3\cdot4x^3sec^2(x^4)+2\cdot4x^3sec^2(x^4)[/tex]

Simplifying

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{3+3}sec^2(x^4)+8x^3sec^2(x^4)[/tex]

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex]

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Answer:

[tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

   Number of cards = 52

 Number of black cards = 13 (club) + 13 (spade)

                                        = 26

[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]

                                     [tex]\sf =\dfrac{1}{2}[/tex]

Answer:

40

Step-by-step explanation:

2 x 10⁷/5 x 10⁵ = 2/5 x 10^5-7 = 2/5 x 10² = 2 x 100/5

There were 40 times more white-tailed deer in 2000 than in 1905

a) The inequality is

P + S + M > 60

b) The solution of the inequality is:

P > 19

Where P is Pedro's age.

c) The oldest brother has more than 21 years-

Let's define the variables:

p = Pedro's age.

S = Sebastian's ae

M = Manuel's age

We know that the sums of their ages is more than 60, then:

P + S + M > 60

This is the inequality.

b) We know that the brother are one year apart, then:

S = P + 1

M = P + 2

replacing that we get:

P + P + 1 + P + 2 > 60

3P + 3 > 60

3P > 60 - 3

3P > 57

P > 57/3 = 19

P > 19

So Pedro has more than 19

c) The oldest brother is 2 years older than Pedro, then:

M > 19 + 2

M > 21

Manuel is more than 21 years old.

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The solution for the variable w according to the given equation; -21 ⅓ w + 6 = 15 as required in the task content is; w = -27/64.

It follows from the task content that the value of variable w is time determined according to the given equation as in the task content.

Given the equation; -21 ⅓ w + 6 = 15.

First, the mixed number must be converted to a fraction so that we have;

-21 ⅓ = -64/3.

Hence, the equation becomes;

-64w/3 + 6 = 15

Multiply both sides of the equation by 3 so that we have;

-64w + 18 = 45

-64w = 45 - 18

-64w = 27

w = -27/64.

Ultimately, the solution for variable w according to the equation as given in the task content is; w = -27/64.

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Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve the system of equations x-y= -2; x+y=4 by the addition method.

The addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.

Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:

  (x -y) +(x +y) = (-2) +(4)

  2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated

  x = 1 . . . . . . divide by 2

  1 +y = 4 . . . . . . . substitute for x in the second equation

  y = 3 . . . . . . . . . subtract 1

The solution is (x, y) = (1, 3).

Answer: 2-i

Step-by-step explanation:

multiply the fraction by 3-i/3-i

Answer:

No

Step-by-step explanation:

It does not make sense becuse 6x9=54

And 4x9(2)=72 so it would make no sense

The complete table of values of the function is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

The equation of the function is given as

f(x) = 2ˣ

On the incomplete table of values, we have the following x values

x = 0, 1, 2, 3

Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ

So, we have:

f(0) = 2⁰ = 1

f(1) = 2¹ = 2

f(2) = 2² = 4

f(2) = 2³ = 8

So, the complete table is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

When represented as ordered pairs, we have

(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

See attachment for the graph

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The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.

The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.

Here,

a. The length of drain= 52 feet

the gradual decrease=0.125 ft

elevation at high end=126.30 feet

elevation at low end,

=126.3-(52*0.125)

=126.3-6.5

=119.8 feet

b. The elevation at one end=94.67 feet

The elevation at other end=84.12 feet

The difference in elevation,

=94.67-84.12

=10.55 feet

=10.55*12

=126.6 inches

The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.

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The required equation of g(x) for reflection of f(x)=x-2 across the y-axis is g(x)=-x-2.

Reflection is basically a mirror image of the shape, in which the image of a given figure changes accordingly to a given line or axis.

Given that,

f(x)=x-2

To find the required equation  for g(x) that is reflected across the y-axis, Use reflection property,

According to reflection property,

Reflection Across the y-axis, the x change in -x and the remaining part of the equation remains same.

The equation of f(x) changes in g(x) as g(x)=-x-2,

So, the equation of g(x)=-x-2 .

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Answer:

Step-by-step explanation: 348 miles and 6 hours

The slope of the line that is parallel to the line -7x-5y=-6 is -7/5

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.

Any two unique places along the line may be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the vertical change to the horizontal change in each case. We shall comprehend how to discover the slope in this piece, along with some of its uses.

Given, line is -7x-5y=-6

We have to write the given line in slope-intercept form

Then, y= (-7/5)x+(6/5)

The slope-intercept form is y= mx +c

By using the slope-intercept form,

Slope=(-7/5)

The lines that are parallel to y= (-7/5)x+(6/5) have the same slope of -7/5

Therefore, the slope of the line that is parallel to the line -7x-5y=-6 is -7/5

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]

[tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]

[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]

Similarly,

[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]

[tex] \textsf{GCD = 2 × 3 = 6 } [/tex]

[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]

[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]

[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]

[tex] \textsf{GCD = 2 × 2 = 4 } [/tex]

[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]

Answer:

Numbers are : 36, 3, 12

36 = 2 × 2 × 2 × 2 × 2 × 1

3 = 3 × 1

12 = 2 × 2 × 3

HCF = product of total common factors of all three numbers, i.e : 2

LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96

Similarly,

2. Numbers are : 6, 54, 12

6 = 2 × 3

54 = 2 × 3 × 3 × 3

12 = 2 × 2 × 3

GCD = 2 × 3 = 6

[ 2 and 3 are the only ones common among all three ]

LCM = 2² × 3³ = 4 × 27 = 108

3. Numbers are : 16, 8, 12

16 = 2 × 2 × 2 × 2

8 = 2 × 2 × 2

12 = 2 × 2 × 3

GCD = 2 × 2 = 4

LCM = 2⁴ × 3 = 16 × 3 = 48

The lines p and q are parallel.

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.

Given a figure,

Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.

Hence, The lines p and q are parallel.

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The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.

Comparing one quantity to another is what it is. For instance, the weight ratio is 1:3 if you weigh 30 kg and your father weighs 90 kg.

Given:

The ratio of vertical and horizontal distance = 1:12,

The vertical distance of  Mrs. Giles's business  = 28 inches,

If for every one unit of vertical distance, the ramp must have 12 units of horizontal distance, so or 28 inches vertical distance the horizontal distance would be = 28 × 12 = 336 inches,

([tex]1 feet = 12inches[/tex])

= 336 / 12 = 28 feet

Therefore, The length of the horizontal distance of the ramp if The entrance to Mrs. Giles's business is 28 inches higher than the parking lot in front of her store is 28 feet.

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A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

The total sector of a circle is 360°

The area of the sector of 270° is 37.68 square meters.

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as:

Area = πr²

We have,

The radius of the circle = 4 m

The total sector of a circle is 360°

The area of the sector with 270°.

= (270°/360°) x πr²

= 0.75 x πr²

= 0.75 x 3.14 x 4²

= 37.68

= 37.7 square meters

Thus,

The area of the sector of 270° is 37.68 square meters.

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Answer: B

Step-by-step explanation:

For 237,629 the 6 is located in the hundreds section so its value is approx. 600.

Now when you multiply 600 by 10 you get 6000

So the number of 6 should be located in the 6,000 range which is only in answer B 426,579

Answer:

B- 426,579

Step-by-step explanation:

The value of 6 in 237,629 is 600

600×10=6,000

Which answer has 6,000 as the value of 6?

- Answer B: 426,579