Factory A has produced 120 pairs of shoes
and produces 40 more each week. Factory B
has produced 70 pairs of shoes and produces
50 more each week. How many weeks (w)
will it be before Factory B produces as many
pairs of shoes (s) as Factory A?
s = 40w + 120
s = 50w + 70
[?] weeks

Answer:

  540x⁴

Step-by-step explanation:

You want the 3rd term of the expansion of (x +6)⁶.

The k-th term of (a +b)^n is ...

   C(n, k)a^(n-k)b^k

where terms are numbered 0 to n.

The third term of (x+6)⁶ is the above expression with k=2:

  C(6, 2)a⁴b²

Where a=x and b=6, this is ...

  15x⁴6² = 540x⁴

__

Additional comment

C(n, k) is the function that represents the number of combinations of n things taken k at a time:

  C(n, k) = n!/(k!(n-k)!)

  C(6, 2) = 6!/(2!·4!) = 6·5/(2·1) = 15

Answer:

Step-by-step explanation:

your going to have to show anwser choices

Work Shown:

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(26) = \frac{x}{5.7}\\\\x = 5.7*\tan(26)\\\\x \approx 2.78007575482541\\\\x \approx 2.8\\\\[/tex]

Make sure your calculator is in degree mode.

Answer:

The area would be 360 because 8 x 6 x 15 = 720 divided by 2 = 360

If Malcolm trains on his kayak every weekend. The speed is 12km/h and the distance is 31.5km.

Let's call Malcolm's paddling speed in still water "v".

When paddling upstream, Malcolm is fighting the current, so his effective speed is v - 3 km/h. And when paddling downstream, his effective speed is v + 3 km/h.

The time it takes for him to paddle upstream= 3.5 hours

Distance he covers in this time =  (v - 3) * 3.5.

The time it takes for him to paddle downstream = 2.1 hours

Distance he covers in this time = (v + 3) * 2.1.

Let  set the sum of these two distances equal to each other and solve for v:

(v - 3) * 3.5 = (v + 3) * 2.1

Expanding both sides:

3.5v - 10.5 = 2.1v + 6.3

Subtracting 2.1v from both sides:

1.4v - 10.5 = 6.3

Adding 10.5 to both sides:

1.4v = 16.8

Dividing both sides by 1.4:

v = 12 km/h

So Malcolm's paddling speed in still water is 12 km/h. To find the distance he paddles upstream, we can use the formula (v - 3) * 3.5, which gives us:

(12 - 3) * 3.5 = 9 * 3.5 = 31.5 km

Therefore  the distance Malcolm paddles upstream is 31.5 km.

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The length of the line segment AB is 11/2 mm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.

Therefore, AC/AB = EC/ED.

22/AB = 44/11.

2/AB = 4/11.

4AB = 22.

AB = 11/2.

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The function represented by the graph is y = |x + 1|

The complete question is added as an attachment

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

The equation of the graph is an absolute value graph

An absolute value graph is represented as

y = |x|

The function is shifted left by 1 units

So, we have

y = |x + 1|

Hence, the function is y = |x + 1|

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Proportionately, if Tony spent a total of 140 minutes studying for his algebra test, and this total was 5 more than 3 minutes the amount of minutes he spent studying for his biology test, the time Tony spent studying for his biology test was 132 minutes.

Proportion refers to the equation of two or more ratios.

Ratios show the relative size of a value compared to another.

Proportions are fractional values like ratios.

The total minutes Tony spent studying for his algebra test = 140

5 more than 3minutes = 8 minutes

140 > 132 by 8 minutes (140 - 8)

The time spent studying biology = 132

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Answer:

279.987

Step-by-step explanation:

Answer:

279.987073 lbs

Step-by-step explanation:

1 kg = 2.20462262 lbs

2.20462262 * 127 = 279.987073

The area of the sector is evaluated to be equal to 15π ft². B) is the correct option.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

the angle of the sector = 150°

the radius = 6 ft

hence the area of the sector is calculated as follows:

(150°/360°) × π × 6 ft × 6 ft

we simplify by division and multiplication

5/12 × π × 6 ft × 6 ft

5/12 × π × 36 ft²

5π × 3 ft²

15π ft²

Therefore, the area of the sector is evaluated to be equal to 15π ft² square meters.

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The area of the quilt block 112.5 square inches.

The correct option is B: one hundred twelve and one half in²

The area of the quilt block = area of a rectangle + area of a triangle

Ares of rectangle = length * breadth

Area of rectangle = 7.5 inches * 13 inches

Area of rectangle = 97.5 square inches

Area of the triangle = base/2 * height

base = 5 inches

height = 6 inches

Area of triangle = 5/2 inches * 6 inches

Area of triangle = 15 square inches

The area of the quilt block = 15 square inches + 97.5 square inches

The area of the quilt block = 112.5 square inches

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Answer:

20s + 36t - 24

Step-by-step explanation:

4(5s + 9t - 6)

20s + 36t - 24

We can go any further, so that is the answer.

Answer:

9

Step-by-step explanation:

54÷6= 9

27÷3= 9

18÷2= 9

hence the answer is 9.

Answer:

Step-by-step explanation:

There would be 1,968 people who hold valid passports.

Answer:

1. 12 inches

2. 36 inches

Step-by-step explanation: Solve for side b using the Pythagorean therom since this is a right triangle.

[tex]a^2+b^2=c^2[/tex] - Where c is the largest side aka hypotenuse(if you are unsure, look at the side opposite to the right angle)

Substitute the given values to solve for the unknown side

[tex]9^2+b^2=15^2[/tex]

Expand

[tex]81+b^2=225[/tex]

Subtract 81 from both sides

[tex]b^2=144[/tex]

Which means

[tex]b=+-12[/tex]

but since its a triangle in the first quadrant and can only contain positive values, we disregard the negative solution. So b=12.

Lastly, for perimeter, just add all the side lengths together.

[tex]P=9+12+15[/tex]

Which means that the perimeter is 36 inches!

The average with two digits after the decimal point followed by a newline is 7.4

An integer is a whole number, either positive or negative, that does not have any decimal points. Non-negative integers are those that are greater than or equal to zero.

To write such a program, we can use a loop to continuously read in integers from the user until a negative integer is entered. We then ignore the negative integer and calculate the maximum and average of the non-negative integers that were entered.

The maximum is simply the largest integer in the set. We can use a variable to keep track of the largest integer as we read in the input. At the end of the loop, the variable will hold the maximum value.

The average is the sum of all the integers divided by the total number of integers.

We add each non-negative integer to the sum and increment the count. At the end of the loop, we divide the sum by the count to get the average.

To output the average with two digits after the decimal point, we can use the printf method, which allows us to format our output. The format string "%.2f\n" specifies that we want to output a floating-point number with two decimal places followed by a newline character.

=> (15 + 20 + 0 + 3 - 1) / 5 = 7.4

In summary, a program that takes any number of non-negative integers as input, and outputs the max and average can be written using a loop, variables to keep track of the maximum, sum, and count, and the printf method to format the output. Understanding the basics of integers and how to perform calculations with them is essential for programming and statistical analysis.

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Answer

Step-by-step explanation:

Answer:

The area of the land can be found using the formula A = 1/2*D1*D2, where D1 and D2 are the diagonals of the parallelogram. In this case, the area is 1/2*25*12 = 150m^2.

Answer:

180m^2

Step-by-step explanation:

since you said that two sides measure 12 and 17 and the diagonal is 25 you can use herons formula to find the area of each individual triangle then multiply it by two

using heron's formula it gives us the answer of 90 m^2 for one triangle so we can multiply it by two to get the area of the whole shape and 90x2=180m^2

The solution of the equation is (3, 0).

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.

Given:

-x+y=-3....................(1)

3x+3y=9...................(2)

Solving Equation (1) and (2) we get

3x + 3(-3 + x) = 9

3x - 9 + 3x= 9

6x = 18

x= 18/ 6

x= 3

and, y= -3+ x

y= -3 + 3

y= 0

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The number of styrofoam is 11.

It is a polygon having six faces.

The volume of a cube is a side³

We have,

The area of the box = 44 square inches

Styrofoam is considered a square shape.

The side length of the styrofoam = 2 in

The area of the foam = 2² = 4 square inches

Now,

The number of styrofoam.

= 44 / 4

= 11

Thus,

11 styrofoam.

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Complete question:

Jason packs a box full of styrofoam pieces in a rectangular shape surface with an area of 44 square inches.

Each styrofoam is a square shape with a side length of 2 inches.

How many square inches of styrofoam can the box fold ?

Part A) The figure shows the prism.

Part B) the surface area of the figure is,

⇒ S.A = 270 in²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

By figure,

The shape shows the rectangular prism.

We know that;

The surface area of prism is,

⇒ S.A = 2B + ph

Where, B is base area, p is perimeter and h is height of prism.

Here, The base area of the prism is,

B = 10 × 5 = 50 in²

The perimeter of the base of prism is,

p = 2 (5 + 10)

  = 100 in

Height of prism = 1.7 in

Hence, We get;

The surface area of prism is,

⇒ S.A = 2B + ph

⇒ S.A = 2 × 50 + 100 × 1.7

⇒ S.A = 100 + 170

⇒ S.A = 270 in²

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The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

Similar triangles have the same corresponding angle measures and proportional side lengths.

Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,

The sum of interior angles of a triangle = 180°

Considering Δ ABC,

∠ A + ∠ B + ∠ C = 180°

∠ C = 180°-(22°+75°)

∠ C = 83°

Since, we know that the similar triangles have congruent corresponding angles,

Therefore,

∠ A = ∠ F, ∠ B = ∠  G and ∠ C = ∠ H

Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°

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1. To decide if the offer presented by your great uncle is to your advantage, you need to consider the time value of money. This means that money available today is worth more than the same amount of money available in the future, due to the potential for earning interest or returns on the money. In this case, you need to compare the value of $1,000 today with the value of $1,200 in five years. If you can earn a rate of return greater than 4% over the next five years, it would be better to take the $1,000 today and invest it to earn a higher return. However, if you cannot earn a return greater than 4%, it would be better to wait and take the $1,200 in five years.

2. Interest rates and compounding periods will vary depending on the financial institution and type of account. As an example, let's assume that you are considering a savings account, checking account, and money market account with the following interest rates and compounding periods:

Using a compound interest calculator, the future value of $1,000 in each account after five years would be:

3. The value of money today can be different from its value in the future due to inflation, changes in interest rates, economic growth, and changes in the supply and demand for goods and services. Inflation is one of the biggest factors that can affect the value of money over time. If the rate of inflation is high, the value of money will decrease over time, meaning that the same amount of money will buy fewer goods and services in the future. On the other hand, if the rate of inflation is low, the value of money will increase over time, meaning that the same amount of money will buy more goods and services in the future. Interest rates can also affect the value of money, as higher interest rates can make it more attractive to save money, while lower interest rates can make it more attractive to borrow money. Economic growth and changes in the supply and demand for goods and services can also affect the value of money, as these factors can affect the overall price level of goods and services in the economy.

The rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 can be found using the Rational Root Theorem.

The Rational Root Theorem states that if a polynomial has a rational root, it will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -1 and the leading coefficient is 1. The factors of -1 are -1 and 1, and the factors of 1 are 1. Therefore, the possible rational roots of this polynomial are -1/1, 1/1, or -1 and 1.

We can test these possible roots by plugging them into the polynomial and seeing if the result is 0.

P(-1) = (-1)^3 + 3(-1)^2 + (-1) - 1 = -1 + 3 - 1 - 1 = 0
P(1) = (1)^3 + 3(1)^2 + (1) - 1 = 1 + 3 + 1 - 1 = 4

Therefore, the only rational root of this polynomial is -1.

So, the rational roots of the polynomial P(x) = x^3 + 3x^2 + x - 1 are -1.

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Answer: 36.2

Step-by-step explanation:

To find the mean, you add up all the values then divide by the number of values present. So, 45+35+35+30+36= 181. 181 divided by 5 is 36.2

The Perimeter of the pentagon ABCDE is 17 units.

If two points in coordinates plane P(a, b) and Q(c, d) then the distance between these points are

PQ = √(c-a)² + (d-b)²

Given:

The coordinates of Pentagon are  A (4, 3), B (7, 3), C (8, 0), and D (2, -3) and E(0, 1).

Using Distance formula

AB = √(7-4)² + (3-3)²

AB = √9

AB = 3

BC = √(8-7)² + (0-3)²

BC = √1 + 9

BC = √10

CD = √(2-8)² + (-3-0)²

CD = √36  + 9

CD = √45

CD = 3√5

DE = √(0-2)² + (-3-1)²

DE = √4 + 16

DE = √20

DE = 2√5

So, Perimeter of the pentagon ABCDE = AB+BC+CD+DE+EA

                                                                 = 3 + √10 + 3√5 + 2√5

                                                                 = 3 + √10 + 5√5

                                                                 = 17.342 unit

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Answer: 22

Step-by-step explanation:

Just because it is right yk.

Answer:

Step-by-step explanation:

EB/BC=15/12=5/4

ED/AC=X+5/Y=5/4

5y=4x+20

y=0.8x+4