Which of the following sentences describes the next step in the construction?

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

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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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

Answer:

Step-by-step explanation:

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

Answer:

please give the complete question..

Step-by-step explanation:

please give the complete question..

The required amount of sauce in each bottle is given by fraction 5/7. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Sum the total amount of sauce in the 7 bottles present at each booth,
Total sauce = 0 × 2 + 1/2×1 + 1×3 + 1 1/2 × 1
                 = 1/2 + 3 + 3/2
                 = 2 + 3 = 5

Now, the ratio of the total sauce to the total number of bottles will give the amount of sauce in each bottle.

So,
= 5/7

Thus, the required amount of sauce in each bottle is given by fraction 5/7.

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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:

2

Step-by-step explanation:

sqrt 16/4 is 4/2

4/2 is 2

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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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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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.

One gallon is a unit of volume that is equivalent to 3.785 liters. This means that one gallon is equal to 3.785 liters.

The gallon is an imperial unit of measurement, which means that it is not used in most countries outside of the United States and the United Kingdom. In the US customary system, the gallon is divided into four quarts, each of which is equal to two pints. One US gallon is equivalent to approximately 0.83 imperial gallons, which are used in the UK.The gallon originated in medieval England as a measure for ale and other alcoholic beverages. It was adopted by the Romans during their invasion of Britain, and the term "gallon" is derived from the Latin term "galleta," which means "a pailful." The gallon was standardized in the 18th century by the British Imperial System.In the United States, the gallon is used in both the customary and imperial systems. In the customary system, the gallon is equal to 128 fluid ounces, while in the imperial system, it is equal to 160 fluid ounces. The US liquid gallon is divided into four quarts, which is equivalent to eight pints. One US dry gallon is equal to 4.4 liters.

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Based on the ratio of the​ office's area to the area of the home, the deductible amount is $760.

The ratio refers to the relative quantity of one value contained in another.

Generally, ratios are depicted as fractions, decimals, or percentages.

Total home area = 2400 ft²

Office area =380 ft² (20 x 19)

The ratio of office to home area = 380/2400

The percentage of office use of the home-related expense = 15.83% (380/2400 x 100)

The Electricity bill for the year = $4,800

The deductible amount for office use = $760 ($4,800 x 380/2400) or ($4,800 x 15.83%)

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Each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

The angles m∠MON and m∠LOM form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.

we shall solve for x as follows:

2x + 7x + 9 = 90

9x + 9 = 90

9x = 90 - 9 {subtract 9 from both sides}

9x = 81

x = 81/9 {divide through by 9}

x = 9

m∠MON = 7(9) + 9 = 72°

m∠LOM = 2(9) = 18°

The angles m∠LOM and m∠POQ are vertical angles formed by the two straight lines MA and LP, hence;

m∠LOM = m∠POQ = 18°

In conclusion, each interior angles of a rectangle is equal to 90° so m∠MON and m∠LOM are complementary as they add up to 90°. The value of x = 9. Angles m∠MON = 72° and m∠LOM = 18°. The angle m∠POQ = 18° because m∠LOM and m∠POQ are vertical angles.

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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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Answer:

Step-by-step explanation:

The rate of deflation of the hot-air balloon is 0.25 feet per minute. Let's represent the diameter of the balloon at any time t in minutes as D(t).

We know that D(0) = 14 feet (initial diameter) and we want to find x when D(x) = 8 feet.

Using the fact that the rate of change of D with respect to time is -0.25 (negative because the diameter is decreasing), we can set up a differential equation:

dD/dt = -0.25

Separating variables and integrating, we get:

∫(1/D) dD = ∫(-0.25) dt

ln|D| = -0.25t + C

where C is the constant of integration.

Using the initial condition D(0) = 14, we get:

ln|14| = C

C = ln(14)

Substituting this value of C into the equation, we get:

ln|D| = -0.25t + ln(14)

Taking the exponential of both sides, we get:

|D| = e^(-0.25t + ln(14)) = e^ln(14) e^(-0.25t) = 14 e^(-0.25t)

Since we are only interested in the positive value of D, we can drop the absolute value sign:

D = 14 e^(-0.25t)

Now we can solve for x by setting D = 8:

8 = 14 e^(-0.25x)

Dividing both sides by 14, we get:

e^(-0.25x) = 8/14 = 4/7

Taking the natural logarithm of both sides, we get:

ln(e^(-0.25x)) = ln(4/7)

-0.25x = ln(4/7)

x = -4 ln(4/7) / 0.25

x ≈ 6.21

Therefore, it will take about 6.21 minutes for the balloon to shrink to a diameter of 8 feet.

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

Answer

Step-by-step explanation:

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!

A quarter pound hamburger is counted as one servings which is four ounces.

A pound is usually a unit which is used to measure the weight of a body.  It is known as one pound is approximately equal to 454 grams. One kilogram is roughly the same as equal to 2.2 lbs. There are 16 ounces in one pound which is mentioned.

This question can be solved due to the rule of proportions.

A pound is an imperial unit of mass or weight measure, it is abbreviated as lb, lbm and one pound is considered to be equal to 0.4535 kilograms.

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Answer:

Quadrant I is located on the top right of the graph (Positive x, Positive y)

Quadrant II is located on the top left of the graph (Negative x , Positive y)

Quadrant III is located on the bottom left of the graph (Negative x, Negative y)

Quadrant IIII is located on the bottom right of the graph (Positive x, Negative y)

The origin is at the center of the graph with (0,0) as its x and y components

Step-by-step explanation: ^^ Please give 5 star and thanks.

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 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.

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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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 ?

Answer:

here u go

Step-by-step explanation:

Sounds like you're very young but here I go!

since 1 inch = 2.5 cm

and 24 inches = 2 feet

multiply inches and cm by 24

answer is 60 cm

i hope it helped it may be wrong tho :(

(C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

In number theory, the breakdown of a composite number into a sum of smaller integers is known as integer factorization.

The procedure is known as prime factorization if these factors are further limited to prime numbers.

The technique of expressing all numbers as the product of primes is known as prime factorization.

So, let's take something like the number 20 as an example.

It can be divided into two components.

"Well, that's 4 times 5," we can respond.

Observe that 5 is a prime number. The number 4 is not a prime.

So, it is necessary to write 48 as the product of its prime elements:

2 * 3 * 2 * 2 * 2

Then,

√48 = √(2 * 2 * 2 * 2 * 2)

Lower radical form: √48

Hence, (C) could be the correct option.

Therefore, (C) 48 = V2 -2 -2 -2 - 3 = 4√3 correctly uses prime factorization to write V48 in simplest form.

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Correct question:

Which calculation correctly uses prime factorization to write V48 in simplest form?

A. 48 = V2 -2 -2 -2 - 3 = 2V12

B. 48 = 14 - 12 = 2/12

C. 48 = V2 -2 -2 -2 - 3 = 4V3

D. V48 = 16 - 3 = 4V3​

Answer:

Step-by-step explanation

It seems like you are to use trig functions to find the missing sides.

soh - cah - toa

Sin(what degree angle you have) = opposite of the angle over the hypotenuse

cosine (what degree angle you have) = adjacent (side that is next to angle that isn't hypotenuse) over hypotenuse

tangent (what degree angle you have) = opposite side from angle over adjacent side to angle

for number 1:

sine59 = d/ 37

cross multiply

sin59 multiplied by 37 which equals 31.7

so this means d is 31.7

use the trig functions to find the rest. it is just a pattern and SOH-CAH-TOA will help.

lmk if you have questions