How many pieces of tape 5mm long can be cut from a piece 15cm long ?

Answer:

x^2+7x+10

Step-by-step explanation:

x×x=x^2

5×x=5x

2×x=2x

5x+2x=7x

5×2=10

a) The probability that the student will answer all 5 correctly is 1/252.

b) The probability that the student will answer at least 4 correctly is 1 - (1/252 + 1/126 + 1/84 + 1/63).

The probability of answering all 5 problems correctly on the final if the student has figured out how to do 7 of the questions is 1/252. This is because there are 10 questions in total and the student has figured out how to do 7 of them. That means there are 3 questions that the student does not know how to do, and therefore the probability of getting all 5 questions correct on the final is 1/252.The probability that the student will answer at least 4 of the problems is 1 - (1/252 + 1/126 + 1/84 + 1/63). This calculation takes into consideration the fact that there are 4 possible combinations of 5 questions that the student could get wrong out of the 10 questions. So, the probability of answering at least 4 questions correctly is 1 minus the probability of getting 4 or 5 questions wrong.

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9514 1404 393

Answer:

  434 -49π ≈ 280.1 cm²

Step-by-step explanation:

The shaded area is the difference between the enclosing rectangle area and the circle area.

The rectangle is 14 cm high and 31 cm wide, so has an area of ...

  A = WH

  A = (31 cm)(14 cm) = 434 cm²

The circle area is given by ...

  A = πr²

  A = π(7 cm)² = 49π cm²

__

The shaded area is the difference of these, so is ...

  shaded area = rectangle - circle

  = (434 - 49π) cm² ≈ 280.1 cm²

Answer:

It's the third choice.

Step-by-step explanation:

IF y varies inversely as x then y = k/x   where k is a constant,

and k = xy    

For the 3rd choice

-1 * -2/7 = 2/7

4 * 1/14 = 2/7 and

6 * 1/21 = 2/7

so, this is inverse variation.

Answer:

C

Step-by-step explanation:

2+4=6

6+4=10

and

18+36=54

54+36=90

you just add hope this helps :))

The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

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Answer:

2 2/5 inches

Step-by-step explanation:

3/5 x 4

3/5 x 4/1

3/5 x 4/1 = 12/5

12/5 = 2 2/5

We have to find the output of a function, if the input is -7.

The input in this case is the value of x, which is the independent variable.

The output is the value of y, and we will calculate it as:

If the input is x=-7, the output will be y=-14.

3) We have another function, and the input is x=-7

We evaluate y as:

The output is y=1 for any input (also x=-7).

The number of minutes it would take Athlete J to run one mile is 12 minutes.

The number of hours it would take Athlete h to run 5 miles is 10/11 hour.

Athlete h runs faster because his average speed is greater than that of  Athlete J.

In order to determine the time it would take Athlete J to run one mile, the average speed has to be determined.

Average speed = total distance / time

2/3 ÷ 8

2/3 x 1/8 = 1/12 mile / minute

Time it would take Athlete J to run one mile = distance / speed

1 ÷ 1/12 = 12 minutes

Average speed of Athlete H = 2 3/4 ÷ 1/2

11/4 x 2 = 5 1/2 miles / hour

Time it would take Athlete H to run 5 miles = distance / speed

5  ÷ 11/2

5 x 2/11 = 10/11 hours

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Answer:

one solution

Step-by-step explanation:

3 -2x=5-x+3+4x

Combine like terms

3-2x = 8+3x

Add 2x to each side

3-2x+2x = 8+3x+2x

3 = 8+5x

Subtract 8 from each side

3-8 =8+5x-8

-5 =5x

Divide by 5

-5/5 = 5x/5

-1 =x

There is one solution

Answer:

1. Sine A = 3/5

2. Cos A = 4/5

3. Tan A = 3/4

4. Sine B = 4/5

5. Cos B = 3/5

6. Tan B = 4/3

Step-by-step explanation:

1. Determination of Sine A

Opposite = 3 in

Hypothenus = 5 in

Sine A =?

Sine A = opposite / Hypothenus

Sine A = 3/5

2. Determination of Cos A

Adjacent = 4 in

Hypothenus = 5 in

Cos A =?

Cos A = Adjacent / Hypothenus

Cos A = 4/5

3. Determination of Tan A

Opposite = 3 in

Adjacent = 4 in

Tan A =?

Tan A = opposite / Adjacent

Tan A = 3/4

4. Determination of Sine B

Opposite = 4 in

Hypothenus = 5 in

Sine B =?

Sine B = Opposite / Hypothenus

Sine B = 4/5

5. Determination of Cos B

Adjacent = 3 in

Hypothenus = 5 in

Cos B =?

Cos B = Adjacent / Hypothenus

Cos B = 3/5

6. Determination of Tan B

Opposite = 4 in

Adjacent = 3 in

Tan B =?

Tan B = opposite / Adjacent

Tan B = 4/3

Answer:

Statement:-                   Reason:-

---------

---------

---------

Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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Answer:

4x3x2x1=24

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

-2

Step-by-step explanation:

First you want to seperate the c. To do that you divide by both sides so -12/c divide -12 cancels out to be just 1/C. 6 divide -12 is -0.5. Know we have 1/c = -0.5 and that is -2. -2 is your answer :)

Answer:

Step-by-step explanation: Here's a step-by-step guide on how to graph the equation -3y + 6x = 6:

Isolate y: To isolate y, first subtract 6x from both sides of the equation: -3y + 6x = 6 => -3y = -6x + 6.

Divide both sides of the equation by -3: Dividing both sides of the equation by -3, we get: -3y / -3 = (-6x + 6) / -3.

Simplify the equation: On simplifying the equation, we get: y = 2x - 2.

Plot the y-intercept: The y-intercept of the equation is when x = 0. So, when x = 0, y = 2 * 0 - 2 = -2. This point is (0, -2). Plot this point on the graph.

Plot a second point: Pick a value of x and plug it into the equation to find the corresponding y value. For example, let's take x = 1. Plugging x = 1 into the equation, we get y = 2 * 1 - 2 = 0. This point is (1, 0). Plot this point on the graph.

Draw the line: Connect the two points plotted on the graph. This line represents the solution set of the equation.

That's it! You have successfully graphed the equation -3y + 6x = 6.

Answer:



Step-by-step explanation:

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer: Sir in what way would you like me to explain this

Step-by-step explanation:

Answer:

Option b, (4,2)

Option d, (8,4)

Option e, (12,6)

Answered by GAUTHMATH

Answer:

Option b, (4,2)

Option d, (8,4)

Option e, (12,6)

Step-by-step explanation:

the person above me is correct

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Answer:

2 is the gcf.

Answer:

In order to find the GCF of no.'s we need to first look at the smallest no (which is 8, in this case)

Next, list down all the factors of 8.

1*8

2*4

4*2

8*1

Now, once you have listed all the factors for 8, find which factor of 8 goes with 18 and 70.

2 is the answer; because 2 goes into 8, 18 and 70.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

On solving the provided question, we can say that - Surface area of the following will be 20 sq unit sq.

A three-dimensional shape's surface area is the total amount of space that surrounds it. Additional distinctions between interface types include: The area that includes the base and curving section is referred to as the gross area. The curved area is the section of the curved portion that is devoid of a base. A plane is a two-dimensional object that occupies space. square units of measurement. The surface area of a three-dimensional object refers to the space it takes up on its outside surface.

Given plane:

\(-\sqrt{20} + 2y + z = 82\\ z = 82 + \sqrt{20} -2y\\\frac{dx}{dy} = \frac{d}{dy}(82 + \sqrt{20} -2y) \\= -2\)

Surface area =

\(\sqrt{1 + (\sqrt{20} )^2 + (-2)^2}\\ \sqrt{(1 + 20 + 2} \\5\)

5 X Area of the Porth

5 X 6

30 unit sq

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Answer:

C) 0.066...

Step-by-step explanation:

1/15 = 0.066...

You could eliminate B and C as 15 (numerator from question) is not a multiple of 10. You can eliminate A as the numerator of 15 from the question is larger than 10 and will result in a number less than 0.1.