A cylindrical jar contains three glass balls each has a diameter of 2cm and their surfaces touch the inner side of the jar as shown below. What is the volume of the gap in the jar?​

Answer:

The faster cyclist is traveling at 72 miles per hour.

Step-by-step explanation:

We know that the two cyclists are 72 miles apart and meet 3 hours later. We also know that the faster cyclist is 3 times as fast as the slower cyclist.

Let's call the speed of the slower cyclist x miles per hour.

If the faster cyclist is 3 times as fast as the slower cyclist, then their speed is 3x miles per hour.

We can use the formula: distance = speed x time

The distance covered by the slower cyclist is:

x * 3 = 72 miles

The distance covered by the faster cyclist is:

3x * 3 = 72 miles

We can use the formula: distance = speed x time again

x * 3 = 72

x = 24 miles/h

So the slower cyclist is traveling at 24 miles per hour.

To find the speed of the faster cyclist, we know that the faster cyclist is 3 times as fast as the slower cyclist.

The speed of the faster cyclist is:

3 * 24 = 72 miles/h

Answer:

3 cuuuuuuuuuuuuuupsssssss offfccccdd saaaaaaaallllytttt

Answer:

---------------------------------

Use the compound interest formula:

Where A - future amount, P - invested amount, r- annual interest rate, n - number of compounds a year, t - number of years

Given:

Substitute known values and solve for P:

Answer: Here it is

Step-by-step explanation:

a) The perimeter of a shape is the sum of the lengths of all its sides. In this case, the shape has sides with lengths of 4, 5h, 7, and 2h. Therefore, the expression for the perimeter of the shape can be written as:

Perimeter = 4 + 5h + 7 + 2h

To simplify this expression, we can combine like terms:

Perimeter = 4 + 7 + (5h + 2h)

Perimeter = 11 + 7h

So, the simplified expression for the perimeter of the shape is 11 + 7h

b) The perimeter of the shape is 42.

We can use this information and the expression we found in part a) to find the value of h. We know that:

Perimeter = 11 + 7h = 42

We can subtract 11 from both sides to get:

7h = 42 - 11 = 31

Finally, we can divide both sides by 7 to find the value of h:

h = 31/7

h = 4.428 (approximately 4.43)

Answer: Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

Step-by-step explanation:

Multiplying the first equation by 2 we get:

Now, once we have amplified the original equations, the sum of the first equation and the second equation leads to:

Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

Polar form of the given problem are expressed below

In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modelled as a union of argument and modulus.

Given, Some numbers that we need to write in polar form

General formula of polar form = r * [tex]e^{ia}[/tex]

For polar/rectangular conversion we use the following transformations

r² = x² + y²

x = r cosa

y = r sina

Where a is angle

For (a) 1/5

r = 1/5

a = 0

Since angle is 0

Polar form = 1/5

For  (b) 4 +4i

r = √4² + 4² = 4√2

a = tan(4/4) = tan (1) = pi/4

Polar form = 4√2 [tex]e^{ipi/4}[/tex]

For (c) -6 + 6 i

r = √-6² + 6² = 6√2

a = tan(-6 /6)

a = -pi/4

Polar form = 6√2[tex]e^{-ipi/4}[/tex]

Therefore, polar form of the given questions written above.

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Answer:

B)  4√2

Step-by-step explanation:

Given expression:

[tex]7 \sqrt{2}-3\sqrt{8}+\sqrt{18}[/tex]

Rewrite 8 as 4 · 2 and 18 as 9 · 2:

[tex]\implies 7 \sqrt{2}-3\sqrt{4 \cdot 2}+\sqrt{9 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7 \sqrt{2}-3\sqrt{4} \sqrt{2}+\sqrt{9} \sqrt{2}[/tex]

Carry out √4 and √9:

[tex]\implies 7 \sqrt{2}-3\cdot 2 \sqrt{2}+3 \sqrt{2}[/tex]

Multiply -3 and 2:

[tex]\implies 7 \sqrt{2}-6 \sqrt{2}+3 \sqrt{2}[/tex]

Factor out √2:

[tex]\implies (7 -6+3) \sqrt{2}[/tex]

Carry out the operations inside the parentheses:

[tex]\implies 4\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

a. The least square regression equation of Y on X is: Y = 3.08X - 127.82

b. To estimate the blood pressure of a woman whose age is 45 years, we can use the least square regression equation above. Substituting X = 45, we get: Y = 3.08(45) - 127.82 = 143.46. Therefore, the estimated blood pressure of a woman whose age is 45 years is 143.46.

The quotient of these two expressions is not a finite value.

A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.

Here,

Given : The quotient of

2-√√√8

and

4+√12

is not a finite value.

Explanation:

The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.

So the expression inside the first square root becomes 8, and the whole first square root becomes 2.

So the final expression would be:

2 - (2) = 0

On the other hand, √12 = √(223) = 2*√3

So the final expression would be:

4+2*√3

Hence, the quotient of these two expressions is not a finite value.

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Answer:

a) The function is growth.

b) The growth rate in % is 4%. This can be determined by taking the natural logarithm of the coefficient (1.04) and multiplying it by 100.

ln(1.04)*100 = 3.98% ≈ 4%.

The missing vertices of the square are B(x, y) = (- 2, 1) and D(x, y) = (6, - 7), respectively.

Squares are quadrilaterals with four sides of equal length and four internal right angles. This kind of quadrilaterals have two diagonals perpendicular to each other. In this case, we know the coordinates of the endpoints of diagonal AC and we need to determine the location of points B and D.

This can be done by means of the following definition: A(x, y) = (a, b), C(x, y) = (c, d), B(x, y) = (a, d), D(x, y) = (c, b). If we know that a = - 2, b = - 7, c = 6 and d = 1, then the location of points B and D are, respectively:

B(x, y) = (- 2, 1), D(x, y) = (6, - 7)

Lastly, we graph the resulting figure.

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Inequality becomes 0.21t + 15,040 <= 100,000

Energy consumption remains a principal source of human caused greenhouse gas emissions the predominant cause of climate change.

After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour.

t be the number of hours

the power usage increases at a rate of 21% per hour

21% = 0.21, constant rate = 0.21 . So slope = 0.21

Prior to 7 a.m., 15,040 kWh have been used.

At 7.am , power used = 15,040kWh. so our y intercept is 15,040

We use slope intercept form y= mx+b

slope m = 0.21  and b = 15040

power usage , y = 0.21 t + 15040

The university has a daily goal to keep their power usage less than or equal to 100,000 kWh

Power usage is less than or equal to 100,000

So inequality becomes 0.21t + 15,040 <= 100,000

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Answer: 8 x 96

Explanation: (Commutative Law: A x B = B x A)

Answer:

D' (9, 10)

E'( 12,-1)

F'(7,8)

Step-by-step explanation:

The coordinates of triangle DEF will be D(9,10), E(12,-1), and F(7,8) after the translation.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The given triangle DEF has vertices D (3,5), E(6,-6), and F(1,3).

Triangle DEF has translated 5 units up and 6 units right.

This means that the x-coordinates of the vertices D, E, and F will each be increased by 6, and the y-coordinates of the vertices will each be increased by 5.

After the translation, the coordinates of vertex D will be (3 + 6, 5 + 5) = (9, 10)

After the translation, the coordinates of vertex E will be (6 + 6, -6 + 5) = (12, -1)

After the translation, the coordinates of vertex F will be (1 + 6, 3 + 5) = (7, 8)

So after the translation, the coordinates of triangle DEF will be D(9,10), E(12,-1), F(7,8)

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Area of figure 1 is 468 cm² and figure 2 is 45 cm².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2

For figure 1

Length of base = 16 + 14 =  30 cm

Length of right rectangle whose side is 14 and 14(smaller one)

Thus, its area = 14 * 14 = 196

Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272

Total area of the figure = 272 + 196 = 468 square cm

For figure 2

If we split them into two shape they will become a square and a triangle

Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9

Area of square = side * side = 6*6 = 36

Thus, total area = 9 + 36 = 45 square cm

Therefore, Area of these given figures(in unit square) are:

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Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.

Trigonometry is a branch of mathematics that studies how square side length The field's initial development took place during the Baroque era, more likely and around third century BC, as a result of the merger of astronomer and geometry studies. Numerous geometric equations and their potential applications to calculations are covered by precise mathematical approaches. Mathematics has six fundamental operations. They are known by a variety of names and abbreviations, including sine, quadrature, parallel, secant, etc (csc). The study of mathematics is focused mostly on the characteristics of right triangles. The ability to understand geometry, however, necessitates familiarity with each polygon's properties.

Here,

Given : Provided: tan = (-5/3)

With the help of the formula below, you may determine the angle's number, which varies at 90 to 180 degrees.

as tan θ = (-5/3)

The value of the perpendicular is 5, and the value of the base is 3.

The hypotenuse is (25 + 9) according to Pythagoras' Theorem.

= √34

The value of sin is (5/34)

=> sin θ = 5 * √34 / 34

=> sin θ = 5/√34

In the second meiotic division, which contains value, sin is positive.

Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.

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Answer:

36290.4$

Step-by-step explanation:

First of all we should find out how much farmer spent on 240 acres

240 × 188.99 = 45357.6

Then, let's find out the price for whole bushels he gets

240 × 60 × 5.67$ = 81648

Therefore his profit is,

81648 - 45357.6 = 36,290.4$//

Answer:

$519

Step-by-step explanation:

We know that the one day sale price of the ski set is $324 and the markdowns are specified.

A markdown means a reduction in price, so to find the original selling price we need to add the amount of markdown to the sale price.

The markdown of the ski set is $75 + $120 = $195

So, to find the original selling price we need to add the markdown amount to the sale price:

$324 + $195 = $519

Therefore, the original selling price of the ski set was $519

Answer:

1) f(-3)

= 2x + 5

= 2×(-3) +5

= -6+5

= -1

2) g(x)- h(x)

= -3x² + 2x - 6 -(-4 - x)

= -3x² + 2x - 6 + 4 + x

= -3x² + 3x - 2

3) f(x) = h(x)

or, 2x + 5 = -4 - x

or, 2x + x = -4 - 5

or, 3x = -9

or, x = -9/3

or, x = -3

4) i am not sure about the last but the answer is between f(x) and h(x). But i think its f(x).

Answer:

Step-by-step explanation:

Assuming that the area is a rectangle with no obstructions or furniture, and that the people are standing shoulder-to-shoulder, then the area can fit approximately 200,000 people. This is calculated by multiplying 250 feet by 250 feet to get the total square feet of the area, which is 62,500 (250 x 250 = 62,500). Then divide the total square feet by the amount of space taken up by one person, which is 2.5 square feet, to get the approximate number of people that can fit in the area. 62,500 / 2.5 = 25,000, so 25,000 x 8 = 200,000 people.

Answer:

An area that is 20 feet wide and 25 feet long will be 20*25 = 500 square feet large. Division tells us how many times one number is contained within a number, so to find how many 2.5 square feet large people fit in a 500 square feet large space, we do 500/2.5 = 200 people.

Step-by-step explanation:

The sine function that matches the graph is given as follows:

y = sin(2πx/7) - 1.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The maximum value is of 0, while the minimum value is of -2, hence the amplitude A is obtained as follows:

2A = 2. (as the difference of the maximum value and the minimum value is of 2).

A = 1.

A sine function with amplitude 1 should oscillate between -1 and 1, while this one oscillates between -2 and 0, hence the vertical shift is given as follows:

C = -1.

The period of the function is of 7 units, hence:

2π/B = 7

7B = 2π

B = 2π/7.

Then the function is defined as follows:

y = sin(2πx/7) - 1.

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The vertex form of the parabola is y + 1 = - 4 · (x + 1)².

Graphically speaking, parabolae can be generated by quadratic equations, whose forms are described below: (Please notice that the parabola described by statement is parallel to y-axis since axis of symmetry is a vertical line)

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

If we know that h = - 1, k = - 1 and (x, y) = (0, - 5), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (- 5 + 1) / (0 + 1)²

C = - 4 / 1²

C = - 4

The equation of the parabola in vertex form is equal to y + 1 = - 4 · (x + 1)².

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Answer:

Step-by-step explanation:

Linear functions can be used in many real-world applications such as:

Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.

Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.

Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.

Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.

Graphing: Linear functions can be used to graph the relationship between different variables.

Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.

Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.

Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.

I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:

1. Receive order

2. Buy jerseys from supplier

3. Resell at an slighly higher price

4. Pay taxes + shipping

Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.

For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:

[tex]y=60x-50x-5x[/tex]

As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:

[tex]y=60x-55x\\ \\y=5x[/tex]

Say "y" is the net revenue:

[tex]y=5(2)\\ \\y=10[/tex]

You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:

[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]

From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.

In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...

The system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds y, of nuts is; 6x + 2y = 40

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution the power of the equation must be in one degree.

We are given that the dried fruits cost $6 per pound

The nuts cost $2 per pound. It costs Simon $40 to make 12 pounds of trail mix.

We need to find  the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used to make 12 pounds of trail mix.

Therefore, the system of equation will be 6x + 2y = 40

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Answer: We can write an inequality to show how many more inches Bobby needs to grow to reach his desired height by using the following information:

Bobby hopes that he will someday be more than 72 inches tall.

He is currently 59 inches tall.

We can use the inequality x + 59 > 72, where x is the number of inches Bobby needs to grow to reach his desired height.

This inequality represents the total height (x + 59) being greater than the desired height (72).

To solve this inequality, we can subtract 59 from both sides:

x > 72 - 59

x > 13

So, Bobby needs to grow 13 inches or more to reach his desired height.

Step-by-step explanation:

Answer:

length = 6 cm , breadth = 4 cm

Step-by-step explanation:

the area (A) of the large rectangle = length × breadth

here length = 12 cm and breadth = 4 + x , then

A = 12(4 + x) cm²

the area (A) of the smaller rectangle = x(x + 2)

given area of larger is 4 times area of smaller then

12(x + 4) = 4x(x + 2) ← distribute parenthesis on both sides

12x + 48 = 4x² + 8x , that is

4x² + 8x = 12x + 48 ( subtract 12x + 48 from both sides )

4x² - 4x - 48 = 0 ( divide through by 4 )

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

but x must be greater than zero, so x = 4

dimensions of smaller rectangle are

length = x + 2 = 4 + 2 = 6 cm

breadth = x = 4 cm

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. The road junction to Timpson is option B. 20.57 miles.

To find the distance between Timpson and the junction point, we can use the Pythagorean theorem. Let's call the distance "d".

d^2 = (60 - 22)^2 + 12^2

d^2 = 38^2 + 144

d^2 = 1444

d = √(1444) = 38.03

So the distance between Timpson and the junction point is 38.03 miles. The distance between the junction point and Ashburn is simply 22 miles, so the total distance from Timpson to Ashburn is 20.57 miles (38.03 + 22).

Therefore, the distance between the road junction to Timpson is option B. 20.57 miles

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The complete question goes thus:

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. How far is the road junction to Timpson

A. 21.57miles

B. 20.57miles

C. 10.57miles

D. 57.12 miles

Answer:

y = 16.25x

Step-by-step explanation:

y is the total number of miles.

x is the number of days.