Working as a team, 8 mathletes solve 20 problems in 10 minutes. At this rate, how many mathletes solve 30 problems in 5 minutes

Step-by-step explanation:

The Radius of the larger semi circle = [tex]\frac{12}{2}[/tex] = [tex]6[/tex][tex]cm[/tex]

Area of the 2 larger semi Circles = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]

                                                  = [tex]\frac{3.14X(6)^{2} }{2} X 2[/tex]

                                                   = [tex]\frac{113.04}{2} X2[/tex]

                                                    = [tex]113.04[/tex] [tex]cm^{2}[/tex]

Radius of the smaller semi circle = [tex]\frac{5}{2} = 2.5cm[/tex]

Area of the smaller semi circle = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]

                                                    = [tex]\frac{3,14X(2.5)^{2} }{2} X 2[/tex]

                                                     = [tex]196.25[/tex][tex]cm^{2}[/tex]

Combined Area = [tex]113.04 + 196.25[/tex]

                           = [tex]309 . 29cm^{2}[/tex]

The time period it will take a principal of $25000 to grow int $28500 at a rate of 4% is approximately 3 years

Compound interest is the interest that is calculated on the initial principal and also on the accumulated interest of previous periods. It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

In the given question, our data is;

The formula is given as

A = P(1 + r/n)^nx

The given expression is

m(n) = 25000(1 + 0.04/ 2)^2n

m(n) = 28500

28500 = 25000(1 + 0.04 / 2)^2n

Solving for n,

n = 3.3

n ≈ 3

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Answer:

{x,y}={6,-2}

Step-by-step explanation:

System of Linear Equations entered :

[1]    3x + 5y = 8

  [2]    2x - 5y = 22

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    2x = 5y + 22

 [2]    x = 5y/2 + 11

// Plug this in for variable  x  in equation [1]

  [1]    3•(5y/2+11) + 5y = 8

  [1]    25y/2 = -25

  [1]    25y = -50

// Solve equation [1] for the variable  y

  [1]    25y = - 50

[1]    y = - 2

// By now we know this much :

   x = 5y/2+11

   y = -2

// Use the  y  value to solve for  x

 x = (5/2)(-2)+11 = 6

Graphic Representation of the Equations :

The answer should be: {x,y}={6,-2}

Answer: ummm B

Step-by-step explanation:

Answer: B

Step-by-step explanation: To make his special energy drink Jerome uses 8 cups of water and 3 cups of drink mix. So the ratio of drink mix to water is 3:8.

The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.

Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:

c² = a² + b² - 2abcosC

Therefore, you can rearrange the equation to solve for angle C:

C = arccos((a² + b² - c²) / (2ab))

For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.

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The distance Issa travelled from school to his house is 9.6 km.

The actual length covered by the body is defined as distance travelled, whereas displacement is the straight path between the initial and final points.

Here,

Let the total distance between school and home be 'x' meters.

Issa jogged two-thirds of x = 2x/3

So the total distance between school and home is = 2x/3 + 3200

However, the total distance from school to home = x

= 2x/3 + 3200 = x

= 3200 = x/3

= 9600 = x

As a result, the total distance from school to home is 9600 meters.

We're now converting it to kilometers.

We know that 1000 meters equals one kilometer.

9600 meters = 1/1000 x 9600

= 9.6 kilometers

Therefore the distance travelled will be 9.6 km.

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Answer:

35 dimes and 65 nickels

Step-by-step explanation:

We will need use a system of equations to find the total number of nickels and dimes.

Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.

Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75

Substitution will be the easiest method to solve:

[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]

The side lengths measuring 9 units , 12 units and 15 units make a Right Triangle because the sides satisfy the condition of the Pythagoras Theorem .

According to the  Pythagoras Theorem , which states that square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ( perpendicular and Base) ,

The side lengths of right triangle are = 9 units , 12 units and 15 units ,

According to the condition of Pythagoras theorem , [tex]15^{2} = 12^{2} + 9^{2}[/tex]

On simplifying ;

we get ;

[tex]225 = 144 + 81[/tex] ;

[tex]225 = 225 ;[/tex]

the condition is satisfied ,

that means the sides form a right triangle .

Therefore , the side 9 units , 12 units and 15 units  make a right triangle .

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The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).

Start with the first equation:

x + 3y + 2z = 1

Isolate x by subtracting 3y and 2z from both sides:

x = 1 - 3y - 2z

Substitute this expression of x into the second equation:

0.3x + y + 5z = 10

Substitute the value of x found in step 2 into this equation:

0.3(1 - 3y - 2z) + y + 5z = 10

0.3 -0.9y -0.6z + y + 5z = 10

0.1y + 4.4z = 9.7

y + 44z = 97

Solve for y by isolating it:

y = 97 - 44z

Substitute this expression of y into the first equation:

x + 3(97 - 44z) + 2z = 1

x + 291 - 132z + 2z = 1

Solve for x:

x = 130z - 290

Substitute this expression of x into the third equation:

-2(130z - 290) - 3(97 - 44z) + z = 7

-260z + 580 - 291 + 132z + z = 7

Solve for z:

127z = 282

z = 282/127

Substitute this value of z into the expression of y:

y = 97 - 44(282/127)

= -89/ 127

Substitute the values of z into the expression of x:

x = 130(282/127) - 290

= - 170/ 127

So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.

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1(t) = 12(t) (2,2,4) +t(2,4,6) and Ia(t) = 12(t) (2,2,4) +t(2,4,6) represents the same line, as they are both equivalent to 12(t)(2,2,4) + t(2,4,6). So Option A is correct.

The equation of a line in 3-dimensional space can be represented in the form "r(t) = a + tb" where "r(t)" is a vector that represents any point on the line, "a" is a vector that represents a point on the line, and "b" is a vector that represents the direction of the line.

The given equations are:

1(t) = 12(t) (2,2,4) +t(2,4,6)

Ia(t) = 12(t) (2,2,4) +t(2,4,6)

As we can see that both equations are identical to equation 12(t) (2,2,4) +t(2,4,6) thus these three equations represent the same line.

The other given options B, C, and D are not equivalent to each other or to the original equation, thus they do not represent the same line.

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Based on the question above, the patient pays $600 and the insurance company pays $2400.

To calculate how much the patient pays, we first need to calculate how much the insurance pays. We can do this by taking the total cost of the treatment ($3000) and multiplying it by the percentage that the insurance pays:

(90% = 0.9).

$3000 x 0.9 = $2700

This means that the insurance pays $2700 of the cost of the treatment. But we also need to subtract the $300 deductible from this amount.

$2700 - $300

= $2400

So the insurance pays $2400 for the medical treatment.

To find out how much the patient pays, we can subtract the amount paid by the insurance from the total cost of the treatment:

$3000 - $2400

= $600

Therefore, the  mathematics involved in solving this problem is very straightforward. We used basic arithmetic operations such as multiplication and subtraction to find the amounts paid by the insurance company and the patient.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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The comparison operator "≥" in logic means that the number is either greater than or equal to a number , the greater than equal to symbol is used to describe the relationship between two terms .

What is a Comparison Operator ?

The Comparison operator in logic is used to compare logic statements ,such as [tex]a > b[/tex] or [tex]a < b[/tex] , by using a , b as variables, the operator compares their values, returns true and false.

The Comparison Operator "≥" , in logic is read as " greater than equal to" , For Example : if the statement is [tex]a \geq b[/tex] , then if the variable is greater than or equal to b , then the operator will return TRUE and if not then it will return FALSE .

The given question is incomplete , the complete question is

What does the comparison  operator "≥"(greater than equal to) mean in logic ?

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Answer:

h = 8

Step-by-step explanation:

5.50h=44

Divided both sides by 5.50

h = 8

Let's check

5.50(8) = 44

44 = 44

So, h = 8 is the correct answer!

Apply arithmetic operations on both sides of the equation to move the variable to one side and all other values to the opposite side.

Let's begin with a basic equation: x + 2 = 7.

How may x be obtained on its own?

x + 2 - 2 = 7 - 2 x = 5 after deducting 2 from both sides.

Put the solution, x = 5, back into the equation to confirm it. We get 5 + 2= 7.

Since LHS = RHS

In the triangle, find x.

Use triangle properties or the Pythagorean theorem to find the value of x, the unknown side or angle in a triangle.

Let's use an example to better understand how to solve for x in a triangle.

Using the Pythagorean theorem, we obtain AC2 = AB2 + BC2 where x2 = 72 + 242 x = 49 + 576 x = 625 x = 25 units.

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Answer:

C.

Step-by-step explanation:

To find the equation of the line that goes through the points (5, 3) and (-1, 2), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

To find the slope of the line, we can use the following formula:

m = (y2 - y1)/(x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (2 - 3)/(-1 - 5) = -1/6

Substituting this value of m and the coordinates of one of the points into the point-slope form, we get:

y - 3 = -1/6(x - 5)

This simplifies to:

6x + y - 13 = 0

Therefore, the equation of the line is:

6x + y - 13 = 0

A triangle with side lengths 12,16, and 20 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

properties of right angle:

The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.

The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.

consider c=20 a=12, b=16 substitute in above formula:

20²=12²+16²

⇒400=144+256

⇒400=400

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More than one applies to the slope.

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.

The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)

The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.

m = 3

It is steeper than one.

As a result, a scale factor other than 1 has been used to dilate the graph.

The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

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The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).

For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.

To satisfy the second condition the points of a should satisfy the equation given

LHS= 2x+3y

RHS=6

A(0,2)

Substituting the values of x and y in 2x+3y,

2(0)+3(2)=6

Therefore LHS=RHS

Hence, at point A(0,2) the graph of the given equation cuts the Y axis.

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The value of x is 45 degree and value of y is 49 degree.We can find by using supplementary and corresponding angles.

Supplementary angles are those angles that sum up to 180 degrees. To find the angle which is supplementary to another angle subtract the given angle from 180 degrees. For example if one angle is 60 degrees then another angle is 180 – 60 = 120 degrees.

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles.

Now we find

according to supplementary angles

3x+45=180

3x=180-45

x=45

According to corresponding angles

y-4=45

y=45+4

y=49

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The equation of line passes through the points (0, 0) and (3a, 5g) will be;

⇒ y = (5g/3a) x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (3a, 5g).

Now,

Since, The equation of line passes through the points (0, 0) and (3a, 5g).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5g - 0) / (3a - 0)

m = 5g / 3a

Thus, The equation of line with slope 5g/3a is,

⇒ y - 0 = 5g/3a (x - 0)

⇒ y = (5g/3a) x

Therefore, The equation of line passes through the points (0, 0) and

(3a, 5g) will be;

⇒ y = (5g/3a) x

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Answer:

An Ideal solution follows the Raoult's law strictly

A Real solution shows deviation from the Raoult's law.

Step-by-step explanation:

Step-by-step explanation:

a linear relationship or function is described by

y = ax + b

that means that the difference from one y value to the next is defined by a constant ratio of y diff / x diff.

so, the first one is not linear.

because the difference ratios are not constant :

(1-0)/(1-0) = 1

(4-1)/(2-1) = 3

(9-4)/(3-2) = 5

the second one is linear.

the difference ratios are constant :

(1-0)/(1-0) = 1

(4-1)/(4-1) = 1

(9-4)/(9-4) = 1

the third one is not linear.

the difference ratios are not constant :

(3-1)/(3-2) = 2

(9-3)/(4-3) = 6

(27-9)/(5-4) = 18

the fourth one is linear.

the difference ratios are constant :

(5-1)/(4-2) = 4/2 = 2

(9-5)/(6-4) = 4/2 = 2

(13-9)/(8-6) = 4/2 = 2

The coordinate of N' is (2, -3)

Now, According to the question:

We have the point n (-2, -3) and we need to rotate it 270 degrees clockwise about the origin.

When rotating 270 clockwise about the origin you switch the x and y coordinate and use the opposite sign of the original y coordinate.

A(x, y) becomes A' (-y, x)

This means that point N becomes:

N (-2, -3) => N'(-(-2), (-3))

              => N'(2,- 3)

Hence, The coordinate of N' is (2, -3)

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The chance you get a odd number of heads from the first coin is 1/3,

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Answer:

To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:

4x - 6 = 8x - 6

4x = 8x

4x - 8x = 0

-4x = 0

x = 0

So, the value of x that makes (4x-6) equal to (8x-6) is x=0.

Answer:

-4x = -12 Divide each side by '-4'.

Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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The equivalent values to the given expressions are -

2/3 and 3/7 respectively.

Given are two expressions as -

1/3 + 1/3

5/7 - 2/7

The given expression are -

1/3 + 1/3

(1 + 1)/3

2/3

5/7 - 2/7

(5 - 2)/7

3/7

Therefore, the equivalent values to the given expressions are -

2/3 and 3/7 respectively.

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