The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Find the radius of the largerwheel in the figure if the smaller wheel rotates 70.0° when the larger wheel rotates 40.0°The radius of the large wheel is approximately ____ cm.

The volume of a Pyramid

Given a pyramid of base area A and height H, the volume is calculated as:

The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:

Solving for b:

The area of the base is the semi-product of the legs:

Now the volume of the pyramid:

The volume of the figure is 319.2 cubic millimeters

It is to be noted that a relations in math can be represented in 8 different ways. See the examples below.

The relation in mathematics is the relationship between two or more sets of values.

The various types of relations and their examples are:

Empty Relation

An empty relation (or void relation) is one in which no set items are related to one another. For instance, if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8. For an empty relationship,

R = φ ⊂ A × A

Universal Relation

A universal (or complete) relation is one in which every member of a set is connected to one another. Consider the set A = a, b, c. R = x, y will now be one of the universal relations, where |x - y| = 0. In terms of universality,

R = A × A

Identity Relation

Every element of a set is solely related to itself via an identity relation. In a set A = a, b, c, for example, the identity relation will be I = a, a, b, b, c, c. In terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation

When one set includes items that are inverse pairings of another set, there is an inverse connection. For example, if A = (a, b), (c, d), then the inverse relation is R-1 = (b, a), (d, c). As a result, given an inverse relationship,

R-1 = {(b, a): (a, b) ∈ R}

Reflexive Relation

Every element in a reflexive relationship maps to itself. Consider the set A = 1, 2, for example. R = (1, 1), (2, 2), (1, 2), (2, 1) is an example of a reflexive connection. The reflexive relationship is defined as- (a, a) ∈ R

Symmetric Relation

If a=b is true, then b=a is also true in a symmetric relationship. In other words, a relation R is symmetric if and only if (b, a) R holds when (a,b) R. R = (1, 2), (2, 1) for a set A = 1, 2 is an example of a symmetric relation. As a result, with a symmetric relationship, aRb ⇒ bRa, ∀ a, b ∈ A.

Transitive Relation

For transitive relation, if (x, y) ∈ R, (y, z) ∈ R, then (x, z) ∈ R. For a transitive relation, aRb and bRc ⇒ aRc ∀ a, b, c ∈ A

Equivalence Relation

If a relation is reflexive, symmetric and transitive at the same time, it is known as an equivalence relation.

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It is found that a relations in math can be represented in 8 different ways.

The relation in mathematics is defined as the relationship between two or more sets of values.

There various types of relations and their examples:

An empty relation (or void relation) is one in which no set items are related to one another.  if A = 1, 2, 3, one of the empty relations might be R = x, y, where |x - y| = 8.

R = φ ⊂ A × A

Universal Relation; It is one in which every member of a set is connected to one another.

R = A × A

Identity Relation; Every element of a set is solely related to itself via an identity .

In a set A = a, b, c, for example, it is I = a, a, b, b, c, c. I

n terms of identity,  I = {(a, a), a ∈ A}

Inverse Relation; When one set of data includes items that are inverse pairings of another set, there is an inverse connection.

For example, if A = (a, b), (c, d), then the inverse is; R-1 = (b, a), (d, c).

R-1 = {(b, a): (a, b) ∈ R}

Equivalence Relation; When a relation is reflexive, symmetric and transitive at the same time, it is calles as an equivalence relation.

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To solve the quotient below;

We simply both the numerator and the denominator as follows;

Take into account that dop plots are usefull for small or moderate sized data sets, and also they are suefull for data with big gaps.

Based on the previous description, you can conclude that the best option for a dot plot is:

16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97

in comparisson with the other data sets, the elements of the rest of data sets are closer to each other.

Answer:

3*10=30

10^-6=1^-6. (10 raised to the power of-6)

therefore 3*1^-6=3

is equal to

4.86*10=48.6

10^-4=1^-4

therefore 48.6*1^-4=48.6

Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.

According to the question,

We have the following information:

Dave has 7 more dimes than nickels and 10 more pennies than nickels.

Now, let's take the number of nickels to be x.

So,

Dimes = (x+7)

Pennies = (x+10)

Now, Dave has $3.52 in his piggy bank.

We will convert nickels, dimes and pennies into dollars.

We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.

Now, we will convert the given numbers of nickel, dime and pennies into dollars.

x Nickels in dollars = $0.05x

(x+7) dimes in dollars = $0.1(x+7)

(x+10) pennies in dollars = $0.01(x+10)

Now, we will them.

0.05x + 0.1(x+7) + 0.01(x+10) = 3.52

0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52

0.16x + 0.8 = 3.52

0.16x = 3.52-0.8

0.16x = 2.72

x = 2.72/0.16

x = 17

Now, we have:

Number of nickels = 17

Number of dimes = (17+7)

Number of dimes = 24

Number of pennies = (17+10)

Number of pennies = 27

Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.

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Given

A circle with a tangent drawn to it forming one side of a triangle

Required

we need to find the diameter of the circle

Explanation

clearly it is a right angled triangle as radius through point of contact is perpendicular to the tangent. let the lenght of missing side be d

Therefore

or

or

or d=16

Answer:

Step-by-step explanation:

50

The algebraic expression for each phrase would be the following:

a. the product of 9 and a number t would be expressed as:

9*t

b. the difference of a number x and 1/2 would be expressed as:

x - 1/2

c. the sum of a number m and 7.1 would be expressed as:

m + 7.1

d. the quotient of 207 and a number n​ would be expressed as:

207 / n

Answer:

[tex]\frac{5}{2}[/tex] or 2.5cm

Step-by-step explanation:

Hello! Let's help you with your question here!

Let's start by working out what we know and what we need. So, we know that P is a circle and Q is the shape of a quarter circle with a radius of 20cm. The area of Q is 9 times the area of P and we must find the radius of P.

To start, we're looking for area, so we should at least start looking at the area of a circle, given radius, which is:

[tex]A=\pi r^2[/tex]

Now, we don't necessarily know r (radius) and the area either. However, we can try to use the quarter circle as our guide for the full circle. So, we want to find the area of the quarter circle, we can do that by using this formula!

[tex]A=\frac{1}{4} \pi r^2[/tex]

The reason why we put a [tex]\frac{1}{4}[/tex] at the front of [tex]\pi r^{2}[/tex] is because we're only solving for a quarter of a circle instead of the entire circle.

Now that we have our formula! We can calculate the area of the quarter circle as follows:

[tex]A=\frac{1}{4}\pi 15^2[/tex]

[tex]A=\frac{\pi 15^2}{4}[/tex]   -We combine the fraction [tex]\frac{1}{4}[/tex] into the rest of the equation.

[tex]A=\frac{225\pi }{4}[/tex]   - Evaluating [tex]15^2[/tex]

Now that we have the area of the quarter circle, we can now work on the full circle. What we know is that the area of A is 9 times of B, since we're finding the radius of B, we can essentially plug in the area and solve for the radius of the full circle. That would be as such:

[tex]A=9\pi r^2[/tex]   -We're using the area of circle A to find the radius of B.

[tex]\frac{225\pi }{4} =9\pi r^2[/tex]   - Plugging in the area of the quarter circle.

[tex]\frac{225\pi }{4}/9\pi =\frac{9\pi r^2}{9\pi }[/tex]   - We divide [tex]9\pi[/tex] to get rid of it on the right side.

[tex]\frac{25}{4} =r^2[/tex] - When dividing by [tex]\pi[/tex], the numerator [tex]\pi[/tex] gets cancelled out.

[tex]\sqrt{\frac{25}{4} }=r[/tex]   -We square root to get rid of the squared.

[tex]\frac{5}{2}=r[/tex]    - Square rooted both numerator and denominator.

And there we have it! We finally get a radius of [tex]\frac{5}{2}[/tex] or 2.5cm.

Given:

Required:

To find the solutions to the given equations.

Explanation:

Put equation 1 in 2, we get

When x=0,

When x=1,

Final Answer:

The solution are

The solution sets are

SOLUTION

The figure above consists of a triangle and a semi-circle.

Area of the figure = Area the of triangle + Area of the semi-circle

Area of composite figure = 112.5 + 88.3125 = 200.8125

Therefore the Area of the figure = 200.81 squared feet to the nearest hundredth

SOLUTION

Step 1 :

In this question, we are meant to know the relationship between Growth factor and Growth Rate.

Growth factor is the factor by which a quantity multiplies itself over time.

Growth rate is the addend by which a quantity increases ( or decreases ) over time.

Step 2 :

From the question, if the growth factor is 1.2 which is also 120 %,

then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2

CONCLUSION:

The Growth Rate = 0. 2

For the given question, we will use the formula from part (b) to answer part (d)

The given function is as follows:

We will find the number of species (S) When A = 813

so, substitute with A = 813, then find S

Rounding the answer to the nearest 10 species

So, the answer will be:

Solution

The final answer

STEP 1:

We write out the formulas and the necessary values

STEP 2

We substitute the values into the formula

If the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] then the domain of the function exists

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

The collection of all potential inputs for a function is its domain.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Let the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Domain of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] :

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

Range of [tex]$\frac{x^3-3 x+1}{8 x-5}:\left[\begin{array}{cc}\text { Solution: } & -\infty < f(x) < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Axis interception points of [tex]$\frac{x^3-3 x+1}{8 x-5}[/tex]

X Intercepts: [tex]$(0.34729 \ldots, 0),(1.53208 \ldots, 0)$[/tex], [tex]$(-1.87938 \ldots, 0)$[/tex],

Y Intercepts: [tex]$\left(0,-\frac{1}{5}\right)$[/tex]

Asymptotes of [tex]$\frac{x^3-3 x+1}{8 x-5}: \quad$[/tex]

Vertical: [tex]$x=\frac{5}{8}$[/tex]

Extreme Points of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Minimum [tex]$(-0.54351 \ldots,-0.26422 \ldots)$[/tex]

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Answer:

Th

Explanation:

Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;

Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.

Without converting the equations to the same form, the property that must be different in the functions is the slope

From the question, the equations are given as

y = x + 5

y + x = 5

From the question, we understand that:

The equations must not be converted to the same form before the question is solved

The equation of a linear function is represented as

y = mx + c

Where m represents the slope and c represents the y-intercept

When the equation y = mx + c is compared to y = x + 5, we have

Slope, m = 1

y-intercept, c = 5

The equation y = mx + c can be rewritten as

y - mx = c

When the equation y - mx = c is compared to y + x = 5, we have

Slope, m = -1

y-intercept, c = 5

By comparing the properties of the functions, we have

Hence, the different properties of the functions are their slopes

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SOLUTION

The equation relating x and y is

The equation connecting x and y is an equation of the form

Since slope is also refers to as changes between two variables,

Hence

Cmparing with the equation given,

Therefore,

The change per minute in the total amount of water in the pond is 27 litres

The starting amount ot water is when the time is at 0 minutes .

Hence, substite x=0 into the equation given and obtain the value of y which stands for the amount of water at the begining.

Therefore,

The starting amount of water is 600 litres

Answer: A) 27 litres B). 600 litres

Consider that the domain are the set of x values with a point on the curve.

In this case, based on the grap, you can notice that the domain is:

domain = (-8,2)

domain = {-8,-7,-6,-5,-4,-3,-2,-1,0,1,2}

In this case you can observe that the circle has a left limit given by x = -8 (this can be notices by the subdivisions of the coordinate system) and a right limit given by x = 2. That's the reason why it is the interval of the domain.

The range are the set of y values with a point on the curve.

range = (-3,7)

range = {-3,-2,-1,0,1,2,3,4,5,6,7}

In this case, you observe the down and up limits of the circle.

1) Since the sum of these angles is written in terms of x, we can write it out:

Notice that to sum these fractions we had to take the LCM(2, 1) = 2 and rewrite it as a sum.

2) Another way of writing the sum of these angles is writing it as a sum of decimal numbers since we can rewrite fractions as decimal numbers.

3/2 = 3÷2 = 1.5

1/2 = 1÷2 =0.5

1

We have to calculate the average temperature change per hour.

We know that the temperature drops from 48 degrees to -12 degrees in 24 hours.

To calculate the average change, in degrees per hour, we calculate the ratio between the variation of the temperature and the interval of time.

We can expres this as:

Answer: The average change in temperature is -2.5 degrees per hour.

Answer:

Assuming this is rounding to the nearest cent, $36.51

Step-by-step explanation:

    1 ) Find the cost of each individual candy.

M&Ms are given at $3.50 per pack.

To find the cost of one Twix bar, divide $7.00 by 15. This makes Twix equal $0.47 per bar.

You don't need to find the individual price of the Hershey's bars because 9 bars cost $3.00 and you need 9 bars in the equation.

    2 ) Now that you have the prices you need, multiply.

For M&Ms 15 x $3.50 = $52.50

For Twix 17 x $0.47 = $7.99

For Hershey's, it is given that 9 bars are $3.00

    3 ) Add all of these up to get the total spent on candy.

$52.50 + $7.99 + $3.00 = $63.49

    4 ) Subtract this from the budget to get the total amount left over.

$100 - $63.49 = $36.51

We have the following equation of a hyperbola:

Let's divide all the equations by 4, just to simplify it

Just to make it easier, let's put the term if "x" isolated

Now we can complete squares on both sides, just remember that

Now let's complete it!

We already completed one side, now let's complete the side with y^2, see that we will add 4 again, then

And now we can write it using the standard equation!

And now we can graph it like all other hyperbolas, the vertices will be:

And the foci

Then the foci are

Now we can plot the hyperbola!

As we can see in the graph the object returned to its original position in t=6.

It's not accelarating because acceleration is the second derivate of the position, and the position is determined by a linear equation.

The answer is C.



Let

x ------> number of switch type A

y -----> number of switch type B

so

Remember that

1 hour=60 min

32 hours=32*60=1,920 minutes

4x+5y=1,920 -------> equation 1

3x+5y=1,740 ------> equation 2

Solve the system of equations

Solve by graphing

using a graphing tool

see the attached figure

Solution is

x=180

y=240

therefore

To solve the system of equations

we need to make the coefficients of one of the variables opposite, that is, they need to have the same value with different sign; let's do this with the y variable, so let's multiply the second equation by 0.7 and the first equation by 0.2; then we have:

Now we add the equations and solve the resulting equation for x:

Now that we have the value of x we plug it in one of the original equations and solve for y:

Therefore, the solution of the system of equation is (4,2)

Given:

The population of a town increases by 9 % annually.

The current population is 4,500.

Required:

We need to find the equation that gives the population of the town.

Explanation:

The population can be found by the following equation.

Let now be the current population of the town =4500.

Let Next be the population of the town.

The population can be found by the following equation.

Take the common term now out.

Final answer: