Find the circumference.
Use 3.14 for T.
r = 4 cm
C = ? cm
C =

Answer:

Step-by-step explanation:

Let AC = x

AB - AC = 4 cm

AB = 4 +x  ----------------(I)

Pythagorean theorem

AB² + AC² =BC²

(4 + x)² + x² = 9²

Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x

4² +2*4*x  +x² + x²= 81

16 + 8x + 2x² = 81

2x² + 8x + 16 - 81 = 0

2x² + 8x - 65= 0

a = 2 ; b = 8 ; c = -65

D = b² - 4ac

   = 8² - 4*2*(-65)

  = 64 +  520

D = 584

√D = √584 = 24.16

\(x=\frac{-b+\sqrt{D}}{2a} \ or \ x =\frac{-b-\sqrt{D}}{2a}\\\\x= \frac{-8+24.16}{2*2} \ or \ x = \frac{-8-24.6}{2*2}\)   {Ignore this as it is negative.}

x = 16.16/4

x = 4.04

AC = 4.04 Cm

AB = 4 + 4.04 = 8.04 cm

Area of triangle ABC = \(\frac{1}{2}* base * height\)

                                   \(=\frac{1}{2}*4.04 *8.04\\\\= 2.02 * 8.04\)

                                   = 16.24 sq.cm

Answer:

7y+24

Step-by-step explanation:

:)

The value of n is 3, value of m is 2 and the value de m + n + p is -2.

In this question we must analyze a null polynomial and determine three unknown variables. A null polynomial is those whose coefficients are equal to zero.

Therefore, we must resolve the following system of linear equations:

3 · n - 9 = 0   (1)

m - 2 = 0       (2)

p + 7 = 0       (3)

The solution of this system of linear equations is: n = 3, m = 2, p = -7. The value of n is 3, value of m is 2 and the value de m + n + p is -2. \(\blacksquare\)

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Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

The probability that the buyer waits more than 10 minutes is 0.0271

From the question, we have the following parameters that can be used in our computation:

Probability function:

fy(y)=0.2e^(-0.2y), y ≥ 0

The inequality expression y ≥ 0 means that

The value of y is atleast 0

The probability that the buyer waits more than 10 minutes means that

y = 10

So, we have the following representation

y = 10 in fy(y)=0.2e^(-0.2y)

Substitute the known values in the above equation, so, we have the following representation

fy(10)=0.2e^(-0.2 * 10)

Evaluate the exponents

fy(10)=0.2 * 0.13533528323

Evaluate the products

fy(10) = 0.0271

Hence, the probability is 0.0271

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Answer:

The angles of the parallelogram are 72 degrees and 108 degrees

Step-by-step explanation:

Set up an equation as follows:

2(x+36) + 2x = 360,

It should be set equal to 360 since that this the total number of degrees in the parallelogram.

Solve for x and x = 72

x + 36 = 108

In the given figure, a transversal line (m) cuts two parallel lines (p) and (q).

The angles h and i are called alternate interior angles.

The alternate interior angles are congruent (equal).

Since the angle, i is equal to 28° the angle h must also be 28° because they are alternate interior angles.

Therefore, the correct option is D.

The two relationships that describe a function in the table are A: Name as a function of hair color, and D: Eye color as a function of hair color.

A function is a relationship between two sets of values in which each element of the first set corresponds to exactly one element of the second set. In this table, for each hair color there is only one associated name, so the relationship between name and hair color is a function. Similarly, for each hair color there is only one associated eye color, so the relationship between eye color and hair color is also a function.

Note that the other relationships listed in the question (B, C, E and F) are not functions because they do not have a one-to-one correspondence between the two sets of values. For example, in the relationship between eye color and name, multiple people (Juan and Keshia) have the same eye color (brown), so this relationship does not describe a function.

Therefore, options A and D are the correct answer.

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Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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Answer:

Yes

Step-by-step explanation:

40000 x .10 is 4000 in tax. Total after tax would be 36,000

45,000 × .15 is 6750. Total after tax would be 38,250 which is more

Step-by-step explanation:

Actuaries in a town. ... his earning is equivalent to the select an answer an Actuaries, and he is making less

The cost-area proportional situations are:

The cost-area non-proportional situation is:

The situation where there is no enough information is

As a general rule:

Proportional situations are situations that can be represented as unit rates

When represented as a graph, they pass through the origin as in graph (d)

Other possible scenarios are:

The information in (b) a concrete patio quoted at a bulk cost for 50 square feet is incomplete because it does not state if the bulk cost is a unit rate

Other scenarios are non-proportional

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Answer:

the is no, 1/2 is greater than 1/3 to 5/4

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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Step-by-step explanation:

Yes, they are similar because if you convert both of the measurements to fractions, which will be 2/3 and 8/12, you can see that if you simplify 8/12, you will get 2/3. That is why they are similar.

Answer:

Step-by-step explanation:

we know the sum in an triangle will be 180-(47+39)=94

The evaluation of the statements with regards to the graph of a function are;

A function maps an input value to an output based on a definition or rule.

First part of the statement;

The graph of a non-vertical straight line has a range of values for the slope, m, of 0 ≤ m < ∞

The equation of a straight line function is of the form; y = m·x + c

Therefore;

The graph of a non-vertical straight line can be represented by the equation, y = m·x + c, where y has possible values of; -∞ < y < ∞, which indicates that as x increases or decreases, y increases (or decreases), such that each value of x maps unto only one value of y, which indicates that the graph is a function. The statement is therefore true.

Second part of the statement.

The graph of the quadratic function; y = a·x² + b·x + c has a shape of a parabola, therefore, the statement, the graph of a function is not always a straight line is true also.

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Answer:

30.769230769231% or 4/13

Step-by-step explanation:

The fraction of people didn’t pass is 4/ 13.

We have,

Total number of people taking the test: 13

Number of people who passed: 9

So, the number of people who didn't pass

Number of people who didn't pass = Total number of people - Number of people who passed

Number of people who didn't pass = 13 - 9

Number of people who didn't pass = 4

So, the fraction of people didn’t pass

= 4/ 13.

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Answer: it might be something like, descending slope, or declining slope, are there answer choices

Answer:

Step-by-step explanation:

Initial coordinates and transformations:

The different sums are possible are 18.

As, the number of different sums possible is given by the equation:

Number of different sums = n x m

In other words, we multiply the number of outcomes for the first spinner by the number of outcomes for the second spinner to get the total number of unique sums.

So, the different sums are possible

= 2 x 3 x 3

= 18

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Answer:

You will have earned $113 in interest.

Step-by-step explanation:

After investing for 4 years at 3% interest, your initial investment of $900 will have grown to $1,013.

To find the amount you need to invest, we can use the formula for simple interest:

\(\displaystyle\sf \text{{Interest}} = \text{{Principal}} \times \text{{Rate}} \times \text{{Time}}\)

Here, the principal is the amount you need to invest, the rate is 3% (or 0.03 as a decimal), and the time is 4 years. We can rearrange the formula to solve for the principal:

\(\displaystyle\sf \text{{Principal}} = \frac{{\text{{Interest}}}}{{\text{{Rate}} \times \text{{Time}}}}\)

Plugging in the given values, we get:

\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.03 \times 4}}\)

Simplifying further:

\(\displaystyle\sf \text{{Principal}} = \frac{{900}}{{0.12}}\)

Calculating the division:

\(\displaystyle\sf \text{{Principal}} = 7500\)

Therefore, you will need to invest $7500 at 3% to have earned $900 in interest in 4 years.

Answer:

D. its a two dimensional object

Answer:

A. It is a polygon

C. It is a one-dimensional object

The shape is a polygon in two dimensions since a polygon must have at least three straight sides.

Showing that this need not be true if f is continuous but not uniformly continuous.

Given :

let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).

( 1 )

If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,

then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,

then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.

( 2 )

Let E = {1, 1/2, 1/3, · ·  } and f(1/n) = 1 is n is odd, f(1/n) = −1 if

n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the

sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.

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The location of the light bulb is (15, 0). Check the reason for the answer been (15, 0) below.

This is also known as  paraboloid or paraboloidal reflector. It is a kind of  dish or a mirror that is said to have a reflective surface which is often used to take in or project any kind of energy e.g., light, sound, etc.

For the above question, the formula is:

y² = 2px

The focus is (p/2, 0)

x- 10 = u

y2 = 20u

So, the focus for U  =  ( \(\frac{20}{4}\); 0)

The focus for x =  ( \(\frac{20}{4}\); 10, 0)

= 5 , 10, 0

= (15, 0)

Therefore, the answer is (15, 0)

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Answer:

\(368.54 = 3*100 + 6.8*10 +5*1/10 + 4*100\)

Step-by-step explanation:

Given

\(368.54 = ( [\ ] * 100) + ( [\ ] * 10) + ( [\ ] * 1/10) + ( [\ ] * 1/100)\)

Required

Fill in the gap

The number can be expressed as:

\(368.54 = 300 + 60 + 8 +0.5 + 0.04\)

Factorize:

\(368.54 = 3*100 + 6*10 + 0.8*10 +5*1/10 + 4*100\)

Factor out 10 in 6 * 10 + 0.8 * 10

\(368.54 = 3*100 + [6 + 0.8]*10 +5*1/10 + 4*100\)

\(368.54 = 3*100 + 6.8*10 +5*1/10 + 4*100\)

Solved

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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